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Development of a neural networks model to predict the diauxic lag length


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i v A C K N O W L E D G M E N T S I w o u l d l i k e t o t h a n k m y c o m m i t t e e m e m b e r s P r o f e s s o r s S p y r o s A S v o r o n o s B e n K o o p m a n a n d T h o m a s E B u l l o c k f o r t h e i r a c a d e m i c a d v i s e m e n t a n d g u i d a n c e o n t h i s p r o j e c t A s p e c i a l t h a n k s g o t o m y c o a d v i s o r s a n d f e l l o w “ d i a u x i e r s ” P r o f e s s o r s S p y r o s A S v o r o n o s P r o f e s s o r B e n K o o p m a n K e i s h a L i s b o n M i c h e a l M c K e a n A n n a C a s a s u s Z a m b r a n a a n d S e u n g Y e o n W e o n f o r t h e i r h e l p s u p p o r t a n d w i l l i n g n e s s t o d i s c u s s t h e i r i d e a s I w o u l d l i k e t o t h a n k t h e C h e m i c a l E n g i n e e r i n g D e p a r t m e n t f o r t h e f i n a n c i a l s u p p o r t t h r o u g h m y c o u r s e o f s t u d y F i n a l l y I w o u l d l i k e t o t h a n k m y m o t h e r P r a s h a n t s i s t e r a n d a l l m y f r i e n d s f o r t h e i r l o v e s u p p o r t a n d p r a y e r s w i t h o u t w h i c h i t w o u l d h a v e b e e n i m p o s s i b l e f o r m e t o c o m p l e t e t h i s t h e s i s

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v T A B L E O F C O N T E N T S p a g e A C K N O W L E D G M E N T S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i v A B S T R A C T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v i iC H A P T E R S1 I N T R O D U C T I O N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 L I T E R A T U R E R E V I E W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 1 I n d u s t r y S t a n d a r d A c t i v a t e d S l u d g e M o d e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 2 C y b e r n e t i c M o d e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 3 M o d e l i n g o f D i a u x i c L a g i n P s e u d o m o n a s D e n t r i f i c a n s . . . . . . . . . . . . . . . . . . 1 0 2 4 H y b r i d M o d e l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 P U R P O S E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 4 E X P E R I M E N T A L M E T H O D S A N D R E S U L T S . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 4 1 N i t r a t e R e d u c t a s e E n z y m e A s s a y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 4 1 1 E x p e r i m e n t a l M e t h o d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 4 1 2 G r o w t h E x p e r i m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 4 1 3 E x p e r i m e n t a l P r o t o c o l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 4 1 4 A n a l y t i c M e t h o d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 4 1 5 E x p e r i m e n t a l R e s u l t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 4 2 E f f e c t s o f D i s s o l v e d O x y g e n L e v e l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 4 2 1 E x p e r i m e n t a l M e t h o d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 4 2 2 G r o w t h E x p e r i m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 4 2 3 E x p e r i m e n t a l P r o t o c o l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...33 4 2 4 A n a l y t i c M e t h o d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 4 2 5 E x p e r i m e n t a l R e s u l t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 4 3 P r e c u l t u r e E x p e r i m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 4 3 1 E x p e r i m e n t a l M e t h o d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 4 3 2 G r o w t h E x p e r i m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 4 3 3 E x p e r i m e n t a l P r o t o c o l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 4 3 4 A n a l y t i c M e t h o d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 4 3 5 E x p e r i m e n t a l R e s u l t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5

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v i 5 N E U R A L N E T W O R K S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1 5 1 A l g o r i t h m U s e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 5 1 1 B a c k P r o p a g a t i o n A l g o r i t h m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 5 1 2 T r a i n i n g b y C o n j u g a t e G r a d i e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4 5 1 3 S i m u l a t e d A n n e a l i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 8 5 1 4 I n t e r l e a v e d S i m u l a t e d A n n e a l i n g a n d C o n j u g a t e G r a d i e n t A l g o r i t h m . . . . 6 8 5 2 N e u r a l N e t w o r k M o d e l f o r L o w D O E x p e r i m e n t s . . . . . . . . . . . . . . . . . . . . . . . 6 9 5 2 1 T r a i n i n g t h e N e t w o r k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 9 5 2 2 T e s t i n g t h e N e t w o r k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 5 3 N e u r a l N e t w o r k M o d e l P r e c u l t u r e E x p e r i m e n t s . . . . . . . . . . . . . . . . . . . . . . . . 7 6 5 3 1 T r a i n i n g t h e N e t w o r k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 6 5 3 2 T e s t i n g t h e N e t w o r k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 6 5 4 D i s c u s s i o n o f R e s u l t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 5 5 H y b r i d M o d e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 6 C O N C L U S I O N S A N D F U T U R E W O R K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 9 A P P E N D I X : P R O G R A M L I S T I N G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1 L I S T O F R E F E R E N C E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 4 B I O G R A P H I C A L S K E T C H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 8

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v i i A b s t r a c t o f T h e s i s P r e s e n t e d t o t h e G r a d u a t e S c h o o l o f t h e U n i v e r s i t y o f F l o r i d a i n P a r t i a l F u l f i l l m e n t o f t h e R e q u i r e m e n t s f o r t h e D e g r e e o f M a s t e r o f S c i e n c e D E V E L O P M E N T O F A N E U R A L N E T W O R K S M O D E L T O P R E D I C T T H E D I A U X I C L A G L E N G T H B y S a n g e e t h a S h e k a r D e c e m b e r 2 0 0 1 C h a i r m a n : D r S p y r o s A S v o r o n o s M a j o r D e p a r t m e n t : C h e m i c a l E n g i n e e r i n g I n w a s t e w a t e r t r e a t m e n t p l a n t s n i t r o g e n i s r e m o v e d b y p a s s i n g t h e w a s t e w a t e r a l t e r n a t i v e l y f r o m a e r o b i c z o n e s t o a n o x i c z o n e s N i t r i f i c a t i o n t a k e s p l a c e i n t h e a e r o b i c z o n e a n d d e n i t r i f i c a t i o n i n t h e a n o x i c z o n e A d i a u x i c l a g m i g h t o c c u r w h e n f o l l o w i n g t h e s w i t c h f r o m o x y g e n t o n i t r a t e a s t h e t e r m i n a l e l e c t r o n a c c e p t o r T h e p r e s e n t r e s e a r c h a t t e m p t s t o u s e a n e u r a l n e t w o r k i n p l a c e o f t h e t r a d i t i o n a l m o d e l s t o p r e d i c t t h e d u r a t i o n o f t h e d i a u x i c l a g u n d e r a g i v e n s e t o f c o n d i t i o n s E x p e r i m e n t a l d a t a g a t h e r e d f r o m s t u d i e s w i t h t h e c u l t u r e P s e u d o m o n a s d e n i t r i f i c a n s ( A T C C 1 3 8 6 7 ) w a s c l a s s i f i e d b a s e d o n d i s s o l v e d o x y g e n c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e a n d t h e r e v i v i n g p h a s e o f t h e c u l t u r e O n e n e u r a l n e t w o r k w a s t r a i n e d t o p r e d i c t t h e d u r a t i o n o f t h e d i a u x i c l a g f o r e x p e r i m e n t s w i t h a n a n o x i c r e v i v i n g p h a s e a n d l o w d i s s o l v e d o x y g e n c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e T h e i n p u t s t o t h i s n e t w o r k w e r e i n i t i a l b i o m a s s c o n c e n t r a t i o n d i s s o l v e d o x y g e n c o n c e n t r a t i o n i n t h e a e r o b i c p h a s e a n d t h e l e n g t h o f t h e a e r o b i c p h a s e i n h o u r s A s e c o n d n e u r a l n e t w o r k w a s t r a i n e d t o

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v i i i p r e d i c t t h e l a g l e n g t h f o r e x p e r i m e n t s w h e r e d i s s o l v e d o x y g e n c o n c e n t r a t i o n w a s m a i n t a i n e d a t a i r s a t u r a t i o n i n t h e a e r o b i c p h a s e w i t h t h e r e v i v i n g p h a s e ( o x i c / a n o x i c ) o f t h e c u l t u r e i n i t i a l b i o m a s s c o n c e n t r a t i o n l e n g t h o f t h e a e r o b i c p h a s e i n h o u r s a n d n i t r a t e c o n c e n t r a t i o n s i n t h e a e r a t i o n p h a s e a s t h e i n p u t v a r i a b l e s A n i n t e r l e a v e d s i m u l a t e d a n n e a l i n g a n d c o n j u g a t e g r a d i e n t s e a r c h a l g o r i t h m w a s u s e d t o t r a i n t h e n e t w o r k s T h e p r e d i c t e d l a g l e n g t h f r o m t h e n e t w o r k s w a s c o m p a r e d t o t h e a c t u a l e x p e r i m e n t a l d a t a a n d f o u n d t o b e w i t h i n r e a s o n a b l e l i m i t s o f a c c u r a c y

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1 C H A P T E R 1 I N T R O D U C T I O N B i o l o g i c a l r e m o v a l o f n i t r o g e n h a s b e c o m e a c o m m o n p r a c t i c e i n m a n y w a s t e w a t e r t r e a t m e n t f a c i l i t i e s e v e r s i n c e t h e h a r m f u l e f f e c t s o f e x c e s s l e v e l s o f n i t r o g e n h a v e b e e n k n o w n T h i s h a s l e d t o f o c u s e d r e s e a r c h o n p r o c e s s e s t h a t r e m o v e n i t r o g e n f r o m w a s t e w a t e r i n a n e f f i c i e n t a n d e c o n o m i c a l m a n n e r I n a t y p i c a l s u s p e n d e d g r o w t h b i o l o g i c a l n i t r o g e n r e m o v a l s y s t e m a c t i v a t e d s l u d g e p a s s e s t h r o u g h c y c l e s o f a e r o b i c a n d a n o x i c z o n e s w h e r e n i t r i f i c a t i o n a n d d e n i t r i f i c a t i o n a r e a c h i e v e d r e s p e c t i v e l y A m m o n i u m i s o x i d i z e d t o n i t r a t e i n n i t r i f i c a t i o n a n d n i t r a t e i s r e d u c e d t o n i t r o g e n g a s t h r o u g h s e v e r a l s t e p s i n d e n i t r i f i c a t i o n M o n o d ( 1 9 4 2 ) f i r s t d e s c r i b e d t h e p h e n o m e n o n o f d i a u x i c l a g t h a t c a n o c c u r w h e n b a c t e r i a s w i t c h b e t w e e n e l e c t r o n d o n o r s ( c a r b o n s u b s t r a t e s ) D i a u x i e i s c h a r a c t e r i z e d b y a d o u b l e g r o w t h c y c l e c o n s i s t i n g o f t w o e x p o n e n t i a l p h a s e s s e p a r a t e d b y a p h a s e i n w h i c h t h e g r o w t h r a t e i s v e r y l o w o r z e r o T h e l a g c o r r e s p o n d s t o t h e t i m e n e c e s s a r y f o r b a c t e r i a t o s y n t h e s i z e a n d a c t i v a t e t h e e n z y m e s n e c e s s a r y t o m e t a b o l i z e t h e l e s s p r e f e r r e d s u b s t r a t e ( M o n o d 1 9 4 2 ; 1 9 4 9 ) K o d a m a e t a l ( 1 9 6 9 ) o b s e r v e d d i a u x i c g r o w t h w h e n P s e u d o m o n a s s t u t z e r i s w i t c h e d f r o m n i t r a t e t o n i t r i t e a s t e r m i n a l e l e c t r o n a c c e p t o r D i a u x i c l a g c a u s e d b y c h a n g i n g b e t w e e n c a r b o n s o u r c e s h a s b e e n s u c c e s s f u l l y m o d e l e d u s i n g a c y b e r n e t i c m o d e l ( K o m a p a l a e t a l 1 9 8 6 ) “ I n d u s t r y S t a n d a r d ” I A W Q A c t i v a t e d S l u d g e M o d e l s N o 1 a n d 2 ( H e n z e e t a l 1 9 8 7 ; 1 9 9 5 ) d o n o t a c c o u n t f o r a n y d i a u x i c l a g w h e n b a c t e r i a s w i t c h b e t w e e n o x y g e n t o n i t r a t e a s e l e c t r o n a c c e p t o r L i u e t a l ( 1 9 9 6 ) d e v e l o p e d a c y b e r n e t i c m o d e l t o p r e d i c t l a g s f o r a n a c t i v a t e d s l u d g e T h i s m o d e l

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2 h o w e v e r c o u l d n o t c a p t u r e t h e o b s e r v e d l o n g e r l a g s o f a p u r e c u l t u r e A n e w m o d e l a c c o u n t i n g f o r e n z y m e s y n t h e s i s a n d a c t i v i t y i n r e s p o n s e t o c u l t u r e c o n d i t i o n s a n d e n z y m e s p e c i f i c l e v e l s w a s t h e n d e v e l o p e d ( L i u e t a l 1 9 9 8 ) I t c o u l d p r e d i c t l e n g t h o f l a g s c o r r e s p o n d i n g t o t h e g r o w t h p a t t e r n T h i s m a n u s c r i p t r e v i e w s t h e l i t e r a t u r e o n t h e m o d e l s d e v e l o p e d t o p r e d i c t d i a u x i c l a g s a n d a l s o d e v e l o p s a n e u r a l n e t w o r k m o d e l t o p r e d i c t t h e l e n g t h o f t h e d i a u x i c l a g T h e n e u r a l n e t w o r k w a s t r a i n e d w i t h e x p e r i m e n t a l d a t a T h e n e t w o r k c a n s u c c e s s f u l l y p r e d i c t t h e l a g l e n g t h i n h o u r s a s a f u n c t i o n o f i n p u t s s u c h a s b i o m a s s i n t e r m s o f a b s o r b a n c e a t t i m e z e r o l e n g t h o f a e r o b i c p h a s e i n h o u r s r e v i v i n g p h a s e o f t h e c u l t u r e d i s s o l v e d o x y g e n c o n c e n t r a t i o n s a n d n i t r a t e c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e

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3 C H A P T E R 2 L I T E R A T U R E R E V I E W M o n o d f i r s t o b s e r v e d t h e p h e n o m e n o n o f d i a u x i e D i a u x i c l a g i s d e f i n e d a s t h e p h a s e t h a t s e p a r a t e s t w o e x p o n e n t i a l g r o w t h p h a s e s i n w h i c h t h e g r o w t h r a t e i s v e r y l o w o r z e r o ( M o n o d 1 9 4 2 ) I n d i a u x i c g r o w t h t h e s e c o n d s u b s t r a t e i s n o t u t i l i z e d u n t i l a f t e r t h e f i r s t s u b s t r a t e i s e x h a u s t e d a n d t h e e n z y m e s r e q u i r e d b y t h e b a c t e r i a t o u t i l i z e t h e s e c o n d a r e n o t s y n t h e s i z e d u n t i l t h e n ( M o n o d 1 9 4 2 ) H a m i l t o n a n d D a w e s ( 1 9 4 5 ) a l s o o b s e r v e d t h e d i a u x i c g r o w t h p h e n o m e n o n i n P s e u d o m o n a s a e r u g i n o s a i n a m e d i u m o f g l u c o s e a n d o r g a n i c a c i d T h e y o b s e r v e d t h a t o r g a n i c a c i d i s p r e f e r e n t i a l l y u s e d o v e r g l u c o s e S t a n d i n g e t a l ( 1 9 7 2 ) o b s e r v e d t h a t E c o l i e x h i b i t s a d i a u x i c b e h a v i o r i n a m i x t u r e o f g l u c o s e a n d x y l o s e T h e y a l s o o b s e r v e d t h a t w h e n E c o l i w a s i n a n i n i t i a l m e d i u m o f g l u c o s e a n d g a l a c t o s e g l u c o s e a n d g a l a c t o s e w e r e u t i l i z e d s e q u e n t i a l l y a n d t h e r e w a s n o l a g p e r i o d b e t w e e n t h e t w o e x p o n e n t i a l g r o w t h p h a s e s T h e r e f o r e i t c a n n o l o n g e r b e a s s u m e d t h a t d i a u x i e i s a l w a y s c h a r a c t e r i z e d b y a l a g p e r i o d S e q u e n t i a l u t i l i z a t i o n o f s u b s t r a t e s w a s a l s o o b s e r v e d i n P r o p i o n i b a c t e r i u m s h e r m a n i i i n a m i x t u r e o f l a c t a t e a n d g l u c o s e w h e r e l a c t a t e w a s c o m p l e t e l y c o n s u m e d b e f o r e g r o w t h o n g l u c o s e t o o k p l a c e ( L e e e t a l 1 9 7 4 ) T h i s p a t t e r n o f s e q u e n t i a l u t i l i z a t i o n w i t h o u t a l a g p e r i o d i s a l s o o b s e r v e d i n K l e s b i e l l a p n e u m o n i a e w h e n t h e n u t r i e n t s o u r c e i s s w i t c h e d t o x y l o s e f r o m g l u c o s e ( B a l o o a n d R a m a k r i s h a n a 1 9 9 1 ) I n e a c h c a s e t h e p r e f e r r e d s u b s t r a t e i s t h e o n e o n w h i c h t h e b a c t e r i a g r o w t h e f a s t e s t T h e r e f o r e d i a u x i c g r o w t h p h e n o m e n a m a y o r m a y n o t b e c h a r a c t e r i z e d b y a l a g p e r i o d b u t i s d i r e c t l y r e l a t e d t o t h e b a c t e r i a l p r e f e r e n c e f o r c o n s u m i n g t h e f a s t e s t g r o w t h s u p p o r t i n g s u b s t r a t e ( R a m a k r i s h n a e t a l 1 9 8 7 )

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4 R a m a k r i s h n a e t a l ( 1 9 8 7 ) a n d B a l o o a n d R a m a k r i s h n a ( 1 9 9 1 ) r e c o r d t h e g e n e r a l g r o w t h c h a r a c t e r i s t i c s o f b a c t e r i a o n m u l t i p l e s u b s t r a t e s K o d a m a e t a l ( 1 9 6 9 ) w e r e t h e f i r s t t o p e r f o r m e x p e r i m e n t s o f d i a u x i c b e h a v i o r b e t w e e n d i f f e r e n t e l e c t r o n a c c e p t o r s T h e i r s t u d i e s s h o w e d a b i p h a s i c g r o w t h p a t t e r n o f P s e u d o m o n a s s t u t z e r i b e t w e e n n i t r a t e a n d n i t r i t e a s e l e c t r o n a c c e p t o r s T h e p r e f e r r e d e l e c t r o n a c c e p t o r n i t r a t e w a s f u l l y c o n s u m e d b e f o r e a n y n i t r i t e w a s c o n s u m e d T h e e x p o n e n t i a l g r o w t h p h a s e s w e r e s e p a r a t e d b y a l a g p e r i o d i n w h i c h t h e g r o w t h r a t e w a s v e r y l o w S e q u e n t i a l u t i l i z a t i o n w a s a l s o o b s e r v e d b y S t e i n b e r g e t a l ( 1 9 9 2 ) i n f r e s h w a t e r s e l e n a t e r e s p i r i n g b a c t e r i a I n t h e p r e s e n c e o f b o t h n i t r a t e a n d s e l e n a t e n i t r a t e w a s c o m p l e t e l y e x h a u s t e d b e f o r e s e l e n a t e c o n s u m p t i o n b e g a n T h e r e w a s n o l a g p e r i o d b e t w e e n g r o w t h o n n i t r a t e a n d s e l e n a t e R e c e n t l y t h e p h e n o m e n a o f d i a u x i e w h e n b a c t e r i a s w i t c h f r o m o x y g e n t o n i t r a t e a s e l e c t r o n a c c e p t o r s w a s d e m o n s t r a t e d f o r b o t h a c t i v a t e d s l u d g e a s w e l l a s p u r e c u l t u r e ( L i u e t a l 1 9 9 8 a ) F o r t h e p u r e c u l t u r e P s e u d o n m o n a s d e n t r i f i c a n s i t w a s o b s e r v e d t h a t l a g s u p t o 7 h o u r s c o u l d t a k e p l a c e b e f o r e t h e s e c o n d e x p o n e n t i a l g r o w t h p h a s e o n n i t r a t e b e g a n D i a u x i c l a g c a u s e d b y c h a n g e i n c a r b o n s o u r c e s h a s b e e n s u c c e s s f u l l y m o d e l e d u s i n g a c y b e r n e t i c m o d e l ( K o m p a l a e t a l 1 9 8 6 ) A c t i v a t e d S l u d g e M o d e l s N o 1 a n d 2 ( H e n z e e t a l 1 9 8 7 ; 1 9 9 5 ) d o n o t a c c o u n t f o r a n y d i a u x i c l a g w h e n b a c t e r i a s w i t c h b e t w e e n o x y g e n t o n i t r a t e a s e l e c t r o n a c c e p t o r A c y b e r n e t i c a p p r o a c h w a s d e v e l o p e d ( L i u e t a l 1 9 9 6 ) w h i c h i n c o r p o r a t e d a s i m p l i f i e d v e r s i o n A c t i v a t e d S l u d g e M o d e l N o 1 ( H e n z e e t a l 1 9 8 7 ) T h i s c y b e r n e t i c a p p r o a c h w a s a b l e t o p r e d i c t l a g s o b s e r v e d w i t h a c t i v a t e d s l u d g e

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5 2 1 I n d u s t r y S t a n d a r d A c t i v a t e d S l u d g e M o d e l I n t h e “ I n d u s t r y S t a n d a r d ” m o d e l s f o r a c t i v a t e d s l u d g e ( A S M – 1 H e n z e e t a l 1 9 8 7 ; A S M 2 H e n z e e t a l 1 9 9 5 ) t h e e f f e c t o f d i s s o l v e d o x y g e n o n t h e r a t e o f g r o w t h o f h e t e r o t r o p h i c b i o m a s s u n d e r a n o x i c c o n d i t i o n s i s r e p r e s e n t e d b y t h e t e r m H O O H O K S K , + ( 2 1 ) w h e r e a s t h e r a t e o f h e t e r o t r o p h i c g r o w t h u n d e r a e r o b i c c o n d i t i o n s i s c o n t r o l l e d b y t h e t e r m H O O O K S S + ( 2 2 ) w h e r e S O i s t h e d i s s o l v e d o x y g e n c o n c e n t r a t i o n a n d K O H t h e o x y g e n h a l f s a t u r a t i o n c o n c e n t r a t i o n T h e f o r m e r t e r m a p p r o a c h e s z e r o w h e n t h e d i s s o l v e d o x y g e n c o n c e n t r a t i o n i s h i g h a n d a p p r o a c h e s 1 0 w h e n d i s s o l v e d o x y g e n c o n c e n t r a t i o n i s l o w T h e l a t t e r t e r m h a s c o m p l e m e n t a r y b e h a v i o r a p p r o a c h i n g 1 0 w h e n D O i s h i g h a n d t e n d i n g t o w a r d s z e r o w h e n D O i s l o w T o g e t h e r t h e t w o t e r m s s u m a l w a y s t o 1 0 t h u s e n s u r i n g t h a t t h e t o t a l r a t e o f g r o w t h u s i n g b o t h e l e c t r o n a c c e p t o r s d o e s n o t e x c e e d t h a t w h i c h i s p o s s i b l e i n a h i g h l y a e r o b i c e n v i r o n m e n t T h i s f e a t u r e h o w e v e r p r e v e n t s e i t h e r m o d e l f r o m a c c u r a t e l y p o r t r a y i n g t h e d r a m a t i c d e c r e a s e o r e v e n c e s s a t i o n o f g r o w t h d u r i n g t h e d i a u x i e A n e x a m p l e o f a c o n v e n t i o n a l m o d e l o f h e t e r o t r o p h i c g r o w t h u n d e r a e r o b i c a n d a n o x i c c o n d i t i o n s w h e n t h e c a r b o n s o u r c e i s n o n l i m i t i n g i s s h o w n i n T a b l e 2 1 T h e m o d e l w h i c h i s a s i m p l i f i e d m o d e l o f A S M 1 c o n t a i n s p r o c e s s r a t e e x p r e s s i o n s f o r a e r o b i c g r o w t h o f h e t e r o t r o p h i c b i o m a s s T h e c o m p o n e n t s i n c l u d e a c t i v e h e t e r o t r o p h i c b i o m a s s ( X B H ) d i s s o l v e d o x y g e n ( S O ) a n d t h e s u m o f n i t r a t e p l u s n i t r o g e n e x p r e s s e d a s e q u i v a l e n t n i t r a t e ( S N O ) b y t h e f o l l o w i n g e q u a t i o n

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6 ] [ 857 2 ) 143 1 857 2 ( ] [2 3N NO N NO SNO+ = ( 2 3 ) T a b l e 2 1 C o n v e n t i o n a l m o d e l f o r h e t e r o t r o p h i c g r o w t h u n d e r a e r o b i c a n d a n o x i c c o n d i t i o n s C o m p o n e n t i 1 2 3 j P r o c e s s S O S N O X B H P r o c e s s r a t e r j M L 3 T 1 1 A e r o b i c G r o w t h o f h e t e r o t r o p h s O H O H Y Y , 1 1 H B O H O O O HX S K S, , ^ +m 2 A n o x i c G r o w t h o f h e t e r o t r o p h s NO H NO H Y Y , 86 2 1 1 H B NO NO NO O H O H O NO HX S K S S K K, , ^ + +m 3 D e c a y o f h e t e r o t r o p h s 1 b H X B H O b s e r v e d c o n v e r s i o n r a t e M L 3 T 1 j j ij irr g = N e i t h e r o f t h e p r o c e s s r a t e e x p r e s s i o n s f o r g r o w t h c o n t a i n s a s u b s t r a t e c o n c e n t r a t i o n t e r m n o r i s t h e s u b s t r a t e s h o w n a s a c o m p o n e n t T h i s i s b e c a u s e t h e c a r b o n s o u r c e ( g l u c o s e ) i s n o t l i m i t i n g g r o w t h F o r t h e r e a s o n e x p l a i n e d a b o v e t h i s t y p e o f m o d e l c a n n o t c a p t u r e t h e d i a u x i c l a g e v e n t h o u g h i t i s a b l e t o m a t c h t h e g r o w t h r a t e s i n a e r o b i c a n d a n o x i c c o n d i t i o n s C l e a r l y a n e w m o d e l i n g a p p r o a c h i s r e q u i r e d t o s u c c e s s f u l l y p o r t r a y t h e d i a u x i c l a g

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7 2 2 C y b e r n e t i c M o d e l C y b e r n e t i c m o d e l i n g ( R a m a k r i s h n a 1 9 8 2 ; R a m a k r i s h n a e t a l 1 9 8 4 ; K o m a p a l a e t a l 1 9 8 6 ; S t r a i g h t a n d R a m a k r i s h n a 1 9 9 1 ; S t r a i g h t a n d R a m a k r i s h n a 1 9 9 4 ; R a m a k r i s h n a e t a l 1 9 9 5 ) h a s b e e n s u c c e s s f u l i n p o r t r a y i n g t h e d i a u x i c l a g o b s e r v e d w h e n t h e b a c t e r i a s w i t c h b e t w e e n e l e c t r o n d o n o r s I t i s b a s e d o n t h e p r e m i s e t h a t b a c t e r i a a r e o p t i m a l s t r a t e g i s t s ( R a m a k r i s h n a e t a l 1 9 8 7 ) a n d t h a t t h e y r e g u l a t e e n z y m e s y n t h e s i s a n d a c t i v i t y s o t o m a x i m i z e t h e i r s p e c i f i c g r o w t h r a t e I n t h e c y b e r n e t i c m o d e l ( L i u e t a l 1 9 9 8 a ) t h e k i n e t i c e x p r e s s i o n s o f T a b l e 2 1 a r e m o d i f i e d i n a m a n n e r a n a l o g o u s t o t h e m o d i f i c a t i o n s o f M o n o d k i n e t i c e x p r e s s i o n s b y K o m p a l a e t a l ( 1 9 8 6 ) T h e d i a u x i c l a g i s a t t r i b u t e d t o t h e f a c t t h a t a p p r o p r i a t e e n z y m e s f o r a l t e r n a t e e l e c t r o n a c c e p t o r s m u s t b e s y n t h e s i z e d T h e r e f o r e t h e L i u e t a l ( 1 9 9 8 a ) m o d e l a d d s a s c o m p o n e n t s t h e c o n c e n t r a t i o n s o f t w o e n z y m e s E O a n d E N O t o r e g u l a t e t h e b i o m a s s s y n t h e s i s i n t h e p r e s e n c e o f o x y g e n a n d n i t r a t e r e s p e c t i v e l y B o t h t h e c o n c e n t r a t i o n s a n d a c t i v i t i e s o f t h e s e e n z y m e s a f f e c t t h e g r o w t h r a t e o f h e t e r o t r o p h i c b i o m a s s I f e k d e n o t e s t h e s p e c i f i c l e v e l o f a n e n z y m e [ i e . e k = E K / X B H f o r k = O ( o x y g e n ) o r N O ( e q u i v a l e n t n i t r a t e ) ] a n d v k d e n o t e s t h e r e l a t i v e a c t i v i t y ( r a n g i n g f r o m 0 t o 1 ) o f t h e r e s p e c t i v e e n z y m e s t h e n t h e e f f e c t s o f e n z y m e l e v e l a n d a c t i v i t y o n b i o m a s s g r o w t h r a t e c a n b e e x p r e s s e d b y a M o n o d g r o w t h r a t e e x p r e s s i o n b y t h e f a c t o r v k e k / e k m a x w h e r e e k m a x i s t h e e n z y m e m a x i m u m s p e c i f i c l e v e l T h i s g i v e s t h e f o l l o w i n g e q u a t i o n f o r a e r o b i c a n d a n o x i c g r o w t h ( 2 4 ) w h e r e K O = K O H H B K k k k k k k H k X S K S e v e max , ^ + =m r

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8 I t i s p o s t u l a t e d t h a t t h e s y n t h e s i s r a t e o f e a c h e n z y m e c a n b e d e s c r i b e d b y t h e e x p r e s s i o n H B k k k k kX S K S u, +a ( 2 5 ) i n w h i c h t h e m a x i m u m s p e c i f i c s y n t h e s i s r a t e d e p e n d s o n a “ c y b e r n e t i c v a r i a b l e ” u k ( r a n g i n g f r o m 0 t o 1 ) t h a t c o n t r o l s w h e t h e r t h e e n z y m e i s s y n t h e s i z e d o r n o t a n d a t w h a t r a t e a n d a k i s a s y n t h e s i s r a t e c o e f f i c i e n t E n z y m e d e c a y i s a s s u m e d t o b e f i r s t o r d e r w i t h r e s p e c t t o e n z y m e c o n c e n t r a t i o n s i n a m a n n e r a n a l o g o u s t o b i o m a s s d e c a y ; i e t h e d e c a y r a t e i s k k Eb ( 2 6 ) I n t h e a b o v e f o r m u l a t i o n t h e v a r i a b l e s u k a n d v k r e p r e s e n t t h e c o n t r o l a c t i o n s o f t h e c e l l u l a r r e g u l a t o r y p r o c e s s e s o f r e p r e s s i o n i n d u c t i o n a n d i n h i b i t i o n a c t i v a t i o n I n t h e c y b e r n e t i c m o d e l i n g a p p r o a c h i t i s p o s t u l a t e d t h a t t h e b a c t e r i a a d j u s t t h e v a l u e s o f t h e s e v a r i a b l e s a s w e l l a s o f e k m a x s o a s t o m a x i m i z e t h e i r i n s t a n t a n e o u s g r o w t h r a t e A s s h o w n b y K o m a p a l a e t a l ( 1 9 8 6 ) t h e s o l u t i o n o f t h e o p t i m i z a t i o n p r o b l e m i s ==1) (k k k k k kv v ur r ( 2 7 ) ) ( maxk k k k k kv v vr r = ( 2 8 ) ^ k H k k kem b a + = ( 2 9 )

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9 T h e c o m p l e t e k i n e t i c m o d e l i s s u m m a r i z e d i n T a b l e 2 2 I t s h o u l d b e n o t e d t h a t t h e t e r m K O H / ( K O H + S O ) w h i c h i s u s e d i n A S M 1 a n d A S M 2 t o s w i t c h o f f g r o w t h o n n i t r a t e w h e n o x y g e n i s p r e s e n t i s n o t i n c l u d e d a s v N O a s s u m e s t h i s f u n c t i o n T o b e t t e r d e f i n e t h e f a c t o r s t h a t i n f l u e n c e s t h e o n s e t a n d l e n g t h o f d i a u x i c l a g s a s t h e a c t i v a t e d s l u d g e s w i t c h e s f r o m o x y g e n t o n i t r a t e a s e l e c t r o n a c c e p t o r f u r t h e r r e f i n e m e n t o f t h e m o d e l w a s r e q u i r e d T a b l e 2 2 P r o c e s s k i n e t i c s a n d s t o i c h i o m e t r y o f t h e c y b e r n e t i c m o d e l o f L i u e t a l ( 1 9 9 8 a ) C o m p o n e n t i 1 2 3 4 5 j P r o c e s s S O S N O X B H E O E N O P r o c e s s r a t e r j M L 3 T 1 1 A e r o b i c g r o w t h o f h e t e r o t r o p h s O H O H Y Y , 1 1 H B O H O O o o o O HX S K S e v e, max , +m 2 A n o x i c g r o w t h o f h e t e r o t r o p h s NO H NO H Y Y , 86 2 1 1 H B NO NO NO NO NO NO NO H X S K S e v e max , +m 3 D e c a y o f h e t e r o t r o p h s 1 b H X B H 4 S y n t h e s i s r a t e o f e n z y m e a s s o c i a t e d w i t h a e r o b i c g r o w t h 1 O H B O H O O Ou X S K S, , +a 5 S y n t h e s i s r a t e o f e n z y m e a s s o c i a t e d w i t h a n o x i c g r o w t h 1 NO H B NO NO NO NO u X S K S +a 6 E n z y m e d e c a y r a t e 1 b O E O 7 E n z y m e d e c a y r a t e 1 b N O E N O O b s e r v e d c o n v e r s i o n r a t e M L 3 T 1 =j j ij irr g

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1 0 M o d e l R e l a t i o n s h i p s ) ( max i i i i i i v v vr r= ==2 1) (i i i i i iv v ur r H B i i X E e = i i i i eb m a+ = max, max w h e r e i = O o r N O r O = r 1 r N O = r 2 2 3 M o d e l i n g o f D i a u x i c L a g i n P s e u d o m o n a s D e n t r i f i c a n s T h e m o d e l p r o p o s e d b y L i u e t a l ( 1 9 9 8 a ) i s b a s e d o n t h e h y p o t h e s i s t h a t t h e d i a u x i c l a g o c c u r s d u e t o t h e l a c k o f e n z y m e s n e e d e d f o r e l e c t r o n a c c e p t o r u t i l i z a t i o n ( n i t r a t e r e d u c t a s e i n t h i s c a s e ) T h e l a g i s t h e p e r i o d w h e n t h e e n z y m e b u i l d s u p a n d w h e n i t r e a c h e s a c e r t a i n l e v e l b e c o m e s a c t i v a t e d a n d e x p o n e n t i a l g r o w t h r e s u m e s L i u e t a l r e v i s e d t h e i r c y b e r n e t i c m o d e l ( 1 9 9 8 b ) O n e m o d i f i c a t i o n i s t h a t t h e c o e f f i c i e n t s o f t h e e n z y m e s y n t h e s i s r a t e s a r e n o t c o n s t a n t b u t a n i n c r e a s i n g f u n c t i o n o f e n z y m e s p e c i f i c l e v e l A t l o w e n z y m e s p e c i f i c l e v e l s l o w a m o u n t o f e n e r g y w i l l b e a v a i l a b l e f o r b i o s y n t h e s i s I n c r e a s i n g e n z y m e l e v e l w o u l d i n c r e a s e t h e e n e r g y a v a i l a b l e a n d t h e r e b y t h e p o t e n t i a l e n z y m e s y n t h e s i s r a t e F u r t h e r m o r e a t h i g h e r t h e e n z y m e s p e c i f i c l e v e l s m o r e m e t a b o l i c m a c h i n e r y w i l l b e a v a i l a b l e f o r u t i l i z i n g t h i s e n e r g y t h e r e f o r e i n c r e a s i n g t h e e f f i c i e n c y o f e n z y m e s y n t h e s i s T h e e x p r e s s i o n f o r e n z y m e a c t i v i t y v N O a l s o d i f f e r s f r o m t h e o n e u s e d i n t h e c y b e r n e t i c m o d e l s I t p r o v i d e s f o r a s h a r p e r t r a n s i t i o n f r o m i n a c t i v e t o a c t i v e e n z y m e b y u t i l i z i n g a l o g i s t i c f u n c t i o n e N O / e N O m a x + = amx No NO NO ce e r s NO e v ,4 1 1 ( 2 1 0 ) F o r l a r g e r v a l u e s o f t h e p a r a m e t e r s v N O i s c l o s e t o z e r o ( i n a c t i v e e n z y m e ) f o r r a t i o e N O / e N O m a x = 0 a n d c l o s e t o o n e ( f u l l a c t i v a t i o n ) f o r e N O / e N O m a x = 1 T h e p a r a m e t e r

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1 1 r c N O ( c r i t i c a l r a t i o ) s e t s t h e v a l u e o f t h e r a t i o f o r w h i c h e n z y m e a c t i v i t y r e a c h e s 5 0 % T h e p a r a m e t e r s ( s h a r p n e s s p a r a m e t e r ) i s t h e s l o p e o f t h e c u r v e a t e N O / e N O m a x = r c N O T a b l e 2 3 P r o c e s s k i n e t i c s a n d s t o i c h i o m e t r y o f t h e m o d e l p r o p o s e d b y L i u e t a l ( 1 9 9 8 b ) C o m p o n e n t i 1 2 3 4 5 j P r o c e s s S O S N O X B H E O E N O P r o c e s s r a t e r j M L 3 T 1 1 A e r o b i c g r o w t h O H O H Y Y , 1 1 B O H O O o o o O HX S K S e v e +, max ,m 2 A n o x i c g r o w t h NO H NO H Y Y , 86 2 1 1 B NO NO NO NO NO NO NO H X S K S e v e + max ,m 3 D e c a y 1 b H X B 4 S y n t h e s i s r a t e o f e n z y m e a s s o c i a t e d w i t h a e r o b i c g r o w t h 1 O B O H O O O O O Ou X S K S e e + +, max 2 1 ,a a 5 S y n t h e s i s r a t e o f e n z y m e a s s o c i a t e d w i t h a n o x i c g r o w t h 1 NO B NO NO NO NO NO NO NO u X S K S e e + + max 2 1 ,a a 6 E n z y m e d e c a y r a t e 1 b O E O 7 E n z y m e d e c a y r a t e 1 b N O E N O O b s e r v e d c o n v e r s i o n r a t e M L 3 T 1 =j j ij irr g M o d e l R e l a t i o n s h i p s + =max ,4 1 1i i i ce e r s i e v ==2 1) (i i i i i iv v ur r B i i X E e = H i i i i i b e + + =b m a a max, 2 1 max w h e r e i = O o r N O r O = r 1 r N O = r 2

