NEUROBIOLOGY OF LEARNING AND MEMORY 65, 82–90 (1996)Article No. 0009

Micro- and Macrostructure of Learning in Active Avoidance:A Quantitative Approach

ALESSANDRO GIULIANI, ANNA MARIA MANCINI, ORLANDO GHIRARDI, MARIA TERESA RAMACCI,TATIANA VORONINA,* PAOLO SIRABELLA,† AND ALFREDO COLOSIMO†,1

Institute for Research on Senescence Sigma-Tau Pomezia, Rome, Italy; *Institute of Pharmacology, Russian Academy of Sciences,Moscow, Russia; and †Department of Biochemistry, University of Rome ‘‘La Sapienza,’’ Rome, Italy

time and spatial scales, thus raising major inter-The dynamics of learning in the Active Avoidance test pretative problems (Aon & Cortassa, 1993; Frau-

was analyzed at the trials level as well as at the level of enfelder, Sligar, & Wolynes, 1991; Savageau, 1991;daily sessions, each comprising numerous trials. The two Selz & Mandell, 1992; Yates, 1982). In the case ofscales (large scale for the sessions and small scale for the biological systems, the problem of analyzing multi-trials) were demonstrated to be mutually independent. ple scale dynamics was faced in the conformationalThe intermediate derived scales (blocks of trials) were

analysis of proteins (Frauenfelder et al., 1991) andfound consistent among themselves and with small scaleelectroencephalography fields (Selz & Mandell,but independent of the large one. Moreover, the two ex-1992; Basar, 1990; Babloyantz & Destexhe, 1986).treme scales were kinetically discriminable. These results

The reference physical system for the study ofpoint to the existence of two independent mechanisms forlarge and small scale learning together with the need to these phenomena was the spin-glass model. Thispostulate a consolidation process during the rest period. model is simple enough to support concepts and the-q 1996 Academic Press, Inc. ory generation and is also endowed with a suffi-

ciently rich dynamics to simulate the behavior ofbiological systems (Stein, 1989; Giuliani, Capuani,

INTRODUCTION Miccheli, Aureli, Ramacci, & Conti, 1994).In this work we applied a methodological approach

The vast majority of physical phenomena have derived from the study of spin glasses and, more incharacteristic time and spatial scales. With regard general, of the Ising models of magnetization (Wil-to spatial dimensions, this feature derives from the son, 1979) in order to study the dynamics of learninghuge diversity among the fundamental force scal- in an Active Avoidance paradigm (Ghirardi, Capri-ings: it is sufficient to examine the difference be- oli, Milano, Giuliani, Ramacci, & Angelucci, 1992;tween the scale relative to the electrostatic interac- McNamara, Benignus, Benignus, & Miller, 1977) attion between two atoms and the scale of the gravita- different time scales.tional phenomena. The separability of the scales This approach highlighted the existence of two dis-makes it possible to concentrate on a single kind tinct learning dynamics on a small and a large timeof interaction, disregarding the other ones (Wilson, scale, respectively.1979; West, 1985). Kinetic analysis allowed us to quantify the time

Likewise, with regard to the time scales, kinetic constants of these two learning processes.processes with very different time constants do notappreciably interact, thus allowing the researcher to

MATERIALS AND METHODSneglect out-of-scale kinetics (Wilson, 1979).Biological phenomena typically involve multiple

Experimental Methods

The experimental data were derived from two in-1 Address all the correspondance to Alessandro Giuliani, Insti-dependent experiments: experiment A, performedtute for Research on Senescence, Sigma-Tau, Via Pontina Km.

30.400, 00040 Pomezia (Roma) Italy. Fax: 06/9107651. using 14 nine-month-old female mice from Stolbo-

821074-7427/96 $12.00Copyright q 1996 by Academic Press, Inc.All rights of reproduction in any form reserved.

