rat behavior detection and video system limitations

8/14/2019 Rat Behavior Detection and Video System Limitations

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Psycho pharm acology (1993) 113 : 177 186 Psychopharmacology S p r i n g e r - V e r l a g 1 9 9 3

Q u an t i t a t ive a s s e s s m e n t o f t h e m ic r os t r u c t u r e o f r a t b e h av ior :I . f ( d ) , T h e e x t e n s ion o f t h e s c a l in g h yp ot h e s i s *M a r t i n P . P a u l u s l 'z , M a r k A . G e y e r 21 Lab oratory of Biological Dynamics and Theoretical M edicine, University o f California, San Diego (0804) La Jolla, California 92093, USA2 Department of Psychiatry, Scho ol of Medicine, University of C alifornia, San Diego (0804) La Jolla, California 92093, USAReceived Octo ber 6, 19 92/F inal version April 20, 1993

A b s t r a c t . P r e v i o u s s t u d i e s d e m o n s t r a t e d t h a t d r u g e f f e c t so n t h e m o v e m e n t s e q u e n c e s o f r a t s i n u n c o n d i t i o n e dm o t o r a c t i v it y p a r a d i g m s c a n b e q u a n t i fi e d b y s c a li n gm e a s u r e s t h a t d e s c r i b e t h e a v e r a g e r e l a t i o n s h i p b e t w e e na v a r i a b l e o f i n t e re s t a n d a n e x p e r i m e n t a l p a r a m e t e r .H o w e v e r , r a t s e n g a g e i n a w i d e v a r i e t y o f g e o m e t r i c a l l yd i s t i n c t m o v e m e n t s t h a t c a n b e i n f l u e n c ed d i f fe r e n ti a l ly b yd r u g s . I n t h i s i n v e s t i g a t i o n , t h e e x t e n d e d s c a l i n g a p p r o a c hi s p r e s e n t e d t o c a p t u r e q u a n t i t a t i v e l y t h e r e l at i v e co n t r i -b u t i o n s o f g e o m e t r i c a l l y d i s t in c t m o v e m e n t s e q u e n c e s t ot h e o v e r a l l p a t h s t r u c t u re . T h e c a l c u l a t i o n o f t h e s p e c t r u mo f l o c a l s p a t i a l s c a l i n g e x p o n e n t s , f ( d ) , i s b a s e d o n e n -s e m b l e m e t h o d s u s e d i n s t a ti s t i c a l p h y s i c s . R e s u l t s o f t h ef ( d ) a n a l y s is c o n f i r m t h a t t h e a m o u n t o f m o t o r a c t i v i ty i sn o t c o r r e l a t e d w i t h t h e g e o m e t r i c a l s t r u c t u r e o f m o v e -m e n t s e q u e n c e s . C h a n g e s i n t h e a v e r a g e s p a t i a l s c a l i n ge x p o n e n t , d , c o r r e s p o n d t o s h i ft in g t h e e n t i r e f ( d ) f u n c t i o n ,a n d i n d i c a t e o v e r a l l c h a n g e s i n p a t h s t r u c t u r e . W i t h t h ee x t e n d e d s c a l i n g a p p r o a c h , s t r a i g h t m o v e m e n t s e q u e n c e sa r e a s s e s s e d i n d e p e n d e n t l y f r o m h i g h l y c i r c u m s c r i b e dm o v e m e n t s . T h u s , t h e r i d ) f u n c t i o n i d e n t i f ie s d r u g e f fe c t so n p a r t i c u l a r r a n g e s o f m o v e m e n t s e q u e n c e s a s d e fi n e d b yt h e g e o m e t r i c a l s t ru c t u r e o f m o v e m e n t s . M o r e g e n e r a l ly ,t h e f ( d ) f u n c t i o n q u a n t i f i e s t h e r e l a t i o n s h i p b e t w e e nm i c r o s c o p i c a l l y r e c o r d e d v a r i a b l es , in t h i s p a r a d i g m c o n -s e c u t i v e (X , y ) l o c a t i o n s , a n d t h e m a c r o s c o p i c b e h a v i o r a lp a t t e r n s t h a t c o n s t i t u t e th e a n i m a l 's r e s p o n s e t o p o g r a p h y .K e y w o r d s : R a t - B e h a v i o r - M i c r o s t r u c t u r e S c a l in gm e a s u r e s

T h e a s s e s s m e n t o f u n c o n d i t i o n e d m o t o r b e h a v i o r i n an i -m a l s h a s b e e n u s e d a s a q u a n t i t a t i v e d e s c r i p t o r o f a r o u s a l .

* Exemplary calculations o f path segments with different geometri-cal characteristics can be obtained from the authors. Questionsregarding the com putational imp lementation of this method shouldbe addressed to M PP preferably via email ([email protected]) orFAX (619-543-2493)Correspondence to: M.P. Paulus