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1 2 T h e r e v i s e d k i n e t i c m o d e l i s p r e s e n t e d i n T a b l e 2 3 D i f f e r e n t y i e l d c o e f f i c i e n t s a r e u s e d f o r a e r o b i c a n d a n o x i c g r o w t h T h e a b o v e m e c h a n i s t i c m o d e l c o u l d f i t q u i t e w e l l t h e e x p e r i m e n t a l d a t a o f L i u e t a l ( 1 9 9 8 a 1 9 9 8 b ) i n w h i c h a l l a e r o b i c g r o w t h s w e r e w i t h h i g h d i s s o l v e d o x y g e n c o n c e n t r a t i o n s ( n e a r s a t u r a t i o n ) H o w e v e r i t w a s c o n s i d e r a b l y l e s s s u c c e s s f u l i n f i t t i n g m o r e r e c e n t e x p e r i m e n t a l d a t a o b t a i n e d i n o u r l a b i n w h i c h d i a u x i c g r o w t h w i t h l o w d i s s o l v e d o x y g e n c o n c e n t r a t i o n s w e r e i n v e s t i g a t e d 2 4 H y b r i d M o d e l s N e u r a l n e t w o r k m o d e l s w e r e i n t r o d u c e d i n t o t h e a c t i v a t e d s l u d g e m o d e l i n g b y L i u e t a l ( 1 9 9 5 ) L i u e t a l ( 1 9 9 5 ) c o m b i n e d a m a t e r i a l b a l a n c e m o d e l w i t h a r t i f i c i a l n e u r a l n e t w o r k s f o r t h e r e a c t i o n r a t e s T h e i n p u t s w e r e t h e s t a n d a r d i n p u t s o f A S M 1 T h i s m o d e l p e r f o r m e d v e r y w e l l w i t h s i m u l a t e d d a t a b u t p o o r l y w i t h e x p e r i m e n t a l d a t a C l e a r l y s o m e i m p o r t a n t i n p u t s t o t h e n e u r a l n e t w o r k w e r e m i s s i n g Z h a o e t a l ( 1 9 9 9 ) u s e d a s i m p l i f i e d v e r s i o n o f t h e A c t i v a t e d S l u d g e M o d e l N o 2 ( S P M ) a n d n e u r a l n e t w o r k s t o m o d e l a c c u r a t e l y t h e p r o c e s s d y n a m i c s o f n i t r o g e n a n d p h o s p h o r o u s ( n u t r i e n t s ) i n a s e q u e n c i n g b a t c h r e a c t o r ( S B R ) T h e S P M p r o v i d e d a p r e l i m i n a r y p r e d i c t i o n o f t h e p r o c e s s b e h a v i o r b a s e d o n a s m a l l e r s e t o f i n p u t s s u c h a s m e a s u r e m e n t s o f i n f l u e n t a m m o n i a a n d p h o s p h a t e C O D a n d t i m e r c o n t r o l s i g n a l s T h e n e u r a l n e t w o r k w a s f e d w i t h t h e a b o v e i n p u t s a n d a d d i t i o n a l p a r a m e t e r s t h a t c o u l d i n f l u e n c e t h e p r o c e s s T h e n e t w o r k w a s t r a i n e d t o p r e d i c t t h e d i f f e r e n c e b e t w e e n t h e a c t u a l p r o c e s s o u t p u t d a t a a n d S P M p r e d i c t i o n s I n o r d e r w o r d s t h e n e t w o r k l e a r n e d t o b i a s t h e S P M I t w a s f o u n d t h a t t h e a b o v e h y b r i d m o d e l w a s m o r e s u i t a b l e f o r o n l i n e p r e d i c t i o n a n d c o n t r o l t h a n t h e S P M m o d e l T h e h y b r i d m o d e l f o r a n a e r o b i c w a s t e w a t e r t r e a t m e n t s y s t e m s d e v e l o p e d b y

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1 3 K a m a r a e t a l ( 2 0 0 0 ) c o m b i n e s a f e e d f o r w a r d n e t w o r k d e s c r i b i n g b a c t e r i a l k i n e t i c s a n d a p r i o r i k n o w l e d g e b a s e d o n t h e m a s s b a l a n c e s o f t h e p r o c e s s c o m p o n e n t s T h e m o d e l ’ s a r c h i t e c t u r e c o n s i s t s o f a s t a t i c m o d e l o f u n m e a s u r e d p r o c e s s p a r a m e t e r s ( k i n e t i c g r o w t h r a t e ) i n t e g r a t e d w i t h a d y n a m i c r e p r e s e n t a t i o n o f t h e p r o c e s s u s i n g a s e t o f d y n a m i c d i f f e r e n t i a l e q u a t i o n s T h e p e r f o r m a n c e o f t h i s a p p r o a c h w a s e v a l u a t e d u s i n g e x p e r i m e n t a l d a t a T a y a n d Z h a n g ( 1 9 9 9 ) d e v e l o p e d a c o n c e p t u a l a d a p t i v e m o d e l f o r a n a e r o b i c w a s t e w a t e r s y s t e m s u s i n g a d v a n c e d n e u r a l f u z z y s y s t e m s i n p l a c e o f t h e c o n v e n t i o n a l k i n e t i c m o d e l s T h e c o n c e p t u a l n e u r a l f u z z y m o d e l h a d t h e r o b u s t n e s s o f f u z z y s y s t e m s t h e l e a r n i n g a b i l i t y o f n e u r a l n e t w o r k s a n d c o u l d a d a p t t o v a r i o u s s i t u a t i o n s T h e c o n c e p t u a l m o d e l w a s u s e d t o s i m u l a t e t h e d a i l y p e r f o r m a n c e o f t w o h i g h r a t e a n a e r o b i c w a s t e w a t e r t r e a t m e n t s y s t e m s H c k a n d K h n e ( 1 9 9 9 ) t r i e d t o d e v i s e a n e w m e t h o d t o e s t i m a t e w a s t e w a t e r p r o c e s s p a r a m e t e r s ( e g C O D ) b a s e d o n o n l i n e m e a s u r e m e n t s o f a u x i l i a r y p a r a m e t e r s T h e y u s e d n e u r a l n e t w o r k s t o e n a b l e d e t e c t i o n o f n o n l i n e a r s t a t i c / d y n a m i c c o r r e l a t i o n b e t w e e n t h e a u x i l i a r y a n d p r o c e s s p a r a m e t e r s b a s e d o n m e a s u r e d v a l u e s o f t h e a u x i l i a r y p a r a m e t e r s T h e n e t w o r k w a s t r a i n e d u s i n g e x p e r i m e n t a l d a t a A m o n g t h e e n t i r e s e t o f h y b r i d o r n e u r a l n e t w o r k m o d e l s t h a t h a v e b e e n d e v e l o p e d s o f a r n o n e o f t h e m o d e l s c a n p r e d i c t t h e d i a u x i c g r o w t h p a t t e r n

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1 4 C H A P T E R 3 P U R P O S E T h e p u r p o s e o f t h i s s t u d y i s t o d e v e l o p a n e u r a l n e t w o r k m o d e l t h a t p r e d i c t s t h e l e n g t h o f t h e d i a u x i c l a g w h e n b a c t e r i a l c u l t u r e s s w i t c h e l e c t r o n a c c e p t o r s ( o x y g e n t o n i t r a t e ) i n a s y n t h e t i c w a s t e w a t e r m e d i u m I n a p r e v i o u s s t u d y p e r f o r m e d b y L i u e t a l ( 1 9 9 6 ) i t w a s s h o w n t h a t d i a u x i c l a g s o c c u r b e t w e e n a e r o b i c g r o w t h a n d a n o x i c g r o w t h i n a n i t r i f i c a t i o n d e n i t r i f i c a t i o n s y s t e m T h e d i a u x i c l a g i s g e n e r a l l y a t t r i b u t e d t o t i m e r e q u i r e d t o s y n t h e s i z e a n d a c t i v a t e i n d u c i b l e e n z y m e s f o r u t i l i z i n g a l t e r n a t e e l e c t r o n a c c e p t o r s T h e m o d e l p r o p o s e d b y L i u e t a l ( 1 9 9 8 a 1 9 9 8 b ) s u g g e s t s t h a t t h e r e i s a d e c r e a s e i n e n z y m e s p e c i f i c l e v e l s u n d e r a e r o b i c c o n d i t i o n s I n e x p e r i m e n t s i n w h i c h P s e u d o m o n a s d e n i t r i f i c a n s w a s r e v i v e d f r o m a g a r p l a t e s a n d t h e n g r o w n i n b a t c h r e a c t o r s f i r s t u n d e r a e r o b i c c o n d i t i o n s a n d t h e n u n d e r a n o x i c c o n d i t i o n s i t w a s o b s e r v e d t h a t t h e l e n g t h o f t h e l a g d e p e n d s o n t h e c o n c e n t r a t i o n s o f n i t r a t e i t w a s e x p o s e d t o b o t h i n t h e r e v i v i n g p h a s e a n d t h e a e r o b i c p h a s e T h e l e n g t h o f t h e l a g i s a l s o o b s e r v e d t o i n c r e a s e w i t h i n c r e a s e i n l e n g t h o f t i m e o f t h e a e r o b i c p h a s e A l s o e x p e r i m e n t a l s t u d i e s s h o w e d t h a t b a c t e r i a l c u l t u r e s u n d e r l o w e r d i s s o l v e d o x y g e n c o n c e n t r a t i o n s d u r i n g t h e a e r o b i c p h a s e h a v e a s h o r t e r d i a u x i c l a g i n c o m p a r i s o n t o c u l t u r e s a t a i r s a t u r a t i o n d u r i n g t h e a e r o b i c p h a s e T h e e x p l a n a t i o n i s t h a t l o w e r d i s s o l v e d o x y g e n s h o u l d h a v e a l e s s i n h i b i t o r y e f f e c t o n t h e d e n i t r i f y i n g e n z y m e s h e n c e s h o r t e n i n g t h e l e n g t h o f t h e d i a u x i c l a g

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1 5 T h e p r e s e n t r e s e a r c h m a k e s a n a t t e m p t t o u s e a n e u r a l n e t w o r k i n p l a c e o f t h e t r a d i t i o n a l m o d e l t o p r e d i c t t h e d u r a t i o n o f t h e d i a u x i c l a g u n d e r a g i v e n s e t o f c o n d i t i o n s T h e a e r o b i c a n d a n o x i c p h a s e g r o w t h c u r v e s c a n b e c a p t u r e d b y t h e t r a d i t i o n a l M o n o d ( 1 9 4 2 ) e x p r e s s i o n s I f t h e s e w e r e i n t e g r a t e d w i t h a n e u r a l n e t w o r k f o r p r e d i c t i n g t h e l a g t h e r e s u l t i n g h y b r i d m o d e l s h o u l d b e a b l e t o d e s c r i b e t h e c o m p l e t e d i a u x i c g r o w t h T h e e x p e r i m e n t a l d a t a w a s c a t e g o r i z e d b a s e d o n t h e r e v i v i n g p h a s e ( a e r o b i c / a n o x i c ) a n d d i s s o l v e d o x y g e n c o n c e n t r a t i o n s T h e n e u r a l n e t w o r k w a s f i r s t t r a i n e d w i t h e x p e r i m e n t a l d a t a f o r w h i c h t h e r e v i v i n g p h a s e w a s a l w a y s a n o x i c a n d c o n c e n t r a t i o n s o f n i t r a t e w e r e v e r y l o w ( a l m o s t z e r o ) i n t h e a e r o b i c p h a s e I n t h i s c a s e t h e i n p u t s t o t h e n e u r a l n e t w o r k w e r e b i o m a s s c o n c e n t r a t i o n i n t e r m s o f a b s o r b a n c e a t t h e s t a r t o f t h e e x p e r i m e n t d i s s o l v e d o x y g e n c o n c e n t r a t i o n s t h r o u g h t h e a e r o b i c p h a s e a n d t h e d u r a t i o n o f t h e a e r o b i c p h a s e i n h o u r s T h e n e u r a l n e t w o r k h a d o n l y o n e o u t p u t n o d e t h a t b e i n g t h e t i m e i n h o u r s o f t h e d i a u x i c l a g T h e r e w a s a s i n g l e h i d d e n l a y e r o f n e u r o n s a n d t h e n u m b e r o f n o d e s i n t h e h i d d e n l a y e r w a s v a r i e d a n d t h e p e r f o r m a n c e w a s c o m p a r e d T h e n e t w o r k a r c h i t e c t u r e t h a t g a v e t h e l o w e s t r o o t m e a n s q u a r e d e r r o r w a s c h o s e n a n d t h e c o r r e s p o n d i n g w e i g h t s s a v e d T h e n e u r a l n e t w o r k w a s t h e n t e s t e d w i t h e x p e r i m e n t a l d a t a d i f f e r e n t f r o m t h e t r a i n i n g d a t a a n d t h e r e s u l t s c o m p a r e d w i t h t h e d e s i r e d o u t p u t A s e c o n d n e u r a l n e t w o r k w a s t r a i n e d w i t h a d d i t i o n a l i n p u t s s u c h a s t h e s t a t u s o f t h e r e v i v i n g p h a s e o f t h e c u l t u r e a n d t h e v a r y i n g c o n c e n t r a t i o n s o f n i t r a t e i n t h e a e r o b i c p h a s e I n t h i s c a s e t h e d i s s o l v e d o x y g e n c o n c e n t r a t i o n w a s m a i n t a i n e d a t 8 7 m g / L T h e n e t w o r k w a s t h e n t e s t e d a n d t h e p r e d i c t e d d i a u x i c l a g l e n g t h f r o m t h e n e u r a l n e t w o r k c o m p a r e d t o t h e a c t u a l e x p e r i m e n t a l r e s u l t s

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1 6 E f f o r t s w e r e a l s o m a d e t o d e v i s e a s t a n d a r d n i t r a t e r e d u c t a s e e n z y m e a s s a y f o r P s e u d o m o n a s d e n i t r i f i c a n s C u l t u r e s o f P s e u d o m o n a s d e n i t r i f i c a n s ( A T C C 1 3 8 6 7 ) w e r e p r e c u l t u r e d i n b o t h a e r o b i c a n d a n o x i c e n v i r o n m e n t s T h i s w o u l d p r o v i d e c a s e s o f b o t h a b s e n c e a n d p r e s e n c e o f d e n i t r i f y i n g e n z y m e s w h e n t h e c u l t u r e s w e r e i n t r o d u c e d i n t o t h e b i o r e a c t o r T h e r e a c t o r w a s a l w a y s h e l d a t a i r s a t u r a t i o n ( 8 7 m g / L ) i n t h e a e r o b i c p h a s e w h i c h t y p i c a l l y l a s t e d 2 3 h o u r s S a m p l e s f o r t h e e n z y m e a s s a y w e r e w i t h d r a w n f r o m t h e b i o r e a c t o r a t d i f f e r e n t p o i n t s i n t h e e n t i r e e x p e r i m e n t a n d s t o r e d o n i c e T h e s a m p l e s w e r e t h e n a s s a y e d a n d t h e e n z y m e a c t i v i t i e s r e c o r d e d

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1 7 C H A P T E R 4 E X P E R I M E N T A L M E T H O D S A N D R E S U L T S T h r e e k i n d s o f e x p e r i m e n t s p e r f o r m e d t h r o u g h t h e c o u r s e o f t h i s s t u d y : H i g h b i o m a s s e x p e r i m e n t s t o m e a s u r e t h e a c t i v i t i e s o f e n z y m e g r o w t h e x p e r i m e n t s t o s t u d y t h e e f f e c t o f d i s s o l v e d o x y g e n o n t h e d i a u x i c l a g a n d g r o w t h e x p e r i m e n t s t o s t u d y t h e e f f e c t o f r e v i v i n g p h a s e o n t h e l e n g t h o f t h e d i a u x i c l a g 4 1 N i t r a t e R e d u c t a s e E n z y m e A s s a y 4 1 1 E x p e r i m e n t a l M e t h o d s T h e d e n i t r i f y i n g b a c t e r i u m u s e d i n t h i s s t u d y w a s P s e u d o m o n a s d e n i t r i f i c a n s – A T C C 1 3 8 6 7 T h e f r e e z e d r i e d b a c t e r i a w e r e r e v i v e d i n f l a s k s o f 1 2 5 m l o f N u t r i e n t B r o t h ( # 0 0 0 3 1 7 8 ) s u p p l i e d f r o m S i g m a C h e m i c a l C o m p a n y T h e d e n i t r i f y i n g b a c t e r i a w e r e p l a c e d i n a s h a k e r a n d a l l o w e d t o g r o w i n t h e m e d i u m f o r t w o d a y s S u b s e q u e n t l y t h e m i c r o b i a l m i x t u r e w a s t r a n s f e r r e d u s i n g 1 0 m l s t e r i l e i n o c u l a t i n g l o o p s o n t o t r y p t i c s o y a g a r p l a t e s u s i n g t h e s t r e a k t e c h n i q u e P s e u d o m o n a s d e n i t r i f i c a n s w e r e g r o w n o n t h e a g a r p l a t e s a t 3 5 0 C i n a F i s h e r M o d e l I s o t e m p 3 0 3 i n c u b a t o r f o r t w o d a y s a n d s t o r e d a t 4 0 C A g a r p l a t e s w e r e k e p t f o r t w o w e e k s f o r u s e i n e x p e r i m e n t s b e f o r e f r e s h p l a t e s w e r e m a d e D e i o n i z e d w a t e r w a s u s e d f o r p r e p a r i n g a g a r a n d l i q u i d m e d i a C u l t u r e s w e r e g r o w n i n s y n t h e t i c l i q u i d m e d i u m m o d i f i e d f r o m ( T a b l e 4 1 ) K o r n a r o s e t a l ( 1 9 9 6 ) w i t h o r w i t h o u t w i t h o u t n i t r a t e d e p e n d i n g o n w h a t k i n d o f p r e c u l t u r e c o n d i t i o n s w e r e r e q u i r e d f o r t h a t e x p e r i m e n t T h e p H o f t h e m e d i u m w a s a d j u s t e d t o 7 0 u s i n g 2 N N a O H b e f o r e a u t o c l a v i n g a n d t h e a d d i t i o n o f n i t r a t e n i t r o g e n ( i f

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1 8 r e q u i r e d ) C u l t u r e m e d i u m i n 2 5 0 m l f l a s k s ( 1 2 5 m l l i q u i d v o l u m e ) w a s i n o c u l a t e d f r o m a g a r p l a t e s F o r o x i c p r e c u l t u r e c o n d i t i o n s t h e f l a s k s w e r e a g i t a t e d i n a s h a k e r b a t h f o r t w o d a y s a t a p p r o x i m a t e l y 2 5 o C F o r a n o x i c p r e c u l t u r e c o n d i t i o n s t h e c u l t u r e s w e r e g r o w n i n a n i t r a t e l i m i t e d s y n t h e t i c l i q u i d m e d i u m ( 4 m g / L N O 3 N ) m o d i f i e d f r o m T a b l e 4 1 a n d a l l o w e d t o s i t u n d e r a s t e r i l e l a m i n a r h o o d f o r t w o d a y s T a b l e 4 1 C o m p o s i t i o n o f t h e s y n t h e t i c m e d i u m C h e m i c a l s D e i o n i z e d w a t e r g / L I n o r g a n i c S a l t s N a C l 1 N H 4 C l 1 M g S O 4 7 H 2 O 0 2 C a C l 2 7 H 2 O 0 0 2 6 4 T r a c e M e t a l s A d r o p a P h o s p h a t e s K 2 H P O 4 5 K H 2 P O 4 1 5 C a r b o n S o u r c e L G l u t a m i c A c i d 5 N i t r o g e n S o u r c e K N O 3 2 8 9 a T r a c e m e t a l s o l u t i o n c o n t a i n i n g 5 % ( w / v ) e a c h o f C u S O 4 F e C l 3 M n C l 2 a n d N a 2 M o O 4 2 H 2 O 4 1 2 G r o w t h E x p e r i m e n t s A M u l t i G e n b e n c h t o p b i o r e a c t o r m o d e l F 2 0 0 0 ( N e w B r u n s w i c k S c i e n t i f i c ) w a s u s e d f o r t h e e x p e r i m e n t s T h e c u l t u r e w a s c o n t i n u o u s l y s t i r r e d a t 3 0 2 0 C T h e p H r a n g e d f r o m 7 0 i n t h e a e r o b i c p h a s e a n d i n c r e a s e d t o 7 2 d u r i n g t h e a n o x i c p h a s e D i s s o l v e d o x y g e n w a s m o n i t o r e d u s i n g M o d e l D O 4 0 ( N e w B r u n s w i c k S c i e n t i f i c ) a n a l y z e r s w i t h g a l v a n i c e l e c t r o d e s T h e e x p e r i m e n t a l s e t u p w a s a s s h o w n i n F i g u r e 4 1 E a c h e x p e r i m e n t c o n s i s t e d o f a n a e r a t i o n p e r i o d o f 3 5 h o u r s d u r i n g w h i c h t h e r e a c t o r w a s m a i n t a i n e d a t a i r s a t u r a t i o n ( 8 7 m g / L ) A e r a t i o n w a s t h e n s t o p p e d a n d r e a c t o r w a s s p a r g e d w i t h n i t r o g e n g a s t o r e m o v e a n y r e s i d u a l d i s s o l v e d o x y g e n T h u s f o l l o w e d b y a

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1 9 A B C D E F i g u r e 4 1 : E x p e r i m e n t a l s e t u p f o r n i t r a t e r e d u c t a s e e x p e r i m e n t G a s F i l t e r R o t a m e t e A i r N i t r o g e n A T h e r m o c o u p l e B T h e r m o m e t e r C D O p r o b e D F e e d E H e a t e r

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2 0 p e r i o d w h e n n i t r a t e w a s t h e t e r m i n a l e l e c t r o n a c c e p t o r N i t r o g e n g a s f l o o d e d t h r o u g h t h e h e a d s p a c e o f t h e c u l t u r e b o t t l e d u r i n g t h e p e r i o d w h e n t h e r e w a s n o a e r a t i o n T h e v a r i a b l e s m o n i t o r e d i n c l u d e b i o m a s s i n t e r m s o f a b s o r b a n c e d i s s o l v e d o x y g e n t e m p e r a t u r e a n d p H 4 1 3 E x p e r i m e n t a l P r o t o c o l E x p e r i m e n t s w e r e c a r r i e d o u t i n o r d e r t o i n v e s t i g a t e s p e c i f i c e n z y m e l e v e l s t h r o u g h t h e c o u r s e o f a d i a u x i c g r o w t h E a c h e x p e r i m e n t c o n s i s t e d o f a s i n g l e r e a c t o r w i t h i n i t i a l b i o m a s s c o n c e n t r a t i o n s o f a b o u t 0 3 i n t e r m s o f a b s o r b a n c e T h e f i r s t s e t o f e x p e r i m e n t s w a s c a r r i e d o u t w i t h o x i c p r e c u l t u r e c o n d i t i o n s P o t a s s i u m n i t r a t e ( 4 0 0 m g / L ) w a s a d d e d t o t h e r e a c t o r i n t h e a n o x i c p h a s e o f t h e e x p e r i m e n t T h e s e c o n d s e t o f e x p e r i m e n t s w a s c a r r i e d o u t u n d e r a n o x i c p r e c u l t u r e c o n d i t i o n s P o t a s s i u m n i t r a t e ( 4 0 0 m g / L ) w a s a d d e d t o t h e r e a c t o r i n t h e o x i c p h a s e o f t h e e x p e r i m e n t 4 1 4 A n a l y t i c M e t h o d s S a m p l e s w e r e w i t h d r a w n f r o m t h e r e a c t o r u s i n g a s y r i n g e c o n n e c t e d t o a p l a s t i c t u b e t h a t e x t e n d e d t h r o u g h t h e c a p t o t h e b o t t o m o f t h e r e a c t o r T h e s a m p l e l i n e w a s f l u s h e d s e v e r a l t i m e s t h e n 2 1 0 m L w a s w i t h d r a w n A p o r t i o n ( 1 0 m L ) o f e a c h s a m p l e w a s u s e d t o m e a s u r e a b s o r b a n c e A b s o r b a n c e o f t h e c u l t u r e w a s m e a s u r e d u s i n g a s p e c t r o p h o t o m e t e r ( M i l t o n R o y S p e c t r o n i c 2 1 D ) a t 5 5 0 n m u s i n g a 1 2 5 c m p a t h l e n g t h T h e r e s t o f t h e w i t h d r a w n s a m p l e ( 2 0 0 m L ) w a s i m m e d i a t e l y p l a c e d o n i c e a n d s t o r e d a t 0 o C T h e s a m p l e s w e r e t h e n a n a l y z e d t h e n e x t d a y f o r n i t r a t e r e d u c t a s e e n z y m e a c t i v i t y T h e s a m p l e s w e r e f i r s t d e g a s s e d f o r t w o m i n u t e s t o c r e a t e a n d o x y g e n f r e e a t m o s p h e r e w a s h e d w i t h 1 M p h o s p h a t e b u f f e r K P O 4 ( p H = 7 0 ) a n d i c e c e n t r i f u g e d a t 8 0 0 0 r p m f o r 5

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2 1 m i n u t e s a t 2 d e g r e e s c e n t i g r a d e T h e s u p e r n a t a n t w a s d r a i n e d a n d 7 m L o f 1 M p h o s p h a t e b u f f e r K P O 4 ( p H = 7 0 ) w a s a d d e d T h e b i o m a s s p e l l e t w a s r e s u s p e n d e d b y v o r t e x i n g a n d d e g a s s e d w i t h n i t r o g e n g a s f o r t w o m i n u t e s T h e s a m p l e s w e r e c o l d c e n t r i f u g e d a t 1 0 0 0 0 r p m f o r 5 m i n u t e s a t 2 d e g r e e s c e n t i g r a d e T h e s u p e r n a t a n t w a s d r a i n e d a n d 1 m L o f 1 M P h o s p h a t e b u f f e r K P O 4 ( p H = 7 0 ) w a s a d d e d a n d t h e b i o m a s s p e l l e t r e s u s p e n d e d b y v o r t e x i n g T h e s a m p l e w a s t h e n t r a n s f e r r e d t o 1 5 m L t u b e s a n d p l a c e d i n a b e a k e r o f i c e O x y g e n f r e e c o n d i t i o n s w e r e m a i n t a i n e d b y s p a r g i n g t h e c o n t a i n e r i n w h i c h t h e b e a k e r w a s p l a c e d w i t h n i t r o g e n E a c h s a m p l e w a s t h e n s o n i c a t e d f o r t w o 1 5 s e c o n d p e r i o d s w i t h a n i n t e r v a l o f 1 5 s e c o n d s a n d p l a c e d b a c k o n t h e i c e b a t h A p o r t i o n o f t h e s a m p l e w a s t h e n p i p e t t e d o u t i n a t e s t t u b e t o w h i c h 0 1 m L o f 5 0 m M N a N O 3 0 0 3 m L o f 1 M P h o s p h a t e b u f f e r K P O 4 ( p H = 7 0 ) b u f f e r a n d 0 0 7 m L o f 1 m M b e n z y l v i o l o g e n w a s a d d e d N e x t 0 0 5 m l s o d i u m d i a t h i o n i d e N a 2 S 2 O 4 2 w a s a d d e d a n d w a s a l l o w e d t o r e a c t f o r 3 0 s e c o n d s T h e r e a c t i o n w a s s t o p p e d b y v o r t e x i n g t h e s a m p l e T h e n i t r i t e w a s e s t i m a t e d b y a d d i n g 0 5 m L 1 % s u l f a n i l a m i d e i n 2 5 N H C l a n d 0 5 m L N 1 N a p t h y l e n e d i a m i n e d i h y d r o c h l o r i d e ( 0 0 2 % i n w a t e r ) a n d t h e s a m p l e v o r t e x t e d 5 m L o f d e i o n i z e d w a t e r w a s a d d e d t h e t e s t t u b e a n d v o r t e x e d a g a i n T h e s a m p l e s w e r e t h e n c e n t r i f u g e d a t 3 3 0 0 r p m f o r 1 5 m i n u t e s T h e n i t r a t e r e d u c t a s e a c t i v i t y w a s m e a s u r e d i n t e r m s o f a b s o r b a n c e u s i n g a s p e c t r o p h o t o m e t e r ( M i l t o n R o y S p e c t r o n i c 2 1 D ) a t 5 4 0 n m u s i n g a 1 2 5 c m p a t h l e n g t h

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2 2 F i g u r e 4 2 N i t r a t e r e d u c t a s e e n z y m e p r o c e d u r e C e l l P r e p a r a t i o n : T a k e t h e s a m p l e f r o m i c e b a t h a n d d e g a s i t f o r 2 m i n u t e s w i t h n i t r o g e n I c e c e n t r i f u g e s a m p l e a t 8 0 0 0 r p m f o r 5 m i n u t e s a t 2 o C D r a i n s u p e r n a t a n t a n d a d d 7 m L o f 1 M p h o s p h a t e b u f f e r K P O 4 ( p H = 7 0 ) a n d d e g a s f o r 2 m i n u t e s w i t h n i t r o g e n V o r t e x s a m p l e a n d i c e c e n t r i f u g e a t 1 0 0 0 0 r p m f o r 5 m i n u t e s a t 2 o C D r a i n s u p e r n a t a n t a n d a d d 1 m L o f 1 M p h o s p h a t e b u f f e r K P O 4 ( p H = 7 0 ) a n d d e g a s f o r 2 m i n u t e s w i t h n i t r o g e n V o r t e x s a m p l e a n d t r a n s f e r s a m p l e t o 1 5 m L t e s t t u b e s a n d p l a c e i n a b e a k e r o f i c e S o n i c a t e s a m p l e s f o r 1 5 s e c o n d s M a i n t a i n a n o x y g e n f r e e e n v i r o n m e n t b y s p a r g i n g c o n t a i n e r w i t h n i t r o g e n P i p e t t e o u t 0 1 m L o f t h e s o n i c a t e d s a m p l e i n t o a t e s t t u b e S m a l l c e n t r i f u g e t u b e 0 3 m L t o t a l s o l u t i o n c o n t a i n i n g : 0 1 m L c e l l s a m p l e 0 2 m L s o l u t i o n o f : 0 1 m L o f 5 0 m M N a N O 3 0 0 3 m l o f 1 M P h o s p h a t e b u f f e r K P O 4 ( p H = 7 0 ) b u f f e r 0 0 7 m l o f 1 m M b e n z y l v i o l o g e n 0 0 5 m L S 2 O 4 2 t o s t a r t t h e r e a c t i o n ( 2 0 m M S 2 O 4 2 i n 2 0 m M N a 2 C O 3 ) P u r p l e c o l o r o b s e r v e d L e t r e a c t i o n p r o c e e d f o r 3 0 s e c s V o r t e x t o o x i d i z e S 2 O 4 2 a n d s t o p t h e r e a c t i o n D e t e r m i n e N O 2

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2 3 F i g u r e 4 3 N i t r a t e r e d u c t a s e e n z y m e p r o c e d u r e ( n i t r i t e d e t e r m i n a t i o n ) 0 3 5 m L s a m p l e c o n t a i n i n g n i t r i t e 0 5 m L 1 % s u l f a n i l a m i d e i n 2 5 N H C l 0 5 m L N 1 N a p t h h y l e n e d i a m i n e d i h y d r o c h o l r i d e ( 0 0 2 % i n w a t e r ) V o r t e x t h e s a m p l e D i l u t e w i t h 5 m L o f D I w a t e r V o r t e x s a m p l e a g a i n C e n t r i f u g e a t 3 3 0 0 r p m f o r 1 5 m i n u t e s T r a n s f e r s u p e r n a t a n t t o s m a l l t e s t t u b e M e a s u r e a b s o r b a n c e o f s u p e r n a t a n t a t 5 4 0 n m

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2 4 4 1 5 E x p e r i m e n t a l R e s u l t s T h e m o d e l p r o p o s e d b y L i u e t a l ( 1 9 9 8 a b ) a t t r i b u t e d t h e d i a u x i c l a g t o t h e l o w c o n c e n t r a t i o n s o f n i t r a t e r e d u c t a s e e n z y m e a n d i n t u r n a c t i v i t y o f t h e e n z y m e i n t h e a e r o b i c p h a s e T h e s h o r t e r l a g s t h a t o c c u r r e d w h e n c u l t u r e h a d b e e n r e v i v e d u n d e r a n o x i c c o n d i t i o n s a n d e x p o s e d t o n i t r a t e i n t h e a e r o b i c p h a s e w e r e a t t r i b u t e d t o t h e s y n t h e s i s o f n i t r a t e r e d u c t a s e d u r i n g t h e a e r o b i c p h a s e a l t h o u g h t h e e n z y m e w a s s t i l l i n a c t i v e T h e e x p e r i m e n t a l r e s u l t s ( F i g u r e 4 4 ) o f m e a s u r e d e n z y m e a c t i v i t y v e r s u s t i m e w h e n t h e c u l t u r e w a s r e v i v e d u n d e r a n o x i c c o n d i t i o n s a n d e x p o s e d t o n i t r a t e i n t h e a e r o b i c p h a s e o f t h e e x p e r i m e n t d o n o t a g r e e w i t h t h e p r o p o s e d h y p o t h e s i s T h e n i t r a t e r e d u c t a s e e n z y m e l e v e l s w e r e f o u n d t o i n c r e a s e a t a r a t e f a s t e r t h a n b i o m a s s a n d d r o p a f t e r t h e o x y g e n s u p p l y w a s t u r n e d o f f O n t h e o t h e r h a n d t h e l e v e l s o f e n z y m e a c t i v i t y t h r o u g h a n e x p e r i m e n t w h e r e t h e c u l t u r e w a s r e v i v e d u n d e r o x i c p r e c u l t u r e c o n d i t i o n s a n d e x p o s e d t o n i t r a t e o n l y w h e n t h e o x y g e n w a s t u r n e d o f f ( F i g u r e s 4 5 ) w e r e f o u n d t o a g r e e c l o s e l y w i t h t h e h y p o t h e s i s p r o p o s e d T h e n i t r a t e r e d u c t a s e e n z y m e a s s a y f o r P s e u d o m o n a s d e n i t r i f i c a n s i s f a r f r o m b e i n g s t a n d a r d i z e d L i t e r a t u r e g i v e s u s a w e a l t h o f i n f o r m a t i o n o n n i t r a t e r e d u c t a s e a s s a y s d e v e l o p e d f o r d i f f e r e n t s t r a i n s o f b a c t e r i a K r u l e t a l ( 1 9 7 7 ) d e v i s e d e n z y m e a s s a y s f o r n i t r a t e r e d u c t a s e e n z y m e i s o l a t e d f r o m s e v e r a l d e n i t r i f y i n g b a c t e r i a I n t h e i r n i t r a t e r e d u c t a s e e n z y m e a s s a y c h l o r a m p h e n i c o l w a s a d d e d t o s t o p p r o t e i n s y n t h e s i s i n t h e c e l l s j u s t a f t e r w a s h i n g w i t h p h o s p h a t e b u f f e r a n d t h e c e l l s w e r e l y s e d b y f i r s t u s i n g a F r e n c h P r e s s a t 2 0 0 0 0 p s i a n d t h e n t r e a t e d w i t h a n u l t r a s o n i c ( M S E ) f o r 2 m i n u t e s T h e y o b s e r v e d t h a t t h e s y n t h e s i s o f d i s s i m i l a t o r y n i t r a t e r e d u c t a s e w a s o n l y p a r t i a l l y r e p r e s s e d b y o x y g e n i n s o m e s t r a i n s o f b a c t e r i a H o w e v e r i f t h e o x y g e n c o n c e n t r a t i o n w a s i n c r e a s e d b e y o n d a i r s a t u r a t i o n t h e n s i g n i f i c a n t r e p r e s s i o n o f e n z y m e s y n t h e s i s o c c u r r e d

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2 5 S i m p k i n a n d B o y l e ( 1 9 8 8 ) e m p h a s i z e d t h e i m p o r t a n c e o f s p a r g i n g t h e c e l l f r e e e x t r a c t s w i t h n i t r o g e n t o c r e a t e a n o x y g e n f r e e e n v i r o n m e n t a n d m a i n t a i n e d a l l t h e i r s a m p l e s i n a c o n s t a n t t e m p e r a t u r e w a t e r b a t h T h e y a l s o p r e s e r v e d t h e w h o l e c e l l s a m p l e s t h a t w e r e w i t h d r a w n f r o m t h e r e a c t o r i n l i q u i d n i t r o g e n i n o r d e r t o s t o p c e l l a c t i v i t y T h e y b a s e d t h e i r c o n c l u s i o n s t h a t n i t r a t e r e d u c t a s e s y n t h e s i s w a s n o t r e p r e s s e d f u l l y b y o x y g e n b y e v a l u a t i n g t h e r a t i o o f ‘ e x p r e s s e d d e n i t r i f y i n g e n z y m e a c t i v i t i e s ’ ( s a m p l e s t h a t w e r e s o n i f i e d a n d a s s a y e d i m m e d i a t e l y ) a n d ‘ p o t e n t i a l d e n i t r i f y i n g e n z y m e a c t i v i t i e s ’ ( s a m p l e s t h a t w e r e i n a n a n o x i c e n v i r o n m e n t f o r a p e r i o d o f t h r e e h o u r s t h e n s o n i f i e d a n d a s s a y e d ) I t r e m a i n s t o b e i n v e s t i g a t e d i f i n c o r p o r a t i o n o f t h e s e s t e p s t o o u r e n z y m e a s s a y w o u l d g i v e m o r e m e a n i n g f u l r e s u l t s 4 2 E f f e c t s o f D i s s o l v e d O x y g e n L e v e l s 4 2 1 E x p e r i m e n t a l M e t h o d s C u l t u r e s w e r e g r o w n i n n i t r a t e l i m i t e d s y n t h e t i c l i q u i d m e d i u m ( 4 m g / L N O 3 N ) m o d i f i e d f r o m ( T a b l e 4 1 ) K o r n a r o s e t a l ( 1 9 9 6 ) T h e p H o f t h e m e d i u m w a s a d j u s t e d t o 7 0 u s i n g 2 N N a O H b e f o r e a u t o c l a v i n g a n d t h e a d d i t i o n o f n i t r a t e n i t r o g e n C u l t u r e m e d i u m i n 2 5 0 m L f l a s k s ( 1 2 5 m L l i q u i d v o l u m e ) w a s i n o c u l a t e d f r o m a g a r p l a t e s ( p r e p a r e d a s d i s c u s s e d i n s e c t i o n 4 1 1 ) a n d a l l o w e d t o s i t u n d e r a s t e r i l e l a m i n a r h o o d f o r t w o d a y s A p r o c e d u r e t e r m e d ‘ s p l i t t i n g ’ w a s t h e n p e r f o r m e d o n t h e c u l t u r e m e d i u m A p p r o x i m a t e l y 2 5 0 m L o f t h e c u l t u r e m e d i u m w a s a d d e d t o a l i t e r o f l i q u i d m e d i u m a n d a l l o w e d t o m i x t o p r e v e n t f l o c c u l a t i o n T h e c u l t u r e w a s t h e n s p l i t i n t o t w o 5 0 0 m L v o l u m e s t r a n s f e r r e d t o e a c h b i o r e a c t o r s i m u l t a n e o u s l y a n d d i l u t e d w i t h l i q u i d m e d i u m t o a n a b s o r b a n c e ( l = 5 5 0 n m 1 2 5 p a t h l e n g t h ) o f 0 0 2 0 0 9 f o r u s e i n e x p e r i m e n t s