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83A QUANTITATIVE APPROACH TO ACTIVE AVOIDANCE

vaya farm and experiment B, performed on 19 five- From the application of the renormalization groupwe obtain, for each individual: (a) the degree of corre-month-old male Wistar rats from Charles River.

Both the experiments made use of a conventional lation on the small scale between time and latency(Pearson’s r between progressive number of trial andshuttle box (U. Basile, Italia) divided into two identi-

cal compartments by a partition provided with an latency Å CORRSS); (b) the degree of correlation onthe large scale between time and latency (Pearson’sopening between them to allow communication. Foot

shock was delivered through the stainless steel grid r between progressive number of session and meanlatency of the session Å CORRLS); (c) the degree offloor. Trials were programmed on a schedule of con-

ditioned stimulus (CS Å light on), followed 3 s later correlation on the intermediate scales between timeand latency (Pearson’s r between progressive num-by an unconditioned stimulus (US Å a 4-s, 0.2-mA

electric shock) (Ghirardi et al., 1992). ber of block and mean latency of the block ÅCORMiS).In experiment A, six consecutive daily sessions of

40 trials were performed. The intertrial intervals For experiment A the intermediate scales con-sisted of 4, 5, 8, and 10 trials, respectively, and forwere 30 s long: the animal was placed in one com-

partment and the start of the trial was signaled by experiment B of 4, 5, and 7 trials, respectively.the CS followed by the delivery of the US. Experi- Principal component analysis. The variables cor-ment B followed an identical schedule but consisted responding to the degree of correlation between timeof seven daily sessions of 20 trials with an intertrial and performance at the different scales were ana-interval of 1 min. In both cases the measured vari- lyzed by principal component analysis (PCA).able was the time to escape from the electrified com- PCA is a well-known multivariate techniquepartment after the delivery of CS (Escape Latency widely used in biology and psychology (Benzecri,or Latency). The measurement unit was 0.1 s. 1980; Benigni & Giuliani, 1986; Giuliani et al., 1991;

Paulus & Geyer, 1993; Giuliani, Ghirardi, Caprioli,Data Analysis Methods Di Serio, Ramacci, & Angelucci, 1994). Referring to

existing literature for the explanation of PCA (Leb-Renormalization group. This name is used to re- art, Morineau, & Warwick, 1984; Preisendorfer,fer to a family of mathematical procedures designed 1988), it is sufficient here to state that principal com-to study phenomena taking place on multiple scales ponents are variables derived from the experimental(Wilson, 1979). measures (in our case the individual correlation coef-Each step of the renormalization procedure con- ficients at the different time scales) which give asists of averaging at a particular scale; at each step representation of the original data set that is devoidthe individual values come from an averaging of the of redundancy. This goal is obtained projecting thepreceding level. The averaging axiomatically corre- data set into a space spanned by new, mutually or-sponds to the elimination of fluctuations in order to thogonal axes (components) explaining most of theallow only the central tendency to survive. At each data set variability (Lebart et al., 1984; Preisend-step, the information arrives at a particular level orfer, 1988).with the variability pertaining to the preceding lev- The number of principal components necessary toels filtered out. Therefore, it becomes possible to describe a system with a significant level of accuracystudy the features of the system typical of each scale can be equated to the number of significant degreesat which the averaging was performed. of freedom of the system itself and can be expressedIn our case the feature of interest was the degree as the number of dynamically independent subsys-of correlation between the time and the escape la- tems (Vautard, Yiou, & Ghil, 1992; Linsker, 1988;tency. This correlation can be interpreted as the de- Preisendorfer, 1988; Paulus & Geyer, 1993).gree of order imposed by time (learning) on the be- The correlation coefficients between componentshavior of each animal (Banerjee, Sibbald, & Maze, and original variables (factor loadings) make it pos-1990). sible to assign a meaning to the components (Bartho-The correlation was studied at the trials scale lomew, 1984; Lebart et al., 1984).(small scale), at the sessions scale (large scale), andat intermediate scales corresponding to averages Kinetic analysis. The basic contribution made by

kinetic analysis to the investigation of natural phe-over blocks of trials. Tables 1a, 1b, and 1c report theapplication of the renormalization group to our data. nomena consists in: (i) the characterization of any

observed process in the time dimension by means ofThe tables refer to experiment A, although experi-ment B was treated in a completely superimposable one or more time constants directly related to char-

acteristic half-life times (e.g., milliseconds for light-manner.