A r o u s a l r e f e r s t o a s t a t e o f a w a k e n e s s r e l a t e d t o t h ea c t i v i t y o f t h e a s c e n d i n g r e t i c u l a r f o r m a t i o n ( H u l l 1 9 4 9;H e b b 1 9 5 5 ; R o b b i n s a n d E v e r i t t 1 9 9 0 ) . B a s e d o nm e a s u r e s o f t h e a m o u n t o f m o t o r a c t iv i t y i n r o d e n t s ,p h a r m a c o l o g i c a l a g e n t s c a n b e c a t e g o r i z e d a sp s y c h o m o t o r s t im u l a n t s o r d e p r e s s a n t s ( H a r v e y 1 9 87 ).H o w e v e r , d i ff e re n t t y p e s o f b e h a v i o r c a n b e a s s o c i a t edw i t h s i m i l a r a m o u n t s o f a c t i v i t y ( G e y e r e t a l. 1 9 86 ). M o r e -o v e r , i t h a s b e e n p r o p o s e d t h a t a r o u s a l i s n o t a s i m p l es c a l a r s t a te b u t c a n b e d i f f e r e n t i a t e d b y d i s t i n c t p a t t e r n s o fa c t i v i t y ( R o b b i n s a n d E v e r i t t 1 9 9 0) . C o n s e q u e n t l y , t h ea s s e s s m e n t o f a r o u s a l r e q u i r e s t h e q u a n t i f i c a t i o n o f d i f fe r -e n t p a t t e r n s o f u n c o n d i t i o n e d m o t o r a c t i v it y to i d e n t i fyb e h a v i o r a l p r o f i le s t h a t m a y h e l p t o d e t e r m i n e t h e m o d e sa n d s i te s o f a c t i o n o f t h e s e s u b s t a n c e s .U n c o n d i t i o n e d m o t o r a c t i v i t y i s f r e q u e n t l y m e a s u r e db y c o u n t i n g i n t e rr u p t i o n s o f p h o t o b e a m s i n a s t a n d a r d -i z e d t e s ti n g e n v i r o n m e n t ( R o b b i n s 1 97 7; R e i t e r a n d M a c -P h a i l 1 9 79 ; G e y e r 1 99 0 ). I n s o m e c a s e s, t r a v e l e d d i s t a n c e sh a v e a l s o b e e n u s e d t o q u a n t i f y t h e a m o u n t o f m o t o ra c t i v i t y ( S a n b e r g e t a l . 1 9 8 7 ) . H o w e v e r , w h e n m e a s u r i n gt h e a m o u n t o f m o t o r a c t iv i t y , i n s t r u m e n t - r e l a t e d f e a t u r e sc r u c i a l ly af fe c t t h e m e a s u r e m e n t . T h e m o s t i m p o r t a n t o ft h e s e f e a t u r e s i n c l u d e t h e d i s t a n c e b e t w e e n p h o t o b e a m s ,t h e r e s o l u t i o n u s e d t o m e a s u r e t h e m o v e m e n t s i n v i d e od e v i c e s , a n d t h e s a m p l i n g f r e q u e n c y . S e v e r a l i n v e s t i g a t o r s( L j u n g b e r g a n d U n g e r s t e d t 1 9 7 7 ; N i c k o l s o n 1 9 8 1 ; G e y e re t a l . 1986; Sanber g e t a l . 1987; S tah le 1987) have d i s t in -g u i s h e d b e t w e e n d i f fe r e n t t y p e s o f m o t o r b e h a v i o r b yi n t r o d u c i n g a p r i o r i d e f i n i t io n s o f d if f er e n t m o v e m e n tp a t t e r n s . O t h e r s ( F r a y e t a l. 1 9 8 t ) h a v e u s e d r a t i n g s c a le st o q u a n t i f y d i f f e re n t c a t e g o r i e s o f b e h a v i o r . B o t h a p -p r o a c h e s a c k n o w l e d g e t h a t t h e a m o u n t o f m o t o r a c t i v it yp r o v i d e s o n l y a p a r t i a l d e s c r i p t i o n o f th e b e h a v i o r , w h i c hs u g g e st s t h a t m e a s u r e s o f p a t t e r n s o f m o t o r a c t iv i t y y i el di m p o r t a n t a d d i t io n a l i n f o r m a t io n .T r a d i t i o n a l l y , t h e a s s e s sm e n t o f b e h a v i o r a l p a t t e r n sa r e b a s e d o n b e h a v i o r a l c a t e g o r i e s t h a t a r e d e f i n e da p r io r i . H o w e v e r , w e (P a u l u s a n d G e y e r 1 9 9 1 a) a n do t h e r s ( S z e c h t m a n e t a l . 1 9 8 8 ) h a v e a r g u e d t h a t d i s c r e t eb e h a v i o r a l c a t e g o r i e s a r e n o t a d e q u a t e d e s c r i p t o r s f o r th em i c r o - a n a l y s i s o f u n c o n d i t i o n e d m o t o r b e h a v i o r . F i rs t . it


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178i s f r e q u e n t l y d i f fi c u lt t o c o m p a r e t h e b e h a v i o r a l e f f ec t s o fd r u g s i n u n c o n d i t i o n e d m o t o r p a r a d i g m s b e c a u s e t h ed e f i n it i o n o f b e h a v i o r a l c a t e g o r i e s d e p e n d s i d i o s y n c r a ti -c a l ly o n t h e s p e c if i c m e a s u r i n g d e v i c e a n d t e s ti n g e n v i r o n -m e n t . S e c o n d , c o r r e l a t i o n s b e t w e e n l a r g e n u m b e r s o fd i f f e r e n t b e h a v i o r a l c a t e g o r i e s p o s e d i f f i c u l t s t a t i s t i c a lp r o b l e m s a n d m a y n o t p r o v i d e a d d i ti o n a l i n f o r m a t i o na b o u t t h e b e h a v i o r o f t h e a n i m a l . T h i rd , t h e b e h a v i o r a le f fe c ts o f s o m e d r u g s , s u c h a s t h e p r o t o t y p i c a l p s y c h o s -t i m u l a n t d - a m p h e t a m i n e , a r e c h a r a c t e r i z e d b y a f r a g -m e n t a t i o n o f b e h a v i o r a l r e sp o n s e s ( L y o n a n d R o b b i n s1 9 7 5 ) , m a k i n g i t d i f f i c u l t t o a s s e s s w h e t h e r a s p e c i f i cb e h a v i o r a l c a t e g o r y h a s b e e n c o m p l e t e d . F o u r t h , t h e d e -t e r m i n a t i o n o f th e n e u r o b i o l o g i c a l s u b s t r a t e s u n d e r l y i n gb e h a v i o r a l e f f e c ts i s c o m p l i c a t e d b y t h e f a c t t h a t a p r i o r id e f i n e d b e h a v i o r a l c a t e g o r i e s m a y n o t c o r r e s p o n d t o d i s -t i n c t n e u r o c h e m i c a l p r o c e s s e s o r n e u r o a n a t o m i c a l s y s -t e m s . F if t h , b e h a v i o r a l c a t e g o r i e s a r e n o t e a s i l y m o n i t o r e dw i t h t h e t e m p o r a l r e s o l u t i o n t h a t i s n e c e s s a r y t o d e t e c ts u b t le c h a n g e s i n t h e r e s p o n s e t o p o g r a p h y o f t h e a n i m a l .A l t e r n a t i v e l y , b e h a v i o r a l p a t t e r n s c a n b e e x t r a c t e d f r o mm e a s u r e s d e s c r i b i n g d i st i n ct c h a r a c t e r i s t i c s o f b e h a v i o r a le v e n t s . C o n s e q u e n t l y , b e h a v i o r a l p a t t e r n s c a n b e d e f i n e da s p a r t i c u l a r c o m b i n a t i o n s o f m e a s u r e s e q u e n c e s o b -s e r v e d w i t h i n a c o l l e c t i o n o f b e h a v i o r a l e v e n t s .