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2 6 E 1 F i g u r e 4 4 E x p e r i m e n t E 1 E x p e r i m e n t w i t h a n o x i c r e v i v i n g p h a s e t o m e a s u r e n i t r a t e r e d u c t a s e e n z y m e a c t i v i t y D a t a p o i n t s s h o w e x p e r i m e n t a l r e s u l t s : b i o m a s s a n d n i t r a t e r e d u c t a s e a c t i v i t y a s s h o w n b y a b s o r b a n c e B i o m a s s a n d N i t r a t e R e d u c t a s e A c t i v i t y v e r s u s t i m e0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 t i m e ( m i n )A b s o r b a n c e0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9N i t r a t e R e d u c t a s e A c t i v i t y i n t e r m s o f a b s o r b a n c e B I O M A S S N a R O x i c P h a s e A n o x i c P h a s e 0 8

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2 7 E 2 F i g u r e 4 5 E x p e r i m e n t E 2 E x p e r i m e n t w i t h o x i c r e v i v i n g p h a s e t o m e a s u r e n i t r a t e r e d u c t a s e e n z y m e a c t i v i t y D a t a p o i n t s s h o w e x p e r i m e n t a l r e s u l t s : b i o m a s s a n d n i t r a t e r e d u c t a s e a c t i v i t y a s s h o w n b y a b s o r b a n c e B i o m a s s a n d N i t r a t e R e d u c t a s e A c t i v i t y v s t i m e 0 0 2 0 4 0 6 0 8 1 1 20 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0 6 0 0t i m e ( m i n )A b s o r b a n c e0 0 0 5 0 1 0 1 5 0 2 0 2 5 0 3 0 3 5 0 4 0 4 5N i t r a t e R e d u c t a s e A c t i v i t y i n t e r m s o f a b s o r b a n c e B I O M A S S N a R O x i c P h a s e A n o x i c P h a s e 6 6

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2 8 E 3 F i g u r e 4 6 E x p e r i m e n t E 3 E x p e r i m e n t w i t h o x i c r e v i v i n g p h a s e t o m e a s u r e n i t r a t e r e d u c t a s e e n z y m e a c t i v i t y D a t a p o i n t s s h o w e x p e r i m e n t a l r e s u l t s : b i o m a s s a n d n i t r a t e r e d u c t a s e a c t i v i t y a s s h o w n b y a b s o r b a n c e 9 6

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2 9 E 4 F i g u r e 4 7 E x p e r i m e n t E 4 E x p e r i m e n t w i t h o x i c r e v i v i n g p h a s e t o m e a s u r e n i t r a t e r e d u c t a s e e n z y m e a c t i v i t y D a t a p o i n t s s h o w e x p e r i m e n t a l r e s u l t s : b i o m a s s a n d n i t r a t e r e d u c t a s e a c t i v i t y a s s h o w n b y a b s o r b a n c e 5 8

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3 0 E 5 F i g u r e 4 8 E x p e r i m e n t E 5 E x p e r i m e n t w i t h o x i c r e v i v i n g p h a s e t o m e a s u r e n i t r a t e r e d u c t a s e e n z y m e a c t i v i t y D a t a p o i n t s s h o w e x p e r i m e n t a l r e s u l t s : b i o m a s s a n d n i t r a t e r e d u c t a s e a c t i v i t y a s s h o w n b y a b s o r b a n c e 9 3

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3 1 E 6 F i g u r e 4 9 E x p e r i m e n t E 6 E x p e r i m e n t w i t h o x i c r e v i v i n g p h a s e t o m e a s u r e n i t r a t e r e d u c t a s e e n z y m e a c t i v i t y D a t a p o i n t s s h o w e x p e r i m e n t a l r e s u l t s : b i o m a s s a n d n i t r a t e r e d u c t a s e a c t i v i t y a s s h o w n b y a b s o r b a n c e 1 0

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3 2 4 2 2 G r o w t h E x p e r i m e n t s T w o m u t i G e n b e n c h t o p b i o r e a c t o r s i n p a r a l l e l ( m o d e l s F 1 0 0 0 a n d F 2 0 0 0 N e w B r u n s w i c k S c i e n t i f i c ) w e r e u s e d f o r t h e e x p e r i m e n t s T h e c u l t u r e w a s c o n t i n u o u s l y s t i r r e d a t 3 0 2 0 C T h e p H r a n g e d f r o m 7 0 i n t h e a e r o b i c p h a s e a n d i n c r e a s e d t o 7 2 d u r i n g t h e a n o x i c p h a s e D i s s o l v e d o x y g e n w a s m o n i t o r e d u s i n g M o d e l D O 4 0 ( N e w B r u n s w i c k S c i e n t i f i c ) a n a l y z e r s w i t h g a l v a n i c e l e c t r o d e s T h e e f f e c t o f v a r i o u s l e v e l s o f d i s s o l v e d o x y g e n c o n c e n t r a t i o n o n d i a u x i c l a g w e r e c o m p a r e d a n d c o n t r a s t e d t o a h i g h d i s s o l v e d o x y g e n c o n c e n t r a t i o n o f 8 7 m g / L ( a i r s a t u r a t i o n ) T h e e x p e r i m e n t a l s e t u p w a s a s s h o w n i n F i g u r e 4 1 0 E a c h e x p e r i m e n t c o n s i s t e d o f a n a e r a t i o n p e r i o d o f 3 5 h o u r s d u r i n g w h i c h o n e r e a c t o r w a s m a i n t a i n e d a t 1 0 0 % a i r s a t u r a t i o n a n d t h e o t h e r a t t h e r e s p e c t i v e l o w D O c o n c e n t r a t i o n T o m a i n t a i n 1 0 0 % a i r s a t u r a t i o n a s t a g e d i l u t i o n w a s u s e d i n w h i c h p r i m a r i l y a i r w a s f e d t h r o u g h a Y c o n n e c t o r g a s f i l t e r a n d i n t o t h e b i o r e a c t o r O x y g e n w a s f e d i n t o t h e b i o r e a c t o r a s n e e d e d t o m a i n t a i n 1 0 0 % a i r s a t u r a t i o n L o w d i s s o l v e d o x y g e n c o n c e n t r a t i o n s ( < 0 0 9 m g / L ) w e r e m a i n t a i n e d b y f e e d i n g p u r e n i t r o g e n t h r o u g h a r o t a m e t e r w h i c h m i x e d w i t h a i r n i t r o g e n m i x t u r e i n w h i c h p u r e a i r w a s f e d t h o r o u g h a s e c o n d r o t a m e t e r L o w d i s s o l v e d o x y g e n c o n c e n t r a t i o n s r a n g i n g f r o m 0 1 8 t o 0 7 0 m g / L w e r e a c h i e v e d b y m a n u a l l y c o n t r o l l i n g t h e a i r f l o w v a l v e o n t h e a i r t a n k b a s e d o n t h e r e a d i n g o f t h e D O m e t e r T h e d i s s o l v e d o x y g e n a n a l y z e r h o w e v e r c o u l d n o t m e a s u r e a c c u r a t e l y c o n c e n t r a t i o n s b e l o w 0 1 5 m g / L A n a l t e r n a t i v e m e t h o d w a s d e v e l o p e d t o m a i n t a i n d i s s o l v e d o x y g e n c o n t r o l I t w a s o b s e r v e d t h a t i n s u c h l o w d i s s o l v e d o x y g e n e x p e r i m e n t s t h e a i r f l o w r a t e c o r r e l a t e d c l o s e l y t o t h e b i o m a s s a b s o r b a n c e ( K L i s b o n 2 0 0 0 ) T h e a i r f l o w r a t e w a s g i v e n b y t h e l i n e a r e q u a t i o n : A i r F l o w R a t e = I n i t i a l s e t t i n g + 1 0 5 9 7 ( A b s o r b a n c e – B e g i n n i n g A b s o r b a n c e )

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3 3 T o b e g i n t h e a n o x i c p h a s e a e r a t i o n w a s s t o p p e d a n d r e a c t o r w a s s p a r g e d w i t h n i t r o g e n g a s t o r e m o v e a n y r e s i d u a l d i s s o l v e d o x y g e n 4 0 0 m g / L o f n i t r a t e n i t r o g e n w a s t h e n a d d e d t o e a c h r e a c t o r s i m u l t a n e o u s l y t h u s s t a r t i n g a p e r i o d w h e n n i t r a t e w a s t h e t e r m i n a l e l e c t r o n a c c e p t o r N i t r o g e n g a s f l o o d e d t h r o u g h t h e h e a d s p a c e o f t h e r e a c t o r s d u r i n g t h e p e r i o d w h e n t h e r e w a s n o a e r a t i o n T h e v a r i a b l e s m o n i t o r e d i n c l u d e d b i o m a s s i n t e r m s o f a b s o r b a n c e d i s s o l v e d o x y g e n t e m p e r a t u r e a n d p H 4 2 3 E x p e r i m e n t a l P r o t o c o l E x p e r i m e n t s w e r e c a r r i e d o u t i n o r d e r t o i n v e s t i g a t e t h e e f f e c t o f v a r i o u s d i s s o l v e d o x y g e n c o n c e n t r a t i o n s o n t h e d u r a t i o n o f d i a u x i c l a g s E a c h e x p e r i m e n t c o n s i s t e d o f t w o p a r a l l e l t r i a l s w i t h t h e s a m e i n i t i a l c u l t u r e c o n d i t i o n s T o e n s u r e t h a t t h e p a r a l l e l c u l t u r e s h a d t h e s a m e i n i t i a l b i o m a s s c o n c e n t r a t i o n s t h e o r i g i n a l c u l t u r e s w a s w e l l m i x e d a n d d i v i d e d b e t w e e n t h e t w o b i o r e a c t o r s T h e f i r s t s e t o f s e t o f e x p e r i m e n t s w e r e c a r r i e d o u t a 0 3 5 m g / L c o n c e n t r a t i o n o f d i s s o l v e d o x y g e n i n o n e b i o r e a c t o r w i t h d i s s o l v e d o x y g e n b e i n g m a i n t a i n e d o v e r 8 7 m g / L i n t h e o t h e r P o t a s s i u m n i t r a t e ( 4 0 0 m g / L ) w a s a d d e d i n t h e a n o x i c p h a s e t o b o t h r e a c t o r s T h e s e e x p e r i m e n t s w e r e r e p e a t e d a t l o w e r d i s s o l v e d o x y g e n c o n c e n t r a t i o n s r a n g i n g f r o m 0 0 1 t o 0 0 7 m g / L 4 2 4 A n a l y t i c M e t h o d s S a m p l e s w e r e w i t h d r a w n f r o m t h e r e a c t o r u s i n g a s y r i n g e c o n n e c t e d t o a p l a s t i c t u b e t h a t e x t e n d e d t h r o u g h t h e c a p t o t h e b o t t o m o f t h e r e a c t o r T h e s a m p l e l i n e w a s f l u s h e d s e v e r a l t i m e s t h e n 3 0 m L w a s w i t h d r a w n A p o r t i o n ( 1 0 m L ) o f e a c h s a m p l e w a s u s e d t o m e a s u r e a b s o r b a n c e A b s o r b a n c e o f t h e c u l t u r e w a s m e a s u r e d u s i n g a s p e c t r o p h o t o m e t e r ( M i l t o n R o y S p e c t r o n i c 2 1 D ) a t 5 5 0 n m u s i n g a 1 2 5 c m p a t h l e n g t h

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3 4 A B C D E A B C D E F i g u r e 4 1 0 E x p e r i m e n t a l s e t u p f o r t h e l o w D O e x p e r i m e n t s G a s F i l t e r R o t a m e t e A i r O x y g e n G a s F i l t e r R o t a m e t e N i t r o g e R o t a m e t e N i t r o g e A i r A T h e r m o c o u p l e B T h e r m o m e t e r C D O p r o b e D F e e d E H e a t e r

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3 5 4 2 5 E x p e r i m e n t a l R e s u l t s F i g u r e 4 1 1 s h o w s t h e r e s u l t s o f t h e r u n s w i t h l o w d i s s o l v e d c o n c e n t r a t i o n s < 0 7 m g / L I n t h e s e e x p e r i m e n t s t h e a e r o b i c g r o w t h r a t e o f t h e r e a c t o r a t h i g h D O w a s h i g h e r t h a n t h e l o w D O r e a c t o r A l s o t h e d i a u x i c l a g o f t h e h i g h D O r e a c t o r w a s s i g n i f i c a n t l y l o n g e r T h e s p e c i f i c a n o x i c g r o w t h r a t e s w e r e h i g h e r i n t h e L o w D O r e a c t o r F i g u r e 4 2 0 s h o w s t h e r e s u l t s o f t h e r u n s w i t h l o w d i s s o l v e d c o n c e n t r a t i o n s > 0 7 m g / L I n t h e s e e x p e r i m e n t s a s i g n i f i c a n t d i f f e r e n c e i n t h e g r o w t h r a t e s i n t h e a e r o b i c p h a s e w a s n o t r e c o r d e d s u g g e s t i n g t h a t P s e u d o m o n a s d e n i t r i f i c a n s c o u l d b e m i c r o a e r o p h i l i c B u t a s i g n i f i c a n t d i f f e r e n c e i n l e n g t h o f l a g a n d a n o x i c s p e c i f i c g r o w t h r a t e s w a s o b s e r v e d T h e r e f o r e n o t o n l y d i d d i s s o l v e d o x y g e n h a v e a n e f f e c t o n t h e l e n g t h o f t h e d i a u x i c l a g b u t i t a l s o a f f e c t e d t h e s p e c i f i c g r o w t h r a t e s i n t h e a e r o b i c a n d a n o x i c p h a s e s 4 3 P r e c u l t u r e E x p e r i m e n t s 4 3 1 E x p e r i m e n t a l M e t h o d s C u l t u r e s w e r e g r o w n i n s y n t h e t i c l i q u i d m e d i u m m o d i f i e d f r o m ( T a b l e 4 1 ) K o r a r o s e t a l ( 1 9 9 6 ) w i t h o r w i t h o u t w i t h o u t n i t r a t e d e p e n d i n g o n w h a t k i n d o f p r e c u l t u r e c o n d i t i o n s w e r e r e q u i r e d f o r t h a t e x p e r i m e n t T h e p H o f t h e m e d i u m w a s a d j u s t e d t o 7 0 u s i n g 2 N N a O H b e f o r e a u t o c l a v i n g a n d t h e a d d i t i o n o f n i t r a t e n i t r o g e n ( i f r e q u i r e d ) C u l t u r e m e d i u m i n 2 5 0 m L f l a s k s ( 1 2 5 m L l i q u i d v o l u m e ) w a s i n o c u l a t e d f r o m a g a r p l a t e s ( p r e p a r e d a s d e s c r i b e d i n s e c t i o n 4 1 1 ) T o m a i n t a i n O x i c p r e c u l t u r e c o n d i t i o n s t h e f l a s k s w e r e a g i t a t e d i n a s h a k e r b a t h f o r t w o d a y s a t a p p r o x i m a t e l y 2 5 o C I f a n o x i c p r e c u l t u r e c o n d i t i o n s w e r e t o b e m a i n t a i n e d t h e c u l t u r e s w e r e g r o w n i n a n i t r a t e l i m i t e d s y n t h e t i c l i q u i d m e d i u m ( 4 m g / L N O 3 N ) m o d i f i e d f r o m T a b l e 4 1 a n d a l l o w e d t o s i t u n d e r a s t e r i l e l a m i n a r h o o d f o r t w o d a y s A p r o c e d u r e t e r m e d ‘ s p l i t t i n g ’

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3 6 E 7 F i g u r e 4 1 1 E x p e r i m e n t E 7 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 0 1 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0 6 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x )A n o x i c P r e c u l t u r e N i t r a t e i n A n o x i c P h a s e 2 1 0 9 3

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3 7 E 8 F i g u r e 4 1 2 E x p e r i m e n t E 8 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 0 1 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0 6 0 0 6 5 0 7 0 0 7 5 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x )A n o x i c P r e c u l t u r e N i t r a t e i n A n o x i c P h a s e 2 8 1 3

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3 8 E 9 F i g u r e 4 1 3 E x p e r i m e n t E 9 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 0 1 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0 6 0 0 6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 0 9 5 0 1 0 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x )A n o x i c P r e c u l t u r e N i t r a t e i n A n o x i c P h a s e 3 0 0 9 5

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3 9 E 1 0 F i g u r e 4 1 4 E x p e r i m e n t E 1 0 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 0 7 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0 9 0 0 1 0 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 1 0 0 1 2 0 0 1 3 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x )A n o x i c P r e c u l t u r e N i t r a t e i n A n o x i c P h a s e 7 6 4 5

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4 0 E 1 1 F i g u r e 4 1 5 E x p e r i m e n t E 1 1 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 0 7 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0 9 0 0 1 0 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 1 0 0 1 2 0 0 1 3 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x )A n o x i c P r e c u l t u r e N i t r a t e i n A n o x i c P h a s e 1 3

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4 1 E 1 2 F i g u r e 4 1 6 E x p e r i m e n t E 1 2 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 0 9 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 1 0 0 1 2 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x )A n o x i c P r e c u l t u r e N i t r a t e i n A n o x i c P h a s e 6 8 1 2

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4 2 E 1 3 F i g u r e 4 1 7 E x p e r i m e n t E 1 3 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 0 9 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0 9 0 0 1 0 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 1 0 0 1 2 0 0 1 3 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x )A n o x i c P r e c u l t u r e N i t r a t e i n A n o x i c P h a s e 4 9 4 2

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4 3 E 1 4 F i g u r e 4 1 8 E x p e r i m e n t E 1 4 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 0 9 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 1 2 0 2 4 0 3 6 0 4 8 0 6 0 0 7 2 0 8 4 0 9 6 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x ) A n o x i c P r e c u l t u r e N O 3 P r e s e n t i n A e r o b i c 2 6 2 4

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4 4 E 1 5 F i g u r e 4 1 9 E x p e r i m e n t E 1 5 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 0 9 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 00 1 2 0 2 4 0 3 6 0 4 8 0 6 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x )A n o x i c P r e c u l t u r e N i t r a t e i n A n o x i c P h a s e 1 2 0 8 5

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4 5 E 1 6 F i g u r e 4 2 0 E x p e r i m e n t E 1 6 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 1 7 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 1 2 0 2 4 0 3 6 0 4 8 0 6 0 0 7 2 0 8 4 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x ) 4 2 0 8 8

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4 6 E 1 7 F i g u r e 4 2 1 E x p e r i m e n t E 1 7 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 1 7 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 1 2 0 2 4 0 3 6 0 4 8 0 6 0 0 7 2 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x ) 1 7 3 2

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4 7 E 1 8 F i g u r e 4 2 2 E x p e r i m e n t E 1 8 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 1 7 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 00 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 1 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x )A n o x i c P r e c u l t u r e N i t r a t e i n A n o x i c P h a s e 2 8 2 8

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4 8 E 1 9 F i g u r e 4 2 3 E x p e r i m e n t E 1 9 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 3 5 m g / l ) 0 0 0 0 0 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0 4 0 0 0 1 2 0 2 4 0 3 6 0 4 8 0 6 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x ) 1 8 0 8 4

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4 9 E 2 0 F i g u r e 4 2 4 E x p e r i m e n t E 2 0 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 3 5 m g / l ) 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 1 2 0 2 4 0 3 6 0 4 8 0 6 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x ) 1 6 1 2

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5 0 E 2 1 F i g u r e 4 2 5 E x p e r i m e n t E 2 1 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 7 0 m g / l ) 0 0 0 0 0 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0 4 0 0 0 1 2 0 2 4 0 3 6 0 4 8 0 6 0 0 7 2 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x ) 3 5 0 7 3

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5 1 E 2 2 F i g u r e 4 2 6 E x p e r i m e n t E 2 2 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 7 m g / l ) 0 0 0 0 0 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0 4 0 0 0 4 5 0 0 1 2 0 2 4 0 3 6 0 4 8 0 6 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x ) 0 4 3 0 5 8

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5 2 E 2 3 F i g u r e 4 2 7 E x p e r i m e n t E 2 3 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e f o l l o w i n g s y m b o l s r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o a s p e c i f i c D O c o n c e n t r a t i o n a n d t h e l e v e l s o f d i s s o l v e d o x y g e n : B I O M A S S ( w / H i g h D O ) H i g h D O ( 8 7 m g / l ) B I O M A S S ( w / L o w D O ) H i g h D O ( 0 7 m g / l ) 0 0 0 0 0 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0 4 0 0 0 4 5 0 0 1 2 0 2 4 0 3 6 0 4 8 0 6 0 0 7 2 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x ) 1 1 1 4

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5 3 w a s t h e n p e r f o r m e d o n t h e c u l t u r e m e d i u m A p p r o x i m a t e l y 2 5 0 m L o f t h e c u l t u r e m e d i u m w a s a d d e d t o a l i t e r o f l i q u i d m e d i u m a n d a l l o w e d t o m i x t o p r e v e n t f l o c c u l a t i o n T h e c u l t u r e w a s t h e n s p l i t i n t o t w o 5 0 0 m L v o l u m e s t r a n s f e r r e d t o e a c h b i o r e a c t o r s i m u l t a n e o u s l y a n d d i l u t e d w i t h l i q u i d m e d i u m t o a n a b s o r b a n c e ( l = 5 5 0 n m 1 2 5 p a t h l e n g t h ) o f 0 0 2 0 0 5 f o r u s e i n e x p e r i m e n t s 4 3 2 G r o w t h E x p e r i m e n t s T w o m u t i G e n b e n c h t o p b i o r e a c t o r s i n p a r a l l e l ( m o d e l s F 1 0 0 0 a n d F 2 0 0 0 N e w B r u n s w i c k S c i e n t i f i c ) w e r e u s e d f o r t h e e x p e r i m e n t s T h e c u l t u r e w a s c o n t i n u o u s l y s t i r r e d a t 3 0 2 0 C T h e p H r a n g e d f r o m 7 0 i n t h e a e r o b i c p h a s e a n d i n c r e a s e d t o 7 2 d u r i n g t h e a n o x i c p h a s e D i s s o l v e d o x y g e n w a s m o n i t o r e d u s i n g M o d e l D O 4 0 ( N e w B r u n s w i c k S c i e n t i f i c ) a n a l y z e r s w i t h g a l v a n i c e l e c t r o d e s T h e e f f e c t o f v a r i o u s p r e c u l t u r e s a n d p r e s e n c e a n d a b s e n c e o f n i t r a t e n i t r o g e n i n a e r o b i c p h a s e w a s c o m p a r e d a n d c o n t r a s t e d a t t h e d i s s o l v e d o x y g e n c o n c e n t r a t i o n o f 8 7 m g / L t h r o u g h t h e a e r o b i c p h a s e T h e e x p e r i m e n t a l s e t u p w a s a s s h o w n i n F i g u r e 4 2 8 E a c h e x p e r i m e n t c o n s i s t e d o f a n a e r a t i o n p e r i o d o f 7 9 h o u r s 4 0 0 m g / L o f n i t r a t e n i t r o g e n w a s a d d e d t o o n e r e a c t o r O n c e t h e b i o m a s s i n t h e r e a c t o r s w a s u p t o 0 2 5 i n t e r m s o f a b s o r b a n c e a o n e l i t e r s a m p l e w a s p u l l e d o u t f r o m t h e r e a c t o r s a n d r e p l a c e d w i t h f r e s h s y n t h e t i c m e d i u m a t 3 0 o C T h i s d i l u t i o n p r o c e s s w a s r e p e a t e d t w o t i m e s A e r a t i o n w a s t h e n s t o p p e d a n d t h e r e a c t o r w a s s p a r g e d w i t h n i t r o g e n g a s t o r e m o v e a n y r e s i d u a l d i s s o l v e d o x y g e n t o m a r k t h e b e g i n n i n g o f t h e a n o x i c p h a s e N i t r o g e n g a s w a s f l o o d e d t h r o u g h t h e h e a d s p a c e o f t h e r e a c t o r s d u r i n g t h e p e r i o d w h e n t h e r e w a s n o a e r a t i o n T h e v a r i a b l e s m o n i t o r e d i n c l u d e b i o m a s s i n t e r m s o f a b s o r b a n c e d i s s o l v e d o x y g e n t e m p e r a t u r e a n d p H

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5 4 A B C D E A B C D E F i g u r e 4 2 8 E x p e r i m e n t a l s e t u p f o r t h e p r e c u l t u r e e x p e r i m e n t s G a s F i l t e r R o t a m e t A i r N i t r o g e n G a s F i l t e r R o t a m e t e A i r N i t r o g e n A T h e r m o c o u p l e B T h e r m o m e t e r C D O p r o b e D F e e d E H e a t e r

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5 5 4 3 3 E x p e r i m e n t a l P r o t o c o l E x p e r i m e n t s w e r e c a r r i e d o u t i n o r d e r t o i n v e s t i g a t e t h e e f f e c t o f v a r i o u s p r e c u l t u r e c o n d i t i o n s a n d t h e n i t r a t e c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e o n t h e d u r a t i o n o f d i a u x i c l a g s E a c h e x p e r i m e n t c o n s i s t e d o f t w o p a r a l l e l t r i a l s o f t h e s a m e i n i t i a l c u l t u r e c o n d i t i o n s T o e n s u r e t h a t t h e p a r a l l e l c u l t u r e s h a d t h e s a m e i n i t i a l b i o m a s s c o n c e n t r a t i o n s t h e o r i g i n a l c u l t u r e w a s w e l l m i x e d a n d d i v i d e d b e t w e e n t h e t w o b i o r e a c t o r s P o t a s s i u m n i t r a t e ( 4 0 0 m g / L ) w a s a d d e d i n t h e a e r o b i c p h a s e t o o n e r e a c t o r O n e s e t o f p a r a l l e l r u n e x p e r i m e n t s w a s p e r f o r m e d w i t h o x i c p r e c u l t u r e c o n d i t i o n s a n d a n o t h e r w i t h a n o x i c p r e c u l t u r e c o n d i t i o n s a n d t h e l e n g t h o f d i a u x i c l a g s w a s c o m p a r e d 4 3 4 A n a l y t i c M e t h o d s S a m p l e s w e r e w i t h d r a w n f r o m t h e r e a c t o r u s i n g a s y r i n g e c o n n e c t e d t o a p l a s t i c t u b e t h a t e x t e n d e d t h r o u g h t h e c a p t o t h e b o t t o m o f t h e r e a c t o r T h e s a m p l e l i n e w a s f l u s h e d s e v e r a l t i m e s a n d 3 0 m L w a s w i t h d r a w n A p o r t i o n ( 1 0 m L ) o f e a c h s a m p l e w a s u s e d t o m e a s u r e a b s o r b a n c e A b s o r b a n c e o f t h e c u l t u r e w a s m e a s u r e d u s i n g a s p e c t r o p h o t o m e t e r ( M i l t o n R o y S p e c t r o n i c 2 1 D ) a t 5 5 0 n m u s i n g a 1 2 5 c m p a t h l e n g t h 4 3 5 E x p e r i m e n t a l R e s u l t s T h e r e s u l t s o f e x p e r i m e n t s s h o w e d t w o t h i n g s c l e a r l y O x i c p r e c u l t u r e c o n d i t i o n s ( F i g u r e 4 3 2 ) e x p e r i m e n t s h a d s i g n i f i c a n t l y l o n g e r d i a u x i c l a g s t h a n c u l t u r e s t h a t w e r e r e v i v e d a n o x i c a l l y ( F i g u r e 4 3 1 ) A l s o t h e d i a u x i c l a g s w e r e l o n g e r f o r c u l t u r e s t h a t h a d n o t b e e n e x p o s e d t o n i t r a t e i n t h e a e r o b i c p h a s e a s s e e n f r o m F i g u r e 4 3 1 P r e s e n c e o f n i t r a t e f a i l e d t o i n f l u e n c e t h e r a t e o f a e r o b i c g r o w t h i n e i t h e r e x p e r i m e n t a s o b s e r v e d i n a l l t h e f i g u r e s T h e s e e x p e r i m e n t s s u p p o r t t h e h y p o t h e s i s i n m o d e l s p r o p o s e d b y L i u e t a l ( 1 9 9 8 a b )

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5 6 E 2 4 F i g u r e 4 2 9 E x p e r i m e n t E 2 4 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e s y m b o l s a s i n t h e c h a r t l e g e n d r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o d i f f e r e n t n i t r a t e c o n c e n t r a t i o n s T h e c u l t u r e w a s r e v i v e d a n o x i c a l l y 0 0 0 5 0 1 0 1 5 0 2 0 2 5 0 3 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 t i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( & o f M a x ) [ N O 3 ] ( m g / L ) B I O M A S S ( w N O 3 ) B I O M A S S ( w / o N O 3 ) D O ( w N O 3 ) [ N O 3 ] ( w N O 3 ) D O ( w / o N O 3 ) [ N O 3 ] ( w / o N O 3 ) 2 5 1 1 6 7

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5 7 E 2 5 F i g u r e 4 3 0 E x p e r i m e n t E 2 5 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e s y m b o l s a s i n t h e c h a r t l e g e n d r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o d i f f e r e n t n i t r a t e c o n c e n t r a t i o n s T h e c u l t u r e w a s r e v i v e d a n o x i c a l l y 3 3 2 6

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5 8 E 2 6 F i g u r e 4 3 1 E x p e r i m e n t E 2 6 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e s y m b o l s a s i n t h e c h a r t l e g e n d r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o d i f f e r e n t n i t r a t e c o n c e n t r a t i o n s T h e c u l t u r e w a s r e v i v e d a n o x i c a l l y 1 5 0 3

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5 9 E 2 7 F i g u r e 4 3 2 E x p e r i m e n t E 2 7 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e s y m b o l s a s i n t h e c h a r t l e g e n d r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o d i f f e r e n t n i t r a t e c o n c e n t r a t i o n s T h e c u l t u r e w a s r e v i v e d i n o x i c c o n d i t i o n s 0 0 0 5 0 1 0 1 5 0 2 0 2 5 0 3 0 3 5 0 4 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 1 0 0 1 2 0 0 1 3 0 0 T i m e ( m i n )A b s o r b a n c e0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0D O ( % o f m a x ) B I O M A S S ( w / o N O 3 ) B I O M A S S ( w N O 3 ) D O ( w / o N O 3 ) D O ( w N O 3 ) 7 3 2 5

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6 0 E 2 8 F i g u r e 4 3 3 E x p e r i m e n t E 2 8 C o m p a r i s o n o f b i o m a s s a b s o r b a n c e a n d d i s s o l v e d o x y g e n l e v e l s a g a i n s t t i m e T h e s y m b o l s a s i n t h e c h a r t l e g e n d r e p r e s e n t p u r e c u l t u r e a b s o r b a n c e e x p o s e d t o d i f f e r e n t n i t r a t e c o n c e n t r a t i o n s T h e c u l t u r e w a s r e v i v e d a n o x i c a l l y 3 5

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6 1 C H A P T E R 5 N E U R A L N E T W O R K S A l l t h e m o d e l s d e v e l o p e d s o f a r h a v e a l l b e e n s u c c e s s f u l i n p r o v i d i n g d e t a i l e d d e s c r i p t i o n s o f t h e p r o c e s s k i n e t i c s a n d r e f l e c t s t a t e o f t h e a r t u n d e r s t a n d i n g o f p r o c e s s e s s u c h a s d e n i t r i f i c a t i o n a n d n i t r i f i c a t i o n T h e h y p o t h e s i s u s e d t o j u s t i f y t h e o c c u r r e n c e o f a d i a u x i c l a g r e m a i n s t o b e v e r i f i e d e x p e r i m e n t a l l y b y t r a c k i n g e n z y m e a c t i v i t y d u r i n g a t y p i c a l e x p e r i m e n t I n c o n t r a s t t o t h e c o n v e n t i o n a l m o d e l s t h e r e i s t h e b l a c k b o x m o d e l i n g t e c h n i q u e w h i c h p r e d i c t s t h e v a l u e o f a v a r i a b l e g i v e n t h e h i s t o r i c v a l u e s o f i t s e l f ( a n d p e r h a p s o t h e r s v a r i a b l e s ) b u t g i v e s l i t t l e i n s i g h t i n t o t h e p r o c e s s k i n e t i c s o r t h e g o v e r n i n g e q u a t i o n s i n t h e m o d e l A n e u r a l n e t w o r k i s c a p a b l e o f g o o d p e r f o r m a n c e e v e n i f t h e d a t a h a v e c o n s i d e r a b l e n o n l i n e a r i t y A n o t h e r o f i t s s i g n i f i c a n t a d v a n t a g e s i s t h a t i t i s a b l e t o d i s c o v e r p a t t e r n s i n t h e d a t a I n s u m m a r y a n e u r a l n e t w o r k c a n p r o b a b l y s o l v e e f f e c t i v e l y p r o b l e m s t h a t c a n n o t b e s o l v e d b y t r a d i t i o n a l m o d e l i n g o r s t a t i s t i c a l m e t h o d s T h e c h o i c e o f a n a p p r o p r i a t e n e t w o r k a n d a p r a c t i c a l a l g o r i t h m i s r e q u i r e d f o r t h e n e t w o r k t o g i v e t h e d e s i r e d p e r f o r m a n c e I n t h e p r e s e n t s t u d y a n e u r a l n e t w o r k i s u s e d t o p r e d i c t t h e d u r a t i o n o f t h e d i a u x i c l a g g i v e n c e r t a i n p a r a m e t e r s s u c h a s t h e b i o m a s s c o n c e n t r a t i o n s i n t e r m s o f a b s o r b a n c e r e v i v i n g p h a s e o f t h e c u l t u r e d i s s o l v e d o x y g e n c o n c e n t r a t i o n s a n d n i t r a t e c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e a n d l e n g t h o f t h e a e r o b i c p h a s e i n h o u r s

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6 2 5 1 A l g o r i t h m U s e d 5 1 1 B a c k P r o p a g a t i o n A l g o r i t h m T h e b a c k p r o p a g a t i o n n e t w o r k i s p r o b a b l y t h e b e s t k n o w n a n d w i d e l y u s e d a m o n g a l l t h e t y p e s o f n e u r a l n e t w o r k s s y s t e m s A t y p i c a l b a c k p r o p a g a t i o n n e t w o r k i s a s d e p i c t e d i n F i g u r e 5 1 E s s e n t i a l l y a b a c k p r o p a g a t i o n n e t w o r k h a s a n i n p u t l a y e r o u t p u t l a y e r a n d o n e o r m o r e h i d d e n l a y e r s T h e i n t e r c o n n e c t i o n s b e t w e e n t h e i n p u t a n d h i d d e n l a y e r s a n d t h e h i d d e n a n d o u t p u t l a y e r s a r e t e r m e d ‘ w e i g h t s ’ L i k e m o s t o t h e r n e u r a l n e t w o r k s y s t e m s i n p u t p a t t e r n s a r e p r e s e n t e d t o t h e n e t w o r k a n d t h e n e t w o r k i s t r a i n e d t o l e a r n t h e c o r r e s p o n d i n g o u t p u t p a t t e r n T h e n u m b e r o f i n p u t p a r a m e t e r s i n o n e i n p u t p a t t e r n d e t e r m i n e s t h e n u m b e r o f n o d e s i n t h e i n p u t l a y e r S i m i l a r l y t h e n u m b e r o f o u t p u t n o d e s i s t h e n u m b e r o f v a r i a b l e s t h e n e u r a l n e t w o r k i s r e q u i r e d t o p r e d i c t I n t h e p r e s e n t s t u d y w e a r e i n t e r e s t e d i n p r e d i c t i n g t h e d u r a t i o n o f t h e d i a u x i e i n h o u r s H e n c e t h e n e u r a l n e t w o r k h a s o n l y o n e o u t p u t n o d e b e i n g t h e l e n g t h o f t h e d i a u x i c l a g i n h o u r s B o t h t h e n u m b e r o f n o d e s i n t h e h i d d e n l a y e r a n d t h e n u m b e r o f h i d d e n l a y e r s a r e n o t s p e c i f i e d T h o u g h s o m e t h e o r e t i c a l g u i d a n c e e x i s t s t o d e t e r m i n e t h e n u m b e r o f h i d d e n l a y e r s a n d h i d d e n n o d e s t h e y a r e u s u a l l y v a r i e d a n d t h e p e r f o r m a n c e o f t h e n e t w o r k r e c o r d e d f o r e a c h c o m b i n a t i o n F i n a l l y t h e c o m b i n a t i o n w h i c h g i v e s t h e b e s t p e r f o r m a n c e i s c h o s e n R u m e l h a r t ( 1 9 8 6 ) f i r s t p r o p o s e d t h e b a s i c b a c k p r o p a g a t i o n a l g o r i t h m T h e n a m e ‘ b a c k p r o p a g a t i o n ’ c o m e s f r o m t h e f a c t t h a t t h e e r r o r ( g r a d i e n t ) o f t h e h i d d e n u n i t s i s d e r i v e d f r o m p r o p a g a t i n g b a c k w a r d t h e e r r o r a s s o c i a t e d w i t h o u t p u t u n i t s T h e f i r s t s t e p o f t h e b a c k p r o p a g a t i o n a l g o r i t h m i s w e i g h t i n i t i a l i z a t i o n w h e r e t h e w e i g h t s a r e s e t t o s m a l l r a n d o m n u m b e r s I n t h e s e c o n d s t e p a n i n p u t p a t t e r n i s p r e s e n t e d t o t h e n e u r a l n e t w o r k a n d t h e o u t p u t n e u r o n a c t i v a t i o n ’ s ( v a l u e s a t t h e o u t p u t n o d e s ) a r e c a l c u l a t e d