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84 GIULIANI ET AL.

TABLE 1a The Renormalization Group Approach

Computation of the large scale correlations

Experiment A

Animal j

1

2

1

2

∫∫∫∫∫∫∫∫40

6 .

∫∫∫∫

Tria

ls

Sess

ions

Computation of the mean valueof Latency over the 40 trials. Thisvalue is considered the Latencyrelative to the correspondent(i) session: L(i)

Computation of the correlation coeÓcient betweenthe Number of Session and L(i) 5

Value of CORRLS for Animal j

TABLE 1b The Renormalization Group Approach

Computation of the small scale correlations

Experiment A

Animal j

1

2

1

2

∫∫∫∫∫∫∫∫40

6.

∫∫∫∫

Tria

ls

Sess

ions

Computation of the correlationcoeÓcient between the Number ofTrial and Latency. For each i sessionwe obtain a separate correlationcoeÓcient (CORRSSi).

Mean of the CORRSSi over the six sessions 5

Value of CORRSS for Animal j

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85A QUANTITATIVE APPROACH TO ACTIVE AVOIDANCE

TABLE 1c The Renormalization Group Approach

Computation of the intermediate scale correlations

Experiment A

Animal j

1

2

1

2

∫∫∫∫∫∫∫∫40

6 .

∫∫∫∫

Tria

ls

1

2

∫∫k

Bloc

ks

Sess

ions

Computation of the mean value of Latency for eachBlock of k Trials. This value is considered the Latencyrelative to the correspondent Block (L(b))

In each session we have P blocks with P 5 40/k. Foreach (i) session we compute the correlation coefficient betweenNumber of Block and L(b): CORMkSi

Mean value of CORMkSi over the six sessions 5

Value of CORMkS for Animal j

ning or hours for tides); (ii) the identification, in the RESULTScase of complex processes, of a minimum number ofunderlying subprocesses on the basis of a corre-

Table 2a reports the correlation values at the dif-sponding number of distinguishable time constantsferent time scales for each animal in experiment A.(e.g., in the allosteric regulation of an enzymatic re-It is evident from the table that all the animals, withaction, the—relatively fast—binding of the effectorthe sole exception of animal No. 12, show a highto the regulatory site and the—relatively slow—degree of order along the sessions (mean value ofconformational transition of the macromolecule in-CORRLS Å 00.71), while on the other time scalesfluencing the reactivity of the catalytic site).ordering induced by learning is absent or very weak.In very general terms, choosing exponential func-

Averaging over the trials eliminated the smalltions to fit the observed time course of the processscale fluctuations, retaining only the central ten-under investigation provides a straightforward esti-dency of each session. These central values aremate of the corresponding time constants. In thehighly consistent and allow the learning dynamics topresent case, the learning dynamics of animals, asbe appreciated. Learning acts as an order parametershown by the decrease of latency time during trials(Preisendorfer, 1988; Stein, 1989; Basar, 1983), ori-and sessions, was described by exponential functionsenting the values of the escape latency (highly nega-in view of the following facts: (i) a large number oftive correlations) but only at the large scale of thebiological (Boyer, 1970) and psychological (Shepard,sessions, while at the small and at the intermediate1987; Killeen, 1992) phenomena are governed by ex-scales the effect of the order parameter is hardlyponential laws; (ii) the alternative and apparentlydistinguishable from the fluctuations at the level ofsimpler linear model, besides lacking any directindividual data (Wilson, 1979).physical interpretation, showed no significant im-

The analysis of the relations that hold between theprovement in fit; (iii) it is well documented that thedifferent observation scales enables us to establishlearning curve tends to reach a plateau as the num-whether the degree of order imposed by learning,ber of training sessions increases, and the way aalthough having very different values at the differ-system approaches equilibrium or stationary states

is typically governed by exponential laws. ent scales, could be considered an unitary phenome-

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86 GIULIANI ET AL.