S e v e r a l a p p r o a c h e s h a v e b e e n d e v e l o p e d t o e x t r a c ti n f o r m a t i o n a b o u t p a t t e r n s o f m o t o r a c t i v it y in r o d e n ts .S t a h l e ( 1 98 7 ) s u g g e s t e d t h a t t h e e x t r a c t i o n o f l i n e a r f a c t o r sb a s e d o n a p a r t i a l l e a s t s q u a r e a n a l y s i s r e l a t i n g m e a s u r -a b l e b e h a v i o r a l o b s e r v a b l e s t o p h a r m a c o l o g i c a l e f f e c t sp r o v i d e s a s u p e r i o r a s s e s s m e n t o f b e h a v i o r a l p a t t e r n sc o m p a r e d t o m u l t i p l e s t a ti s t ic a l c o m p a r i s o n s o f i n di -v i d u a l m e a s u r e s . K e r n a n e t a l . ( 1 9 8 8 ) h a v e u s e d t e m p o r a lc o r r e l a t i o n f u n c t io n s b a s e d o n s t a ti s ti c s o f s p a t i a l p o i n tp r o c e s s e s t o d e t e c t p a t t e r n s i m i l a r i t i e s a n d e x p l o r e t h eb e h a v i o r a l r e p e r t o i r e o f r a t s in a s p o n t a n e o u s m o t o r a c -t i v it y p a r a d i g m . T e i t e l b a u m e t a l. ( 19 8 2) h a v e u s e d t i m ef r a m e a n a l y s i s t o d e c o m p o s e b e h a v i o r a l r e s p o n s e s i n t oe l e m e n t a r y e v e n t s a n d a s s e ss t h e i r in d i v i d u a l c o n t r i b u -t i o n s . T h e s e a p p r o a c h e s h a v e p r o v i d e d a d d i t i o n a l a n di m p o r t a n t i n f o r m a t i o n a b o u t m o t o r a c t iv i ty p a tt e rn s .H o w e v e r , c o m m o n s h o r t c o m i n g s o f t he s e m e t h o d s i n -c l u d e t h e i r d e p e n d e n c e o n b o t h p r e d e f i n e d b e h a v i o r a lc a t e g o r i e s a n d a p a r t i c u l a r m e a s u r i n g r e s o l u ti o n .R e c e n t l y , w e i n t r o d u c e d s c a l in g m e a s u r e s q u a n t i f y i n gt h e f u n c t i o n a l r e l a t io n s h i p b e t w e e n a n e x p e r i m e n t a l p a r a -m e t e r a n d a v a r i a b l e o f i nt e r e s t d e s c r ib i n g a c h a r a c t e r i s t i cf e a t u r e o f t h e e x p e r i m e n t a l s y s t e m . T h e s e m e a s u r e s a s s e sst h e r e l a t io n s h i p b e t w e e n i n d i v i d u a l b e h a v i o r a l e v e n t s a n dt h u s q u a n t i f y b e h a v i o r a l p a t t e r n s o f r a t s e x p o s e d t o t h eB e h a v i o r a l P a t t e r n M o n i t o r ( B P M ) ( P a u l u s a n d G e y e r1 99 1a ). T h e c o m p u t a t i o n o f t h e s e m e a s u r e s i s b a s e d o ns e q u e n c e s o f m i c r o - e v e n t s , d e f i n e d b y t h e s m a l l e s t r e s o lv -a b l e c h a n g e i n t h e e v e n t s p a c e . U s i n g t h e s c a l i n ga p p r o a c h , t h e s e m e a s u r e s s u m m a r i z e t h e i n f o r m a t i o nc o n t a i n e d o n d i f f e r e n t s p a t i o - t e m p o r a l s c a l e s . T e m -p o r a l l y , t h e c o n t r i b u t i o n o f s h o r t - d u r a t i o n m i c r o - e v e n t si n r e l a ti o n t o l o n g - d u r a t i o n m i c r o - e v e n t s is q u a n ti f ie d b yt h e t e m p o r a l s c a l i n g e x p o n e n t c~. S p a t i a l l y , t h e a v e r a g ep a t h l e n g t h b e t w e e n m i c r o o e v e n t s s e p a r a t e d b y k m i c r o -e v e n t s i s q u a n t i f i e d b y t h e s p a t i a l s c a l i n g e x p o n e n td ( P a u l u s a n d G e y e r 1 9 9 1a ). T h i s a p p r o a c h a s s u m e d t h a t

t h e a v e r a g e s c a l i n g r e l a t i o n s h i p a d e q u a t e l y r e f l e c t s t h ea n i m a l ' s b e h a v i o r a n d p r o v i d e d n o d e t a i le d i n f o r m a t i o na b o u t t h e f l u c t u a t i o n o f t h e s c a l i n g r e l a t i o n s h i p .

I n t h i s in v e s t i g a t i o n , t h e s c a l i n g a p p r o a c h w a s e x -t e n d e d t o a s s e ss t h e g e o m e t r i c a l c h a r a c t e r i st i c s o f m i c r o -e v e n t s u b s e q u e n c e s . T h e s p e c t r u m o f l o c a l s p a ti a l s c a l in ge x p o n e n t s , f ( d ) , d e s c r ib e s f u n c t i o n a l ly t h e c o n t r i b u t i o n o fm i c r o ~ e v e n t s u b s e q u e n c e s w i t h d i ff e r e n t lo c a l s p a t i a l s c a l -i n g e x p o n e n t s , d i . T h u s , t h i s f u n c t i o n q u a n t i f i e s h o w s e -q u e n c e s o f b e h a v i o r a l e v e n t s f o r m m a c r o s c o p i cb e h a v i o r a l p a t t e r n s . T h i s p a p e r f o c u s es o n t h r e e a i m s : I )t o i n t r o d u c e t h e c o m p u t a t i o n a l m e t h o d s r e q u i r e d t o o b -t a i n t h e f ( d ) f u n c t i o n ; 2 ) t o c o m p a r e t h e r e l a t i o n s h i pb e t w e e n t h e a v e r a g e s c a l i n g b e h a v i o r a n d t h e f ( d ) f u n c -t io n ; a n d 3 ) t o s u p p l y p o s s i b le b e h a v i o r a l i n t e r p r e t a t i o n so f c h a n g e s i n t h e f ( d ) b a s e d o n a n e x e m p l a r y d a t a s e t.A c o m p a n i o n p a p e r d e t a i ls t h e a p p l i c a t i o n o f t hi s m e t h o dt o a n a l y z e d i f f e r e n c e s b e t w e e n c l a s s i c a l d o p a m i n e r g i cp s y c h o s t i m u l a n t s a n d r e l at i ve l y se l e c ti v e d o p a m i n e r e u p -t a k e i n h i b i t o r s ( P a u l u s e t a l . 1 9 9 3 ) .

M a t e r i a l s a n d m e t h o d s

Bas ic sca l ing assumpt ion . The scaling approach is based on theassumption that the relationship between experimental parametersand variables of interest provides impo rtant information ab out thestructural a nd sequen tial characteristics of sequences. In general,behavioral observables are giv en by a set of coordinates ina predefined even t space. Typically, discrete se ts of coordinates areused to ob ain variables of interest. These v ariables of interest arecollected for specific experime ntal conditions to yie ld meas ures ofthe observe d beh avior. F or exam ple, the (x, y) positions of a rat ina test environment and the time spent at that position provide a setof coordinates defining a m icro-event of a b ehavior in a three-dimensional event space. The variable of interest to determine thegeom etrical characteristics of pa th patterns is the distance or path-length between two micro-events that are separated by k micro-events. For example, the distance between consecutive micro-events,i.e. k = 1, is always 1 by definition of the micro-event as the sm allestresolvable change in the event spac e. Here, k corresponds to theexperimental param eter that is use d to extract the structural in-formation and is also called the resolution with which the pathlengthis obtained. Sp ecifically, the geom etrical structure of move mentsequences is extracted from the functional relationship betweenk and the pathlength. The particular functional forms relating thesequantit ies are derived from scaling approa ches in physical systems,which have yielded a rem arkable universality (Stanley 1987; Barn-sley 1988; Feder 1988), as we ll as from the description of a geom etri-cal obje ct using its fractal dimension (M andelbrot 1977). This func-tional form can be stated m ost generally as[variable o f interest] ([pa ram ete r A]) ~ [pa ram eter A ] ~"li~g 0xp ....x [variable o f interest]

x ( [param eter B])Specifically, the average distance betwee n micro-events separated bythree micro-events, (L(3)), is related to the average distance separ-ated by one micro-event, (L(1)) via(L(3)) ~ 32-d(L(1))The scaling relationship is described quantitatively by the spatialscaling exponent, d. Fo r a straight line , the distance a fter threemicro-even ts (e.g. L (3 )= 3) is three times the distance after onemicro-even t, whieh by definition is one (e_g. L(1) -- I), ie, 3 ,= 32 -d t.The value of d that solves this equation is 1. In contrast , a pa thpatte rn of tour m icro-events characterized by two 90 degree right