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6 3 F i g u r e 5 1 B a c k p r o p a g a t i o n n e t w o r k … … … … … … … … … … … … S A c t u a l O u t p u t T a r g e t O u t p u t + I n p u t w e i g h t s F o r w a r d i n f o r m a t i o n f l o w B a c k w a r d e r r o r p r o p a g a t i o n F o r w a r d i n f o r m a t i o n f l o w F o r w a r d i n f o r m a t i o n f l o w I N P U T L A Y E R H I D D E N L A Y E R O U T P U T L A Y E R

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6 4 T h e t h i r d s t e p i s w e i g h t u p d a t i n g w h e r e t h e w e i g h t s a r e a d j u s t e d ( b a c k w a r d s f r o m t h e o u t p u t t o h i d d e n l a y e r s r e c u r s i v e l y ) t o r e d u c e t h e e r r o r T h e s e c o n d a n d t h i r d s t e p s a r e r e p e a t e d f o r e a c h t r a i n i n g p a t t e r n ( i n p u t a n d c o r r e s p o n d i n g o u t p u t p a t t e r n ) T h e n u m b e r o f s u c h d i s t i n c t t r a i n i n g p a t t e r n s p r e s e n t e d t o t h e n e t w o r k i s c a l l e d e p o c h s i z e w h e r e a n e p o c h i s o n e p a s s o f t h e a b o v e t h r e e s t e p s f o r a l l t h e t r a i n i n g p a t t e r n s T h e e r r o r m e a s u r e u s e d h e r e i s m e a n s q u a r e e r r o r i n t h e o u t p u t a c t i v a t i o n s T h e m e a n s q u a r e e r r o r f o r a s i n g l e p a s s i s t h e s q u a r e o f t h e d i f f e r e n c e b e t w e e n t h e a t t a i n e d a n d d e s i r e d o u t p u t a c t i v a t i o n f o r t h e o u t p u t n e u r o n T h e e p o c h e r r o r i s c o m p u t e d a s t h e a v e r a g e o f e r r o r s i n t r a i n i n g p r e s e n t a t i o n s w i t h i n t h a t e p o c h M a t h e m a t i c a l l y i f w e w e r e p r o c e s s i n g t r a i n i n g p a t t e r n p w h e r e t h e d e s i r e d o u t p u t a c t i v a t i o n w a s t p a n d t h e a c t u a l a t t a i n e d a c t i v a t i o n w a s o p t h e n e r r o r f o r t h a t s i n g l e r e p r e s e n t a t i o n i s g i v e n b y 2 ) ( p p p o t E = ( 5 1 ) I f t h e r e w e r e m s u c h p r e s e n t a t i o n s i n a n e p o c h t h e e p o c h e r r o r i s g i v e n b y = = 1 0 1 m p p E m E ( 5 2 ) R u m e l h a r t ( 1 9 8 6 ) d e s c r i b e s t h e e q u a t i o n s g o v e r n i n g t h e b a c k p r o p a g a t i o n a l g o r i t h m i n g r e a t d e t a i l A l t h o u g h t h e b a c k p r o p a g a t i o n a l g o r i t h m i s s i m p l e a n d e a s y t o i m p l e m e n t i t s s u c c e s s c r u c i a l l y d e p e n d s o n u s e r d e f i n e d p a r a m e t e r s s u c h a s l e a r n i n g r a t e a n d m o m e n t u m c o n s t a n t H e n c e i n m a n y s i t u a t i o n s i t l a n d s u p h a v i n g p o o r c o n v e r g e n c e r a t e s C o n j u g a t e g r a d i e n t s e a r c h a l g o r i t h m s a i m a t m i n i m i z i n g s o m e o f t h e s e d i s a d v a n t a g e s 5 1 2 T r a i n i n g b y C o n j u g a t e G r a d i e n t s F r o m a n o p t i m i z a t i o n p o i n t o f v i e w l e a r n i n g i n a n e u r a l n e t w o r k i s e q u i v a l e n t t o m i n i m i z i n g a g l o b a l e r r o r f u n c t i o n w h i c h i s a m u l t i v a r i a t e f u n c t i o n t h a t d e p e n d s o n t h e

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6 5 w e i g h t s i n t h e n e t w o r k S u p p o s e w e a p p r o x i m a t e t h e g l o b a l e r r o r f u n c t i o n t o a q u a d r a t i c f u n c t i o n o f t h e f o r m g ( x ) = c – b x + 2 1x A x ( 5 3 ) w h e r e x i s t h e w e i g h t v e c t o r T h e f u n c t i o n i s m i n i m i z e d w h e n i t s g r a d i e n t g = A x – b x ( 5 4 ) i s z e r o T h e m i n i m i z a t i o n i s c a r r i e d o u t b y g e n e r a t i n g a s u c c e s s i o n o f s e a r c h d i r e c t i o n s h k a n d i m p r o v e d m i n i m i z e r s x k ( w e i g h t v e c t o r s ) A t e a c h s t a g e a q u a n t i t y a k ( s t e p s i z e ) i s a l s o i s a l s o f o u n d t h a t m i n i m i z e s f ( x k + a k h k ) a n d x k + 1 i s s e t e q u a l t o t h e n e w p o i n t x k + a k h k T h e s e a r c h d i r e c t i o n v e c t o r h k a n d t h e w e i g h t v e c t o r x k a r e b u i l t i n s u c h a w a y t h a t x k + 1 i s a l s o t h e m i n i m i z e r o f t h e f u n c t i o n f o v e r a l l t h e v e c t o r s p a c e s o f d i r e c t i o n s a l r e a d y t a k e n n a m e l y { h 1 h 2 … h k } T h e r e f o r e i n N i t e r a t i o n s w e a r r i v e a t t h e m i n i m u m o v e r t h e e n t i r e v e c t o r s p a c e T h e s e a r c h d i r e c t i o n v e c t o r h k + 1 i s g i v e n b y t h e f o l l o w i n g e q u a t i o n h k + 1 = g k + 1 + g k h k ( 5 5 ) T h e P o l a k R i b i e r e a l g o r i t h m d e f i n e s t h e s c a l a r g k a s f o l l o w s g k = k k g g g ). g (g 1 k k 1 k + + ( 5 6 ) w h e r e g k i s t h e n e g a t i v e g r a d i e n t o f f a t s o m e p o i n t P k ( i e ) g k = f ( P k ) ( 5 7 ) I f w e p r o c e e d e d f r o m P k a l o n g t h e d i r e c t i o n h k t o t h e l o c a l m i n i m a o f f l o c a t e d a t p o i n t P k + 1 t h e n g k + 1 c a n b e w r i t t e n a s g k + 1 = f ( P k + 1 ) ( 5 8 )

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6 6 T h e a b o v e t o l o g i c c a n b e i m p l e m e n t e d i n t w o m a j o r s t a g e s r e c u r s i v e l y : S t a g e 1 : T o f i n d t h r e e p o i n t s s u c h t h a t m i d d l e p o i n t i s l e s s t h a n t h e f i r s t p o i n t T h e s t e p s o f t h e a l g o r i t h m i n c l u d e : ( 1 ) S a v e t h e w e i g h t s a s t h e y c o m e i n t o t h e c o n j u g a t e g r a d i e n t m o d u l e a n d c o m p u t e t h e n e g a t i v e g r a d i e n t o f t h e w e i g h t v e c t o r g k a t p o i n t P k L e t P k b e t h e f i r s t o f t h e t h r e e p o i n t s w e a r e t r y i n g t o d e t e r m i n e ( 2 ) S e t t h e i n t i a l d i r e c t i o n v e c t o r h k e q u a l t o g k i f k = 0 I f k > 0 c o m p u t e h k u s i n g e q u a t i o n s ( 5 ) a n d ( 6 ) ( 3 ) F i n d a s e c o n d p o i n t P k + 1 i n t h e d i r e c t i o n h k s u c h t h a t f ( P k + 1 ) < f ( P k ) ( 4 ) E s t i m a t e a t h i r d p o i n t u s i n g t h e g o l d e n r a t i o n r u l e a n d c o m p u t e t h e v a l u e o f t h e e r r o r f u n c t i o n a t t h a t p o i n t T h e v a l u e o f t h e e r r o r f u n c t i o n a t t h i s t h i r d p o i n t n e e d n o t b e l e s s t h a n t h e s e c o n d p o i n t W e n o w h a v e t h r e e p o i n t s t h a t d e f i n e a n i n t e r v a l S i n c e t h e e r r o r f u n c t i o n i s a p p r o x i m a t e d t o a q u a d r a t i c e q u a t i o n w e c a n f i t t h e t h r e e p o i n t s i n a p a r a b o l a S t a g e 2 : T o r e f i n e t h i s i n t e r v a l c o n t a i n i n g t h e m i n i m a u n t i l w i t h i n s a t i s f a c t o r y l i m i t s o f a c c u r a c y a n d t r y t o l o c a t e t h e l o c a l m i n i m u m L e t t h e f i r s t p o i n t b e P 1 i t s e r r o r e 1 s e c o n d p o i n t b e P 2 a n d i t s e r r o r e 2 a n d s o o n W e t a k e a ‘ s t e p ’ i n t h e n e g a t i v e g r a d i e n t d i r e c t i o n f r o m P 2 a l o n g t h e p a r a b o l a a n d c o m p u t e t h e v a l u e o f t h e f u n c t i o n a t t h a t p o i n t T h e f o l l o w i n g c a s e s a r i s e :

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6 7 ( 1 ) I f t h e f u n c t i o n v a l u e a t P 3 i s l e s s t h a n t h a t a t P 2 a n d t h e ‘ s t e p ’ i s b e t w e e n P 2 a n d P 3 : T h e f u n c t i o n v a l u e a t t h i s n e w l y s t e p p e d o u t p o i n t i s c o m p u t e d a n d c o m p a r e d t o e 3 I f t h e f u n c t i o n v a l u e i s l e s s t h a n e 3 t h e n t h e m i n i m u m i s a n i n t e r n a l p o i n t ( b e t w e e n P 2 a n d P 3 ) a n d w e a r e d o n e I n t h i s c a s e P 1 a n d P 2 a r e u p d a t e d a l o n g w i t h t h e i r f u n c t i o n v a l u e s a s f o l l o w s : P 2 b e c o m e s P 1 a n d t h e m i n i m u m b e c o m e s P 2 ( 2 ) I f t h e f u n c t i o n v a l u e a t P 3 i s l e s s t h a n t h a t a t P 2 a n d t h e ‘ s t e p ’ i s b e y o n d P 3 b u t w i t h i n t h e m a x i m u m s t e p : P 3 i s u p d a t e d a l o n g w i t h i t s f u n c t i o n v a l u e t o ‘ s t e p ’ a n d t h e f u n c t i o n v a l u e a t t h i s n e w l y s t e p p e d o u t p o i n t ( 3 ) I f t h e f u n c t i o n v a l u e a t P 3 i s l e s s t h a n t h a t a t P 2 a n d i f t h e n e w p o i n t w a s a b o v e a n a r b i t r a r y l i m i t b e y o n d P 3 t h e n w e r e e s t i m a t e t h e n e w p o i n t b y t a k i n g a ‘ s t e p ’ o f t h e m a x i m u m s i z e a n d r e t u r n i n g t o o n e o f t h e c a s e s a b o v e I f t h e n e w p o i n t w e r e a n y w h e r e e l s e t h e n i t i s n o t d e s i r e d a n d h e n c e w e u s e t h e g o l d e n r a t i o r u l e t o s t e p o u t s i d e t o a n e w p o i n t ( 4 ) I f t h e f u n c t i o n v a l u e a t P 2 i s l e s s t h a n t h a t a t P 3 a n d t h e n e w p o i n t ( ‘ s t e p ’ ) i s b e t w e e n P 2 a n d P 3 : I n t h i s c a s e P 1 a n d P 2 a r e u p d a t e d a l o n g w i t h t h e i r f u n c t i o n v a l u e s a s f o l l o w s : P 1 b e c o m e s P 2 a n d P 2 b e c o m e s n e w p o i n t ‘ s t e p ’ ( 5 ) I f t h e f u n c t i o n v a l u e a t P 2 i s l e s s t h a n t h a t a t P 3 a n d t h e n e w p o i n t ( ‘ s t e p ’ ) i s b e t w e e n P 1 a n d P 2 : I n t h i s c a s e P 2 a n d P 3 a r e u p d a t e d a l o n g w i t h t h e i r f u n c t i o n v a l u e s a s f o l l o w s : P 3 b e c o m e s P 2 a n d P 2 b e c o m e s n e w p o i n t ‘ s t e p ’ ( 6 ) I f t h e n e w p o i n t w e r e a n y w h e r e e l s e t h e n i t i s n o t d e s i r e d a n d h e n c e w e u s e t h e g o l d e n r a t i o r u l e t o s t e p o u t s i d e t o a n e w p o i n t

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6 8 T h e c o n j u g a t e g r a d i e n t a l g o r i t h m t h o u g h s i m i l a r t o t h e b a c k p r o p a g a t i o n a l g o r i t h m w i t h m o m e n t u m d i f f e r s f r o m i t i n t w o w a y s O n e t h e s t e p s i z e i s n o t f i x e d T w o t h e m o m e n t u m t e r m g v a r i e s i n a n o p t i m a l w a y r a t h e r t h a n b e i n g f i x e d t h r o u g h o u t 5 1 3 S i m u l a t e d A n n e a l i n g A n n e a l i n g i s a t e r m f r o m m e t a l l u r g y W h e n t h e a t o m s i n a m e t a l a r e a l i g n e d r a n d o m l y t h e m e t a l i s b r i t t l e m o r e l i k e l y t o g e t f r a c t u r e d H e n c e w h e n a m e t a l i s h e a t e d t o v e r y h i g h t e m p e r a t u r e s ( t h e a t o m s a r e c o m p l e t e l y r a n d o m ) a n d c o o l e d r a p i d l y i t i s m o r e l i k e l y t h a t t h e a t o m s s e t t l e d o w n i n r a n d o m u n s t a b l e s t a t e O n t h e o t h e r h a n d o f t h e m e t a l w e r e c o o l e d g r a d u a l l y t h e a t o m s t e n d t o f a l l i n t o p a t t e r n s t h a t a r e r e l a t i v e l y s t a b l e f o r t h a t t e m p e r a t u r e T h e s a m e i d e a i s u s e d i n o p t i m i z a t i o n T h e i n d e p e n d e n t v a r i a b l e s a r e r a n d o m l y p e r t u r b e d ( w e i g h t s i n t h e c a s e o f a n e u r a l n e t w o r k ) w h i l e k e e p i n g t r a c k o f t h e b e s t ( l o w e s t e r r o r ) f u n c t i o n v a l u e f o r e a c h r a n d o m i z e d s e t o f v a r i a b l e s A h i g h s t a n d a r d d e v i a t i o n f o r t h e r a n d o m n u m b e r g e n e r a t o r i s u s e d A f t e r m a n y s u c h t r i e s t h e s e t t h a t p r o d u c e d t h e b e s t f u n c t i o n v a l u e i s u s e d a s t h e c e n t e r f o r p e r t u r b a t i o n f o r t h e n e x t t e m p e r a t u r e T h e t e m p e r a t u r e ( s t a n d a r d d e v i a t i o n ) i s d e c r e a s e d a n d n e w t r i e s a r e p e r f o r m e d 5 1 4 I n t e r l e a v e d S i m u l a t e d A n n e a l i n g a n d C o n j u g a t e G r a d i e n t A l g o r i t h m I n t h e p r e s e n t s t u d y t h e a n n e a l i n g p a r a m e t e r s n a m e l y s t a r t i n g a n d s t o p p i n g t e m p e r a t u r e s w h i c h r e p r e s e n t s t a n d a r d d e v i a t i o n s a r e s e t t o h i g h a n d l o w v a l u e s r e s p e c t i v e l y i n i t i a l l y T h e t e m p e r a t u r e i s r e d u c e d b y a f a c t o r o f c e a c h t i m e w h e r e c i s g i v e n b y t h e r e l a t i o n 1 ) / ln( -=n start stope c ( 5 9 )

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6 9 W h e r e s t a r t a n d s t o p a r e t h e s t a r t i n g a n d t h e s t o p p i n g s t a n d a r d d e v i a t i o n s n t h e n u m b e r o f t e m p e r a t u r e s T h e s t a r t i n g w e i g h t s a r e e s t i m a t e d b y u s i n g t h e s i m u l a t e d a n n e a l i n g a l g o r i t h m T h e c o n j u g a t e g r a d i e n t a l g o r i t h m t h e n f i n d s t h e l o c a l m i n i m a r a p i d l y O n c e t h e r e s i m u l a t e d a n n e a l i n g c a s t s a b o u t a n d t r y i n g t o e s c a p e t o a l o w e r p o i n t T h i s a l t e r n a t i o n i s c o n t i n u e d u n t i l w e a r e u n a b l e t o e s c a p e f r o m t h e l o c a l m i n i m a A n o t h e r p o i n t t o n o t e i s t h a t a l i m i t h a s b e e n s e t o n t h e s i z e o f w e i g h t s s o t h a t e x t r e m e l y l a r g e a c t i v a t i o n l e v e l s c a n b e a v o i d e d S h o u l d t h e r e b e n o l i m i t o n t h e s i z e o f t h e w e i g h t s t h e n a n y u p d a t i n g o f t h e w e i g h t s m a y n o t h a v e a n y e f f e c t a s t h e w e i g h t s m a y b e e i t h e r e x t r e m e l y l a r g e o r s m a l l h e n c e t h e l i m i t 5 2 N e u r a l N e t w o r k M o d e l f o r L o w D O E x p e r i m e n t s 5 2 1 T r a i n i n g t h e N e t w o r k A s e t o f e i g h t e e n e x p e r i m e n t s ( E 7 t o E 2 3 ) w a s s p i l t i n t o t w o s e t s – t r a i n i n g a n d t e s t d a t a T a b l e 5 1 g i v e s t h e d a t a u s e d t o t r a i n t h e n e u r a l n e t w o r k m o d e l t o p r e d i c t t h e d u r a t i o n o f t h e l e n g t h o f t h e d i a u x i c l a g i n h o u r s I n p u t s t o t h e n e u r a l n e t w o r k i n c l u d e b i o m a s s i n t e r m s o f a b s o r b a n c e a t t h e s t a r t o f t h e e x p e r i m e n t d u r a t i o n o f t h e a e r a t i o n p h a s e i n h o u r s a n d c o n c e n t r a t i o n o f d i s s o l v e d o x y g e n i n m g / l ( a s i n F i g u r e 5 2 ) A l l t h e t r a i n i n g d a t a w a s n o r m a l i z e d a n d t h e n p a s s e d t o t h e n e t w o r k T h e n u m b e r o f n o d e s i n t h e h i d d e n l a y e r w a s v a r i e d a n d t h e m e a n s q u a r e d e r r o r s r e c o r d e d ( F i g u r e 5 3 ) T h e m e a n s q u a r e e r r o r w a s t h e l o w e s t w h e n t h e n u m b e r o f n o d e s i n t h e h i d d e n l a y e r w a s t h r e e T h e w e i g h t s a f t e r t r a i n i n g w e r e s a v e d a n d w e r e u s e d t o t e s t t h e n e t w o r k F i g u r e 5 4 s h o w s t h e r e s u l t s w h e n t h e t r a i n i n g d a t a w a s p a s s e d b a c k t o t h e n e u r a l n e t w o r k t o v e r i f y i f t h e n e t w o r k h a d l e a r n t a l l t h e e x p e r i m e n t a l d a t a p r e s e n t e d t o i t

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7 0 F i g u r e 5 2 : N e u r a l n e t w o r k u s e d t o p r e d i c t t h e d u r a t i o n o f t h e d i a u x i c l a g f o r l o w D O e x p e r i m e n t s B i o m a s s a s a b s o r b a n c e a t t i m e z e r o C o n c e n t r a t i o n o f d i s s o l v e d o x y g e n i n m g / l L e n g t h o f a e r o b i c p h a s e i n h o u r s H i d d e n L a y e r L a g l e n g t h i n h o u r s N e t w o r k O u t p u t

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7 1 T a b l e 5 1 T r a i n i n g d a t a f o r n e u r a l n e t w o r k m o d e l f o r l o w D O e x p e r i m e n t s I n p u t s t o N e t w o r k D e s i r e d O u t p u t E x p e r i m e n t N u m b e r L e n g t h o f A e r o b i c P h a s e ( h r s ) B i o m a s s i n t e r m s o f a b s o r b a n c e a t t i m e z e r o D O C o n c e n t r a t i o n ( m g / l ) L e n g t h o f d i a u x i c l a g ( h r s ) E 7 4 2 5 0 0 0 6 2 8 7 m g / L 2 1 0 0 E 7 4 2 5 0 0 0 6 8 0 1 m g / L 0 9 3 0 E 8 4 2 5 0 0 0 8 0 8 7 m g / L 2 8 0 0 E 8 4 2 5 0 0 0 8 0 0 1 m g / L 1 3 0 0 E 1 1 4 7 5 0 0 0 5 2 8 7 m g / L 1 3 0 0 E 1 1 4 7 5 0 0 0 5 2 0 7 m g / L 0 0 0 0 E 1 2 5 2 5 0 0 0 4 5 8 7 m g / L 6 8 0 0 E 1 2 5 2 5 0 0 0 4 5 0 9 m g / L 1 2 0 0 E 1 3 4 7 5 0 0 0 4 9 8 7 m g / L 4 9 0 0 E 1 3 4 7 5 0 0 0 5 1 0 9 m g / L 4 2 0 0 E 1 4 5 0 0 0 0 0 4 7 8 7 m g / L 2 6 0 0 E 1 4 5 0 0 0 0 0 4 7 0 9 m g / L 2 4 0 0 E 1 7 3 1 6 7 0 1 3 0 8 7 m g / L 3 2 0 0 E 1 7 3 1 6 7 0 1 2 9 1 7 m g / L 1 7 0 0 E 1 8 4 4 1 7 0 0 5 4 8 7 m g / L 2 8 0 0 E 1 8 4 4 1 7 0 0 5 4 1 7 m g / L 2 8 0 0 E 1 9 3 4 1 7 0 0 6 7 8 7 m g / L 1 8 0 0 E 1 9 3 4 1 7 0 0 6 7 3 5 m g / L 0 8 4 0 E 2 1 3 8 3 3 0 0 6 9 8 7 m g / L 3 5 0 0 E 2 1 3 8 3 3 0 0 7 0 7 0 m g / L 0 7 3 0 E 2 2 3 5 0 0 0 0 7 4 8 7 m g / L 0 5 8 0 E 2 2 3 5 0 0 0 0 7 6 7 0 m g / L 0 4 3 0 E 2 3 3 3 3 3 0 0 7 7 8 7 m g / L 1 4 0 0 E 2 3 3 3 3 3 0 0 8 2 7 0 m g / L 1 1 0 0

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7 2 5 2 2 T e s t i n g t h e N e t w o r k T a b l e 5 2 g i v e s t h e s e t o f d a t a u s e d t o t e s t t h e n e t w o r k w i t h t h e w e i g h t s f o u n d a f t e r t r a i n i n g F i g u r e 5 5 s h o w s t h e r e s u l t s o f p a s s i n g t h e t e s t d a t a t o t h e t r a i n e d n e u r a l n e t w o r k T a b l e 5 2 T e s t d a t a f o r n e u r a l n e t w o r k m o d e l f o r l o w D O e x p e r i m e n t s I n p u t s t o N e t w o r k D e s i r e d O u t p u t E x p e r i m e n t N u m b e r L e n g t h o f A e r o b i c P h a s e ( h r s ) B i o m a s s i n t e r m s o f a b s o r b a n c e a t t i m e z e r o D O C o n c e n t r a t i o n ( m g / l ) L e n g t h o f d i a u x i c l a g ( h r s ) E 9 4 7 5 0 0 0 5 2 8 7 m g / L 3 0 0 0 E 9 4 7 5 0 0 0 5 2 0 4 m g / L 0 9 5 0 E 1 0 7 7 5 0 0 0 3 7 8 7 m g / L 7 6 0 0 E 1 0 7 7 5 0 0 0 3 7 0 7 m g / L 4 5 0 0 E 1 5 5 0 0 0 0 0 5 0 8 7 m g / L 1 2 0 0 E 1 5 5 0 0 0 0 0 5 0 0 9 m g / L 0 8 5 0 E 1 6 4 0 0 0 0 0 6 5 8 7 m g / L 4 2 0 0 E 1 6 4 0 0 0 0 0 6 5 1 7 m g / L 0 8 8 0 E 2 0 3 4 1 7 0 0 9 9 8 7 m g / L 1 6 0 0 E 2 0 3 4 1 7 0 0 9 8 3 5 m g / L 1 2 0 0

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7 3 F i g u r e 5 3 G r a p h s h o w i n g t h e v a r i a t i o n o f r o o t m e a n s q u a r e e r r o r w i t h t h e n u m b e r o f n o d e s i n t h e h i d d e n l a y e r f o r n e u r a l n e t w o r k f o r l o w D O e x p e r i m e n t s 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 1 2 3 4 5 6 7 N u m b e r o f n o d e s i n h i d d e n l a y e rR M S E r r o r i n h o u r s

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7 4 F i g u r e 5 4 C o m p a r i s o n o f t h e o u t p u t f r o m t h e n e u r a l n e t w o r k a n d t h e d e s i r e d l a g l e n g t h w h e n t h e t r a i n i n g d a t a w a s p a s s e d b a c k t o t h e t r a i n e d n e t w o r k f o r l o w D O e x p e r i m e n t s T h e f o l l o w i n g s y m b o l s r e p r e s e n t t h e d a t a p o i n t s i n t h e g r a p h : L a g L e n g t h p r e d i c t e d b y t h e n e t w o r k D e s i r e d O u t p u t l a g l e n g t h 0 1 2 3 4 5 6 7 8 0 5 1 0 1 5 2 0 2 5 3 0 D a t a p o i n t sT i m e i n h o u r s

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7 5 F i g u r e 5 5 C o m p a r i s o n o f t h e o u t p u t f r o m t h e n e u r a l n e t w o r k a n d t h e d e s i r e d l a g l e n g t h w h e n t h e t e s t d a t a w a s p a s s e d b a c k t o t h e t r a i n e d n e t w o r k f o r l o w D O e x p e r i m e n t s T h e f o l l o w i n g s y m b o l s r e p r e s e n t t h e d a t a p o i n t s i n t h e g r a p h : L a g L e n g t h p r e d i c t e d b y t h e n e t w o r k D e s i r e d O u t p u t l a g l e n g t h 0 1 2 3 4 5 6 7 8 9 0 2 4 6 8 1 0 1 2 D a t a P o i n t sT i m e i n h o u r s

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7 6 5 3 N e u r a l N e t w o r k M o d e l P r e c u l t u r e E x p e r i m e n t s 5 3 1 T r a i n i n g t h e N e t w o r k A s e t o f n i n e e x p e r i m e n t s ( E 3 t o E 6 a n d E 2 4 t o E 2 8 ) w a s s p l i t i n t o t w o s e t s – t r a i n i n g a n d t e s t d a t a T a b l e 5 3 g i v e s t h e d a t a u s e d t o t r a i n t h e n e u r a l n e t w o r k m o d e l t o p r e d i c t t h e d u r a t i o n o f t h e l e n g t h o f t h e d i a u x i c l a g i n h o u r s I n a l l t h e s e e x p e r i m e n t s t h e d i s s o l v e d o x y g e n c o n c e n t r a t i o n w a s m a i n t a i n e d a t 8 7 m g / L t h r o u g h t h e a e r o b i c p h a s e a n d t h e r e f o r e w a s n o t a n i n p u t t o t h e n e u r a l n e t w o r k B i o m a s s i n t e r m s o f a b s o r b a n c e a t t h e s t a r t o f t h e e x p e r i m e n t d u r a t i o n o f t h e a e r a t i o n p h a s e i n h o u r s a n d c o n c e n t r a t i o n o f n i t r a t e i n t h e a e r o b i c p h a s e r e v i v i n g p h a s e o f t h e c u l t u r e w e r e t h e i n p u t s t o t h e n e t w o r k ( F i g u r e 5 6 ) A n o x i c r e v i v i n g p h a s e t r a n s a l a t e d t o a n i n p u t o f z e r o t o t h e n e t w o r k w h i l e a n a n o x i c r e v i v i n g p h a s e w a s d e n o t e d b y a n i n p u t v a l u e o f o n e A l l t h e o t h e r i n p u t s w e r e n o r m a l i z e d a n d t h e n p a s s e d t o t h e n e t w o r k T h e n u m b e r o f n o d e s i n t h e h i d d e n l a y e r w a s c h o s e n t o b e t h r e e a s t h a t g a v e t h e l o w e s t m e a n s q u a r e e r r o r ( F i g u r e 5 7 ) T h e w e i g h t s a f t e r t r a i n i n g w e r e s a v e d a n d w e r e u s e d t o t e s t t h e n e t w o r k F i g u r e 5 8 s h o w s t h e r e s u l t s w h e n t h e t r a i n i n g d a t a w a s p a s s e d b a c k t o t h e n e u r a l n e t w o r k t o v e r i f y i f t h e n e t w o r k h a d l e a r n t a l l t h e e x p e r i m e n t a l d a t a p r e s e n t e d t o i t 5 3 2 T e s t i n g t h e N e t w o r k T a b l e 5 4 g i v e s t h e s e t o f d a t a u s e d t o t e s t t h e n e t w o r k w i t h t h e w e i g h t s f o u n d a f t e r t r a i n i n g F i g u r e 5 9 s h o w s t h e r e s u l t s o f p a s s i n g t h e t e s t d a t a t o t h e t r a i n e d n e u r a l n e t w o r k

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7 7 F i g u r e 5 6 : N e u r a l n e t w o r k u s e d t o p r e d i c t t h e d u r a t i o n o f t h e d i a u x i c l a g f o r p r e c u l t u r e e x p e r i m e n t s B i o m a s s a s a b s o r b a n c e a t t i m e z e r o C o n c e n t r a t i o n o f d i s s o l v e d n i t r a t e i n t h e a e r o b i c p h a s e i n m g / l L e n g t h o f a e r o b i c p h a s e i n h o u r s H i d d e n L a y e r L a g l e n g t h i n h o u r s N e t w o r k O u t p u t R e v i v i n g p h a s e – A n o x i c / O x i c

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7 8 T a b l e 5 3 T r a i n i n g d a t a f o r n e u r a l n e t w o r k m o d e l f o r p r e c u l t u r e e x p e r i m e n t s I n p u t s t o N e t w o r k D e s i r e d O u t p u t E x p e r i m e n t N u m b e r L e n g t h o f A e r o b i c P h a s e ( h r s ) R e v i v i n g p h a s e o f t h e c u l t u r e B i o m a s s i n t e r m s o f a b s o r b a n c e a t t i m e z e r o C o n c e n t r a t i o n o f n i t r a t e i n t h e a e r o b i c p h a s e ( g / l ) L e n g t h o f d i a u x i c l a g ( h r s ) E 2 4 5 8 3 3 A n o x i c 0 0 3 0 0 2 5 0 0 E 2 4 5 8 3 3 A n o x i c 0 0 3 0 4 0 1 1 6 7 E 2 6 8 1 6 7 A n o x i c 0 0 4 0 0 1 5 0 0 E 2 6 8 1 6 7 A n o x i c 0 0 4 0 4 0 0 3 3 3 E 2 7 9 1 6 7 O x i c 0 0 4 0 0 7 3 3 3 E 2 7 9 1 6 7 O x i c 0 0 4 0 4 0 2 5 0 0 E 2 8 8 3 3 3 A n o x i c 0 0 3 0 0 3 5 0 0 E 2 8 8 3 3 3 A n o x i c 0 0 3 0 4 0 0 0 0 0 E 5 2 5 0 0 O x i c 0 0 3 5 4 0 9 3 3 3 E 4 1 6 6 7 O x i c 0 0 3 0 4 0 5 8 3 3

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7 9 F i g u r e 5 7 G r a p h s h o w i n g t h e v a r i a t i o n o f r o o t m e a n s q u a r e e r r o r w i t h t h e n u m b e r o f n o d e s i n t h e h i d d e n l a y e r f o r n e u r a l n e t w o r k f o r p r e c u l t u r e e x p e r i m e n t s 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 2 0 1 2 3 4 5 6 7 N u m b e r o f n o d e s i n t h e h i d d e n l a y e rR o o t m e a n s q u a r e d e r r o r n h o u r s

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8 0 F i g u r e 5 8 C o m p a r i s o n o f t h e o u t p u t f r o m t h e n e u r a l n e t w o r k a n d t h e d e s i r e d l a g l e n g t h w h e n t h e t r a i n i n g d a t a w a s p a s s e d b a c k t o t h e t r a i n e d n e t w o r k f o r p r e c u l t u r e e x p e r i m e n t s T h e f o l l o w i n g s y m b o l s r e p r e s e n t t h e d a t a p o i n t s i n t h e g r a p h : L a g L e n g t h p r e d i c t e d b y t h e n e t w o r k D e s i r e d O u t p u t l a g l e n g t h 0 1 2 3 4 5 6 7 8 9 1 0 0 2 4 6 8 1 0 1 2 D a t a P o i n t sT i m e i n h o u r s

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8 1 F i g u r e 5 9 C o m p a r i s o n o f t h e o u t p u t f r o m t h e n e u r a l n e t w o r k a n d t h e d e s i r e d l a g l e n g t h w h e n t h e t e s t d a t a w a s p a s s e d b a c k t o t h e t r a i n e d n e t w o r k f o r p r e c u l t u r e e x p e r i m e n t s T h e f o l l o w i n g s y m b o l s r e p r e s e n t t h e d a t a p o i n t s i n t h e g r a p h : D e s i r e d O u t p u t l a g l e n g t h L a g L e n g t h p r e d i c t e d b y t h e n e t w o r k 0 2 4 6 8 1 0 1 2 0 1 2 3 4 5 D a t a P o i n t sT i m e i n h o u r s

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8 2 T a b l e 5 4 T e s t d a t a f o r n e u r a l n e t w o r k m o d e l f o r p r e c u l t u r e e x p e r i m e n t s I n p u t s t o N e t w o r k D e s i r e d O u t p u t E x p e r i m e n t N u m b e r L e n g t h o f A e r o b i c P h a s e ( h r s ) R e v i v i n g p h a s e o f t h e c u l t u r e B i o m a s s i n t e r m s o f a b s o r b a n c e a t t i m e z e r o C o n c e n t r a t i o n o f n i t r a t e i n t h e a e r o b i c p h a s e ( g / l ) L e n g t h o f d i a u x i c l a g ( h r s ) E 2 5 4 1 6 7 A n o x i c 0 0 4 0 0 3 3 3 3 E 2 5 4 1 6 7 A n o x i c 0 0 4 0 4 0 2 6 6 7 E 6 2 0 0 0 O x i c 0 0 3 5 4 0 1 0 5 0 0 E 3 1 7 5 0 O x i c 0 0 4 0 4 0 9 6 6 7 5 4 D i s c u s s i o n o f R e s u l t s T h e n e u r a l n e t w o r k u s e d t o p r e d i c t t h e d i a u x i c l a g l e n g t h s f o r l o w D O e x p e r i m e n t s h a d a l a r g e r s e t o f t r a i n i n g d a t a t h a n t h e n e t w o r k u s e d t o p r e d i c t t h e l a g l e n g t h f o r p r e c u l t u r e e x p e r i m e n t s A l a r g e r t e s t s e t o f d a t a w a s u s e f u l i n t h a t i t p r e s e n t e d a b r o a d e r r a n g e o f d a t a t o t h e n e t w o r k b u t i t d i d n o t h e l p i n i m p r o v i n g t h e p e r f o r m a n c e o f t h e n e t w o r k d u e t h e l a r g e v a r i a t i o n i n e x p e r i m e n t a l d a t a w i t h p r a c t i c a l l y t h e s a m e i n p u t v a r i a b l e s T h e l o w e s t r o o t m e a n s q u a r e e r r o r c a l c u l a t e d f o r t h e t r a i n i n g d a t a w a s 0 0 2 h o u r s T h i s c a n b e a t t r i b u t e d t o t h e n a t u r e o f t h e t r a i n i n g d a t a H o w e v e r t h e n e t w o r k i s a b l e t o p r e d i c t t h e d i a u x i c l a g l e n g t h w i t h c o n s i d e r a b l e a c c u r a c y ( F i g u r e 5 5 ) a n d p r e d i c t e d s h o r t e r d i a u x i e s f o r l o w D O c o n c e n t r a t i o n s c o m p a r e d t o h i g h D O c o n c e n t r a t i o n s T h e n e t w o r k u s e d t o t r a i n t h e p r e c u l t u r e e x p e r i m e n t a l d a t a h a d a v e r y s m a l l t r a i n i n g s e t s i z e T h e l o w e s t r o o t m e a n s q u a r e e r r o r f o r t h e t r a i n i n g d a t a s e t o f t h i s n e t w o r k w a s 0 0 0 8 h o u r s w i t h t h r e e n o d e s i n t h e h i d d e n l a y e r F i g u r e 5 9 s h o w s t h a t t h e n e t w o r k p r e d i c t s h i g h e r l a g l e n g t h s f o r e x p e r i m e n t s w i t h o x i c r e v i v i n g p h a s e I t c o u l d a l s o p r e d i c t h i g h e r l a g l e n g t h s f o r b a c t e r i a t h a t w e r e n o t e x p o s e d t o n i t r a t e i n t h e a e r o b i c p h a s e