TABLE 2aValues of the Correlations at the Different Time Scales for Each Animal

of Experiment A with Descriptive Statistics

CORRSS CORM4S CORM5S CORM8S CORM10S CORRLS

00.04 00.153 00.052 00.127 00.053 00.9200.37 00.617 00.518 00.585 00.520 00.8500.44 00.628 00.618 00.608 00.592 00.95

0.09 0.195 0.185 0.175 0.135 00.9000.12 00.185 00.170 00.172 00.100 00.9600.15 00.232 00.252 00.248 00.237 00.6600.08 00.182 00.293 00.158 00.118 00.6000.12 0.267 00.268 00.218 00.205 00.4200.24 00.407 00.413 00.382 00.352 00.8000.05 00.108 00.165 00.140 00.133 00.9600.13 00.315 00.240 00.198 00.427 00.8100.18 00.288 00.287 00.270 00.253 0.2900.40 00.642 00.688 00.622 00.595 00.6000.30 00.708 00.665 00.565 00.480 00.86

Mean 00.181 00.286 00.317 00.294 00.281 00.714SD 0.152 0.298 0.245 0.231 0.220 0.332

Note. This table is the raw data matrix for the subsequent elaborations (correlation matrix and PCA).

non. If so, the variables describing the amount of The problem is if, at the individual level, the ani-mals that learn better at the small scale level areorder at the different scales must correlate.

This is a crucial point: as we will see by the appli- the animals that learn better at the large scale, too.In other words, the problem is to discover if thecation of kinetic analysis, there is a significant gen-

eral effect of trials on learning as well as of sessions. learning at the small scale is uniformable to the

TABLE 2bValues of the Correlations at the Different Time Scales for Each Animal

of Experiment B with Descriptive Statistics

CORRSS CORM4S CORM5S CORM7S CORRLS

00.094 00.20 00.168 00.200 00.9300.030 00.16 00.210 00.120 00.5300.004 0.02 00.055 00.011 00.1000.064 00.12 00.100 00.095 00.5100.078 00.12 0.090 00.093 00.5500.164 00.36 00.385 00.296 00.7900.410 00.81 00.820 00.666 00.95

0.091 0.10 0.235 0.145 00.710.063 0.20 0.208 0.118 00.88

00.187 00.52 00.428 00.428 00.910.111 0.27 0.187 0.171 00.870.196 0.33 0.327 0.333 00.38

00.333 00.61 00.662 00.545 00.6000.120 00.34 00.232 00.181 00.82

0.090 0.08 0.202 0.131 00.220.058 0.43 0.257 0.310 00.82

00.077 00.26 00.163 00.140 00.8400.600 00.12 0.042 0.080 0.0600.063 00.06 00.020 00.055 00.80

Mean 00.057 00.119 00.089 00.081 00.639SD 0.149 0.323 0.317 0.270 0.297

Note. This table is the raw data matrix for the subsequent elaborations (correlation matrix and PCA).

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87A QUANTITATIVE APPROACH TO ACTIVE AVOIDANCE

TABLE 3aCorrelation Matrix Among the Individual Correlations at the Different Time Scales for Experiment A

CORRLS CORRSS CORM4S CORM5S CORM8S CORM10S

CORRLS 1.000 00.023 0.116 00.059 00.011 00.016CORRSS 1.000 0.864 0.947 0.982 0.947CORM4S 1.000 0.852 0.880 0.853CORM5S 1.000 0.974 0.929CORM8S 1.000 0.943CORM10S 1.000

large scale one, even if the small scale learning is the relation between the large time scale and theothers (Aon & Cortassa, 1993).obscured by noise effects.