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t u r n s w i l l y ie l d t h e s a m e d i s t a n c e f o r t w o m i c r o - e v e n t s s e p a r a t e d b yt h r e e m i c r o - e v e n t s ( e. g. L ( 3 ) = 1 ) a s f o r t w o c o n s e c u t i v e m i c r o -ev en ts ( e .g . L(1 ) = 1 ). i .e . 1 = 3 2 - a l . Th e v a lu e o f d th a t so lv es th i se q u a t i o n i s 2 . I n g e n e r a l , s t r a i g h t m o v e m e n t s a r e a s s o c i a t e d w i t ha l o w s p a t i a l s c a l in g e x p o n e n t , d , h i g h ly c i r c u m s c r i b e d m o v e m e n t swi th m an y tu rn s an d rev e rsa l s r e su l t in a h ig h sp a t ia l s ca l in g ex p o -n en t (Pau lu s an d Gey e r 1 9 9 1 a ) .Th e tem p o ra l s ca l in g ex p o n en t , c~, r e la te s th e n u m b er o f mic ro -e v e n t s t o t h e m i c r o - e v e n t d u r a t i o n , c~ q u a n t i fi e s t h e a m o u n t o f m o t o ra c t i v i ty b a s e d o n a l o c a l " d e g r e e o f a c t i n g " b y e v a l u a t i n g t h e r a t i o o fsh o r t d u ra t io n mic ro -ev en ts (h ig h lo ca l d eg ree o f ac t in g ) v e r su s lo n gd u ra t io n mic ro -ev en ts ( lo w lo ca l d eg ree o f ac t in g ), d an d e cand i f f er e n t ia t e u n c o n d i t i o n e d m o t o r e f fe c ts o f p h a r m a c o l o g i c a l a g e n t sev en wh en th e se su b s tan ces r e su l t in s imi la r l ev e l s o f ac t iv i ty .

Exten ded sca ling assumpt ion . P a t t e r n s o f b e h a v i o r a r e n o t q u a n t i f ie dsu f f ic ien t ly b y av e rag e measu re s . T h e ex ten d ed sca l in g a s su m p t io n i sb a s e d o n t h e i d e a t h a t t h e l o c al s c a l in g r e l a t i o n s h ip b e t w e e n t h ev a r i a b l e o f in t e r e s t a n d t h e e x p e r i m e n t a l p a r a m e t e r i s c h a r a c t e r i z e db y a r an g e o f s ca l in g ex p o n en ts , d ~ , in s tead o f o n ly th e a v e rag esca l in g ex p o n en t , d . Th e te rm lo ca l r e fe r s to a sp a t ia l ly o r t emp o ra l lyl imi t in g co n d i t io n , i . e . th e g eo me t r ica l ch a rac te r i s t i c s a re ca lcu la tedf o r c i r c u m s c r i b e d m i c r o - e v e n t s e g m e n t s c o r r e s p o n d i n g t o c o n s e c u t -i v e m o v e m e n t s o f t h e a n i m a l . T h i s i d e a r e f l e c t s t h e e x p e r i m e n t a lo b s e r v a t i o n t h a t a n i m a l s d i s p l a y a v a r i e t y o f d i f fe r e n t m o v e m e n tseq u en ces . Th e o b jec t iv e o f th i s ap p ro a ch i s to q u an t i fy h o w f re -q u en t ly sp ec i f ic d~ d esc r ib e th e sca l in g re la t io n sh ip o f mic ro -ev e n ts e g m e n t s. T o q u a n t i f y t h e c o n t r i b u t i o n s o f m o v e m e n t s h a v i r i g d i f fe r -e n t g e o m e t r i c a l c h a r a c t e r s i t i c s i n a m a n n e r t h a t i s i n d e p e n d e n t o fth e re so lu t io n k , a fu n c t io n i s d e f in ed th a t d e sc r ib e s th e re la t io n sh ipb e tween th e o ccu r ren ce p ro b ab i l i ty o f sp ec i f ic d r an d th e re so lu t io nk . Sp ec i fica l ly , th e n u m b er o f s eg men ts wi th a sp ec i f i c dr fo r k = 3 ,N(d~, 3), is re la ted to the numl~er of N(d i , 1 ) b y th e same fu n c t io n a lfo rm d esc r ib ed ab o v e , i . e .N(d~, 3) ~ 3s~0T h e r e s o l u t i o n - i n d e p e n d e n c e o f t h is f u n c t i o n i s a n i m p o r t a n t f e a t u red u e to th e fac t th a t th e o c cu r ren ce p ro b a b i l i ty o f sp eci f i c d~ ch an g esfo r d i ffe ren t v a lu es o f k . Th is s ca l in g fu n c t io n h as b een d ev e lo p ed tod e s c r i be q u a n t a t i v e l y o b j e c t s w i t h d i v e rs e a n d c o m p l e x g e o m e t r i c a lch a rac te r i s t i c s (Ha lsey e t a l . 1 9 8 6 ) an d i s c a l l ed th e spectrum of localspatial scatin9 exponents, f(d).Graphical example. A s c h e m a t i c e x a m p l e s h o u l d c l a r i f y t h e b a s i cs tep s o f ca lcu la t in g th e sp ec t ru m o f lo ca l sp a t ia l s ca l in g ex p o n en ts ,f (d ) . In F ig . 1 , fo u r d i f fe ren t s eg me n ts co n s t ru c ted f ro m f iv e mic ro -ev en ts a t d i f fe ren t l ev e l s o f r e so lu t io n a re co n s id e red . Th e ca lcu -la t io n o f th e p a th len g th s o f th e se seg men ts fo r k = 1 an d k = 4 y ie ld sd~ = 1 for the s t ra igh t l ine , de ~ 1 .2 for the seg me nt wit h tr ia ngu lardeflec t ion , de = 1 .5 for the b ent segm ent, a nd d~ = 2 for the s tar-sh ap ed seg m en t . Fo r i l lu s t r a t iv e p u rp o ses , a p a th p a t te rn i s co n -s t ru c ted f ro m th ese seg men ts o n th ree l ev e l s o f r e so lu t io n , I , I I , an dI l l , co r re sp o n d in g ap p ro x ima te ly to k = 1 ,2 an d 4 , re sp ec t iv e ly .B a s e d o n t h e d e f i n it i o n o f f ( d ) g i v e n a b o v e a n d t h e f r e q u e n c y o f t h edifferen t segmen ts a t k = 1 (1 for a l l segm ents) and k = 4 (3 , 4 , 8, andI4 ) , th e f (d ) v a lu es fo r th e fo u r d i f fe ren t s eg men ts a re 0 .79 , 1 .0 , 1 .5 ,an d t . 9 0 , r e sp ec t iv e ly . Th e f ( d ) fu n c t io n fo r th e fo u r d i f fe ren t s eg -m en ts rea ds (1,0.79), (1.2, 1), (1.5, 1.5), an d (2.0, 1.9). Ho w ev er, thep a t h p a t t e r n a l s o c o n si s t s o f c o m b i n a t i o n s o f th e s e s e g m e n ts , w h i c hy ie ld s th e fu n c t io n a l ex ten s io n b e tween th e se in d iv id u a l p o in t s .Loca l spatial scalin9 exponents and the spectrum of local scalin9exponents. F o r t h e a n a l y si s o f r at m o v e m e n t s , t h e E u c l i d e a n d i s -tan ce , A , b e tween two mic ro -ev en ts i s c a lcu la ted fo r d i f fe ren t s eg -men ts , i , a t d i f f e ren t l ev e ls o f r e so lu t io n , k . In ad d i t io n , th e d i s tan cesf o r d i f f e r e n t k a r e a v e r a g e d w i t h i n e a c h s e g m e n t t o i m p r o v e t h ees t im a t io n o f de . Th e seg m en t s ize was ch o sen a s a co mp ro m iseb e tween two co mp e t in g o b jec t iv e s . Th e f i r s t o b jec t iv e was to d i f fe r -e n t i a t e o p t i m a l l y t h e g e o m e t r i c a l c h a r a c t er i s i ti c s o f d i ff e r e nt m o v e -men ts , wh ich req u i re d th e u se o f sma l l s eg m en t s ize s. Th e seco n do b jec t iv e was to o b ta in an accu ra te l e a s t sq u a re s f i t fo r d i f fe ren t d ~ ,wh ich imp ro v es wi th l a rg e seg men t s ize s . Ex ten s iv e v a r ia t io n s o f