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8 3 5 5 H y b r i d M o d e l T h e c o m p l e t e h y b r i d m o d e l u s e s t h e m a t e r i a l b a l a n c e m o d e l f o r b o t h t h e a e r o b i c a n d a n o x i c g r o w t h p h a s e s a n d t h e n e u r a l n e t w o r k t o p r e d i c t t h e d i a u x i c l a g T h e e q u a t i o n g o v e r n i n g t h e a e r o b i c g r o w t h w i t h c o n s t a n t s p e c i f i c g r o w t h r a t e i s : X B ( t ) = X B ( 0 ) e m O t ( 1 0 ) W h e r e X B ( t ) i s t h e b i o m a s s c o n c e n t r a t i o n a t t i m e t X B ( 0 ) i s t h e b i o m a s s c o n c e n t r a t i o n a t t i m e z e r o A n d m O i s t h e s p e c i f i c g r o w t h r a t e i n t h e a e r o b i c p h a s e A n a n a l o g o u s e x p r e s s i o n f o r b i o m a s s c o n c e n t r a t i o n i n t h e a n o x i c p h a s e a s s u m i n g n o n l i m i t i n g n i t r a t e c o n c e n t r a t i o n s i s g i v e n b y : X B ( t ) = X B ( t 0 ) e m N ( t t 0 ) ( 1 1 ) W h e r e m N i s t h e s p e c i f i c g r o w t h r a t e i n t h e a n o x i c p h a s e a n d t 0 t h e t i m e a t t h e e n d o f t h e d i a u x i c l a g w h e n e x p o n e n t i a l g r o w t h r e s u m e s ( a n o x i c g r o w t h c u r v e ) T h e s p e c i f i c g r o w t h ( o x i c a n d a n o x i c ) r a t e s u s e d i n t h e m o d e l a r e f r o m L i s b o n ( 2 0 0 1 ) F i g u r e 5 1 0 s h o w s t h e c o m p a r i s o n o f t h e g r o w t h c u r v e s a s p r e d i c t e d b y t h e h y b r i d m o d e l a n d e x p e r i m e n t a l v a l u e s f o r h i g h d i s s o l v e d o x y g e n c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e f o r e x p e r i m e n t E 2 1 I n t h i s c a s e t h e s p e c i f i c g r o w t h r a t e s ( b o t h o x i c a n d a n o x i c ) o f t h i s e x p e r i m e n t a n d t h e a v e r a g e s p e c i f i c g r o w t h r a t e s a g r e e c l o s e l y H e n c e w e c a n s e e g r o w t h c u r v e s p r e d i c t e d b y t h e m o d e l c l o s e l y m a t c h w i t h t h e a c t u a l e x p e r i m e n t a l d a t a F i g u r e 5 1 1 s h o w s a c o m p a r i s o n o f t h e g r o w t h c u r v e s a s p r e d i c t e d b y t h e h y b r i d m o d e l a n d e x p e r i m e n t a l v a l u e s f o r l o w d i s s o l v e d o x y g e n c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e f o r e x p e r i m e n t E 2 1

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8 4 F i g u r e 5 1 0 C o m p a r i s o n o f t h e g r o w t h c u r v e s a s p r e d i c t e d b y t h e h y b r i d m o d e l a n d e x p e r i m e n t a l v a l u e s f o r h i g h d i s s o l v e d o x y g e n c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e f o r e x p e r i m e n t E 2 1 0 0 0 5 0 1 0 1 5 0 2 0 2 5 0 3 0 3 5 0 4 0 4 5 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 T i m e i n m i n u t e sA b s o r b a n c e b i o m a s s e x p e r i m e n t a l H i g h D O b i o m a s s f r o m h y b r i d m o d e l H i g h D O

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8 5 F i g u r e 5 1 1 C o m p a r i s o n o f t h e g r o w t h c u r v e s a s p r e d i c t e d b y t h e h y b r i d m o d e l a n d t h e a c t u a l e x p e r i m e n t a l v a l u e s f o r l o w d i s s o l v e d o x y g e n ( 0 7 m g / L ) c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e f o r e x p e r i m e n t E 2 1 0 0 0 5 0 1 0 1 5 0 2 0 2 5 0 3 0 3 5 0 4 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 T i m e i n m i n u t e sA b s o r b a n c e b i o m a s s e x p e r i m e n t a l l o w D O b i o m a s s f r o m h y b r i d m o d e l l o w D O

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8 6 I n e x p e r i m e n t E 1 4 t h e m o d e l p r e d i c t i o n d o e s n ’ t c l o s e l y a g r e e w i t h t h e e x p e r i m e n t a l g r o w t h c u r v e s T h i s c o u l d b e a t t r i b u t e d s e v e r a l r e a s o n s F i r s t l y t h e a v e r a g e s p e c i f i c g r o w t h r a t e s a r e h i g h e r t h a n t h e s p e c i f i c g r o w t h r a t e s o f t h i s p a r t i c u l a r e x p e r i m e n t S e c o n d l y t h e p r e s e n t h y b r i d m o d e l d o e s n ’ t a c c o u n t f o r a n y d i a u x i c l a g a t t h e b e g i n n i n g o f t h e a e r o b i c p h a s e F i g u r e 5 1 2 s h o w s t h e c o m p a r i s o n o f t h e g r o w t h c u r v e s a s p r e d i c t e d b y t h e h y b r i d m o d e l a n d e x p e r i m e n t a l v a l u e s f o r h i g h d i s s o l v e d o x y g e n c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e f o r e x p e r i m e n t E 1 4 A l t h o u g h t h e m o d e l c a p t u r e s t h e l a g a c c u r a t e l y i t i s n o t a b l e t o c a p t u r e t h e a e r o b i c a n d a n o x i c g r o w t h c u r v e s F i g u r e 5 1 3 s h o w s t h e c o m p a r i s o n o f t h e g r o w t h c u r v e s a s p r e d i c t e d b y t h e h y b r i d m o d e l a n d e x p e r i m e n t a l v a l u e s f o r l o w d i s s o l v e d o x y g e n c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e f o r e x p e r i m e n t E 1 4

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8 7 F i g u r e 5 1 2 C o m p a r i s o n o f t h e g r o w t h c u r v e s a s p r e d i c t e d b y t h e h y b r i d m o d e l a n d e x p e r i m e n t a l v a l u e s f o r h i g h d i s s o l v e d o x y g e n c o n c e n t r a t i o n s i n t h e a e r o b i c p h a s e f o r e x p e r i m e n t E 1 4 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 T i m e i n m i n u t e sA b s o r b a n c e b i o m a s s e x p e r i m e n t a l h i g h D O b i o m a s s f r o m h y b r i d m o d e l h i g h D O

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8 8 F i g u r e 5 1 3 C o m p a r i s o n o f t h e g r o w t h c u r v e s a s p r e d i c t e d b y t h e h y b r i d m o d e l a n d e x p e r i m e n t a l v a l u e s f o r l o w d i s s o l v e d o x y g e n c o n c e n t r a t i o n s ( 0 0 9 m g / L ) i n t h e a e r o b i c p h a s e f o r e x p e r i m e n t E 1 4 0 0 2 0 4 0 6 0 8 1 1 2 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 T i m e i n m i n u t e sA b s o r b a n c e b i o m a s s e x p e r i m e n t a l l o w D O b i o m a s s f r o m h y b r i d m o d e l l o w D O

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8 9 C H A P T E R 6 C O N C L U S I O N S A N D F U T U R E W O R K T h i s r e s e a r c h h a s s h o w n t h a t a n e u r a l n e t w o r k m o d e l c a n p r e d i c t t h e l e n g t h o f t h e d i a u x i c l a g g i v e n c e r t a i n p a r a m e t e r s a s i n p u t s A l t h o u g h t h e n e t w o r k d o e s n o t p r o v i d e a n y i n s i g h t i n t o p r o c e s s d y n a m i c s o r g o v e r n i n g e q u a t i o n s i t c e r t a i n l y i s v e r y p o w e r f u l a s i t c a n l e a r n e x p e r i m e n t a l d a t a v e r y q u i c k l y I n a t y p i c a l n i t r o g e n r e m o v a l p l a n t t h e e n t i r e h i s t o r y o f d a t a c a n b e u s e d t o t r a i n t h e n e u r a l n e t w o r k E s t i m a t i o n o f t h e l e n g t h o f d i a u x i c l a g c a n h a v e s i g n i f i c a n t e c o n o m i c a d v a n t a g e s i n t r e a t m e n t p l a n t s C o n s i d e r a b l e e x p e r i m e n t a l w o r k n e e d s t o b e d o n e t o e x p a n d t h e s i z e o f t h e d a t a s e t a v a i l a b l e f o r t r a i n i n g A c o m p r e h e n s i v e n e t w o r k t h a t t a k e s i n a l l p a r a m e t e r s s u c h a s b i o m a s s i n t e r m s o f a b s o r b a n c e l e n g t h o f t h e a e r a t i o n p h a s e d i s s o l v e d o x y g e n c o n c e n t r a t i o n s n i t r a t e c o n c e n t r a t i o n s i n a e r o b i c p h a s e t o p r e d i c t t h e d u r a t i o n o f t h e d i a u x i c l a g c a n b e d e v e l o p e d I t m i g h t a l s o b e i n t e r e s t i n g t o r e p l a c e t h e d u r a t i o n o f t h e a e r a t i o n p h a s e a n d t h e b i o m a s s a t t i m e z e r o w i t h t h e r a t i o o f t h e b i o m a s s a t t h e e n d o f t h e a e r a t i o n p h a s e t o t h e b i o m a s s a t t i m e z e r o a s a n i n p u t T h i s n e t w o r k c a n t h e n b e i n t e g r a t e d w i t h t h e s i m p l e M o n o d t y p e m o d e l s f o r b o t h t h e a e r o b i c a n d a n o x i c p h a s e s t o g i v e a c o m p l e t e h y b r i d m o d e l N i t r a t e r e d u c t a s e e n z y m e a c t i v i t y t h r o u g h t h e c o u r s e o f a n e x p e r i m e n t a l s o r e m a i n s a n u n r e s o l v e d p r o b l e m P o s s i b l e i m p r o v i s a t i o n s i n t h e e n z y m e a s s a y s u c h a s f r e e z i n g t h e w h o l e c e l l s a m p l e s i n l i q u i d n i t r o g e n t o s t o p c e l l a c t i v i t y o n c e w i t h d r a w n f r o m t h e r e a c t o r c o u l d g i v e m o r e a c c u r a t e r e s u l t s A r e l i a b l e a s s a y f o r n i t r a t e r e d u c t a s e

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9 0 a n d b e i n g a b l e t o t r a c k e n z y m e a c t i v i t y t h r o u g h t h e c o u r s e o f a n e x p e r i m e n t w o u l d h e l p a m a j o r p i e c e o f t h e p u z z l e f a l l i n t o p l a c e

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9 1 A P P E N D I X P R O G R A M L I S T I N G T h e f o l l o w i n g p r o g r a m a c c e p t s f r o m t h e u s e r t h e f o l l o w i n g i n f o r m a t i o n : N u m b e r o f n o d e s i n t h e I n p u t L a y e r N u m b e r o f n o d e s i n t h e H i d d e n L a y e r T r a i n i n g d a t a f i l e n a m e w i t h e x t e n s i o n T e s t d a t a f i l e n a m e w i t h e x t e n s i o n N u m b e r o f d a t a p o i n t s T h e p r o g r a m u s e s S i m u l a t e d A n n e a l i n g c o u p l e d w i t h c o n j u g a t e g r a d i e n t s e a r c h t o f i n d t h e p o i n t o f m i n i m a a n d t r a i n s t h e n e t w o r k f o r t h e g i v e n t r a i n i n g d a t a O n c e t h e n e t w o r k h a s b e e n t r a i n e d t h e t e s t d a t a i s p a s s e d t o t h e n e u r a l n e t w o r k a n d t h e r e s u l t s a r e w r i t t e n t o f i l e A l s o t h e w e i g h t s f r o m t h e i n p u t t o h i d d e n l a y e r a n d h i d d e n t o o u t p u t l a y e r a r e w r i t t e n t o f i l e P r e d e f i n e d c o n s t a n t s a n d v a r i a b l e n a m e s u s e d : V a r i a b l e / C o n s t a n t n a m e W h a t i t s t a n d s f o r M A X D A T A M a x i m u m n u m b e r o f d a t a p o i n t s M A X I N P M a x i m u m n u m b e r o f i n p u t n o d e s M A X H I D M a x i m u m n u m b e r o f h i d d e n n o d e s S T A R T T E M P S t a r t i n g t e m p e r a t u r e f o r t h e s i m u l a t e d a n n e a l i n g S T O P T E M P S t o p p i n g t e m p e r a t u r e f o r t h e s i m u l a t e d a n n e a l i n g N T E M P S N u m b e r o f i t e r a t i o n s t o f i n d t h e b e s t s e e d v a l u e W m a x M a x i m u m v a l u e o f t h e w e i g h t s W m i n M i n i m u m v a l u e o f t h e w e i g h t s P R O G R A M L I S T I N G / / N E U R A L N E T W O R K S C O D E F O R V A R I A B L E N U M B E R O F I N P U T N O D E S A N D S I N G L E O U T P U T N O D E / / S t a n d a r d L i b r a r i e s i n c l u d e d # i n c l u d e < i o s t r e a m h > # i n c l u d e < s t d l i b h > # i n c l u d e < t i m e h > # i n c l u d e < c t y p e h >

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9 2 # i n c l u d e < m a t h h > # i n c l u d e < s t r i n g h > # i n c l u d e < s t d i o h > / / C o n s t a n t s f o r N e t w o r k A r c h i t e c t u r e # d e f i n e M A X D A T A 3 0 # d e f i n e M A X I N P 3 0 # d e f i n e M A X H I D 3 0 / / C o n s t a n t s f o r S i m u l a t e d A n n e a l i n g # d e f i n e G O L D E N R A T I O 1 6 1 8 0 3 4 / / G l o b a l v a r i a b l e s p r e d e f i n e d f l o a t E P = 1 e 4 0 ; f l o a t S T A R T T E M P = 2 ; f l o a t S T O P T E M P = 0 2 ; i n t N T E M P S = 2 ; f l o a t w m a x = 5 0 ; f l o a t w m i n = 5 0 ; f l o a t a = 0 9 ; / / V a r i a b l e s u s e d i n t h e c o d e i n t t e s t d a t a ; i n t n o o f d a t a i n p n o d e s h i d n o d e s ; f l o a t i n p d a t a [ M A X D A T A ] [ M A X I N P ] m a x i [ M A X I N P ] m i n i [ M A X I N P ] i n p h i d w [ M A X I N P ] [ M A X H I D ] h i d o u t w [ M A X H I D ] d e s o p [ M A X D A T A ] ; f l o a t h i d [ M A X H I D ] ; f l o a t n e w i h w [ M A X I N P ] [ M A X H I D ] n e w h o w [ M A X H I D ] s a v i h w [ M A X I N P ] [ M A X H I D ] s a v h o w [ M A X H I D ] ; f l o a t d e r i i h w [ M A X I N P ] [ M A X H I D ] d e r i h o w [ M A X H I D ] f d e r i i h w [ M A X I N P ] [ M A X H I D ] f d e r i h o w [ M A X H I D ] ; f l o a t o l d d i h w [ M A X I N P ] [ M A X H I D ] o l d d h o w [ M A X H I D ] ; f l o a t t e s t [ M A X D A T A ] [ M A X I N P ] m a x t e s t d a t a [ M A X I N P ] m i n t e s t d a t a [ M A X I N P ] ; f l o a t n w ; f l o a t a 1 a 2 a 3 ; f l o a t n n 1 n n 2 n n 3 e n n 1 e n n 2 e n n 3 ; f l o a t t 1 t 2 d e n o m s t e p d i f f s t e p e r r r m s m a x s t e p ; f l o a t t e m p t e m p m u l t ; f l o a t n n o p d h o d h i ; f l o a t e e e e r e r r o r e e e ;

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9 3 / / F i l e v a r i a b l e s F I L E i p t r o p t r ; c h a r i n p f i l e [ 2 0 ] ; f l o a t f v a l u e ; i n t i j k ; i n t f l a g f l a g g g i v e u p ; i n t s e e d b e s t s e e d ; / / F u n c t i o n P r o t o t y p e s f l o a t e r r o r c a l f n 0 ( ) ; f l o a t e r r o r c a l f n 1 ( ) ; f l o a t w e r r o r c a l f n ( ) ; f l o a t r n d ( ) ; m a i n ( ) { / / A c c e p t f r o m u s e r t h e n u m b e r o f i n p u t d a t a f i l e w i t h e x t e n s i o n d a t a p o i n t s / / N u m b e r o f i n p u t n o d e s n u m b e r o f t e s t d a t a p o i n t s a n d h i d d e n n o d e s c o u t < < \ n N e u r a l N e t w o r k s M o d e l o f t h e D i a u x i c l a g \ n ; c o u t < < \ n E n t e r t h e N a m e o f t h e I n p u t D a t a F i l e w i t h E x t e n s i o n : ; c i n > > i n p f i l e ; c o u t < < \ n E n t e r t h e N u m b e r o f D a t a P o i n t s : ; c i n > > n o o f d a t a ; c o u t < < \ n E n t e r t h e N u m b e r o f I n p u t N o d e s : ; c i n > > i n p n o d e s ; c o u t < < \ n E n t e r t h e N u m b e r o f T e s t D a t a P o i n t s : ; c i n > > t e s t d a t a ; c o u t < < \ n E n t e r t h e N u m b e r o f N o d e s i n H i d d e n L a y e r : ; c i n > > h i d n o d e s ; / / A d d a b i a s t o t h e n u m b e r o f I n p u t a n d H i d d e n l a y e r i = i n p n o d e s + 1 ; j = h i d n o d e s + 1 ;

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9 4 / / R e a d t h e t r a i n i n g d a t a f r o m t h e d a t a f i l e i p t r = f o p e n ( i n p f i l e r ) ; / / S e t t h e b i a s i n t h e i n p u t d a t a t o o n e f o r ( i = 0 ; i < n o o f d a t a ; i + + ) i n p d a t a [ i ] [ 0 ] = 1 ; / / R e a d i n g t h e i n p u t d a t a f r o m f i l e i n t o t h e a r r a y f o r ( i = 0 ; i < n o o f d a t a ; i + + ) f o r ( j = 1 ; j < = i n p n o d e s ; j + + ) { f s c a n f ( i p t r % f & f v a l u e ) ; i n p d a t a [ i ] [ j ] = f v a l u e ; p r i n t f ( % f \ t i n p d a t a [ i ] [ j ] ) ; } / / C l o s e t h e f i l e f c l o s e ( i p t r ) ; / / R e a d t h e d e s i r e d o u t p u t d a t a f r o m u s e r e n t e r e d d a t a n a m e f i l e w i t h e x t e n s i o n c o u t < < \ n E n t e r t h e n a m e o f t h e d e s i r e d o u t p u t d a t a f i l e w i t h e x t e n s i o n : ; c i n > > i n p f i l e ; i p t r = f o p e n ( i n p f i l e r ) ; f o r ( i = 0 ; i < n o o f d a t a ; i + + ) { f s c a n f ( i p t r % f & f v a l u e ) ; d e s o p [ i ] = f v a l u e ; p r i n t f ( % f \ t d e s o p [ i ] ) ; } f c l o s e ( i p t r ) ; / / A c c e p t t e s t d a t a f i l e n a m e f r o m u s e r a n d r e a d d a t a f r o m f i l e c o u t < < \ n E n t e r t h e n a m e o f t h e t e s t d a t a f i l e w i t h e x t e n s i o n : ; c i n > > i n p f i l e ; i p t r = f o p e n ( i n p f i l e r ) ; f o r ( i = 0 ; i < t e s t d a t a ; i + + ) f o r ( j = 1 ; j < = i n p n o d e s ; j + + ) {

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9 5 f s c a n f ( i p t r % f & f v a l u e ) ; t e s t [ i ] [ j ] = f v a l u e ; p r i n t f ( % f \ t t e s t [ i ] [ j ] ) ; } f c l o s e ( i p t r ) ; / / F i n d t h e M a x i m u m e a c h v e c t o r o f t h e i n p u t d a t a f o r ( j = 1 ; j < = i n p n o d e s ; j + + ) { m a x i [ j ] = m i n i [ j ] = 0 ; } f o r ( j = 1 ; j < = i n p n o d e s ; j + + ) { m a x i [ j ] = i n p d a t a [ 0 ] [ j ] ; f o r ( i = 0 ; i < n o o f d a t a ; i + + ) { i f ( i n p d a t a [ i ] [ j ] > m a x i [ j ] ) m a x i [ j ] = i n p d a t a [ i ] [ j ] ; } } / / F i n d t h e M i n i m u m e a c h v e c t o r o f t h e i n p u t d a t a f o r ( j = 1 ; j < = i n p n o d e s ; j + + ) { m i n i [ j ] = i n p d a t a [ 0 ] [ j ] ; f o r ( i = 0 ; i < n o o f d a t a ; i + + ) { i f ( i n p d a t a [ i ] [ j ] < m i n i [ j ] ) m i n i [ j ] = i n p d a t a [ i ] [ j ] ; } } / / S c a l i n g t h e I n p u t d a t a p r i n t f ( \ n ) ; f o r ( i = 1 ; i < = i n p n o d e s ; i + + ) f o r ( j = 0 ; j < n o o f d a t a ; j + + ) { i n p d a t a [ j ] [ i ] = ( i n p d a t a [ j ] [ i ] m i n i [ i ] ) / ( m a x i [ i ] m i n i [ i ] ) ; } p r i n t f ( \ n s c a l e d v a l u e s : \ n ) ; f o r ( i = 0 ; i < n o o f d a t a ; i + + )

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9 6 f o r ( j = 1 ; j < = i n p n o d e s ; j + + ) { p r i n t f ( % f \ t i n p d a t a [ i ] [ j ] ) ; } / / S c a l i n g t h e O u t p u t d a t a f l o a t m i n d e s o p m a x d e s o p ; m i n d e s o p = m a x d e s o p = d e s o p [ 0 ] ; f o r ( i = 0 ; i < n o o f d a t a ; i + + ) { i f ( m i n d e s o p > d e s o p [ i ] ) m i n d e s o p = d e s o p [ i ] ; i f ( m a x d e s o p < d e s o p [ i ] ) m a x d e s o p = d e s o p [ i ] ; } f o r ( i = 0 ; i < n o o f d a t a ; i + + ) { d e s o p [ i ] = ( d e s o p [ i ] m i n d e s o p ) / ( m a x d e s o p m i n d e s o p ) ; } / / T o f i n d t h e m a x i m u m e a c h v e c t o r o f t h e t e s t d a t a f o r ( j = 1 ; j < = i n p n o d e s ; j + + ) { m a x t e s t d a t a [ j ] = m i n t e s t d a t a [ j ] = 0 ; } f o r ( j = 1 ; j < = i n p n o d e s ; j + + ) { m a x t e s t d a t a [ j ] = t e s t [ 0 ] [ j ] ; f o r ( i = 0 ; i < t e s t d a t a ; i + + ) { i f ( t e s t [ i ] [ j ] > m a x t e s t d a t a [ j ] ) m a x t e s t d a t a [ j ] = t e s t [ i ] [ j ] ; } } / / T o f i n d t h e m i n i m u m e a c h v e c t o r o f t h e t e s t d a t a f o r ( j = 1 ; j < = i n p n o d e s ; j + + ) { m i n t e s t d a t a [ j ] = t e s t [ 0 ] [ j ] ; f o r ( i = 0 ; i < t e s t d a t a ; i + + ) { i f ( t e s t [ i ] [ j ] < m i n t e s t d a t a [ j ] ) m i n t e s t d a t a [ j ] = t e s t [ i ] [ j ] ;

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9 7 } } / / S c a l i n g t h e t e s t d a t a p r i n t f ( \ n ) ; f o r ( i = 1 ; i < = i n p n o d e s ; i + + ) f o r ( j = 0 ; j < t e s t d a t a ; j + + ) { t e s t [ j ] [ i ] = ( t e s t [ j ] [ i ] m i n i [ i ] ) / ( m a x i [ i ] m i n i [ i ] ) ; } p r i n t f ( \ n s c a l e d v a l u e s : \ n ) ; f o r ( i = 0 ; i < t e s t d a t a ; i + + ) f o r ( j = 1 ; j < = i n p n o d e s ; j + + ) { p r i n t f ( % f \ t t e s t [ i ] [ j ] ) ; } t i m e t B e g i n T i m e E n d T i m e ; t i m e ( & B e g i n T i m e ) ; / / I n i t i a l i z a t i o n o f t h e w e i g h t s i n t h e I n p u t H i d d e n l a y e r f o r ( i = 1 ; i < = h i d n o d e s ; i + + ) f o r ( j = 0 ; j < = i n p n o d e s ; j + + ) i n p h i d w [ j ] [ i ] = 0 ; / / I n i t i a l i z a t i o n o f t h e w e i g h t s i n t h e H i d d e n O u t p u t l a y e r f o r ( j = 0 ; j < = h i d n o d e s ; j + + ) h i d o u t w [ j ] = 0 ; / / I n i t i a l e s t i m a t i o n o f t h e e r r o r e r r o r = e r r o r c a l f n 0 ( ) ; / / S i m u l a t e d A n n e a l i n g / / N u m b e r o f i t e r a t i o n s t o f i n d t h e b e s t s e e d n w = 3 0 ( 5 h i d n o d e s + 1 ) ; d o {

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9 8 f l a g = 0 ; / / S t a r t i n g t e m p e r a t u r e o f t h e s i m u l a t e d a n n e a l i n g t e m p = S T A R T T E M P ; / / t e m p m u l t = e x p ( l o g ( S T A R T T E M P / S T O P T E M P ) / ( N T E M P S 1 ) ) ; f o r ( i n t i t e m p = 0 ; i t e m p < N T E M P S ; i t e m p + + ) { f l a g g = 0 ; f o r ( k = 1 ; k < = n w ; k + + ) { / / S e t t h e s e e d v a l u e s e e d = k ; / / S e e d t h e r a n d o m n u m b e r g e n e r a t o r s r a n d ( ( u n s i g n e d ) s e e d ) ; / / S e t t h e n e w h i d d e n o u t p u t n o d e w e i g h t s t o z e r o f o r ( j = 0 ; j < = h i d n o d e s ; j + + ) n e w h o w [ j ] = 0 0 ; / / S e t t h e n e w i n p u t h i d d e n n o d e w e i g h t s t o z e r o f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) { n e w i h w [ o ] [ j ] = 0 0 ; } / / E v a l u a t e t h e w e i g h t s f o r ( j = 0 ; j < = h i d n o d e s ; j + + ) { n e w h o w [ j ] = h i d o u t w [ j ] + t e m p r n d ( ) ; }

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9 9 p r i n t f ( \ n ) ; f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) { n e w i h w [ o ] [ j ] = i n p h i d w [ o ] [ j ] + t e m p r n d ( ) ; } / / C h e c k t o s e e i f t h e w e i g h t v a l u e s a r e w i t h i n b o u n d s f o r ( j = 0 ; j < = h i d n o d e s ; j + + ) { i f ( n e w h o w [ j ] > w m a x ) n e w h o w [ j ] = w m a x ; i f ( n e w h o w [ j ] < w m i n ) n e w h o w [ j ] = w m i n ; } f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) { i f ( n e w i h w [ o ] [ j ] > w m a x ) n e w i h w [ o ] [ j ] = w m a x ; i f ( n e w i h w [ o ] [ j ] < w m i n ) n e w i h w [ o ] [ j ] = w m i n ; } / / C a l c u l a t e t h e e r r o r w i t h t h e s e w e i g h t s e r = e r r o r c a l f n 1 ( ) ; / / I f t h e e r r o r h a s i m p r o v e d t h e n t h i s i s t h e b e s t s e e d f o u n d s o f a r i f ( e r < e r r o r ) { f l a g g = 1 ; b e s t s e e d = s e e d ; e = e r ; } } / / k l o o p e n d s h e r e / / I f t h e r e w a s a n y i m p r o v e m e n t i n e r r o r t h e n u p d a t e t h e w e i g h t s w i t h t h i s r a n d o m n u m b e r a n d s e e d i f ( f l a g g = = 1 ) { f l a g = 1 ; / / S e e d t h e r a n d o m n u m b e r g e n e r a t o r

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1 0 0 s r a n d ( b e s t s e e d ) ; / / W e i g h t U p d a t i o n f o r ( j = 0 ; j < = h i d n o d e s ; j + + ) h i d o u t w [ j ] = h i d o u t w [ j ] + t e m p r n d ( ) ; f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) i n p h i d w [ o ] [ j ] = i n p h i d w [ o ] [ j ] + t e m p r n d ( ) ; / / C h e c k t o s e e i f t h e w e i g h t v a l u e s a r e w i t h i n b o u n d s f o r ( j = 0 ; j < = h i d n o d e s ; j + + ) { i f ( h i d o u t w [ j ] > w m a x ) h i d o u t w [ j ] = w m a x ; i f ( h i d o u t w [ j ] < w m i n ) h i d o u t w [ j ] = w m i n ; } f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) { i f ( i n p h i d w [ o ] [ j ] > w m a x ) i n p h i d w [ o ] [ j ] = w m a x ; i f ( i n p h i d w [ o ] [ j ] < w m i n ) i n p h i d w [ o ] [ j ] = w m i n ; } / / C a l c u l a t e t h e e r r o r w i t h t h e w e i g h t s a n d s a v e i t e = e r r o r c a l f n 0 ( ) ; / / R e s e t t h e r a n d o m n u m b e r g e n e r a t o r s r a n d ( b e s t s e e d / 2 + 9 9 9 ) ; } / / e n d i f t h e i f f l a g g ( i e ) i f t h e r e w a s a n y i m p r o v e m e n t / / U p d a t e t h e t e m p v a l u e t e m p = t e m p m u l t ; } / / i t e m p l o o p e n d s h e r e / / I f t h e r e w a s a n i m p r o v e m e n t i n t h e e r r o r t h e n c a l c u l a t e t h e e r r o r d e r i v a t i v e s i f ( f l a g = = 1 ) {

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1 0 1 / / I n i t i a l i z e t h e d e r i v a t i v e s t o z e r o f o r ( j = 0 ; j < = h i d n o d e s ; j + + ) { f d e r i h o w [ j ] = 0 ; d e r i h o w [ j ] = 0 ; } f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) { f d e r i i h w [ o ] [ j ] = 0 ; d e r i i h w [ o ] [ j ] = 0 ; } / / T e s t i n g t o s e e i f t h i s n e w p o i n t o f r e d u c e d e r r o r i s a l o c a l m i n i m a d o { / / S a v i n g t h e o l d d e r i v a t i v e v a l u e s f o r ( j = 0 ; j < = h i d n o d e s ; j + + ) { o l d d h o w [ j ] = d e r i h o w [ j ] ; d e r i h o w [ j ] = 0 ; } f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) { o l d d i h w [ o ] [ j ] = d e r i i h w [ o ] [ j ] ; d e r i i h w [ o ] [ j ] = 0 ; } / / N e w G r a d i e n t C a l c u l a t i o n f o r t h e e n t i r e d a t a s e t / / C o m p u t i n g t h e v a l u e s a t t h e h i d d e n l a y e r f o r ( i = 0 ; i < n o o f d a t a ; i + + ) { h i d [ 0 ] = 1 ; / / C o m p u t i n g t h e v a l u e s a t t h e h i d d e n l a y e r f o r ( k = 1 ; k < = h i d n o d e s ; k + + )

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1 0 2 { f o r ( j = 0 ; j < = i n p n o d e s ; j + + ) { h i d [ k ] = h i d [ k ] + i n p d a t a [ i ] [ j ] i n p h i d w [ j ] [ k ] ; } i f ( h i d [ k ] < 1 0 0 ) h i d [ k ] = 1 0 0 ; h i d [ k ] = 1 0 / ( 1 0 + e x p ( h i d [ k ] ) ) ; } / / C o m p u t i n g t h e v a l u e s a t t h e o u t p u t l a y e r o p = d h o = 0 ; f o r ( k = 0 ; k < = h i d n o d e s ; k + + ) { o p = o p + h i d [ k ] h i d o u t w [ k ] ; } i f ( o p < 1 0 0 ) o p = 1 0 0 ; o p = 1 0 / ( 1 0 + e x p ( o p ) ) ; / / E r r o r a t t h e o u t p u t l a y e r t o b e b a c k p r o p a g a t e d d h o = ( 1 0 o p ) ( o p ) ( d e s o p [ i ] o p ) ; / / D e r i v a t e o f t h e w e i g h t s f r o m h i d d e n t o o u t p u t l a y e r f o r ( k = 0 ; k < = h i d n o d e s ; k + + ) { d e r i h o w [ k ] + = h i d [ k ] d h o ; } / / D e r i v a t i v e o f t h e w e i g h t s f r o m i n p u t t o h i d d e n l a y e r f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) { d h i = h i d [ j ] ( 1 h i d [ j ] ) d h o h i d o u t w [ j ] ; f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) d e r i i h w [ o ] [ j ] + = d h i i n p d a t a [ i ] [ o ] ; } } / / i l o o p e n d s h e r e / / C o n j u g a t e G r a d i e n t C a l c u l a t i o n f o r ( k = 0 ; k < = h i d n o d e s ; k + + ) { a 1 + = o l d d h o w [ k ] o l d d h o w [ k ] ;

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1 0 3 a 2 + = d e r i h o w [ k ] d e r i h o w [ k ] ; a 3 + = d e r i h o w [ k ] o l d d h o w [ k ] ; } f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) { a 1 + = o l d d i h w [ o ] [ j ] o l d d i h w [ o ] [ j ] ; a 2 + = d e r i i h w [ o ] [ j ] d e r i i h w [ o ] [ j ] ; a 3 + = d e r i i h w [ o ] [ j ] o l d d i h w [ o ] [ j ] ; } i f ( a 1 = 0 ) a = ( a 2 a 3 ) / a 1 ; e l s e a = 0 ; / / G r a d i e n t C a l c u l a t i o n f o r ( k = 0 ; k < = h i d n o d e s ; k + + ) { f d e r i h o w [ k ] = d e r i h o w [ k ] + a f d e r i h o w [ k ] ; } f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) { f d e r i i h w [ o ] [ j ] = d e r i i h w [ o ] [ j ] + a f d e r i i h w [ o ] [ j ] ; } / / S a v e t h e o l d w e i g h t s f o r b a c k u p f o r ( k = 0 ; k < = h i d n o d e s ; k + + ) { s a v h o w [ k ] = h i d o u t w [ k ] ; } f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) { s a v i h w [ o ] [ j ] = i n p h i d w [ o ] [ j ] ; } n n = 5 ; / / C a l c u l a t e t h e e r r o r f o r t h e s e u p d a t e d w e i g h t s

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1 0 4 d o { n n = n n / 2 ; e e e = w e r r o r c a l f n ( ) ; } w h i l e ( e e e > e ) ; n n 1 = 0 0 ; n n 2 = n n ; e n n 1 = e ; e n n 2 = e e e ; n n 3 = n n 2 + G O L D E N R A T I O n n ; e n n 3 = w e r r o r c a l f n ( ) ; / / P a r a b o l i c F i t t o e s t i m a t e t h e L o c a l M i n i m a w h i l e ( e n n 3 < e n n 2 ) { t 1 = ( n n 2 n n 1 ) ( e n n 2 e n n 3 ) ; t 2 = ( n n 2 n n 3 ) ( e n n 2 e n n 1 ) ; d e n o m = 2 0 ( t 2 t 1 ) ; i f ( ( f a b s ( d e n o m ) < E P ) & & ( d e n o m > 0 0 ) ) { d e n o m = E P ; } e l s e { d e n o m = E P ; } / / S t e p c a l c u l a t i o n a n d m a x s t e p t o s e e t h a t w e d o n ’ t j u m p t o o f a r s t e p = n n 2 + ( ( n n 2 n n 1 ) t 1 ( n n 2 n n 3 ) t 2 ) / d e n o m ; m a x s t e p = n n 2 + 2 0 0 0 ( n n 3 n n 2 ) ; / / I f i t s b e t w e e n n n 1 a n d n n 2 / / T h e n n n 3 s h i f t s t o n n 2 / / A n d n n 2 i s t h e i n t e r m e d i a t e v a l u e s t e p i f ( ( n n 2 s t e p ) ( s t e p n n 1 ) > 0 0 ) { / / c a l c u l a t e t h e e r r o r s t e p e r r = w e r r o r c a l f n ( ) ; n n 3 = n n 2 ; n n 2 = s t e p ; e n n 3 = e n n 2 ; e n n 2 = s t e p e r r ; g o t o N E X T T E S T ; }

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1 0 5 / / i f i t s b e t w e e n n n 2 a n d n n 3 e l s e i f ( ( n n 2 s t e p ) ( s t e p n n 3 ) > 0 0 ) { s t e p e r r = w e r r o r c a l f n ( ) ; / / n n 1 s h i f t s t o n n 2 / / a n d n n 2 i s t h e i n t e r m e d i a t e v a l u e s t e p i f ( s t e p e r r < e n n 3 ) { n n 1 = n n 2 ; n n 2 = s t e p ; e n n 1 = e n n 2 ; e n n 2 = s t e p e r r ; g o t o N E X T T E S T ; } / / t h e p o i n t i s t o t h e l e f t o f n n 3 / / s h i f t n n 3 t o s t e p e l s e i f ( s t e p e r r > e n n 2 ) { n n 3 = s t e p ; e n n 3 = s t e p e r r ; g o t o N E X T T E S T ; } / / i f i t i s o u t o f t h e r a n g e s i m p l y a p p l y t h e g o l d e n r a t i o r u l e e l s e { s t e p = n n 3 + G O L D E N R A T I O ( n n 3 n n 2 ) ; s t e p e r r = w e r r o r c a l f n ( ) ; } } / / i f t h e s t e p v a l u e i s t o t h e r i g h t o f n n 3 e l s e i f ( ( n n 3 s t e p ) ( s t e p m a x s t e p ) > 0 0 ) { s t e p e r r = w e r r o r c a l f n ( ) ; / / s h i f t n n 2 t o n n 3 a n d n n 3 t o s t e p

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1 0 6 i f ( s t e p e r r < e n n 3 ) { n n 2 = n n 3 ; n n 3 = s t e p ; s t e p = n n 3 + G O L D E N R A T I O ( n n 3 n n 2 ) ; e n n 2 = e n n 3 ; e n n 3 = s t e p e r r ; s t e p e r r = w e r r o r c a l f n ( ) ; } } / / s t e p m a y b e e v e n b e y o n d m a x s t e p e l s e i f ( ( s t e p m a x s t e p ) ( m a x s t e p n n 3 ) > = 0 0 ) { s t e p = m a x s t e p ; s t e p e r r = w e r r o r c a l f n ( ) ; i f ( s t e p e r r < e n n 3 ) { n n 2 = n n 3 ; n n 3 = s t e p ; s t e p = n n 3 + G O L D E N R A T I O ( n n 3 n n 2 ) ; e n n 2 = e n n 3 ; e n n 3 = s t e p e r r ; s t e p e r r = w e r r o r c a l f n ( ) ; } } / / u s e g o l d e n r a t i o t o u p d a t e t h e s t e p v a l u e s e l s e { s t e p = n n 3 + G O L D E N R A T I O ( n n 3 n n 2 ) ; s t e p e r r = w e r r o r c a l f n ( ) ; } n n 1 = n n 2 ; n n 2 = n n 3 ; n n 3 = s t e p ; e n n 1 = e n n 2 ; e n n 2 = e n n 3 ; e n n 3 = s t e p e r r ;