17 9

g 8 18 s lope c 16 s lope d

P'T ?1 !I l I I I ] I I I I I I I I I I I I I I I I I Il og2( resolu t ion)

f(d) & -~ o

dFig , 1 . Th is f ig u re sch ema t ica l ly d i sp lay s th e co n s t ru c t io n o f th efu n c t io n d esc r ib in g th e sp ec t ru m o f lo ca l sp a t ia l s ca l in g ex p o n en ts ,f (d ) . Deta i l s a re d e sc r ib ed in th e t ex t

th e se p a rame te r s r e su l ted in th e se lec t io n o f a s eg m en t s ize o f 1 6mic r o -ev en ts an d th e re so lu t io n ran g e , k = 1 -1 2 . In ad d i t io n , th ec o n t r i b u t i o n o f a r t i fa c t u a l ly s m a l l d i s t a n ce s b e t w e e n c o n s e c u t i v em i c r o - e v e n t s d u e t o t h e l o w e r r e s o l u t i o n l i m i t o f t h e r e c o r d i n gi n s t r u m e n t i s r e d u c e d b y " d a t a d i t h e r i n g " . T h i s t e c h n i q u e u s e sa sma l l r a n d o m n u m b er , ~ , w i th m ag n i tu d e le s s th a n 6 = 21 o f th esma l le s t mic ro -ev e n t d i s tan ce , th a t i s ad d ed to th e (x , y ) p o s i t io n too b t a i n t h e p a t h l e n g t h b a s e d o n m e a s u r i n g t h e d i s t a n c e b e tw e e n t w osma l l a rea s o f s id e len g th 2 6 .

T h r e e m i c r o - e v e n t s e g m e n t s c o n s i s t i n g o f 1 6 m i c r o - e v e n t s b a s e do n a c t u a l r a t m o v e m e n t s a f t e r " d a t a d i t h e r i n g " a r e s h o w n i n F i g . 2 .T h r e e i m p o r t a n t c o n c l u s i o n s c an b e d r a w n f r o m t h e c a l c u l a t i o n o f d lfo r th e se seg m en ts u s in g k = 1 to k = 1 2. F i r s t , th e lo g - lo g p lo t s o fth e p a th len g th v e r su s k su p p o r t s th e sp ec i fi c fu n c t io n a l fo rm o f th esca l in g h y p o th es i s d e sc r ib ed ab o v e . Seco n d , th e s tan d a rd d ev ia t io n so f t h e d~s ( ab o u t 1 % o f th e d i v a lu e ) sh o w th a t lo ca l sp a t ia l s ca l in ge x p o n e n t s c a n b e e s t i m a t e d r e l i a b l y a n d a c c u r a t e l y f r o m t h e s emic ro -ev en t s eg men ts . Th i rd , th e l a rg e ra n g e o f d r ( t . 1 9 -1 .9 2 ) sh o wsth a t th e av e rag e d d o es n o t su f f ic ien t ly d e sc r ib e th e d i f fe ren t p a thp a t t e r n s a n d s u p p o r t s t h e e x t e n d e d s c a li n g a ss u m p t i o n . D e s p i t e t h es a m e a m o u n t o f a c t i v i t y (counts = 1 6 mic ro -ev en ts ) , th e g eo m e t r ica lch a rac te r i s t i c s o f th e se seg men ts d i f fe r d ra s t i ca l ly . Wh i le th e mo v e -men ts in th e f i r s t s eg m en t (F ig . 2 , to p l ef t) a re h ig h ly lo ca l ized a lo n gt h e c e n t e r o f t h e s h o r t w a l l i n t h e B P M c h a m b e r , t h e s e c o n d s e g m e n tsh o ws a mean d e r in g p a t te rn (F ig . 2 , mid d le l e f t ) , an d th e p a t te rn o fth e l a s t s eg men t (F ig . 2 , b o t to m le f t ) i s ch a rac te r ized b y s t r a ig h tm o v e m e n t s a l o n g t h e p e r i m e t e r o f t h e B P M c h a m b e r , B e h a v i o r a l l y ,s m a l l d l v a l u e s a r e a s s o c i a t e d w i t h d i r e c t e d m o v e m e n t s f r o m o n ep a r t o f t h e e n c l o s u r e t o a n o t h e r , o f t en s e r v i n g d i v e r s iv e e x p l o r a t i o n(Ber ly n e 1 9 6 0) , b u t c a n a l so re su l t f ro m p e rsev e ra t iv e s t r a ig h t m o v e -men ts a lo n g th e wa l l (Pau lu s an d Ge y e r 1 9 91 a ). H ig h lo ca l d ~ v a lu esa r e o b t a i n e d f r o m a n i m a l s e n g a g i n g e x t e n s i ve l y in l o c a l b e h a v i o r s ,e .g . g r o o m i n g , r e a r i n g , o r h o l e p o k i n g , b u t c a n a l s o o c c u r f o r a n i m a l sd i sp lay in g fo ca l s t e reo ty p ic b eh av io r , e . g . r ep ea ted h o tep o k in g ,g n a w i n g , o r h e a d b o b b i n g .


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18 0

d = 1 . 9 2 8 s ( d ) = 0 . 0 3 9 2

1 1 . 5 2 3 5 7 i 0 1 5 2 0log(k)

d = 1 . 6 1 2 s ( d ) = 0 . 0 3 5 3

O.

0 ,2

0. I 1 . 5 2 3 5 7 0 1 5 2 0l o g ( k )

i

d = 1 . 1 9 6 s ( d ) = 0 . 0 2 5 42 o g ( L ( k ) )

1 . 5 2 3 5 7 i 0 1 5 2 0l o g ( k )Fig . 2 . Th is f ig u re d isp lay s th ree seg men ts o f 1 6 co n secu t iv e mic ro -e v e n t s a f t e r " d a t a d i t h e r i n g " f o r a r a t in t h e B P M . E a c h m i c r o - e v e n tco r re sp o n d s to a p o in t , w i th su ccess iv e mic ro -ev en ts b e in g co n n ec -

Calculat ion o f local spatial scaling exponents and the spectrum of localspatial scaling exponents. In th e g rap h ica l ex amp le in F ig . 1 , th e f (d )f u n c t i o n w a s e s t i m a t e d d i r e c t l y f r o m t h e s l o p e o f t h e d o u b l y l o g a r -i t h m i c p l o t o f t h e o c c u r r e n c e f r e q u e n c y o f m i c r o - e v e n t s e g m e n t swi th a g iv en d~ v e r su s th e m easu r in g re so lu t io n s , k . In p rac t ice ,h o w e v e r , d i r e c t e s t im a t i o n s o f t h e f ( d ) f u n c t i o n d e p e n d s e n s it i v el y o nth e ran g e o f th e lo ca l sp a t ia l s ca l in g ex p o n en t , ~d ; , u sed to e s t im a teth e i r o ccu r ren ce f req u en cy . Fo r p rac t ica l c a lcu la t io n s , a d i f fe ren tme th o d h as b een p ro p o sed (Ha lsey e t a l . 1 9 8 6 ) th a t i s b a sed o n th ef o r m a l a n a l o g y o f th i s f u n c t i o n a l f o r m a l i s m w i t h s t a t is t i ca l m e c h a n -i c s a n d t h e r m o d y n a m i c s ( C h a n d l e r 1 9 8 7) . T h i s a n a l o g y h a s b e e nd ev e lo p ed fo r f r ac ta l o b jec t s (Fed e r !9 8 8 ) an d fo r d y n a mica l sy s tems(Ru e l le 1 9 8 9) an d i s su mm ar ized co m p reh en s iv e ly in Bad i i (19 8 9) . Ins ta t i s t i c a l p h y s ic s , en semb le me th o d s b ased o n p a r t i t io n fu n c t io n sa re u sed to o b ta in re lev an t m easu re s . Sp ec i f ica l ly , a p a r t i t io n fu n c -t io n , Z(q, n) , i s d e f in ed b ased o n a " f i l t e red su m ma t io n " o f th ep a t h l e n g t h s o f t h e m i c r o - e v e n t s e g m e n ts . T h e b e h a v i o r o f Z(q, n) fo rd i f fe ren t v a lu es o f th e f i l t e r p a ram e te r , q , i s u sed to ca lcu la te b o th th elo ca l sp a t ia l s ca l in g ex p o n e n ts an d th e f lu c tu a t io n sp e c t ru m o f lo ca lsp a t ia l s ca l in g ex p o n en ts ( fo r d e ta i l s , s ee Ap p en d ix ) .Bo th d i an d f (d i ) d ep en d imp l ic i t ly o n th e f i l t e r p a rame te r , q ,s in ce b o th d esc r ip to r s a re o b ta in ed f ro m Z (q , n ). F i r s t , m ic ro -ev en ts e g m e n t s a r e o b t a i n e d f r o m t h e s e q u e n ce s o f m i c r o - e v e n t s g e n e r a te db y t h e a n i m a l d u r i n g t h e e x p o s u r e i n t h e B P M . S e c o n d , t h r e equan t i t i e s , d q , f ( d q ) , an d Z (q , n ), a re ca lcu la ted fo r a r an g e o f q v a lu esfo r th e se seg men ts . Th e ran g e o f q v a lu es i s s e lec ted to a l lo w th eca lcu la t io n o f a su f f ic ien t r an g e fo r th e f (d ) fu n c t io n , su ch th a t th ec o n t r i b u t i o n s o f b o t h l o w a n d h i g h l o c a l s p at i a l s c a l in g e x p o n e n t sa re d e te rmin ed . Ty p ica l q v a lu es r an g e f ro m - 4 to + 6. Sp ec i f i -ca l ly , th e av e rag e sp a t ia l s ca l in g ex p o n en t , d , p rev io u s ly u sed a sa g l o b a l d e s c r i p t o r o f t h e g e o m e t r i c a l p a t h s t r u c t u r e ( P a u l u s a n dGey e r 1 9 9 ia ) , i s r eco v e red fo r q = I , an d d l = f (d t ) . Grap h ica l ly , th ed v a l u e c a n b e l o c a t e d a t t h e t a n g e n t o f t h e f ( d ) f u n c t i o n w i t h t h eid en t i ty l in e (x = y ) . Th i rd , th e dq, f(dq), a n d Z ( q , n ) ca Icu la ted fo re a c h r a t a r e a v e r a g e d f o r a ll a n i m a l s o f a t r e a t m e n t g r o u p t o o b t a i nt h e g r o u p a v e r a g e s a n d t h e g r o u p s t a n d a r d d e v i a t i o n d q , a(dq),Z ( q , n ) , a ( Z ( q , n ) ) , f ( d q ) a n d a( f (dq) ) , r e sp ec t iv e ly . Fo r ex amp le , fo reach q v a lu e

Z ( q , n )2 (q, n) = [animals]n u m b e r o f an i m a l sTh ese g ro u p fu n c t io n s can b e u sed to q u an t i fy th e e f fec t s o f t r ea t -m e n t s o n t h e g e o m e t r i c a l p a t h s t r u c t u r e .Statis t ical comparisons between group averages of d and f(d) . A d e -ta i l ed .q u an t i t a t iv e a s se s sm en t o f d ru g e f fect s o n th e p a th s t ru c tu re i so b t a i n e d f r o m t h e c o m p a r i s o n s o f d[q] an d th e f ( d [ q ] ) fu n c t io n sre la t iv e to th e co n t ro l g ro u p . Pre l im in a ry re su l t s in d ica te th a t th ed is t r ib u t io n o f sp a t ia l s ca l in g ex p o n en ts in a l a rg e g ro u p o f co n t ro la n i m a l s d o e s n o t d e v i a t e s i gn i f i ca n t l y f r o m a n o r m a l d i s t r i b u ti o n(Pau lu s an d Gey e r 1 9 93 ). Th u s , th e s ig n i f ican ce o f a d ru g e ffec t c anb e e x p re s s e d b y a z - t r a n sf o r m e d n o r m a l s c o re . H o w e v e r , s o m e d r u gt r e a t m e n t s m a y c h a n g e t h e v a r i a n c e o f th e a v e r a g e s p a t i a l s c a li n ge x p o n e n t . T h e r e f o r e , a m o d i f i e d z - t r a n s f o r m a t i o n w a s u s e d t o o b -ta in a co n se rv a t iv e e s t ima te o f th e s ig n i f ican ce o f t r ea tmen t e f fec t s .T h i s t r a n s f o r m a t i o n i n c l u d es t h e s t a n d a r d d e v i a t i o n s o f t h e c o n t r o lg r o u p , ac( f (d ) ) , a n d o f t h e t r e a t m e n t g r o u p , crA(f(d)). Th e d i f fe ren cecurve s , f~ . ~(d) a re cal led local pattern differences and s ignify" a l ter-a t io n s o f th e co n t r ib u t io n s o f sp ec i f i c dzs r e la t iv e to co n t ro l s , b u t d o