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1 0 7 } / / C o d e j u m p s h e r e i f w e h a v e m a d e o n e i m p r o v i s a t i o n N E X T T E S T : g i v e u p = 0 ; d o { t 1 = ( n n 2 n n 1 ) ( e n n 2 e n n 3 ) ; t 2 = ( n n 2 n n 3 ) ( e n n 2 e n n 1 ) ; d e n o m = 2 0 ( t 2 t 1 ) ; i f ( f a b s ( d e n o m ) < E P ) { i f ( g i v e u p = = 1 ) { g i v e u p = 2 ; } i f ( g i v e u p = = 0 ) { g i v e u p = 1 ; } i f ( d e n o m > 0 0 ) d e n o m = E P ; e l s e d e n o m = E P ; } / / N a r r o w d o w n t h e s e a r c h f o r m i n i m a u n t i l t h e e r r o r r e d u c e s b e l o w t h e t h r e s h o l d r e q u i r e d s t e p = n n 2 + ( ( n n 2 n n 1 ) t 1 ( n n 2 n n 3 ) t 2 ) / d e n o m ; s t e p e r r = w e r r o r c a l f n ( ) ; i f ( ( n n 2 s t e p ) ( s t e p n n 1 ) > 0 0 ) { n n 3 = n n 2 ; n n 2 = s t e p ; e n n 3 = e n n 2 ; e n n 2 = s t e p e r r ; } e l s e i f ( ( n n 2 s t e p ) ( s t e p n n 3 ) > 0 0 ) { n n 1 = n n 2 ; n n 2 = s t e p ; e n n 1 = e n n 2 ; e n n 2 = s t e p e r r ; } e l s e b r e a k ;

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1 0 8 i f ( g i v e u p = = 2 ) b r e a k ; } w h i l e ( f a b s ( n n 3 n n 1 ) > 0 0 0 0 0 1 ) ; e e e = w e r r o r c a l f n ( ) ; p r i n t f ( E r r o r ( e e e ) : % f \ n e e e ) ; d i f f = e e e e ; p r i n t f ( d i f f : % f \ n d i f f ) ; e = e e e ; } w h i l e ( f a b s ( e e e ) > 0 0 0 0 0 0 1 ) ; } S T A R T T E M P = 2 ; S T O P T E M P = 2 ; N T E M P S = 0 ; } w h i l e ( f l a g = = 1 ) ; / / C l o c k s t h e t i m e t a k e n f o r t h e t r a i n i n g t i m e ( & E n d T i m e ) ; p r i n t f ( T i m e E l a p s e d i n s e c o n d s : % l u \ n E n d T i m e B e g i n T i m e ) ; p r i n t f ( S u m o f E r r o r S q u a r e d : % f \ n e e e ) ; r m s = s q r t ( e e e / n o o f d a t a ) ; p r i n t f ( U n s c a l e d R o o t M e a n S q u a r e d E r r o r : % f \ n r m s ) ; / / W r i t i n g t h e f i n a l w e i g h t s t o f i l e o p t r = f o p e n ( w e i g h t s d a t " w ) ; f o r ( k = 0 ; k < = h i d n o d e s ; k + + ) { f p r i n t f ( o p t r % f \ t h i d o u t w [ k ] ) ; } f p r i n t f ( o p t r \ n ) ; f o r ( j = 1 ; j < = h i d n o d e s ; j + + ) f o r ( i n t o = 0 ; o < = i n p n o d e s ; o + + ) { f p r i n t f ( o p t r % f \ t i n p h i d w [ o ] [ j ] ) ; }

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1 0 9 f p r i n t f ( o p t r U n s c a l e d R o o t M e a n S q u a r e d E r r o r : % f \ n r m s ) ; / / W r i t i n g t h e r e s u l t s o f p a s s i n g b a c k t h e t r a i n i n g d a t a t o f i l e f o r ( i = 0 ; i < n o o f d a t a ; i + + ) { h i d [ 0 ] = 1 ; f o r ( k = 1 ; k < = h i d n o d e s ; k + + ) { f o r ( j = 0 ; j < = i n p n o d e s ; j + + ) { h i d [ k ] = h i d [ k ] + i n p d a t a [ i ] [ j ] i n p h i d w [ j ] [ k ] ; } i f ( h i d [ k ] < 1 0 0 ) h i d [ k ] = 1 0 0 ; h i d [ k ] = 1 0 / ( 1 0 + e x p ( h i d [ k ] ) ) ; } o p = 0 ; f o r ( k = 0 ; k < = h i d n o d e s ; k + + ) { o p = o p + h i d [ k ] h i d o u t w [ k ] ; } i f ( o p < 1 0 0 ) o p = 1 0 0 ; o p = 1 0 / ( 1 0 + e x p ( o p ) ) ; o p = o p ( m a x d e s o p m i n d e s o p ) + ( m i n d e s o p ) ; f p r i n t f ( o p t r % f \ n o p ) ; } f p r i n t f ( o p t r U n s c a l e d R o o t M e a n S q u a r e d E r r o r : % f \ n r m s ) ; / / E v a l u a t i o n o f n e t w o r k p e r f o r m a n c e f o r t h e t e s t d a t a f o r ( i = 0 ; i < t e s t d a t a ; i + + ) { h i d [ 0 ] = 1 ; f o r ( k = 1 ; k < = h i d n o d e s ; k + + ) { f o r ( j = 0 ; j < = i n p n o d e s ; j + + ) { h i d [ k ] = h i d [ k ] + t e s t [ i ] [ j ] i n p h i d w [ j ] [ k ] ; } i f ( h i d [ k ] < 1 0 0 ) h i d [ k ] = 1 0 0 ; h i d [ k ] = 1 0 / ( 1 0 + e x p ( h i d [ k ] ) ) ; } o p = 0 ;

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1 1 0 f o r ( k = 0 ; k < = h i d n o d e s ; k + + ) { o p = o p + h i d [ k ] h i d o u t w [ k ] ; } i f ( o p < 1 0 0 ) o p = 1 0 0 ; o p = 1 0 / ( 1 0 + e x p ( o p ) ) ; o p = o p ( m a x d e s o p m i n d e s o p ) + ( m i n d e s o p ) ; f p r i n t f ( o p t r % f \ n o p ) ; } f p r i n t f ( o p t r U n s c a l e d R o o t M e a n S q u a r e d E r r o r : % f \ n r m s ) ; f c l o s e ( o p t r ) ; } / / e n d o f m a i n / / F u n c t i o n E r r o r c a l t o c a l c u l a t e t h e e r r o r w i t h t h e p r e s e n t s e t o f w e i g h t s f l o a t e r r o r c a l f n 0 ( ) { i n t i i j j k k ; f l o a t f n 0 e e = 0 o p = 0 f n 0 e e e = 0 ; f o r ( k k = 1 ; k k < = h i d n o d e s ; k k + + ) h i d [ k k ] = 0 0 ; f o r ( i i = 0 ; i i < n o o f d a t a ; i i + + ) { h i d [ 0 ] = 1 ; f o r ( k k = 1 ; k k < = h i d n o d e s ; k k + + ) { f o r ( j j = 0 ; j j < = i n p n o d e s ; j j + + ) { h i d [ k k ] = h i d [ k k ] + i n p d a t a [ i i ] [ j j ] i n p h i d w [ j j ] [ k k ] ; } i f ( h i d [ k k ] < 1 0 0 ) h i d [ k k ] = 1 0 0 ; h i d [ k k ] = 1 0 / ( 1 0 + e x p ( h i d [ k k ] ) ) ; } o p = 0 ; f o r ( k k = 0 ; k k < = h i d n o d e s ; k k + + ) { o p = o p + h i d [ k k ] h i d o u t w [ k k ] ; } i f ( o p < 1 0 0 ) o p = 1 0 0 ;

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1 1 1 o p = 1 0 / ( 1 0 + e x p ( o p ) ) ; f n 0 e e = 0 ; f n 0 e e = ( d e s o p [ i i ] o p ) ( d e s o p [ i i ] o p ) ; f n 0 e e e + = f n 0 e e ; } r e t u r n f n 0 e e e ; } / / F u n c t i o n s a m e a s a b o v e w i t h t h e n e w w e i g h t s f l o a t e r r o r c a l f n 1 ( ) { i n t i i j j k k ; f l o a t f n 1 e e = 0 f n 1 e e e = 0 o p = 0 ; f o r ( k k = 1 ; k k < = h i d n o d e s ; k k + + ) h i d [ k k ] = 0 0 ; f o r ( i i = 0 ; i i < n o o f d a t a ; i i + + ) { h i d [ 0 ] = 1 ; f o r ( k k = 1 ; k k < = h i d n o d e s ; k k + + ) { f o r ( j j = 0 ; j j < = i n p n o d e s ; j j + + ) { h i d [ k k ] = h i d [ k k ] + i n p d a t a [ i i ] [ j j ] n e w i h w [ j j ] [ k k ] ; } i f ( h i d [ k k ] < 1 0 0 ) h i d [ k k ] = 1 0 0 ; h i d [ k k ] = 1 0 / ( 1 0 + e x p ( h i d [ k k ] ) ) ; } o p = 0 ; f o r ( k k = 0 ; k k < = h i d n o d e s ; k k + + ) { o p = o p + h i d [ k k ] n e w h o w [ k k ] ; } i f ( o p < 1 0 0 ) o p = 1 0 0 ; o p = 1 0 / ( 1 0 + e x p ( o p ) ) ; f n 1 e e = 0 ; f n 1 e e = ( d e s o p [ i i ] o p ) ( d e s o p [ i i ] o p ) ; f n 1 e e e + = f n 1 e e ; }

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1 1 2 r e t u r n f n 1 e e e ; } / / F u n c t i o n t o c a l c u l a t e t h e e r r o r i n t h e c o n j u g a t e g r a d i e n t m o d u l e f l o a t w e r r o r c a l f n ( ) { i n t i i j j k k o o ; f l o a t w e e = 0 w e e e = 0 ; f o r ( k k = 0 ; k k < = h i d n o d e s ; k k + + ) { h i d o u t w [ k k ] = s a v h o w [ k k ] + n n f d e r i h o w [ k k ] ; } f o r ( j j = 1 ; j j < = h i d n o d e s ; j j + + ) f o r ( i n t o o = 0 ; o o < = i n p n o d e s ; o o + + ) { i n p h i d w [ o o ] [ j j ] = s a v i h w [ o o ] [ j j ] + n n f d e r i i h w [ o o ] [ j j ] ; } f o r ( i i = 0 ; i i < n o o f d a t a ; i i + + ) { h i d [ 0 ] = 1 ; f o r ( k k = 1 ; k k < = h i d n o d e s ; k k + + ) { f o r ( j j = 0 ; j j < = i n p n o d e s ; j j + + ) { h i d [ k k ] = h i d [ k k ] + i n p d a t a [ i i ] [ j j ] i n p h i d w [ j j ] [ k k ] ; } i f ( h i d [ k k ] < 1 0 0 ) h i d [ k k ] = 1 0 0 ; h i d [ k k ] = 1 0 / ( 1 0 + e x p ( h i d [ k k ] ) ) ; } o p = 0 ; f o r ( k k = 0 ; k k < = h i d n o d e s ; k k + + ) { o p = o p + h i d [ k k ] h i d o u t w [ k k ] ; } i f ( o p < 1 0 0 ) o p = 1 0 0 ; o p = 1 0 / ( 1 0 + e x p ( o p ) ) ; w e e = 0 ;

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1 1 3 w e e = ( d e s o p [ i i ] o p ) ( d e s o p [ i i ] o p ) ; w e e e + = w e e ; } r e t u r n w e e e ; } / / R a n d o m n u m b e r g e n e r a t o r f l o a t r n d ( ) { t i m e t t ; s r a n d ( ( u n s i g n e d ) t i m e ( & t ) ) ; f l o a t r n d = 0 0 ; f l o a t R A N D M A X = p o w ( 2 1 5 ) 1 0 ; r n d = ( ( f l o a t ) r a n d ( ) + ( f l o a t ) r a n d ( ) ( f l o a t ) r a n d ( ) ( f l o a t ) r a n d ( ) ) / ( 2 0 ( f l o a t ) R A N D M A X ) 3 4 6 4 1 0 1 6 1 5 ; r e t u r n ( r n d ) ; }

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1 1 4 L I S T O F R E F E R E N C E S A i d a T H a t a S a n d K u s o n o k i H ( 1 9 8 4 ) T e m p o r a r y L o w O x y g e n C o n d i t i o n s f o r t h e F o r m a t i o n o f N i t r a t e R e d u c t a s e a n d N i t r o u s O x i d e R e d u c t a s e b y D e n i t r i f y i n g P s e u d o m o n a s s p G 5 9 C a n a d i a n J o u r n a l o f M i c r o b i o l o g y 3 2 5 4 3 5 4 7 B a l o o S a n d R a m k r i s h n a D ( 1 9 9 1 ) M e t a b o l i c R e g u l a t i o n i n B a c t e r i a l C o n t i n u o u s C u l t u r e s : I I B i o t e c h n o l o g y a n d B i o e n g i n e e r i n g 3 8 1 3 5 3 1 3 6 3 D o d d J R a n d B o n e H ( 1 9 7 5 ) N i t r a t e R e d u c t i o n b y D e n i t r i f y i n g B a c t e r i a i n S i n g l e a n d T w o S t a g e C o n t i n o u s F l o w W a t e r R e s 9 3 2 3 3 2 8 H c k M a n d K h n e M ( 1 9 9 9 ) E s t i m a t i o n o f W a s t e w a t e r P r o c e s s P a r a m e t e r s u s i n g N e u r a l N e t w o r k s W a t e r S c i e n c e a n d T e c h n o l o g y 3 3 1 0 1 1 1 5 H a m i l t o n W A a n d D a w e s E A ( 1 9 5 9 ) A D i a u x i c E f f e c t w i t h P s e u d o m o n a s a e r u g i n o s T h e B i o c h e m i c a l J o u r n a l 7 1 2 5 P 2 6 P H e n z e M G r a d y C P L G u j e r W M a r a i s G V R a n d M a t s u o T ( 1 9 8 7 ) A c t i v a t e d S l u d g e M o d e l N o 1 I A W P R C S c i e n t T e c h R e p N o 1 I A W P R C L o n d o n U K H e n z e M G u j e r W M i n o T M a t s u o T a n d W e n t z e l M C ( 1 9 9 5 ) A c t i v a t e d S l u d g e M o d e l N o 2 I A W P R C S c i e n t T e c h R e p N o 3 I A W P R C L o n d o n U K H u r d C L B e r g e s J A O s b o r n e J a n d H a r r i s o n P J ( 1 9 9 5 ) O p t i m i z a t i o n a n d C h a r a c t e r i z a t i o n o f t h e E n z y m e f o r F u c u s G a r d n e r i ( P h a e o p h t y t a ) J o u r n a l o f P h a r m a c o l o g y 3 1 8 3 5 K a m a r a A B e r n a r d O G e n o v e s i A D o c h a i n D B e n h a m m o u A S t e y e r J P ( 2 0 0 0 ) H y b r i d M o d e l l i n g o f A n a e r o b i c W a s t e w a t e r T r e a t m e n t P r o c e s s e s W a t e r S c i e n c e & T e c h n o l o g y 4 3 4 3 – 5 0 K o d a m a T S h i m a d a K a n d M o r i T ( 1 9 6 9 ) S t u d i e s o n A n a e r o b i c B i p h a s i c G r o w t h o f a D e n i t r i f y i n g B a c t e r i u m P s e u d o m o n a s s t u t z e r i P l a n t & C e l l p h y s i o l o g y 1 0 8 5 5 8 6 5 K o i k e I a n d H a t t o r i A ( 1 9 7 5 ) G r o w t h y i e l d o f a D e n i t r i f y i n g B a c t e r i u m P s e u d o m o n a s d e n i t r i f i c a n s u n d e r A e r o b i c a n d D e n i t r i f y i n g C o n d i t i o n s J o u r n a l o f G e n e r a l M i c r o b i o l o g y 8 8 1 1 0

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1 1 5 K o m a p a l a D S R a m a k r i s h n a D J a n s e n B B a n d T s a o G T ( 1 9 8 6 ) I n v e s t i g a t i o n o f B a c t e r i a l G r o w t h o n M i x e d S u b s t r a t e s : E x p e r i m e n t a l E v a l u a t i o n o f C y b e r n e t i c M o d e l s B i o t e c h n o l o g y a n d B i o e n g i n e e r i n g 2 8 1 0 4 4 1 0 5 5 K o r n a r o s M a n d L y b e r t o s G ( 1 9 9 8 ) K i n e t i c M o d e l l i n g o f P s e u d o m o n a s d e n i t r i f i c a n s G r o w t h a n d D e n i t r i f i c a t i o n U n d e r A e r o b i c A n o x i c a n d T r a n s i e n t O p e r a t i n g C o n d i t i o n s W a t e r E n v i r o n m e n t R e s e a r c h 3 2 6 1 9 1 2 1 9 2 2 K o r n a r o s M Z a f i r i C a n d L y b e r t o s G ( 1 9 9 6 ) K i n e t i c s o f d e n i t r i c a t i o n b y P s e u d o m o n a s d e n i t r i f i c a n s u n d e r G r o w t h C o n d i t i o n s L i m i t e d b y C a r b o n a n d / o r N i t r a t e o r N i t r i t e W a t e r E n v i r o n m e n t R e s e a r c h 6 8 5 9 3 4 9 4 5 K o r n e r H a n d Z u m f t W G ( 1 9 8 9 ) E x p r e s s i o n o f D e n i t r i f i c a t i o n E n z y m e s i n R e s p o n s e t o t h e D i s s o l v e d O x y g e n L e v e l a n d R e s p i r a t o r y S u b s t r a t e i n C o n t i n o u s C u l t u r e o f P s e u d o m o n a s s t u t z e r A p p l i e d a n d E n v i r o n m e n t a l M i c r o b i o l o g y 5 5 7 1 6 7 0 1 6 7 6 K r u l J M a n d V e e n i n g e n R ( 1 9 7 7 ) T h e S y n t h e s i s o f t h e D i s s i m i l a t o r y N i t r a t e R e d u c t a s e U n d e r A e r o b i c C o n d i t i o n s I n a N u m b e r o f D e n i t r i f y i n g B a c t e r i a I s o l a t e d f r o m A c t i v a t e d S l u d g e a n d D r i n k i n g W a t e r W a t e r R e s e a r c h 1 1 3 9 4 3 L e e I H F r e d r i c k s o n A G a n d T s u c h i y a H M ( 1 9 7 4 ) D i a u x i c G r o w t h o f P r o p i o n i b a c t e r i m s h e r m a n i i A p p l i e d M i c r o b i o l o g y 1 1 3 9 4 3 L i M F ( 1 9 9 4 ) N e u r a l N e t w o r k s i n C o m p u t e r I n t e l l i g e n c e M c G r a w H i l l I n c N e w Y o r k L i s b o n K M c K e a n M S h e k a r S S v o r o n o s S a n d K o o p m a n B ( 2 0 0 1 ) D i a u x i c L a g o f P s e u d o m o n a s d e n i t r i f i c a n s i n T r a n s i t i o n f r o m O x i c t o A n o x i c G r o w t h : E f f e c t o f D i s s o l v e d O x y g e n C o n c e n t r a t i o n J o u r n a l o f E n v i r o n m e n t a l E n g i n e e r i n g ( U n d e r p u b l i c a t i o n ) L i u P P o t t e r T S v o r o n o s S A a n d K o o p m a n B ( 1 9 9 5 ) H y b r i d M o d e l o f N i t r o g e n D y n a m i c s i n a P e r i o d i c W a s t e w a t e r T r e a t m e n t P r o c e s s P r e s e n t e d a t 1 9 9 5 A I C h E A n n u a l M e e t i n g M i a m i B e a c h F L L i u P Z h a n G S v o r o n o s S A a n d K o o p m a n B ( 1 9 9 6 ) C y b e r n e t i c A p p r o a c h t o M o d e l l i n g D e n i t r i f i c a t i o n i n A c t i v a t e d S l u d g e P r e s e n t e d a t 1 9 9 6 A I C h E N a t i o n a l M e e t i n g C h i c a g o L i u P Z h a n G S v o r o n o s S A a n d K o o p m a n B ( 1 9 9 8 a ) D i a u x i c L a g f r o m C h a n g i n g E l e c t r o n A c c e p t o r s i n A c t i v a t e d S l u d g e T r e a t m e n t W a t e r R e s e a r c h 3 2 1 1 3 4 5 2 3 4 6 0

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1 1 6 L i u P S v o r o n o s S A a n d K o o p m a n B ( 1 9 9 8 b ) E x p e r i m e n t a l a n d M o d e l i n g S t u d y o f D i a u x i c L a g o f P s e u d o m o n a s d e n i t r i f i c a n s S w i t c h i n g f r o m O x i c t o A n o x i c C o n d i t i o n s B i o t e c h n o l o g y a n d B i o e n g i n e e r i n g 6 0 6 6 4 9 6 5 5 M a r s h a l l R O D i s h b u r g e r H J M a c V i c a r R a n d H a l l m a r k G D ( 1 9 5 3 ) S t u d i e s o n t h e E f f e c t o f A e r a t i o n o n N i t r a t e R e d u c t i o n b y P s e u d o m o n a s S p e c i e s u s i n g N 1 5 J o u r n a l o f B a c t e r i o l o g y 6 4 2 5 4 2 5 8 M a s t e r s T ( 1 9 9 3 ) P r a c t i c a l N e u r a l N e t w o r k R e c i p i e s i n C + + A c a d e m i c P r e s s N e w Y o r k M o n o d J ( 1 9 4 2 ) R e c h e r c h e s s u r l a C r o i s s a n c e d e s C u l t u r e s B a c t e r i e n n e s A c t u a l i t e s S c i e n t i f i q u e e t I n d u s t r i e l l e s 9 1 1 1 2 1 5 M o n o d J ( 1 9 4 7 ) T h e P h e n o m e n o n o f E n z y m a t i c A d a p t a t i o n a n d I t s B e a r i n g s o n P r o b l e m s o f G e n e t i c a n d C e l l u l a r D i f f e r e n t i a t i o n G r o w t h 1 1 2 2 3 2 8 9 M o n o d J ( 1 9 4 9 ) T h e G r o w t h o f B a c t e r i a l C u l t u r e s A n n u a l R e v i e w o f M i c r o b i o l o g y 3 3 7 1 3 9 4 P a y n e W J ( 1 9 8 1 ) D e n i t r i f i c a t i o n W i l e y N e w Y o r k P a y n e W J ( 1 9 8 3 ) B a c t e r i a l D e n i t r i f i c a t i o n : A s s e t o f D e f e c t ? B i o s c i e n c e 3 3 5 3 1 9 3 2 5 R a m a k r i s h n a D ( 1 9 8 2 ) A C y b e r n e t i c P e r s p e c t i v e o f M i c r o b i a l G r o w t h i n F o u n d a t i o n s o f B i o c h e m i c a l E n g i n e e r i n g i n K i n e t i c s a n d T h e r m o d y n a m i c s i n B i o l o g i c a l S y s t e m s P a p o u t s a k i s E I S t e p h a n o p o l o u s G T a n d B l a n c h H W E d s A m e r i c a n C h e m i c a l S o c i e t y W a s h i n g t o n D C 1 6 1 1 7 8 R a m k r i s h n a D K o m p a l a D S a n d T s a o G T ( 1 9 8 4 ) C y b e r n e t i c M o d e l i n g o f M i c r o b i a l P o p u l a t i o n s i n F r o n t i e r s o f C h e m i c a l R e a c t i o n E n g D o r i a s w a m y L K E d s W i l e y E a s t e r n L i m t e d N e w D e l h i R a m k r i s h n a D K o m p a l a D S a n d T s a o G T ( 1 9 8 7 ) A r e M i r c o b e s O p t i m a l S t r a t e g i s t s ? B i o t e c h n o l o g y P r o c e s s 3 3 1 2 1 1 2 6 R a m a k r i s h n a D R a m k r i s h n a R a n d K o n o p k a A E ( 1 9 9 5 ) C y b e r n e t i c M o d e l l i n g o f G r o w t h i n M i x e d S u b s t i t u t a b l e S u b s t r a t e E n v i r o n m e n t s P r e f e r e n t i a l a n d S i m u l t a n e o u s U t i l i z a t i o n P r e s e n t e d a t 1 9 9 5 A I C h E N a t i o n a l M e e t i n g M i a m i B e a c h S a d a n a A a n d R a j u R R ( 1 9 9 0 ) S t a b i l i t y I n d e x f o r E n z y m e s D e a c t i v a t i n g b y D i f f e r e n t M e c h a n i s m s J o u r n a l o f B i o t e c h n o l 1 3 3 2 7 3 3 5

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1 1 7 S c h u l p J A a n d S t o u t h a m e r A H ( 1 9 7 0 ) T h e I n f l u e n c e o f O x y g e n G l u c o s e a n d N i t r a t e u p o n t h e F o r m a t i o n o f N i t r a t e R e d u c t a s e a n d t h e R e s p i r a t o r y S y s t e m i n B a c i l l u s l i c h e n i f o r m i s J o u r n a l o f G e n e r a l M i c r o b i o l g y 6 4 1 9 5 2 0 3 S i m p k i n T J a n d B o y l e W C ( 1 9 8 8 ) T h e L a c k o f R e p r e s s i o n B y O x y g e n o f t h e D e n i t r i f y i n g E n z y m e s i n A c t i v a t e d S l u d g e W a t e r R e s e a r c h 2 2 2 2 0 1 2 0 6 S t a n d i n g C N F r e d r i c k s o n A G a n d T s u c h i y a H M ( 1 9 7 2 ) B a t c h a n d C o n t i n o u s C u l t u r e T r a n s i e n t s f o r T w o S u b s t r a t e S y s t e m s A p p l i e d M i c r o b i o l o g y 2 3 2 3 5 4 3 5 9 S t e i n b e r g N A B l u m J S H o c h e s t e i n L a n d O r e m l a n d R S ( 1 9 9 2 ) N i t r a t e I s a P r e f e r r e d E l e c t r o n A c c e p t o r f o r G r o w t h o f F r e s h w a t e r S e l e n a t e R e s p i r i n g B a c t e r i a A p p l i e d a n d E n v i r o n m e n t M i c r o b i o l o g y 5 8 4 2 6 4 2 8 S t o u t h a m e r A H ( 1 9 8 0 ) B i o e n e r g e t i c s t u d i e s o n P a r a c o c c u s d e n i t r i f i c a n s T r e n d s i n B i o c h e m i c a l S c i e n c e s 5 1 6 4 1 6 6 S t r a i g h t J V a n d R a m a k r i s h n a D ( 1 9 9 1 ) C o m p l e x G r o w t h D y n a m i c s i n B a t c h C u t l t u r e s : E x p e r i m e n t s a n d C y b e r n e t i c M o d e l s B i o t e c h n o l B i o e n g 3 7 8 9 5 9 0 9 S t r a i g h t J V a n d R a m a k r i s h n a D ( 1 9 9 4 ) C y b e r n e t i c M o d e l l i n g a n d R e g u l a t i o n o f M e t a b o l i c P a t h w a y s G r o w t h o n C o m p l i m e n t a r y N u t r i e n t s B i o t e c h n o l P r o g 1 0 5 7 4 5 8 7 T a y J H a n d Z h a n g X ( 1 9 9 9 ) N e u r a l F u z z y M o d e l i n g o f A n a e r o b i c B i o l o g i c a l W a s t e w a t e r T r e a t m e n t S y s t e m s J o u r n a l o f E n v i r o n m e n t a l E n g i n e e r i n g 1 2 5 1 1 4 9 1 1 5 9 Z h a o H I s s a c s S H S o e b e r g H a n d K u m m e l M ( 1 9 9 4 ) A N o v e l C o n t r o l S t r a t e r g y f o r I m p r o v e d N i t r o g e n R e m o v a l i n a n A l t e r n a t i n g A c t i v a t e d S l u d g e P r o c e s s P a r t I P r o c e s s A n a l y s i s W a t e r R e s e a r c h 2 8 5 2 1 5 3 4 Z h a o H I s a a c s S H S p i e l b e r g H a n d K u m m e l M ( 1 9 9 4 ) N o v e l C o n t r o l S t r a t e g y f o r I m p r o v e d N i t r o g e n R e m o v a l i n a n A l t e r n a t i n g A c t i v a t e d S l u d g e P r o c e s s P a r t I I C o n t r o l D e v e l o p m e n t W a t e r R e s e a r c h 2 8 5 3 5 5 4 2 Z h a o H H a o O J a n d M c A v o y J T ( 1 9 9 9 ) A p p r o a c h e s t o M o d e l i n g N u t r i e n t D y n a m i c s : A S M 2 S i m p l i f i e d M o d e l a n d N e u r a l N e t s W a t e r S c i e n c e a n d T e c h n o l o g y 3 9 2 2 7 2 3 4

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1 1 8 B I O G R A P H I C A L S K E T C H S a n g e e t h a S h e k a r w a s b o r n o n J u n e 2 0 t h 1 9 7 7 i n M a d r a s I n d i a S h e r e c e i v e d h e r b a c h e l o r ’ s d e g r e e i n c h e m i c a l e n g i n e e r i n g f r o m B i r l a I n s t i t u t e o f T e c h n o l o g y a n d S c i e n c e s P i l a n i I n d i a I n 1 9 9 8 s h e w a s a c c e p t e d t o t h e U n i v e r s i t y o f F l o r i d a t o p u r s u e a M a s t e r o f S c i e n c e S h e c u r r e n t l y i s p u r s u i n g a s e c o n d m a s t e r ’ s i n c o m p u t e r a n d i n f o r m a t i o n s c i e n c e s a n d e n g i n e e r i n g


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Permanent Link: http://ufdc.ufl.edu/UFE0000351/00001

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Title: Development of a neural networks model to predict the diauxic lag length
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Copyright Date: 2008

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Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
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Material Information

Title: Development of a neural networks model to predict the diauxic lag length
Physical Description: Mixed Material
Copyright Date: 2008

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Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
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DEVELOPMENT OF A NEURAL NETWORKS MODEL TO PREDICT THE
DIAUXIC LAG LENGTH

















By

SANGEETHA SHEKAR


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2001




























Copyright 2001

by

Sangeetha Shekar



























Dedicated to my Mother and Prashant















ACKNOWLEDGMENTS


I would like to thank my committee members- Professors Spyros A. Svoronos,

Ben Koopman, and Thomas E. Bullock-for their academic advisement and guidance on

this project.

A special thanks go to my co-advisors and fellow "diauxiers"- Professors Spyros

A. Svoronos, Professor Ben Koopman, Keisha Lisbon, Micheal McKean, Anna Casasus

Zambrana, and Seung-Yeon Weon-for their help, support, and willingness to discuss their

ideas.

I would like to thank the Chemical Engineering Department for the financial

support through my course of study.

Finally I would like to thank my mother, Prashant, sister and all my friends for

their love, support, and prayers without which it would have been impossible for me to

complete this thesis.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S .................................................................................................. iv

A B STR A C T ............. ..........................................................................................vii

CHAPTERS

1 INTRODUCTION ....................... .................. 1

2 L IT E R A T U R E R E V IE W ....................................................... .................................... 3

2.1 Industry Standard Activated Sludge Model ........... ............................... 5
2.2 C ybernetic M odel .... ...... .......... .... .. .. ...... .... ....... ......... ...... .. ...... .. 7
2.3 Modeling of Diauxic Lag in Pseudomonas Dentrificans ............. .............. 10
2.4 Hybrid M odels.............................. ............ 12

3 PU R P O SE .................... ................................ ........ ......... ...... 14

4 EXPERIMENTAL METHODS AND RESULTS.......................... ............ ..... 17

4.1 N itrate R eductase Enzym e A ssay.............................................. ... ... .............. 17
4.1.1 Experim ental M ethods ........................................... .......................... 17
4.1.2 G row th Experim ents .............. ........................................................... 18
4.1.3 Experim ental Protocol ........ .................. ................. ... ............... 20
4.1.4 A nalytic M methods ......... ................................... ................................ 20
4.1.5 Experimental Results......... .......................... .................. 24
4.2 Effects of Dissolved Oxygen Levels........... ................... ................... .............25
4.2.1 Experim mental M methods ....... .... ............... ......... ..... ....... .... ........... 25
4.2.2 Growth Experiments ................... ................. ................... 32
4.2.3 Experim mental Protocol ........... ........ .. ................. .......... ............... 33
4.2.4 A nalytic M ethods ............. ................. ................. .... ....................... 33
4.2.5 Experimental Results........ ........ .................. ..... ........... ... 35
4.3 Preculture Experim ents ......................................................... .............. 35
4.3.1 E xperim ental M ethods ..................................................................... .. .... 35
4.3.2 G row th Experim ents ......................................................... ........ ...... 53
4.3.3 Experim ental Protocol ............................................. ............................... 55
4.3.4 A nalytic M ethods ............................................. ......... ............ 55
4 .3 .5 E x perim ental R esults.......................................................... ... ................. 55



v









5 N E U R A L N E T W O R K S ................................................................................................ 6 1

5.1 A lgorithm U sed ..................................................................... .......... ....... ....62
5.1.1 Back Propagation Algorithm.......... .................... ..............62
5.1.2 Training by Conjugate Gradients ......................................................... 64
5.1.3 Sim ulated A nnealing ..................................................... ......... ................ 68
5.1.4 Interleaved Simulated Annealing and Conjugate Gradient Algorithm ........68
5.2 Neural Network Model for Low DO Experiments ....................................... 69
5.2.1 Training the Network .............. ................ .. ... .............. 69
5.2.2 Testing the Network ............................ .......................... 72
5.3 Neural Network Model Preculture Experiments..............................................76
5.3.1 Training the Network .............. ........... .............. 76
5.3.2 Testing the Network ....................................... 76
5.4 D iscu ssion of R results ................................... ............ ............. ........................ 82
5.5 Hybrid Model ............. ..... ......... ............... 83

6 CONCLUSIONS AND FUTURE WORK ........................................................ 89

A PPEN D IX : PR O GR AM LISTIN G ....................................................... .................... 91

L IST O F R E F E R E N C E S ................................................................................................ 114

BIOGRAPH ICAL SKETCH ................. ................................................ .............. 118















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

DEVELOPMENT OF A NEURAL NETWORKS MODEL TO PREDICT THE
DIAUXIC LAG LENGTH
By

Sangeetha Shekar

December 2001


Chairman: Dr. Spyros A. Svoronos
Major Department: Chemical Engineering

In wastewater treatment plants nitrogen is removed by passing the wastewater

alternatively from aerobic zones to anoxic zones. Nitrification takes place in the aerobic

zone and denitrification in the anoxic zone. A diauxic lag might occur when following

the switch from oxygen to nitrate as the terminal electron acceptor. The present research

attempts to use a neural network in place of the traditional models to predict the duration

of the diauxic lag under a given set of conditions.

Experimental data gathered from studies with the culture Pseudomonas

denitrificans (ATCC 13867) was classified based on dissolved oxygen concentrations in

the aerobic phase and the reviving phase of the culture. One neural network was trained

to predict the duration of the diauxic lag for experiments with an anoxic reviving phase

and low dissolved oxygen concentrations in the aerobic phase. The inputs to this network

were initial biomass concentration, dissolved oxygen concentration in the aerobic phase

and the length of the aerobic phase in hours. A second neural network was trained to









predict the lag length for experiments where dissolved oxygen concentration was

maintained at air saturation in the aerobic phase with the reviving phase (oxic/anoxic) of

the culture, initial biomass concentration, length of the aerobic phase in hours and nitrate

concentrations in the aeration phase as the input variables. An interleaved simulated

annealing and conjugate gradient search algorithm was used to train the networks. The

predicted lag length from the networks was compared to the actual experimental data and

found to be within reasonable limits of accuracy.














CHAPTER 1
INTRODUCTION

Biological removal of nitrogen has become a common practice in many

wastewater treatment facilities ever since the harmful effects of excess levels of nitrogen

have been known. This has led to focused research on processes that remove nitrogen

from wastewater in an efficient and economical manner. In a typical suspended growth

biological nitrogen removal system, activated sludge passes through cycles of aerobic and

anoxic zones where nitrification and denitrification are achieved respectively.

Ammonium is oxidized to nitrate in nitrification and nitrate is reduced to nitrogen gas

through several steps in denitrification.

Monod (1942) first described the phenomenon of diauxic lag that can occur when

bacteria switch between electron donors (carbon substrates). Diauxie is characterized by a

double growth cycle consisting of two exponential phases separated by a phase in which

the growth rate is very low or zero. The lag corresponds to the time necessary for bacteria

to synthesize and activate the enzymes necessary to metabolize the less preferred

substrate (Monod 1942; 1949). Kodama et al. (1969) observed diauxic growth when

Pseudomonas stutzeri switched from nitrate to nitrite as terminal electron acceptor.

Diauxic lag caused by changing between carbon sources has been successfully

modeled using a cybernetic model (Komapala et al. 1986). "Industry Standard" IAWQ

Activated Sludge Models No. 1 and 2 (Henze et al., 1987; 1995) do not account for any

diauxic lag when bacteria switch between oxygen to nitrate as electron acceptor. Liu et al.

(1996) developed a cybernetic model to predict lags for an activated sludge. This model









however could not capture the observed longer lags of a pure culture. A new model

accounting for enzyme synthesis and activity in response to culture conditions and

enzyme specific levels was then developed (Liu et al. 1998). It could predict length of

lags corresponding to the growth pattern.

This manuscript reviews the literature on the models developed to predict diauxic

lags and also develops a neural network model to predict the length of the diauxic lag.

The neural network was trained with experimental data. The network can successfully

predict the lag length in hours as a function of inputs such as biomass in terms of

absorbance at time zero, length of aerobic phase in hours, reviving phase of the culture,

dissolved oxygen concentrations and nitrate concentrations in the aerobic phase.