ted b y l in e s . Th e lo ca l sp a t ia l s ca l in g ex p o n en t , d , an d i t s s t an d a rdd e v i a t i o n ( S D ) a r e s h o w n f o r e a c h p a t h s e g m e n t. T h e c o r r e s p o n d i n gp l o t s o f th e l o g a r i t h m o f th e p a t h l e n g t h v e r s us t h e l o g a r i t h m o f th ere so lu t io n a re d i sp lay ed o n th e r ig h t o f each seg men t . Th e s t r a ig h tl in e s ig n i f ie s th e re su l t o f a l e a s t sq u a re s f i t t in g p ro ced u re ; th e s lo p ed e te rmin es th e lo ca l sp a t ia l s ca l in g ex p o n en t


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181not indicate o verall changes in the p ath structure. These changes areassessed most easily by z-transformed differences between the aver-age spatial scaling exponen ts, d~ (Paulus and Geye r 19 91a). Theseoverall changes are displayed comprehensively in the d - e plane,which simultaneously describes changes in b oth the tempo ral scalingexpon ent, cq and the spatial scaling exponent, d. Therefore, bo th th ez-transformed d -differences and the local pa ttern differences yieldspecific and different information abo ut the g eome trical path struc-ture. W hile the d~ indicates the glob al changes in the g eometricalpath structure, the ft. A d) quantif ies local changes in the m ovementseq uences.

Rat locomotorbehavior assessment.The Behavioral Pattern Monitorand general experimental procedures are described in the compan-ion p aper (P aulus et al. 19 93). Briefly, or each exp eriment, anima lsreceived subcutaneous injections of drugs 10 min prior to testing.Typically, animals we re exposed to the BPM for 120 rain, but onlythe fi rst 60 min we re used to calculate the f (d) functions shownbelow. Detailed descriptions of the drug treatments for the RU24969 animal can be found in R em pel et at (1993), for the 2,5-dimethoxy-4-iodo-amphetamine (DOI) animal in Paulus and Gey er(1992), and for the quinpirole a nimal in Paulus and Geyer (1991b).

. R e s u l t s

E x a m p l e s o f d i f fe r e n t f ( d ) f u n c t i o n sF i g u r e 3 d i s p la y s t h e r e s u l t s o f fi v e e x e m p l a r y a n i m a l st r e a t e d w i t h s a l in e , t h e d o p a m i n e ( D A ) D - 2 a g o n i s t q u i n -p i r o l e (0 .0 6 25 m g / k g ) , t h e D A u p t a k e i n h i b i t o r n o m i f e n -s i ne ( 5 . 0 m g / k g ) , t h e s e r o t o n i n 5 - H T z a g o n i s t D O I( 0 . 2 7 m g / k g ) , a n d t h e 5 - H T1 B a g o n i s t R U 2 4 9 6 9( 1.2 5 m g / k g ) , r e s p e c t i v e l y . T h e s e s e l e c t e d a n i m a l s e x e m p -l if y c o m b i n a t i o n s o f th e a v e r a g e s p a t ia l s c a li n g e x p o n e n t ,d , a n d t h e t e m p o r a l s c a li n g e x p o n e n t , e , in a l l f o u r q u a d -r an t s o f the d - ~ p lane . Th e d - e p lan e i l lus t r a tes d if f e r -e n t i a l ef fe c ts o f d r u g s o n t h e a m o u n t a n d a v e r a g e p a t hs t r u c t u r e o f u n c o n d i t i o n e d m o t o r a c t i v it y ( P a u l u s a n dG e y e r 1 99 1 a) . T h e s y m b o l s i n t h e s c h e m a t i c i z e d d - c~p l a n e i n d i c a t e t h e a p p r o x i m a t e l o c a t i o n o f t h e d r u gt r e a t e d a n i m a l s . T h e s a l i n e c o n t r o l a n i m a l i s l o c a t e d a t t h eo r i g i n .T h e l o c o m o t o r p a t h s o f i n d i v i d u a l a n i m a l s a r e d is -p l a y e d b y t h e l i n es c o n n e c t i n g c o n s e c u t i v e ( x , y ) lo c a t i o n si n th e B P M . T h e r e s o l u t i o n l i m i t o f t h i s i n s t r u m e n t , a g r i do f 7 x 1 5 p o s s i b l e l o c a t i o n s , i s e v i d e n t i n t h e g r a p h ' ss q u a r e p a t t e r n s . T h e p a t h s a r e d i s p l a y e d f o r 6 0 m i n o fu n c o n d i t i o n e d m o t o r a c ti v it y in t h e B P M c h a m b e r . In -s t e a d o f p l o t t i n g t h e e x a c t ( x , y ) l o c a t i o n o f t h e a n i m a l s ,t h e d i s p l a y e d ( x , y ) p o s i t i o n is o b t a i n e d b y c h o o s i n g r a n -do m ly f r om a r a nge of va lues ( x _+ 0 .4 , y _+ 0 .4) sur r o un d-i n g t h e e x a c t l o c a ti o n . T h i s p r o c e d u r e a v o i d s r e t r a c i n g t h es a m e l i n e s a n d t h e r e b y f a c il i t a t e s t h e v i s u a l r e c o g n i t i o n o ff r e q u e n t l y v is i t e d a r e a s . T h e p a t h s t r u c t u r e o f t h e s a l i n ec o n t r o l a n i m a l i s c h a r a c t e ri z e d b y f r e q u e n t l y v i si t ed l o c a -t i o n s, w h i c h h a v e b e e n c a l l e d t h e h o m e a r e a ( G e y e r t 9 9 0 ),a s w el l a s p re f e r re d p a t h s t h r o u g h o u t t h e B P M c h a m b e r .S t r a i g h t m o v e m e n t s c a n b e f o u n d a l o n g t h e l o n g w a l ls o ft h e B P M e n c l o s u r e , w h i l e l o c a l m o v e m e n t s a r e o b s e r v e dp a r t i c u l a r ly a l o n g t h e s h o r t w a l l s a n d i n t h e c o r n e r s o f t h ec h a m b e r . W h i l e t h e q u i n p i r o l e - a n d n o m i f e n s i n e - t r e a t e da n i m a l s d i f f er v a s t l y in t h e a m o u n t o f m o t o r a c t i v i ty

e x h i b i t e d ( 1 7 0 5 a n d 9 7 4 5 m i c r o - e v e n t c o u n t s d u r i n g t h ef i rs t 6 0 r a i n , r e s p e c ti v e l y ) , t h e p a t h p a t t e r n s s h a r e s o m es i m i l a ri t ie s . S p e c i f i c a ll y , l o c a l a r e a s o f i n c r e a s e d m o v e -m e n t d e n s i t y r e f le c t f r e q u e n t l o c a l m o v e m e n t s e q u e n c esc h a r a c t e r i z e d b y h i g h l o c a l d i v a l u e s . I n a d d i t i o n , o c c a -s i o n a l l o n g s t r a i g h t m o v e m e n t s c a n b e o b s e r v e d a l o n g t h ew a l ls o f t h e B P M c h a m b e r . S i m i l a rl y , t h e D O I - a n d R U2 4 9 6 9 - t r e a t e d a n i m a l s a r e d i s t i n g u i s h e d b y t h e i r a m o u n to f m o t o r a c t i v it y (3 7 9 3 a n d 1 0 3 16 m i c r o - e v e n t c o u n t sd u r i n g t h e f i r s t 6 0 m i n , r e s p e c ti v e l y ). T h e m o v e m e n t p a t -t e r n s o f b o t h a n i m a l s, h o w e v e r , a r e d o m i n a t e d b y l o n gs t r a ig h t p a t h s p r i m a r i l y a l o n g t h e w a ll s o f t h e B P M c h a m -b e r . C o r r e s p o n d i n g l y , m o v e m e n t s i n t o t h e c e n t e r a r e a o ft h e e n c l o s u r e a r e i n f r e q u e n t .T h e o v e r a l l p a t h s t r u c t u r e f o r q u i n p i r o l e - a n dn o m i f e n s i n e - t r e a t e d a n i m a l s y i e l d s i m i l a r a v e r a g ed va lues , o f 1 .71 an d 1 .70 r espec t ive ly . I n co nt r as t , the pa ths t r u c t u r e o f D O I - a n d R U 2 4 9 6 9 - t r e a t e d a n i m a l s r e s u l te din aver a ge d va lue s of 1 .48 an d 1 .49 , r espec t ive ly . Th ea v e r a g e d , t h e r e f o r e , d i s t i n g u i s h e s t h e d i f f e re n t p a t h s t r u c -t u r e s o f d r u g s t h a t e i t h e r r e d u c e o r i n c r e a se u n c o n d i -t i o n e d m o t o r a c t i v i t y . H o w e v e r , c l o s e r e x a m i n a t i o n o ft h e s e p a t h s t r u c t u r e s a l s o d i s c l o s e s d if f e re n c e s b o t h b e -t w e e n q u i n p i r o l e a n d n o m i f e n s i n e a n d b e t w e e n D O I a n dR U 2 4 96 9 . F o r e x a m p l e , l o c a ti o n s o f h i g h l y c ir c u m s c r i b e dm o v e m e n t s s e t a p a r t t h e p a t h s t r u c t u r e o f t h e n o m i f e n s i n ea n i m a l f r o m t h e p a t h s t r u c t u r e o f t h e q u i n p i r o l e a n i m a l .W h i l e t h i s d e s c r i p t i v e a s s e s s m e n t o f th e s e s u b t l e p a t hc h a r a c t e r i s t i c s i s c o m p l i c a t e d b y t h e c o n f o u n d i n g i n f l u -e n c e o f t h e d i ff e re n c e i n t h e a m o u n t o f m o t o r a c t i v i ty , t h es p e c t r u m o f s p a t i a l s c a l in g e x p o n e n t s , f ( d ) , e n a b l e sa q u a n t i f i c a t i o n o f t h e p a t h s t r u c t u r e i n d e p e n d e n t o f th ea m o u n t o f m o t o r a c ti v it y .

T h e f ( d ) f u n c t i o n s f o r a l l f i v e a n i m a l s a r e d i s p l a y e dw i t h t h e c o r r e s p o n d i n g s y m b o l s a t t h e p o i n t s w h e r e t h ef u n c t i o n h a s b e e n e v a l u a t e d u s i n g t h e q - d e p e n d e n t m a s ss c a li n g e x p o n e n t . T y p i c a l l y , t h e s e f u n c t i o n s r a n g e f r o m1 .0 _< d i < 1 . 5 , d e s c r i b i n g e x t r e m e l y s t r a i g h t o r d i r e c t e dmo vem ent s , to 2 .0 _< d l < 2 .5, r e f lec t ing h igh ly c i r cu m-s c r i b e d m o v e m e n t s . T h e f ( d ) f u n c t i o n f o r t h e s a l i n ec o n t r o l a n i m a l i s s h o w n w i t h o u t a s y m b o l . W h i l e t h eq u i n p i r o l e a n d n o m i f e n s i n e tr e a t m e n t s s h if t t h e f ( d ) f u n c -t i o n t o t h e r ig h t , D O I a n d R U 2 4 9 6 9 t r e a t m e n t s s h if t t h ef ( d ) f u n c t i o n t o t h e l e f t . I n b o t h c a s e s , t h e l e f t a s c e n d i n gb r a n c h o f t h e f ( d ) f u n c t i o n s o f l o w d i v al u e s o v e r l ap . T h u s ,t h e q u i n p i r o l e - a n d n o m i f e n s i n e - t r e a t e d r a t s a r e s i m i l a rw i t h r e g a r d t o t h e c o n t r i b u t i o n s o f m i c r o - e v e n t s e g m e n t sw i t h s t r a i g h t m o v e m e n t s . S i m i l a r l y , t h e r e l a t i v e c o n t r i b u -t i o n s o f s tr a i g h t m o v e m e n t s d o e s n o t d i ff e r f o r t h e D O I -a n d R U 2 4 9 6 9 t r e a t m e n t s . H o w e v e r , t h e r ig h t d e s c e n d i n gb r a n c h o f th e f ( d ) f u n c t i o n r e v e a l s t h a t t h e n o m i f e n s i n e -t r e a t e d a n i m a l e x h i b i t e d a n i n c r e a s e d c o n t r i b u t i o n o fh i g h l y l o c a l m o v e m e n t s c o m p a r e d t o t h e q u i n p i r o l e -t r e a t e d a n i m a l . H i g h l y l o c a l m o v e m e n t s a l s o c o n t r i b u t em o r e t o t h e o v e r a ll p a t h s t r u c t u r e f o r t h e D O I a n i m a lr e l a t i v e to t h e R U 2 4 9 6 9 a n i m a l . I n b o t h c a s e s, th e s e l o c a ld i f f e r ences a r e w e l l w i th in th e g lob a l sh i f t s o f the f ( d )f u n c t i o n s . T h e s e d i f f e r e n c e s w i t h i n t h e o v e r a l l s h i f t o f t h ef u n c t i o n s i n d i c a t e t h a t , a l t h o u g h r e l a t i v e d i ff e r e n c e s e x i s tb e t w e e n q u i n p i ro l e a n d n o m i f en s i ne o r D O I a n d R U2 4 9 6 9 , t h e s e c h a n g e s a r e b e l o w a n d a b o v e t h e r e s p e c t i v ec o n t r i b u t i o n s o f di v a l u e s f o r t h e s a l in e a n i m a l .


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rat behavior detection and video system limitations

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