CHAPTER 2
LITERATURE REVIEW


Monod first observed the phenomenon of diauxie. Diauxic lag is defined as the

phase that separates two exponential growth phases in which the growth rate is very low

or zero (Monod, 1942). In diauxic growth the second substrate is not utilized until after

the first substrate is exhausted and the enzymes required by the bacteria to utilize the

second are not synthesized until then (Monod, 1942). Hamilton and Dawes (1945) also

observed the diauxic growth phenomenon in Pseudomonas aeruginosa in a medium of

glucose and organic acid. They observed that organic acid is preferentially used over

glucose. Standing et al. (1972) observed that E. coli exhibits a diauxic behavior in a

mixture of glucose and xylose. They also observed that when E. coli was in an initial

medium of glucose and galactose, glucose and galactose were utilized sequentially and

there was no lag period between the two exponential growth phases. Therefore, it can no

longer be assumed that diauxie is always characterized by a lag period. Sequential

utilization of substrates was also observed in Propionibacterium shermanii in a mixture

of lactate and glucose where lactate was completely consumed before growth on glucose

took place (Lee et al., 1974). This pattern of sequential utilization without a lag period is

also observed in Klesbiella pneumoniae when the nutrient source is switched to xylose

from glucose (Baloo and Ramakrishana, 1991). In each case the preferred substrate is the

one on which the bacteria grow the fastest. Therefore diauxic growth phenomena may or

may not be characterized by a lag period but is directly related to the bacterial preference

for consuming the fastest growth supporting substrate (Ramakrishna et al., 1987).

3









Ramakrishna et al. (1987) and Baloo and Ramakrishna (1991) record the general growth

characteristics of bacteria on multiple substrates.

Kodama et al. (1969) were the first to perform experiments of diauxic behavior

between different electron acceptors. Their studies showed a biphasic growth pattern of

Pseudomonas stutzeri between nitrate and nitrite as electron acceptors. The preferred

electron acceptor nitrate was fully consumed before any nitrite was consumed. The

exponential growth phases were separated by a lag period in which the growth rate was

very low. Sequential utilization was also observed by Steinberg et al. (1992) in fresh-

water selenate respiring bacteria. In the presence of both nitrate and selenate, nitrate was

completely exhausted before selenate consumption began. There was no lag period

between growth on nitrate and selenate.

Recently, the phenomena of diauxie when bacteria switch from oxygen to nitrate

as electron acceptors was demonstrated for both activated sludge as well as pure culture

(Liu et al. 1998a). For the pure culture Pseudonmonas dentrificans it was observed that

lags up to 7 hours could take place before the second exponential growth phase on nitrate

began.

Diauxic lag caused by change in carbon sources has been successfully modeled

using a cybernetic model (Kompala et al. 1986). Activated Sludge Models No. 1 and 2

(Henze et al. 1987; 1995) do not account for any diauxic lag when bacteria switch

between oxygen to nitrate as electron acceptor. A cybernetic approach was developed

(Liu et al. 1996) which incorporated a simplified version Activated Sludge Model No. 1

(Henze et al. 1987). This cybernetic approach was able to predict lags observed with

activated sludge.









2.1 Industry Standard Activated Sludge Model

In the "Industry Standard" models for activated sludge (ASM -1, Henze et al.,

1987; ASM-2, Henze et al., 1995), the effect of dissolved oxygen on the rate of growth of

heterotrophic biomass under anoxic conditions is represented by the term

KOH (2-1)
So +KO,H

where as the rate of heterotrophic growth under aerobic conditions is controlled by the

term

So (2-2)
So +KO,H

where So is the dissolved oxygen concentration and KO,H the oxygen half-saturation

concentration. The former term approaches zero when the dissolved oxygen

concentration is high, and approaches 1.0 when dissolved oxygen concentration is low.

The latter term has complementary behavior, approaching 1.0 when DO is high and

tending towards zero when DO is low. Together, the two terms sum always to 1.0, thus

ensuring that the total rate of growth using both electron acceptors does not exceed that

which is possible in a highly aerobic environment. This feature, however, prevents either

model from accurately portraying the dramatic decrease or even cessation of growth

during the diauxie.

An example of a conventional model of heterotrophic growth under aerobic and

anoxic conditions when the carbon source is non-limiting is shown in Table 2.1. The

model, which is a simplified model of ASM-1, contains process rate expressions for

aerobic growth of heterotrophic biomass. The components include active heterotrophic

biomass (XB,H), dissolved oxygen (So), and the sum of nitrate plus nitrogen expressed as

equivalent nitrate (SNo) by the following equation










(N2.857 -1.143)
Sno = [NO N] + [NO, N]I
2.857


Table 2.1 Conventional model for heterotrophic
conditions
Component- i 1 2 3

j Process So SNo XB,H

1 Aerobic 1- YH 1
Yr H,O


UJlOWLII 01

heterotrophs

2 Anoxic

Growth of

heterotrophs

3 Decay of

heterotrophs

Observed

conversion rate,

ML3T-1


1 -YH,NO
2.86YH,NO


growth under aerobic and anoxic


Neither of the process rate expressions for growth contains a substrate

concentration term, nor is the substrate shown as a component. This is because the carbon

source (glucose) is not limiting growth.

For the reason explained above this type of model cannot capture the diauxic lag

even though it is able to match the growth rates in aerobic and anoxic conditions. Clearly

a new modeling approach is required to successfully portray the diauxic lag.


Process rate, pj, ML-3T


^H,o B,H
SKO,H + So




H K' SNO
OHNO NO
bHX, H +So Kno +SNO B,H




bHXB,H


(2-3)


r, = r P









2.2 Cybernetic Model

Cybernetic modeling (Ramakrishna, 1982; Ramakrishna et al., 1984; Komapala et

al., 1986; Straight and Ramakrishna, 1991; Straight and Ramakrishna, 1994;

Ramakrishna et al., 1995) has been successful in portraying the diauxic lag observed

when the bacteria switch between electron donors. It is based on the premise that bacteria

are optimal strategists (Ramakrishna et al., 1987) and that they regulate enzyme synthesis

and activity so to maximize their specific growth rate. In the cybernetic model (Liu et al.

1998a), the kinetic expressions of Table 2.1 are modified in a manner analogous to the

modifications of Monod kinetic expressions by Kompala et al. (1986).

The diauxic lag is attributed to the fact that appropriate enzymes for alternate

electron acceptors must be synthesized. Therefore the Liu et al. (1998a) model adds as

components the concentrations of two enzymes, Eo and ENO, to regulate the biomass

synthesis in the presence of oxygen and nitrate, respectively. Both the concentrations and

activities of these enzymes affect the growth rate of heterotrophic biomass. If ek denotes

the specific level of an enzyme [ i.e.. ek = EK/XB,H for k=O (oxygen) or NO (equivalent

nitrate)] and Vk denotes the relative activity (ranging from 0 to 1) of the respective

enzymes, then the effects of enzyme level and activity on biomass growth rate can be

expressed by a Monod growth rate expression by the factor Vkek/ek,max, where ek,max is the

enzyme maximum specific level. This gives the following equation for aerobic and

anoxic growth

ekv, k Sk )
Pk = /U H,k X B,H
ek,max Kk + SK ) (2-4)


where Ko=KO,H.









It is postulated that the synthesis rate of each enzyme can be described by the

expression


akk Sk B,H (2-5)
K k +Sk

in which the maximum specific synthesis rate depends on a "cybernetic variable" uk

(ranging from 0 to 1) that controls whether the enzyme is synthesized or not and at what

rate, and Gk is a synthesis rate coefficient.

Enzyme decay is assumed to be first order with respect to enzyme concentrations,

in a manner analogous to biomass decay; i.e. the decay rate is

fkEk (2-6)

In the above formulation the variables uk and Vk represent the control actions of

the cellular regulatory processes of repression-induction and inhibition-activation. In the

cybernetic modeling approach it is postulated that the bacteria adjust the values of these

variables, as well as of ek,max, so as to maximize their instantaneous growth rate. As

shown by Komapala et al. (1986), the solution of the optimization problem is


k PkVk (2-7)
(P,/~vk)
k=l


vk = Pk/k (2-8)
maxk(pk vk)


ek = ak (2-9)
A+ lHk









The complete kinetic model is summarized in Table 2.2. It should be noted that

the term KO,H/(KO,H + So) which is used in ASM-1 and ASM-2 to switch off growth on

nitrate when oxygen is present, is not included, as VNO assumes this function.

To better define the factors that influences the onset and length of diauxic lags as

the activated sludge switches from oxygen to nitrate as electron acceptor further

refinement of the model was required.



Table 2.2 Process kinetics and stoichiometry of the cybernetic model of Liu et al. (1998a)
Component- i 1 2 3 4 5
j Process So SNO XB, E EN Process rate, pj, ML-3T
H O O
1 Aerobic 1-YH, 1 eoVo So s
growth of H- O H e.. KO, + SO BH
heterotrophs HO0

2 Anoxic growth 1-YH,NO 1 eNO NO SNO Bw
of heterotrophs 2.86YHNO HNO eNO K + SN

3 Decay of -1 bHXB,H
heterotrophs
4 Synthesis rate 1 So B
of enzyme o KOH SOBH
associated with
aerobic growth
5 Synthesis rate 1 ( SNO B
of enzymeNO SNO + S BHNO
associated with
anoxic growth
6 Enzyme decay -1 3oEo
rate
7 Enzyme decay -1 PNOENO
rate
Observed r, = 7"y
conversion rate,
ML-3T-









Model Relationships
P, /v, p- V, E e,
v= u= e= e =
max, (p /v,) XBH ,max, + ma ,

where i = O or NO,
Po=P1,
PNO=P2


2.3 Modeling of Diauxic Lag in Pseudomonas Dentrificans

The model proposed by Liu et al. (1998a) is based on the hypothesis that the

diauxic lag occurs due to the lack of enzymes needed for electron acceptor utilization

(nitrate reductase in this case). The lag is the period when the enzyme builds up and when

it reaches a certain level becomes activated and exponential growth resumes.

Liu et al. revised their cybernetic model (1998b). One modification is that the co-

efficients of the enzyme synthesis rates are not constant but an increasing function of

enzyme specific level. At low enzyme specific levels, low amount of energy will be

available for bio -synthesis. Increasing enzyme level would increase the energy available

and thereby the potential enzyme synthesis rate. Furthermore, at higher the enzyme

specific levels, more metabolic machinery will be available for utilizing this energy,

therefore increasing the efficiency of enzyme synthesis.

The expression for enzyme activity, VNO also differs from the one used in the

cybernetic models. It provides for a sharper transition from inactive to active enzyme by

utilizing a logistic function eNo/eNo,max

1
S 4rNO- eo (2-10)

l+e ( eNo,.

For larger values of the parameter s, vNo is close to zero (inactive enzyme) for

ratio eNo/eNo,max = 0 and close to one (full activation) for eNo/eNo,max = 1. The parameter










rc,NO (critical ratio) sets the value of the ratio for which enzyme activity reaches 50%. The

parameter s (sharpness parameter) is the slope of the curve at eNo/eNo,max = rc,NO.


Table 2.3 Process kinetics and stoichiometry of the model pro
Component- i 1 2 3 4 5
j Process 4 So SNO XB, E EN
H 0 0
1 Aerobic 1- Y 1


growth


2 Anoxic growth



3 Decay
4 Synthesis rate
of enzyme
associated with
aerobic growth
5 Synthesis rate
of enzyme
associated with
anoxic growth
6 Enzyme decay
rate
7 Enzyme decay
rate
Observed
conversion rate,
ML-3T-


HO


1- YH,NO
2.86YH.NO


=;CYrp,


posed by Liu et al. (1998b)


Process rate, pj, ML-3 T-


eoVo So
eo,mx KO,H +So


,, eNO VNO SNO
eNOmax -NO + NNO


bHXB


I0,1 + ao02 eo So "Bo




+ O, NO e+,2-- BNO
eNO, ..m JKo +So0)

PoEo

PNoENo


Model Relationships
1 P,/V, E, a,i, + a,,2
v = u e e =

i+e X Y (p V XB max max b
1=1
where i = O or NO,
Po=P1,
po=p2'
PNO=P2









The revised kinetic model is presented in Table 2.3. Different yield coefficients

are used for aerobic and anoxic growth.

The above mechanistic model could fit quite well the experimental data of Liu et

al. (1998a, 1998b), in which all aerobic growths were with high dissolved oxygen

concentrations (near saturation). However, it was considerably less successful in fitting

more recent experimental data obtained in our lab, in which diauxic growth with low

dissolved oxygen concentrations were investigated.



2.4 Hybrid Models

Neural network models were introduced into the activated sludge modeling by

Liu et al. (1995). Liu et al. (1995) combined a material balance model with artificial

neural networks for the reaction rates. The inputs were the standard inputs of ASM-1.

This model performed very well with simulated data but poorly with experimental data.

Clearly some important inputs to the neural network were missing. Zhao et al. (1999)

used a simplified version of the Activated Sludge Model No. 2 (SPM) and neural

networks to model accurately the process dynamics of nitrogen and phosphorous

(nutrients) in a sequencing batch reactor (SBR). The SPM provided a preliminary

prediction of the process behavior based on a smaller set of inputs such as measurements

of influent ammonia and phosphate, COD, and timer control signals. The neural network

was fed with the above inputs and additional parameters that could influence the process.

The network was trained to predict the difference between the actual process output data

and SPM predictions. In order words the network learned to bias the SPM. It was found

that the above hybrid model was more suitable for on-line prediction and control than the

SPM model. The hybrid model for anaerobic wastewater treatment systems developed by









Kamara et al. (2000) combines a feed forward network, describing bacterial kinetics and

a priori knowledge based on the mass balances of the process components. The model's

architecture consists of a static model of unmeasured process parameters (kinetic growth

rate) integrated with a dynamic representation of the process, using a set of dynamic

differential equations. The performance of this approach was evaluated using

experimental data. Tay and Zhang (1999) developed a conceptual adaptive model for

anaerobic wastewater systems using advanced neural fuzzy systems in place of the

conventional kinetic models. The conceptual neural fuzzy model had the robustness of

fuzzy systems, the learning ability of neural networks and could adapt to various

situations. The conceptual model was used to simulate the daily performance of two high-

rate anaerobic wastewater treatment systems. Hack and Kohne (1999) tried to devise a

new method to estimate wastewater process parameters (e.g. COD) based on on-line

measurements of auxiliary parameters. They used neural networks to enable detection of

non-linear static/dynamic correlation between the auxiliary and process parameters based

on measured values of the auxiliary parameters. The network was trained using

experimental data.

Among the entire set of hybrid or neural network models that have been

developed so far, none of the models can predict the diauxic growth pattern.














CHAPTER 3
PURPOSE


The purpose of this study is to develop a neural network model that predicts the

length of the diauxic lag when bacterial cultures switch electron acceptors (oxygen to

nitrate) in a synthetic wastewater medium. In a previous study performed by Liu et al.

(1996) it was shown that diauxic lags occur between aerobic growth and anoxic growth in

a nitrification- denitrification system. The diauxic lag is generally attributed to time

required to synthesize and activate inducible enzymes for utilizing alternate electron

acceptors. The model proposed by Liu et al (1998a, 1998b) suggests that there is a

decrease in enzyme specific levels under aerobic conditions. In experiments in which

Pseudomonas denitrificans was revived from agar plates and then grown in batch reactors

first under aerobic conditions and then under anoxic conditions it was observed that the

length of the lag depends on the concentrations of nitrate it was exposed to both in the

reviving phase and the aerobic phase. The length of the lag is also observed to increase

with increase in length of time of the aerobic phase. Also experimental studies showed

that bacterial cultures under lower dissolved oxygen concentrations during the aerobic

phase have a shorter diauxic lag in comparison to cultures at air saturation during the

aerobic phase. The explanation is that lower dissolved oxygen should have a less

inhibitory effect on the denitrifying enzymes hence shortening the length of the diauxic

lag.









The present research makes an attempt to use a neural network in place of the

traditional model to predict the duration of the diauxic lag under a given set of conditions.

The aerobic and anoxic phase growth curves can be captured by the traditional Monod

(1942) expressions. If these were integrated with a neural network for predicting the lag

the resulting hybrid model should be able to describe the complete diauxic growth.

The experimental data was categorized based on the reviving phase

(aerobic/anoxic) and dissolved oxygen concentrations. The neural network was first

trained with experimental data for which the reviving phase was always anoxic and

concentrations of nitrate were very low (almost zero) in the aerobic phase. In this case the

inputs to the neural network were biomass concentration in terms of absorbance at the

start of the experiment, dissolved oxygen concentrations through the aerobic phase and

the duration of the aerobic phase in hours. The neural network had only one output node,

that being the time in hours of the diauxic lag. There was a single hidden layer of neurons

and the number of nodes in the hidden layer was varied and the performance was

compared. The network architecture that gave the lowest root mean squared error was

chosen and the corresponding weights saved. The neural network was then tested with

experimental data different from the training data and the results compared with the

desired output. A second neural network was trained with additional inputs such as the

status of the reviving phase of the culture and the varying concentrations of nitrate in the

aerobic phase. In this case the dissolved oxygen concentration was maintained at 8.7

mg/L. The network was then tested and the predicted diauxic lag length from the neural

network compared to the actual experimental results.









Efforts were also made to devise a standard nitrate reductase enzyme assay for

Pseudomonas denitrificans. Cultures of Pseudomonas denitrificans (ATCC 13867) were

pre-cultured in both aerobic and anoxic environments. This would provide cases of both

absence and presence of denitrifying enzymes when the cultures were introduced into the

bioreactor. The reactor was always held at air saturation (8.7 mg/L) in the aerobic phase,

which typically lasted 2-3 hours. Samples for the enzyme assay were withdrawn from

the bioreactor at different points in the entire experiment and stored on ice. The samples

were then assayed and the enzyme activities recorded.














CHAPTER 4
EXPERIMENTAL METHODS AND RESULTS

Three kinds of experiments performed through the course of this study: High

biomass experiments to measure the activities of enzyme, growth experiments to study

the effect of dissolved oxygen, on the diauxic lag and growth experiments to study the

effect of reviving phase on the length of the diauxic lag.



4.1 Nitrate Reductase Enzyme Assay

4.1.1 Experimental Methods

The denitrifying bacterium used in this study was Pseudomonas denitrificans -

ATCC 13867. The freeze-dried bacteria were revived in flasks of 125ml of Nutrient

Broth (#0003-17-8) supplied from Sigma Chemical Company. The denitrifying bacteria

were placed in a shaker and allowed to grow in the medium for two days. Subsequently,

the microbial mixture was transferred, using 10pl sterile inoculating loops, onto tryptic

soy agar plates using the streak technique. Pseudomonas denitrificans were grown on the

agar plates at 350C in a Fisher Model Isotemp 303 incubator for two days and stored at

40C. Agar plates were kept for two weeks for use in experiments before fresh plates were

made. De-ionized water was used for preparing agar and liquid media.

Cultures were grown in synthetic liquid medium modified from (Table 4.1)

Kornaros et al. (1996) with or with out without nitrate depending on what kind of

preculture conditions were required for that experiment. The pH of the medium was

adjusted to 7.0 using 2N NaOH before autoclaving and the addition of nitrate-nitrogen (if









required). Culture medium in 250ml flasks (125 ml liquid volume) was inoculated from

agar plates. For oxic preculture conditions the flasks were agitated in a shaker bath for

two days at approximately 250 C. For anoxic preculture conditions, the cultures were

grown in a nitrate limited synthetic liquid medium (4mg/L NO3- N) modified from Table

4.1 and allowed to sit under a sterile laminar hood for two days.




Table 4.1. Composition of the synthetic medium
Chemicals De-ionized water, g/L
Inorganic Salts NaCl 1
NH4C1 1
MgSO4.7H20 0.2
CaCl2.7H20 0.0264
Trace Metals A drop
Phosphates K2HPO4 5
KH2PO4 1.5
Carbon Source L-Glutamic Acid 5
Nitrogen Source KNO3 28.9
aTrace metal solution containing .5% (w/v) each of CuSO4, FeCl3, MnC12, and Na2MoO4.2H20.



4.1.2 Growth Experiments

A MultiGen bench-top bio-reactor, model F-2000 (New Brunswick Scientific)

was used for the experiments. The culture was continuously stirred at 3020C. The pH

ranged from 7.0 in the aerobic phase and increased to 7.2 during the anoxic phase.

Dissolved oxygen was monitored using Model DO-40 (New Brunswick Scientific)

analyzers with galvanic electrodes. The experimental setup was as shown in Figure 4.1.

Each experiment consisted of an aeration period of 3-5 hours during which the reactor

was maintained at air saturation (8.7 mg/L). Aeration was then stopped and reactor was

sparged with nitrogen gas to remove any residual dissolved oxygen. Thus followed by a

















-D


A- Thermocouple B-Thermometer
C-DO probe D-Feed
E-Heater


Gas Filter



Rotamete







Air Nitrogen


Figure 4.1: Experimental setup for nitrate reductase experiment


m


'A _B


c9t











period when nitrate was the terminal electron acceptor. Nitrogen gas flooded through the

head space of the culture bottle during the period when there was no aeration. The

variables monitored include biomass in terms of absorbance, dissolved oxygen,

temperature and pH.


4.1.3 Experimental Protocol

Experiments were carried out in order to investigate specific enzyme levels

through the course of a diauxic growth. Each experiment consisted of a single reactor

with initial biomass concentrations of about 0.3 in terms of absorbance. The first set of

experiments was carried out with oxic preculture conditions. Potassium nitrate (400

mg/L) was added to the reactor in the anoxic phase of the experiment. The second set of

experiments was carried out under anoxic preculture conditions. Potassium nitrate (400

mg/L) was added to the reactor in the oxic phase of the experiment.


4.1.4 Analytic Methods

Samples were withdrawn from the reactor using a syringe connected to a plastic

tube that extended through the cap to the bottom of the reactor. The sample line was

flushed several times, then 210 mL was withdrawn. A portion (10 mL) of each sample

was used to measure absorbance. Absorbance of the culture was measured using a

spectrophotometer (Milton Roy Spectronic 21D) at 550 nm using a 1.25 cm path length.

The rest of the withdrawn sample (200 mL) was immediately placed on ice and stored at

0 C. The samples were then analyzed the next day for nitrate reductase enzyme activity.

The samples were first degassed for two minutes to create and oxygen free atmosphere,

washed with 1M phosphate buffer KPO4 (pH=7.0) and ice centrifuged at 8000 rpm for 5









minutes at 2 degrees centigrade. The supernatant was drained and 7mL of 1M phosphate

buffer KPO4 (pH=7.0) was added. The bio mass pellet was re-suspended by vortexing

and degassed with nitrogen gas for two minutes. The samples were cold centrifuged at

10000 rpm for 5 minutes at 2 degrees centigrade. The supernatant was drained and ImL

of 1M Phosphate buffer KPO4 (pH=7.0) was added and the biomass pellet re-suspended

by vortexing. The sample was then transferred to 1.5 mL tubes and placed in a beaker of

ice. Oxygen free conditions were maintained by sparging the container in which the

beaker was placed with nitrogen. Each sample was then sonicated for two 15 second

periods with an interval of 15 seconds and placed back on the ice bath. A portion of the

sample was then pipetted out in a test-tube to which 0.lmL of 50mM NaNO3, 0.03mL of

1M Phosphate buffer KPO4 (pH = 7.0) buffer, and 0.07 mL of ImM benzylviologen was

added. Next, 0.05ml sodium-diathionide Na2S2042- was added and was allowed to react

for 30 seconds. The reaction was stopped by vortexing the sample. The nitrite was

estimated by adding 0.5 mL 1 % sulfanilamide in 2.5 N HC1 and 0.5mL N-1-

Napthylene -diamine dihydrochloride (0.02 % in water) and the sample vortexted. 5mL

of deionized water was added the test-tube and vortexed again. The samples were then

centrifuged at 3300rpm for 15 minutes. The nitrate reductase activity was measured in

terms of absorbance using a spectrophotometer (Milton Roy Spectronic 21D) at 540 nm

using a 1.25 cm path length.


































. Small centrifuge tube


0.3 mL total solution
containing:
0.1 mL cell sample
S 0.2 mL solution of:
S* 0.lmL of 50mM NaNO3
0.03ml of 1M Phosphate
buffer KPO4 (pH = 7.0)
buffer
0.07 ml of ImM
benzylviologen


Vortex to oxidize S2042-
and stop the reaction


0.05 mL S2042- to
start the reaction
(20 mM S2042 in 20
mM Na2CO3)


V
Purple color observed
Let reaction proceed for
30 secs


Determine NO2


Figure 4.2. Nitrate reductase enzyme procedure


Cell Preparation:
* Take the sample from ice bath and de-gas it for 2 minutes with
nitrogen
* Ice centrifuge sample at 8000 rpm for 5 minutes at 20C
* Drain supernatant and add 7mL of 1M phosphate buffer KPO4
(pH=7.0) and de-gas for 2 minutes with nitrogen
* Vortex sample and ice centrifuge at 10000 rpm for 5 minutes at
20C
* Drain supernatant and add ImL of 1M phosphate buffer KPO4
(pH=7.0) and de-gas for 2 minutes with nitrogen
* Vortex sample and transfer sample to 1.5 mL test tubes and
place in a beaker of ice
* Sonicate samples for 15 seconds. Maintain an oxygen free
environment by sparging container with nitrogen
* Pipette out 0.1 mL of the sonicated sample into a test tube

















0.35 mL sample
containing nitrite


0.5 mL N-1-Napthhylene-
diamine dihydrocholride
(0.02% in water)


0.5 mL 1% sulfanilamide
in 2.5 N HCl


Figure 4.3. Nitrate reductase enzyme procedure (nitrite determination)


* Vortex the sample
* Dilute with 5 mL of DI water
* Vortex sample again
* Centrifuge at 3300 rpm for 15 minutes
* Transfer supernatant to small test tube
* Measure absorbance of supernatant at 540 nm









4.1.5 Experimental Results

The model proposed by Liu et al. (1998 a, b) attributed the diauxic lag to the low

concentrations of nitrate reductase enzyme and in turn activity of the enzyme in the

aerobic phase. The shorter lags that occurred when culture had been revived under anoxic

conditions and exposed to nitrate in the aerobic phase were attributed to the synthesis of

nitrate reductase during the aerobic phase although the enzyme was still inactive. The

experimental results (Figure 4.4) of measured enzyme activity versus time when the

culture was revived under anoxic conditions and exposed to nitrate in the aerobic phase

of the experiment do not agree with the proposed hypothesis. The nitrate reductase

enzyme levels were found to increase at a rate faster than biomass and drop after the

oxygen supply was turned off. On the other hand, the levels of enzyme activity through

an experiment where the culture was revived under oxic preculture conditions and

exposed to nitrate only when the oxygen was turned off (Figures 4.5) were found to agree

closely with the hypothesis proposed.

The nitrate reductase enzyme assay for Pseudomonas denitrificans is far from

being standardized. Literature gives us a wealth of information on nitrate reductase

assays developed for different strains of bacteria. Krul et al. (1977) devised enzyme

assays for nitrate reductase enzyme isolated from several denitrifying bacteria. In their

nitrate reductase enzyme assay chloramphenicol was added to stop protein synthesis in

the cells just after washing with phosphate buffer and the cells were lysed by first using a

French Press at 20,000 psi and then treated with an ultrasonic (MSE) for 2 minutes. They

observed that the synthesis of dissimilatory nitrate reductase was only partially repressed

by oxygen in some strains of bacteria. However if the oxygen concentration was

increased beyond air saturation then significant repression of enzyme synthesis occurred.









Simpkin and Boyle (1988) emphasized the importance of sparging the cell free extracts

with nitrogen to create an oxygen free environment and maintained all their samples in a

constant temperature water bath. They also preserved the whole cell samples that were

withdrawn from the reactor in liquid nitrogen inorder to stop cell activity. They based

their conclusions that nitrate reductase synthesis was not repressed fully by oxygen by

evaluating the ratio of 'expressed denitrifying enzyme activities' (samples that were

sonified and assayed immediately) and 'potential denitrifying enzyme activities' (samples

that were in an anoxic environment for a period of three hours, then sonified and

assayed). It remains to be investigated if incorporation of these steps to our enzyme assay

would give more meaningful results.



4.2 Effects of Dissolved Oxygen Levels

4.2.1 Experimental Methods

Cultures were grown in nitrate limited synthetic liquid medium (4mg/L NO3- N)

modified from (Table 4-1) Kornaros et al. (1996). The pH of the medium was adjusted to

7.0 using 2N NaOH before autoclaving and the addition of nitrate-nitrogen. Culture

medium in 250mL flasks (125 mL liquid volume) was inoculated from agar plates

(prepared as discussed in section 4.1.1) and allowed to sit under a sterile laminar hood for

two days. A procedure termed 'splitting' was then performed on the culture medium.

Approximately 250 mL of the culture medium was added to a liter of liquid medium and

allowed to mix to prevent flocculation. The culture was then split into two 500 mL

volumes, transferred to each bioreactor simultaneously and diluted with liquid medium to

an absorbance (k=550 nm, 1.25 path length) of 0.02- 0.09 for use in experiments.























Bomass and Nitrate Reductase Activity versus time


Anoxic Phase


-0 BIOMASS
--0-- NaR


0 50 100 150 200
time (min)


250 300 350 400


Figure 4.4. Experiment E-1. Experiment with anoxic reviving phase to measure nitrate

reductase enzyme activity. Data points show experimental results: biomass and nitrate

reductase activity as shown by absorbance


Oic Phase


c
007
io

006 '

a)
005


004 tU


003 5


002 a

z






















Biomass and Nitrate Reductase Activity vs. time


1 Oxic Phase


Anoxic Phase


p p


6.6

- BIOMASS
..O -.R [R


'-"-


0.3



02



0.15


0.1 2


....o.-..........................


0 50 100 150 200 250 300 350 400 450 500 550 600
time (nin)


Figure 4.5. Experiment E-2. Experiment with oxic reviving phase to measure nitrate
reductase enzyme activity. Data points show experimental results: biomass and nitrate
reductase activity as shown by absorbance

















E-3

0.9 80


0.8
70

0.7
60

0.6
P- 50

0.5 --BIOMASS 9.6
--NR ave
S40 o
S--DO
30
30
0.3

20
0.2


0.1 10


0 0- -
0 100 200 300 400 500 600 700 800

Time (min)


Figure 4.6. Experiment E-3. Experiment with oxic reviving phase to measure nitrate
reductase enzyme activity. Data points show experimental results: biomass and nitrate
reductase activity as shown by absorbance


















E-4

100

0.7
90


0.6 80


70
0.5

60

S0.4 E
-E 5.8 so50

S|----BIOMASS o
0.3 -NR Average 40
-- DO

30
02
.0
............. 20

0.1
..* 10


0 I ----*-0--- ---- ----r--II-*----I-I--* ****
0 100 200 300 400 500 600 700 800
Time (min)


Figure 4.7. Experiment E-4. Experiment with oxic reviving phase to measure nitrate
reductase enzyme activity. Data points show experimental results: biomass and nitrate
reductase activity as shown by absorbance

















E-5

0.9 100

90
08
80

0.7
9.3
70
0.6
60
B-- BIOMASS
S0.5 NR(30min)
S--DO 50

0.4
S/ 40

03 30


0.2 20


0.1 10
n -a06- .9r -- 0.066

0 0
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
time (min)






Figure 4.8. Experiment E-5. Experiment with oxic reviving phase to measure nitrate
reductase enzyme activity. Data points show experimental results: biomass and nitrate
reductase activity as shown by absorbance

















E-6

100

1 -+-BIO "MASS
NR (30 min) 90
---DO
80
08
70

60
r 0.6




0,2 20
o"==-* == 50 o


40
0 10

30


0.2 20

,---



0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500

time (min)



Figure 4.9. Experiment E-6. Experiment with oxic reviving phase to measure nitrate
reductase enzyme activity. Data points show experimental results: biomass and nitrate
reductase activity as shown by absorbance









4.2.2 Growth Experiments

Two mutiGen bench-top bio-reactors in parallel (models F-1000 and F-2000, New

Brunswick Scientific) were used for the experiments. The culture was continuously

stirred at 3020C. The pH ranged from 7.0 in the aerobic phase and increased to 7.2

during the anoxic phase. Dissolved oxygen was monitored using Model DO-40 (New

Brunswick Scientific) analyzers with galvanic electrodes. The effect of various levels of

dissolved oxygen concentration on diauxic lag were compared and contrasted to a high

dissolved oxygen concentration of 8.7 mg/L (air saturation). The experimental setup was

as shown in Figure 4.10. Each experiment consisted of an aeration period of 3-5 hours

during which one reactor was maintained at 100 % air saturation and the other at the

respective low DO concentration. To maintain 100% air saturation, a stage dilution was

used in which primarily air was fed through a Y-connector, gas filter, and into the bio-

reactor. Oxygen was fed into the bioreactor as needed to maintain 100% air saturation.

Low dissolved oxygen concentrations (<0.09 mg/L) were maintained by feeding pure

nitrogen through a rotameter which mixed with air-nitrogen mixture in which pure air

was fed thorough a second rotameter. Low dissolved oxygen concentrations ranging from

0.18 to 0.70 mg/L were achieved by manually controlling the airflow valve on the air

tank based on the reading of the DO meter. The dissolved oxygen analyzer, however,

could not measure accurately concentrations below 0.15 mg/L. An alternative method

was developed to maintain dissolved oxygen control. It was observed that in such low

dissolved oxygen experiments the airflow rate correlated closely to the biomass

absorbance (K. Lisbon, 2000). The air flow rate was given by the linear equation:

Air Flow Rate = Initial setting + 105.97(Absorbance Beginning Absorbance).









To begin the anoxic phase, aeration was stopped and reactor was sparged with nitrogen

gas to remove any residual dissolved oxygen. 400 mg/L of nitrate-nitrogen was then

added to each reactor simultaneously, thus starting a period when nitrate was the terminal

electron acceptor. Nitrogen gas flooded through the head-space of the reactors during the

period when there was no aeration. The variables monitored included biomass in terms of

absorbance, dissolved oxygen, temperature and pH.


4.2.3 Experimental Protocol

Experiments were carried out in order to investigate the effect of various

dissolved oxygen concentrations on the duration of diauxic lags. Each experiment

consisted of two parallel trials with the same initial culture conditions. To ensure that the

parallel cultures had the same initial biomass concentrations, the original cultures was

well mixed and divided between the two bioreactors. The first set of set of experiments

were carried out a 0.35 mg/L concentration of dissolved oxygen in one bioreactor with

dissolved oxygen being maintained over 8.7 mg/L in the other. Potassium nitrate (400

mg/L) was added in the anoxic phase to both reactors. These experiments were repeated

at lower dissolved oxygen concentrations ranging from 0.01 to 0.07mg/L.


4.2.4 Analytic Methods

Samples were withdrawn from the reactor using a syringe connected to a plastic

tube that extended through the cap to the bottom of the reactor. The sample line was

flushed several times, then 30 mL was withdrawn. A portion (10 mL) of each sample was

used to measure absorbance. Absorbance of the culture was measured using a

spectrophotometer (Milton Roy Spectronic 21D) at 550 nm using a 1.25 cm path length.



























































A- Thermocouple B-Thermometer
Air C-DO probe D-Feed
Oxygen E-Heater

Figure 4.10. Experimental setup for the low DO experiments









4.2.5 Experimental Results

Figure 4.11 shows the results of the runs with low dissolved concentrations < 0.7

mg/L. In these experiments the aerobic growth rate of the reactor at high DO was higher

than the low DO reactor. Also the diauxic lag of the high DO reactor was significantly

longer. The specific anoxic growth rates were higher in the Low DO reactor. Figure 4.20

shows the results of the runs with low dissolved concentrations > 0.7 mg/L. In these

experiments a significant difference in the growth rates in the aerobic phase was not

recorded suggesting that Pseudomonas denitrificans could be microaerophilic. But a

significant difference in length of lag and anoxic specific growth rates was observed.

Therefore not only did dissolved oxygen have an effect on the length of the diauxic lag

but it also affected the specific growth rates in the aerobic and anoxic phases.


4.3 Preculture Experiments

4.3.1 Experimental Methods

Cultures were grown in synthetic liquid medium modified from (Table 4-1)

Koraros et al. (1996) with or with out without nitrate depending on what kind of

preculture conditions were required for that experiment. The pH of the medium was

adjusted to 7.0 using 2N NaOH before autoclaving and the addition of nitrate-nitrogen (if

required). Culture medium in 250mL flasks (125 mL liquid volume) was inoculated from

agar plates (prepared as described in section 4.1.1). To maintain Oxic preculture

conditions the flasks were agitated in a shaker bath for two days at approximately 250 C.

If anoxic preculture conditions were to be maintained, the cultures were grown in a

nitrate limited synthetic liquid medium (4mg/L NO3- N) modified from Table 4-1 and

allowed to sit under a sterile laminar hood for two days. A procedure termed 'splitting'





















Anoxic Precultire- Nitrate in Anoxic Phase
S--..- A .. A---A- ---A- -- -A... --- -A--- 100

0.500 --90

80
0.400
70


S-60x
0.300 2.1 E
e ,. -500
500

X .40g
0.200
0.93 --30
30

0.100 20

10

0.000 "'".- .. ..--. I '-i-i---- -x-x- 0
0 50 100 150 200 250 300 350 400 450 500 550 600
Time (min)





Figure 4.11. Experiment E-7. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.01 mg/1)






















Anoxic Preculture- Nitrate in Anoxic Phase
.----A---A---A---A- ----- A M100

0.500- -90

80
0.400
70

t 2.8 60
c0.300 E
- 50 o
o

40 1
0.200
1.3
30


0.100- 20

10

0.000 ) X X X X-X X, ,X 1 9 1 X X-- A A 0
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750
Time (min)


Figure 4.12. Experiment E-8. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.01 mg/1)






















Anoxic Preculture- Nitrate in Anoxic Phase
0.800 -A-- -A--A-A- A-A--A-... ar 100

90
0.700 90

S80
0.600
70

S60 -
o
E
S0.400- -50 o

" 3.0 40 a
0.300

30

S20

0.100
0.95 + 10

0.000 --- X --X- -x XX-N'',-- X 9-XN-I'X K,- -- -- ,,i 0
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000
Time(min)


Figure 4.13. Experiment E-9. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.01 mg/1)
















E-10



Anoxic Preculture- Nitrate in Anoxic Phase
1.000 :-x-x-x-x-x-x-x-x-x-x-xx 100

0.900 90

0.800 80

0.700 70

W 0.600 60
c E
0.500 50 0

0.400 40

0.300 7 30

0.200 20

0.100 10
4.5
0.000 0
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
Time (min)


Figure 4.14. Experiment E-10. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.07 mg/l)
















E-11



Anoxic Preculture- Nitrate in Anoxic Phase
1.000 --x-x-x-x. x. 100
X "
0.900 ) 90

0.800 80

0.700- 70

0.600 60
S/ E
2 0.500 50

S0.400 1.3 40 o

0.300 30

0.200 20

0.100 ~10

0.000o '''A'A'A'A -'-A...].-. -.. ,--- 0
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
Time (min)


Figure 4.15. Experiment E- 1. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.07 mg/l)

















E-12



Anoxic Preculture- Nitrate in Anoxic Phase
0.800 A-A-A-A-a-A-A-A-AA 100

90
0.700

80
0.600
70

a -60~
U 6.8
cO E
0.400 -50 o
'0 408

0.300
1.2 -30

20

0.100
10

0.000 1-I K INI -0
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
Time(min)


Figure 4.16. Experiment E-12. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.09 mg/l)
















E-13



Anoxic Preculture- Nitrate in Anoxic Phase
1.000 -x(-x-x-x-x-x-x-x-x 100

0.900 90

0.800 80

0.700 70

0.600 / 60 "
c E
- 0.500 50 0

0
0.400 4.9 -40 O

0.300 / -30

0.200 20

0.1000 10
4.2
0.000 --- 00
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
Time(min)


Figure 4.17. Experiment E-13. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.09 mg/l)

















E-14


Anoxic
Preculture N03 Present in Aerobic

------A. -A- -A- -A- -A- -A- A- 100

0.500 90

80

0.400
70

S-60
S0.300 2.4 E
- 50 6

408
0.203
30
2.630

0.10- 20

10

0.000 K."W N-- x, ,, ..x. X" _,, _, ,_,, K -, 9 ,,, 0
0 120 240 360 480 600 720 840 960
Time (min)


Figure 4.18. Experiment E-14. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.09 mg/1)

















E-15




Anoxic Preculture- Nitrate in Anoxic Phase
-- -A----A- A-- ----A --A----A 100

0500 90


80

0400
70

60
a 0.85 60
S0300 E


50 2001
030
-400
0200
30


0100 20

10

0000 0"x' ---- -x- -x----Xx----X,.. ..- .... ..... X- .X X- A 0
0 120 240 360 480 600
Time(min)


Figure 4.19. Experiment E-15. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.09 mg/1)
















E-16


Figure 4.20. Experiment E-16. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.17 mg/l)


..A--.A--A--A--A---A--A 100

0.500 90



0.400
70

/^60
c 0.300 4.2 E



0.200
30
0.88
0.100 20
10

0 .-X--x--X--X--X --X--X
0.000X,, N-ENl- 0
0 120 240 360 480 600 720 840
Time (min)


















E-17


0
c


--A- -- -a- -a-- -a


0.500



n40m


S70
1.7
S^0< ^^^-60 7
0.300 E
-50 6

/ -40
0.200- 3.2
30
-30

-20
0.100

10

0.000 1., ". X-- -X- -X-;- -X,.....-- 0
0 120 240 360 480 600 720
Time (min)


Figure 4.21. Experiment E-17. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.17 mg/l)

















E-18



Anoxic Preculture- Nitrate in Anoxic Phase
0.800 a--A-A- A- -A--A-A 100

90
0.700

80
0.600
70

0.500
a 60
a
c E
S0.400 50 0
0
Q 2.8 0
40

30
0.200
20

0.100 2.8
10

0.000X- .X .".- it-I-1 0
0 100 200 300 400 500 600 700 800 900 1000 1100
Time (min)


Figure 4.22. Experiment E-18. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.17 mg/l)

















E-19


Figure 4.23. Experiment E-19. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.35 mg/l)


0.400- -----A- aA- --- -A-----A- 100

90
0.35090

80
0.300 1.8
70

0.250
60 x
o
CE
2 0.200 50 s

S0.84 0
S40 0
0.150

30
0.100
20

0.050
10
0.000 | X. .... X ... X .... X .... X... -X... .... X....- .. -X .... X0
0.000 0
0 120 240 360 480 600
Time (min)

















E-20


Figure 4.24. Experiment E-20. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.35 mg/l)


0.400 -

1.6
-60
c 0.300- E
I 50

0

30
0.200 -
1.2
30


0.100 0

10
..X----X---x- ---x----X----x ,
0.000 i-" 1'- --iR --W I A 1 i- 0
0 120 240 360 480 600
Time (min)

















E-21


Figure 4.25. Experiment E-21. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.70 mg/1)


0.400 -A-----A---A-------A-----A 100

90
0.350 90

-80
0.300 3.5
S70

0.250
-60-
C E
* 0.200 0.73 -50 '
0

'- 40 8
0.150 -

0 .0 30
0.100
20

0.050 ..,x,, x .x,
x 10
X A. A-* *A* -A- -A***A ** A -*A- -** A- .* A- -A* A* ** A
0.X0 X---X- -- ---X---X--- X- -X-- -x -X--- X- X-X- --x -----X
0 120 240 360 480 600 720
Time (min)

















E-22


Figure 4.26. Experiment E-22. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.7 mg/1)


0.450- A--- A---- ---- ---A- -- A-A 100

: 1490
0.400 90

-80
0.350 80

70
0.300 0.43 70
S. 60 -
S0.250
I 50 0
. 0.200 i 0.58 0
30
400
0.150
--30

0.100- 20


0.050 10
X . X . X .. -X -X X X
'' -A -- -* -- -- -A-* -A- -A- -A -A
QO0W 0
0 120 240 360 480 600
Time (min)

















E-23


Figure 4.27. Experiment E-23. Comparison of biomass absorbance and dissolved oxygen
levels against time. The following symbols represent pure culture absorbance exposed to
a specific DO concentration and the levels of dissolved oxygen:


BIOMASS (w/ High DO)
High DO (8.7 mg/l)


BIOMASS (w/ Low DO)
High DO (0.7 mg/l)


0.450 9-, 100
A- A-- -A- -A-- -A
0.400 90

-80
0.350 80

70
0.300 1 70
60
0.250 E

0 -50
S0.200
1.4 0
-40 0
0.150
30

0.100 20
20

0.050,, 10
0 X---X---X---X---X---X
S --A- -A-- -A -A-- -A- A- --- -A- A- A- -A- A-- -A A
0.000 kx-- -- X- Xx Ix x 0
0 120 240 360 480 600 720
Time (rin)









was then performed on the culture medium. Approximately 250 mL of the culture

medium was added to a liter of liquid medium and allowed to mix to prevent flocculation.

The culture was then split into two 500 mL volumes, transferred to each bioreactor

simultaneously and diluted with liquid medium to an absorbance (k=550 nm, 1.25 path

length) of 0.02- 0.05 for use in experiments.


4.3.2 Growth Experiments

Two mutiGen bench-top bio-reactors in parallel (models F-1000 and F-2000, New

Brunswick Scientific) were used for the experiments. The culture was continuously

stirred at 3020C. The pH ranged from 7.0 in the aerobic phase and increased to 7.2

during the anoxic phase. Dissolved oxygen was monitored using Model DO-40 (New

Brunswick Scientific) analyzers with galvanic electrodes. The effect of various

precultures and presence and absence of nitrate-nitrogen in aerobic phase was compared

and contrasted at the dissolved oxygen concentration of 8.7 mg/L through the aerobic

phase. The experimental setup was as shown in Figure 4.28. Each experiment consisted

of an aeration period of 7-9 hours. 400 mg/L of nitrate-nitrogen was added to one reactor.

Once the biomass in the reactors was up to 0.25 in terms of absorbance, a one liter

sample was pulled out from the reactors and replaced with fresh synthetic medium at 300

C. This dilution process was repeated two times. Aeration was then stopped and the

reactor was sparged with nitrogen gas to remove any residual dissolved oxygen to mark

the beginning of the anoxic phase. Nitrogen gas was flooded through the head space of

the reactors during the period when there was no aeration. The variables monitored

include biomass in terms of absorbance, dissolved oxygen, temperature and pH.







C DE


A- Thermocouple
B-Thermometer
C-DO probe
D-Feed
E-Heater


Figure 4.28. Experimental setup for the preculture experiments


A B


i


B









4.3.3 Experimental Protocol

Experiments were carried out in order to investigate the effect of various

preculture conditions and the nitrate concentrations in the aerobic phase on the duration

of diauxic lags. Each experiment consisted of two parallel trials of the same initial culture

conditions. To ensure that the parallel cultures had the same initial biomass

concentrations, the original culture was well mixed and divided between the two

bioreactors. Potassium nitrate (400 mg/L) was added in the aerobic phase to one reactor.

One set of parallel run experiments was performed with oxic preculture conditions and

another with anoxic preculture conditions and the length of diauxic lags was compared.


4.3.4 Analytic Methods

Samples were withdrawn from the reactor using a syringe connected to a plastic

tube that extended through the cap to the bottom of the reactor. The sample line was

flushed several times, and 30 mL was withdrawn. A portion (10 mL) of each sample was

used to measure absorbance. Absorbance of the culture was measured using a

spectrophotometer (Milton Roy Spectronic 21D) at 550 nm using a 1.25 cm path length.


4.3.5 Experimental Results

The results of experiments showed two things clearly. Oxic preculture conditions

(Figure 4.32) experiments had significantly longer diauxic lags than cultures that were

revived anoxically (Figure 4.31). Also the diauxic lags were longer for cultures that had

not been exposed to nitrate in the aerobic phase as seen from Figure 4.31. Presence of

nitrate failed to influence the rate of aerobic growth in either experiment as observed in

all the figures. These experiments support the hypothesis in models proposed by Liu et. al

(1998 a, b).

















E-24




0.3 A--A----A --A --A-- 100
A -u- BIOMASS (w N03)
A --- BIOMASS (w/o N03) 90
0 /--+--DO (wNO3)
25 [N03] (w N03) 80
-** DO (w/o N03)
A -- [N03] (w/o N03) 70
0.2
02 -2.5
W -26 0
CE
S0.15 50 o-

S40 0o





S-10

0 0
"A-.- A.-- ---..A. A ..A-. A "..-. A..


0 100 200 300 400 500 600 700 800
time (min)





Figure 4.29. Experiment E-24. Comparison of biomass absorbance and dissolved oxygen
levels against time. The symbols as in the chart legend represent pure culture absorbance
exposed to different nitrate concentrations. The culture was revived anoxically.







57







E-25


0.4 100
w o ...... 90


-- --DO (wo 80
03
0.3 w__. ____ 0


S0.25 60

0,2-5


015

2.6 o
0.1
S20
20



0 .... ....0. < J^- -_.....

0 100 200 300 400 500 600 700 900




Figure 4.30. Experiment E-25. Comparison of biomass absorbance and dissolved oxygen
levels against time. The symbols as in the chart legend represent pure culture absorbance
exposed to different nitrate concentrations. The culture was revived anoxically.
















E-26
0.5 100
--- BIOMASS (w/o N03)
0.45 ix -- BIOtl) SS (w N03) 90
S\x o* DO(w/oNO3)
0.4 \ --DO (w N03) 80

0.35 1.5 70

S 0.3 60

e 0.25 50 O E

S I 0.3
0.2 403

0.15 I30

0.1 20

0.05 i 10
1 0
0 0 --------- -- l-f-- U E-. -ENtU-mnilEHUifElNUUE 0
0 100 200 300 400 500 600 700 800 900 1000
time (min)



Figure 4.31. Experiment E-26. Comparison of biomass absorbance and dissolved oxygen
levels against time. The symbols as in the chart legend represent pure culture absorbance
exposed to different nitrate concentrations. The culture was revived anoxically.








59








E-27




0.4 100

BIOMASS (w/o NO3)
0.35- -- BIOMASS (w NC3)
--+--DO(w/oNCO3)
**o-DO(w NC0) -80
0.3"" 2.5
70

0. 25 60

0.2 --50 1


0.15
/ 'A7


30

20

0.05 1
0 10


0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
Time(min)






Figure 4.32. Experiment E-27. Comparison of biomass absorbance and dissolved oxygen
levels against time. The symbols as in the chart legend represent pure culture absorbance
exposed to different nitrate concentrations. The culture was revived in oxic conditions.







60







E-28

0.45 100


0.4 90
S80

0.35
570





|35 50 3
0.4
eea











--Biomass w NO3 ;
0.25 OwoN3 1
S-0.2- 0


0.15
30








0 100 200 300 400 500 600 700 800 900

Time(min)



Figure 4.33. Experiment E-28. Comparison ofbiomass absorbance and dissolved oxygen

levels against time. The symbols as in the chart legend represent pure culture absorbance
exposed to different nitrate concentrations. The culture was revived anoxically.














CHAPTER 5
NEURAL NETWORKS


All the models developed so far have all been successful in providing detailed

descriptions of the process kinetics and reflect state of the art understanding of processes

such as denitrification and nitrification. The hypothesis used to justify the occurrence of a

diauxic lag remains to be verified experimentally by tracking enzyme activity during a

typical experiment. In contrast to the conventional models there is the black box

modeling technique, which predicts the value of a variable given the historic values of

itself (and perhaps others variables) but gives little insight into the process kinetics or the

governing equations in the model. A neural network is capable of good performance even

if the data have considerable non-linearity. Another of its significant advantages is that it

is able to discover patterns in the data. In summary, a neural network can probably solve

effectively problems that cannot be solved by traditional modeling or statistical methods.

The choice of an appropriate network and a practical algorithm is required for the

network to give the desired performance. In the present study a neural network is used to

predict the duration of the diauxic lag given certain parameters such as the biomass

concentrations in terms of absorbance, reviving phase of the culture, dissolved oxygen

concentrations and nitrate concentrations in the aerobic phase and length of the aerobic

phase in hours.









5.1 Algorithm Used

5.1.1 Back Propagation Algorithm

The back propagation network is probably the best known and widely used among

all the types of neural networks systems. A typical back propagation network is as

depicted in Figure 5.1. Essentially a back propagation network has an input layer, output

layer and one or more hidden layers. The inter -connections between the input and hidden

layers and the hidden and output layers are termed 'weights'. Like most other neural

network systems, input patterns are presented to the network and the network is trained to

learn the corresponding output pattern .The number of input parameters in one input

pattern determines the number of nodes in the input layer. Similarly the number of output

nodes is the number of variables the neural network is required to predict. In the present

study, we are interested in predicting the duration of the diauxie in hours. Hence the

neural network has only one output node, being the length of the diauxic lag in hours.

Both the number of nodes in the hidden layer and the number of hidden layers are not

specified. Though some theoretical guidance exists to determine the number of hidden

layers and hidden nodes, they are usually varied and the performance of the network

recorded for each combination. Finally the combination which gives the best performance

is chosen.

Rumelhart (1986) first proposed the basic back propagation algorithm. The name

'back propagation' comes from the fact that the error (gradient) of the hidden units is

derived from propagating backward the error associated with output units. The first step

of the back propagation algorithm is weight initialization where the weights are set to

small random numbers. In the second step an input pattern is presented to the neural

network and the output neuron activation's (values at the output nodes) are calculated.






63






Target Output

+


Actual Output



Backward error
propagation
Forward information flow propagation
OUTPUT


0 0 0 ............ 0


Forward information flow

HIDDEN





.... ..........
Forward
information .
flow weights
now^

0 0 0 ... 0


INPUT LAYER



Input


Figure 5.1. Backpropagation network









The third step is weight updating, where the weights are adjusted (backwards from the

output to hidden layers recursively) to reduce the error. The second and third steps are

repeated for each training pattern (input and corresponding output pattern). The number

of such distinct training patterns presented to the network is called epoch size where an

epoch is one pass of the above three steps for all the training patterns. The error measure

used here is mean square error in the output activations. The mean square error for a

single pass is the square of the difference between the attained and desired output

activation for the output neuron. The epoch error is computed as the average of errors in

training presentations within that epoch. Mathematically, if we were processing training

pattern p, where the desired output activation was tp and the actual attained activation was

Op then error for that single representation is given by

E, =(t- o) (5-1)

If there were m such presentations in an epoch, the epoch error is given by

1 m-1
E= E (5-2)
m p=o

Rumelhart (1986) describes the equations governing the back propagation algorithm in

great detail. Although the back propagation algorithm is simple and easy to implement,

its success crucially depends on user defined parameters such as learning rate and

momentum constant. Hence in many situations it lands up having poor convergence rates.

Conjugate gradient search algorithms aim at minimizing some of these disadvantages.


5.1.2 Training by Conjugate Gradients

From an optimization point of view, learning in a neural network is equivalent to

minimizing a global error function, which is a multivariate function that depends on the









weights in the network. Suppose we approximate the global error function to a quadratic

function of the form


f(x) = c b.x + I x.A.x (5-3)
2

where, x is the weight vector

The function is minimized when its gradient

V f= A.x -b x (5-4)

is zero. The minimization is carried out by generating a succession of search directions hk

and improved minimizer's xk (weight vectors). At each stage a quantity ak (step size) is

also is also found that minimizesf(xk+ Uk hk), and Xk+1 is set equal to the new point

Xk + ak *hk. The search direction vector hk and the weight vector Xk are built in such a

way that Xk+1 is also the minimizer of the function f over all the vector spaces of

directions already taken namely {hi, h2, ... hk }. Therefore in N iterations we arrive at the

minimum over the entire vector space. The search direction vector hk+1 is given by the

following equation

hk+l = gk+1 + ^hk (5-5)

The Polak-Ribiere algorithm defines the scalar k as follows


k (gk+l -gk )gk (5-6)
'Yk= (5-6)
gk .gk

where gk is the negative gradient off at some point Pk(i.e.)

gk = -Vf(Pk) (5-7)

If we proceeded from Pk along the direction hk to the local minima off located at point

Pk+1 then gk+1 can be written as

gk+ = -Vf(Pk+l) (5-8)











The above to logic can be implemented in two major stages recursively:

Stage 1: To find three points such that middle point is less than the first point.

The steps of the algorithm include:

(1) Save the weights as they come into the conjugate gradient module and compute the

negative gradient of the weight vector gk at point Pk. Let Pk be the first of the three

points we are trying to determine.

(2) Set the initial direction vector hk equal to gk if k =0. If k>0 compute hk using equations

(5) and (6).

(3) Find a second point Pk+1 in the direction hk such thatf(Pk+1) <(Pk).

(4) Estimate a third point using the golden ration rule and compute the value of the error

function at that point. The value of the error function at this third point need not be

less than the second point.

We now have three points that define an interval. Since the error function is

approximated to a quadratic equation, we can fit the three points in a parabola.



Stage 2: To refine this interval containing the minima until within satisfactory limits of

accuracy and try to locate the local minimum



Let the first point be P1, its error el, second point be P2 and its error e2 and so on. We take

a 'step' in the negative gradient direction from P2 along the parabola and compute the

value of the function at that point.

The following cases arise:









(1) If the function value at P3 is less than that at P2 and the 'step' is between P2 and P3:

The function value at this newly stepped out point is computed and compared to e3. If

the function value is less than e3 then the minimum is an internal point (between P2

and P3) and we are done. In this case P1 and P2 are updated along with their function

values as follows: P2 becomes P1 and the minimum becomes P2.

(2) If the function value at P3 is less than that at P2 and the 'step' is beyond P3 but within

the maximum step: P3 is updated along with its function value to 'step' and the

function value at this newly stepped out point.

(3) If the function value at P3 is less than that at P2 and if the new point was above an

arbitrary limit beyond P3 then we re-estimate the new point by taking a 'step' of the

maximum size and returning to one of the cases above. If the new point were

anywhere else then it is not desired and hence we use the golden ratio rule to step

outside to a new point.

(4) If the function value at P2 is less than that at P3 and the new point ('step') is between

P2 and P3: In this case Pi and P2 are updated along with their function values as

follows: Pi becomes P2 and P2 becomes new point 'step'.

(5) If the function value at P2 is less than that at P3 and the new point ('step') is between

P1 and P2: In this case P2 and P3 are updated along with their function values as

follows: P3 becomes P2 and P2 becomes new point 'step'.

(6) If the new point were anywhere else then it is not desired and hence we use the

golden ratio rule to step outside to a new point.









The conjugate gradient algorithm though similar to the back propagation algorithm

with momentum differs from it in two ways. One, the step size is not fixed. Two, the

momentum term y varies in an optimal way rather than being fixed throughout.


5.1.3 Simulated Annealing

Annealing is a term from metallurgy. When the atoms in a metal are aligned

randomly the metal is brittle more likely to get fractured. Hence when a metal is heated to

very high temperatures (the atoms are completely random) and cooled rapidly it is more

likely that the atoms settle down in random unstable state. On the other hand of the metal

were cooled gradually, the atoms tend to fall into patterns that are relatively stable for

that temperature. The same idea is used in optimization. The independent variables are

randomly perturbed (weights in the case of a neural network) while keeping track of the

best (lowest error) function value for each randomized set of variables. A high standard

deviation for the random number generator is used. After many such tries the set that

produced the best function value is used as the center for perturbation for the next

temperature. The temperature (standard deviation) is decreased and new tries are

performed.


5.1.4 Interleaved Simulated Annealing and Conjugate Gradient Algorithm

In the present study, the annealing parameters namely starting and stopping

temperatures, which represent standard deviations are set to high and low values

respectively initially. The temperature is reduced by a factor of c each time where c, is

given by the relation

In(stop / start)
c = e n-1 (5-9)









Where start and stop are the starting and the stopping standard deviations n the number of

temperatures. The starting weights are estimated by using the simulated annealing

algorithm. The conjugate gradient algorithm then finds the local minima rapidly. Once

there, simulated annealing casts about and trying to escape to a lower point. This

alternation is continued until we are unable to escape from the local minima. Another

point to note is that a limit has been set on the size of weights so that extremely large

activation levels can be avoided. Should there be no limit on the size of the weights then

any updating of the weights may not have any effect, as the weights may be either

extremely large or small, hence the limit.


5.2 Neural Network Model for Low DO Experiments

5.2.1 Training the Network

A set of eighteen experiments (E-7 to E-23) was spilt into two sets training and

test data. Table 5.1 gives the data used to train the neural network model to predict the

duration of the length of the diauxic lag in hours. Inputs to the neural network include

biomass in terms of absorbance at the start of the experiment, duration of the aeration

phase in hours and concentration of dissolved oxygen in mg/1 (as in Figure 5.2). All the

training data was normalized and then passed to the network. The number of nodes in the

hidden layer was varied and the mean squared errors recorded (Figure 5.3). The mean

square error was the lowest when the number of nodes in the hidden layer was three. The

weights after training were saved and were used to test the network. Figure 5.4 shows the

results when the training data was passed back to the neural network to verify if the

network had learnt all the experimental data presented to it.

















Network Output





Lag length in
hours


Concentration of
dissolved oxygen
in mg/1


Hidden Layer


Figure 5.2: Neural network used to predict the duration of the diauxic lag for low DO
experiments














Table 5.1. Training da s


Experiment
Number


E-7
E-7
E-8
E-8
E-11
E-11
E-12
E-12
E-13
E-13
E-14
E-14
E-17
E-17
E-18
E-18
E-19
E-19
E-21
E-21
E-22
E-22
E-23
E-23


Inputs to Network Desired Output
Length of Biomass in terms DO Length of
Aerobic Phase of absorbance at Concentration diauxic lag
(hrs) time zero (mg/1) (hrs)

4.250 0.062 8.7 mg/L 2.100
4.250 0.068 .01 mg/L 0.930
A 45n A A00 8'7 mr /T O800


4.250
4.250
4.750
4.750
5.250
5.250
4.750
4.750
5.000
5.000167
3.167
3.167
4.417
4.417
3.417
3.417
3.833
3.833
3.500
3.500
3.333
3.333


0.080 .01 mg/L 1.300
0.052 8.7 mg/L 1.300
0.052 .07 mg/L 0.000
0.045 8.7 mg/L 6.800
0.045 .09 mg/L 1.200
0.049 8.7 mg/L 4.900
0.051 .09 mg/L 4.200
0.047 8.7 mg/L 2.600
0.047 .09 mg/L 2.400
0.130 8.7 mg/L 3.200
0.129 .17 mg/L 1.700
0.054 8.7 mg/L 2.800
0.054 .17 mg/L 2.800
0.067 8.7 mg/L 1.800
0.067 .35 mg/L 0.840
0.069 8.7 mg/L 3.500
0.070 .70 mg/L 0.730
0.074 8.7 mg/L 0.580
0.076 .70 mg/L 0.430
0.077 8.7 mg/L 1.400
0.082 .70 mg/L 1.100


-. \


v,. ,'J ,


u. I Iliat! 1-














5.2.2 Testing the Network


Table 5.2 gives the set of data used to test the network with the weights found

after training. Figure 5.5 shows the results of passing the test data to the trained neural

network.


Table 52 Test data for n s


Experiment
Number


E-9
E-9
E-10
E-10
E-15
E-15
E-16
E-16
E-20
E-20


Inputs to Network Desired Output
Length of Biomass in terms DO Length of
Aerobic Phase of absorbance at Concentration diauxic lag
(hrs) time zero (mg/1) (hrs)

4.750 0.052 8.7 mg/L 3.000


4.750
7.750
7.750
5.000
5.000
4.000
4.000
3.417
3.417


0.052


0.950


.04 mg/L


0.037 8.7 mg/L 7.600
0.037 .07 mg/L 4.500
0.050 8.7 mg/L 1.200
0.050 .09 mg/L 0.850
0.065 8.7 mg/L 4.200
0.065 .17 mg/L 0.880
0.099 8.7 mg/L 1.600
0.098 .35 mg/L 1.200








73














007



006-



005-



.E
0
I 004



S003
coo


002



001 -




0 1 2 3 4 5 6 7
Number of nodes in hidden layer








Figure 5.3. Graph showing the variation of root mean square error with the number of
nodes in the hidden layer for neural network for low DO experiments








74













8-


7-


6


5-
0
c4
E 9
3


2





0 -
0 5 10 15 20 25 30
Data points










Figure 5.4. Comparison of the output from the neural network and the desired lag length
when the training data was passed back to the trained network, for low DO experiments.
The following symbols represent the data points in the graph:





Lag Length predicted by the network


* Desired Output lag length























9


8


7


6



C
I-
4-


3


2




0
0 2 4 6 8 10 12
Data Points


Figure 5.5. Comparison of the output from the neural network and the desired lag length
when the test data was passed back to the trained network, for low DO experiments. The
following symbols represent the data points in the graph:





Lag Length predicted by the network


* Desired Output lag length











5.3 Neural Network Model Preculture Experiments

5.3.1 Training the Network

A set of nine experiments (E-3 to E-6 and E-24 to E-28) was split into two sets -

training and test data. Table 5.3 gives the data used to train the neural network model to

predict the duration of the length of the diauxic lag in hours. In all these experiments the

dissolved oxygen concentration was maintained at 8.7mg/L through the aerobic phase

and therefore was not an input to the neural network. Biomass in terms of absorbance at

the start of the experiment, duration of the aeration phase in hours and concentration of

nitrate in the aerobic phase, reviving phase of the culture were the inputs to the network

(Figure 5.6). An oxic reviving phase translated to an input of zero to the network while

an anoxic reviving phase was denoted by an input value of one. All the other inputs were

normalized and then passed to the network. The number of nodes in the hidden layer was

chosen to be three as that gave the lowest mean square error (Figure 5.7). The weights

after training were saved and were used to test the network. Figure 5.8 shows the results

when the training data was passed back to the neural network to verify if the network had

learnt all the experimental data presented to it.


5.3.2 Testing the Network

Table 5.4 gives the set of data used to test the network with the weights found

after training. Figure 5.9 shows the results of passing the test data to the trained neural

network.

















Biomass as
absorbance at
time zero


-00-

Length of aerobic
phase in hours



Concentration of
dissolved nitrate in
the aerobic phase
in mg/1


Network Output





Lag length in
hours


Hidden Layer


Reviving phase -
Anoxic/Oxic





Figure 5.6: Neural network used to predict the duration of the diauxic lag for preculture
experiments














Table 5.3. Training data for neural network model for preculture experiments


Inputs to Network


Experiment
Number


E-24
E-24
E-26
E-26
E-27
E-27
E-28
E-28
E-5
E-4


Length
Aerobic
Phase (hrs


5.833
5.833
8.167
8.167
9.167
9.167
8.333
8.333
2.500
1.667


of Reviving
phase of the
) culture

Anoxic
Anoxic
Anoxic
Anoxic
Oxic
Oxic
Anoxic
Anoxic
Oxic
Oxic


Biomass in
terms of
absorbance
at time zero
0.030
0.030
0.040
0.040
0.040
0.040
0.030
0.030
0.035
0.030


Concentration
of nitrate in
the aerobic
phase (g/l)
0
40
0
40
0
40
0
40
40
40


Desired
Output
Length of
diauxic lag
(hrs)

2.500
1.167
1.500
0.333
7.333
2.500
3.500
0.000
9.333
5.833








79














0.12



0.1


0
c 0.08



0.06



E 0.04


0.02




0 1 2 3 4 5 6 7
Number of nodes in the hidden layer










Figure 5.7. Graph showing the variation of root mean square error with the number of
nodes in the hidden layer for neural network for preculture experiments
nodes in the hidden layer for neural network for preculture experiments








80














10

9

8

7

6-

c 5
0
4

3

2

1

0 -
0 2 4 6 8 10 12
Data Points








Figure 5.8. Comparison of the output from the neural network and the desired lag length
when the training data was passed back to the trained network, for preculture
experiments. The following symbols represent the data points in the graph:





Lag Length predicted by the network


* Desired Output lag length








81













12



10



8


o
.c6
E
I-

4



2-



0
0 1 2 3 4 5
Data Points










Figure 5.9. Comparison of the output from the neural network and the desired lag length
when the test data was passed back to the trained network, for preculture experiments.
The following symbols represent the data points in the graph:





Desired Output lag length


* Lag Length predicted by the network









Table 5.4. Test data for neural network model for preculture experiments
Inputs to Network

Experiment Length of Reviving Biomass in Concentration
Number Aerobic phase of the terms of of nitrate in
Phase (hrs) culture absorbance the aerobic
at time zero phase (g/l)
E-25 4.167 Anoxic 0.040 0
E-25 4.167 Anoxic 0.040 40
E-6 2.000 Oxic 0.035 40
E-3 1.750 Oxic 0.040 40


Desired
Output
Length of
diauxic lag
(hrs)

3.333
2.667
10.500
9.667


5.4 Discussion of Results

The neural network used to predict the diauxic lag lengths for low DO

experiments had a larger set of training data than the network used to predict the lag

length for preculture experiments. A larger test set of data was useful in that it presented

a broader range of data to the network but it did not help in improving the performance of

the network due the large variation in experimental data with practically the same input

variables. The lowest root mean square error calculated for the training data was 0.02

hours. This can be attributed to the nature of the training data. However the network is

able to predict the diauxic lag length with considerable accuracy (Figure 5.5) and

predicted shorter diauxies for low DO concentrations compared to high DO

concentrations. The network used to train the preculture experimental data had a very

small training set size. The lowest root mean square error for the training data set of this

network was 0.008 hours with three nodes in the hidden layer. Figure 5.9 shows that the

network predicts higher lag lengths for experiments with oxic reviving phase. It could

also predict higher lag lengths for bacteria that were not exposed to nitrate in the aerobic

phase.









5.5 Hybrid Model

The complete hybrid model uses the material balance model for both the aerobic

and anoxic growth phases and the neural network to predict the diauxic lag. The equation

governing the aerobic growth with constant specific growth rate is:

XB (t)= XB (0) e"ot (10)

Where XB (t) is the biomass concentration at time t

XB(O) is the biomass concentration at time zero

And "ois the specific growth rate in the aerobic phase

An analogous expression for biomass concentration in the anoxic phase assuming non-

limiting nitrate concentrations is given by:

XB (t)= XB (to) elN(t-t) (11)

Where IN is the specific growth rate in the anoxic phase

and to the time at the end of the diauxic lag when exponential growth resumes anoxicc

growth curve).

The specific growth (oxic and anoxic) rates used in the model are from Lisbon (2001).

Figure 5.10 shows the comparison of the growth curves as predicted by the hybrid model

and experimental values for high dissolved oxygen concentrations in the aerobic phase

for experiment E-21. In this case the specific growth rates (both oxic and anoxic) of this

experiment and the average specific growth rates agree closely. Hence we can see growth

curves predicted by the model closely match with the actual experimental data. Figure

5.11 shows a comparison of the growth curves as predicted by the hybrid model and

experimental values for low dissolved oxygen concentrations in the aerobic phase for

experiment E-21.








84













0.45


0.4
---biomass experimental High DO

0.35 -m-bomassfrom hybrid model High DO


0.3


u 0.25

o
S0.2


0.15


0.1


0.05


0
0 100 200 300 400 500 600 700
1ime in minutes







Figure 5.10. Comparison of the growth curves as predicted by the hybrid model and
experimental values for high dissolved oxygen concentrations in the aerobic phase for
experiment E-21
























0.4



0.35 -4-biomass experimental low DO

-U-biomassfrom hybrid model low DO
0.3



0.25

c

S0.2
0


0.15



0.1



0.05



0
0 50 100 150 200 250 300 350 400 450 500
1ime in minutes


Figure 5.11. Comparison of the growth curves as predicted by the hybrid model and the
actual experimental values for low dissolved oxygen (0.7mg/L) concentrations in the
aerobic phase for experiment E-21











In experiment E-14 the model prediction doesn't closely agree with the

experimental growth curves. This could be attributed several reasons. Firstly, the average

specific growth rates are higher than the specific growth rates of this particular

experiment. Secondly, the present hybrid model doesn't account for any diauxic lag at the

beginning of the aerobic phase. Figure 5.12 shows the comparison of the growth curves

as predicted by the hybrid model and experimental values for high dissolved oxygen

concentrations in the aerobic phase for experiment E-14. Although the model captures the

lag accurately it is not able to capture the aerobic and anoxic growth curves. Figure 5.13

shows the comparison of the growth curves as predicted by the hybrid model and

experimental values for low dissolved oxygen concentrations in the aerobic phase for

experiment E-14.








87















0.7



0.6

-- biomass expnmental high DO

0.5 -m- biomas from hybrid model high DO



S0.4

-2
0
4 0.3



0.2



0.1



0
0 100 200 300 400 500 600 700 800 900
Time in minutes







Figure 5.12 Comparison of the growth curves as predicted by the hybrid model and
experimental values for high dissolved oxygen concentrations in the aerobic phase for
experiment E-14








88














1.2




1 -

-- bomass experimental low DO

0.8 --- bomass from hybrid model ow DO


U

0.6



0.4



0.2




0
0 100 200 300 400 500 600 700 800 900
1ime in minutes










Figure 5.13 Comparison of the growth curves as predicted by the hybrid model and
experimental values for low dissolved oxygen concentrations (0.09 mg/L) in the aerobic
phase for experiment E-14














CHAPTER 6
CONCLUSIONS AND FUTURE WORK



This research has shown that a neural network model can predict the length of the

diauxic lag given certain parameters as inputs. Although the network does not provide

any insight into process dynamics or governing equations it certainly is very powerful as

it can learn experimental data very quickly. In a typical nitrogen removal plant the entire

history of data can be used to train the neural network. Estimation of the length of diauxic

lag can have significant economic advantages in treatment plants.

Considerable experimental work needs to be done to expand the size of the data

set available for training. A comprehensive network that takes in all parameters such as

biomass in terms of absorbance, length of the aeration phase, dissolved oxygen

concentrations, nitrate concentrations in aerobic phase to predict the duration of the

diauxic lag can be developed. It might also be interesting to replace the duration of the

aeration phase and the biomass at time zero with the ratio of the biomass at the end of the

aeration phase to the biomass at time zero as an input. This network can then be

integrated with the simple Monod type models for both the aerobic and anoxic phases to

give a complete hybrid model.

Nitrate reductase enzyme activity through the course of an experiment also

remains an unresolved problem. Possible improvisations in the enzyme assay such as

freezing the whole cell samples in liquid nitrogen to stop cell activity once withdrawn

from the reactor could give more accurate results. A reliable assay for nitrate reductase






90


and being able to track enzyme activity through the course of an experiment would help a

major piece of the puzzle fall into place.














APPENDIX
PROGRAM LISTING



The following program accepts from the user the following information:
Number of nodes in the Input Layer
Number of nodes in the Hidden Layer
Training data file name with extension
Test data file name with extension
Number of data points

The program uses Simulated Annealing coupled with conjugate gradient search to find
the point of minima and trains the network for the given training data. Once the network
has been trained the test data is passed to the neural network and the results are written to
file. Also the weights from the input to hidden layer and hidden to output layer are
written to file.


Predefined constants
Variable/Constant
name
MAXDATA
MAXINP
MAXHID
STARTTEMP
STOPTEMP
NTEMPS
Wmax
Wmin


s and variable names used:
What it stands for

Maximum number of data points
Maximum number of input nodes
Maximum number of hidden nodes
Starting temperature for the simulated annealing
Stopping temperature for the simulated annealing
Number of iterations to find the best seed value
Maximum value of the weights


Minimum value of the we


ights


PROGRAM LISTING

// NEURAL NETWORKS CODE FOR VARIABLE NUMBER OF INPUT NODES
AND SINGLE OUTPUT NODE

// Standard Libraries included

# include
# include
# include
# include









# include
# include
# include

// Constants for Network Architecture

# define MAXDATA 30
# define MAXINP 30
# define MAXHID 30

// Constants for Simulated Annealing

# define GOLDENRATIO 1.618034

// Global variables predefined

float EP =le-40;
float STARTTEMP = 2;
float STOPTEMP =0.2;
int NTEMPS = 2;
float wmax= 5.0;
float wmin= -5.0;
float a =0.9;

// Variables used in the code

int testdata;
int noofdata, inpnodes, hidnodes;
float inpdata[MAXDATA][MAXINP], maxi[MAXINP], mini[MAXINP],
inphidw[MAXINP][MAXHID], hidoutw[MAXHID], desop[MAXDATA];
float hid[MAXHID];
float newihw[MAXINP] [MAXHID],
newhow[MAXHID],savihw[MAXINP][MAXHID], savhow[MAXHID];
float deriihw[MAXINP] [MAXHID],
derihow[MAXHID],fderiihw[MAXINP][MAXHID], fderihow[MAXHID];
float olddihw[MAXINP] [MAXHID], olddhow[MAXHID];
float test[MAXDATA] [MAXINP], maxtestdata[MAXINP], mintestdata[MAXINP];

float nw;
float al,a2,a3;
float nnl,nn2,nn3,ennl,enn2,enn3;
float tl, t2,denom, step, diff, step_err, rms,max_step;
float temp, tempmult;
float nn, op, dho, dhi;
float e,ee, er, error,eee;