The low absolute values of correlation on the smallTable 3a reports the correlation matrix among thescale match the high within-individual variability ofmeasured variables: it is immediately apparent thatthe latency over the trials. Figure 1 shows clearlythe degree of order on the small scale (CORRSS)that high levels of noise are persistent even at thecorrelates with the orderings relative to the interme-last sessions, when the animals have learned thediate scales (CORMiS), which are in turn mutuallytask.intercorrelated. Conversely, the degree of order on

In order to get a global quantification of the dy-the large scale (CORRLS) is independent of the de-namics of learning on the large and small scales wegree of order at the lower levels. PCA confirms thisfitted an exponential model to the variation of meanobservation generating a two-components descrip-escape latency over the sessions and over the trialstion of the data set: the first component is linked to(Shepard, 1987). This analysis implied an averagingthe small and intermediate scale orderings and theover the entire set of data with the subsequent elimi-second one to the large scale ordering (Table 4a).nation of the variability. As for the small scale theThese two components exhaustively describe theaveraging eliminates the heterogeneity of the indi-data set (95% of explained variability) and representvidual time-latency relations (Fig. 1).two independent aspects of the animals’ response to

The exponential model generates an estimate ofthe test.the time constant (B) of 0.102 sessions01. Bearing inThe principal components correspond to the inde-mind that the sessions are spaced out at 24-h inter-pendent modes of the studied dynamics (Softky &vals B corresponds to 6.94 ∗ 1005 min01. Figure 2Kammen, 1991; Anderson, Silverstein, Ritz, & Ran-reports the graph of the function.dall, 1977; Vautard et al., 1992). The orderings rela-

The same model applied to the trials scale givestive to the small and intermediate scales are heavilyan estimate of B of 0.005 trials01 corresponding toloaded on the first component. This implies that they5 ∗ 1003 min01. Figure 3 reports the graph of thecorrespond to the same process. The large scale or-function. It is worth noting that the experimentaldering is loaded on the second component (orthogo-

nal to the first one), thus being independent of thesmall and intermediate scale learning.

TABLE 4aThis result highlights the strong nonlinearity ofLoadings of the Original Variables on the

Components for Experiment A

PRIN1 PRIN2TABLE 3bCorrelation Matrix among the Individual Correla-

CORRLS 0.000 0.998tions at the Different Time Scales for Experiment BCORRSS 0.982 00.028CORM4S 0.919 0.140CORRLS CORRSS CORM4S CORM5S CORM7SCORM5S 0.973 00.067CORM8S 0.989 00.016CORRLS 1.000 00.290 0.236 0.303 0.345CORM10S 0.967 00.020CORRSS 1.000 0.949 0.956 0.961

CORM4S 1.000 0.954 0.974Note. The loadings are the correlation coefficients of the originalCORM5S 1.000 0.975

variables with the components. The two components space ex-CORM7S 1.000plains 95% of the original variance.

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88 GIULIANI ET AL.

TABLE 4b The biological interpretation of this result is farLoadings of the Original Variables on the more complicated. The nonlinearity of the passage

Components for Experiment B from the small to the large scale can depend on manyfactors.

PRIN1 PRIN2 A plausible explanation could make this nonline-arity derive from the change of meaning of escapeCORRLS 0.384 0.923latency due to the experimental scheme. This changeCORRSS 0.976 00.092

CORM4S 0.974 00.152 of meaning relies on the observation that variationsCORM5S 0.982 00.080 between 0 and 3 s of latency have no adaptive valueCORM7S 0.993 00.039 (and thus could not be learned) because all the val-

ues of latency within this range correspond to avoid-Note. The loadings are the correlation coefficients of the originalances of the painful stimulus. This interpretation isvariables with the components. The two component space ex-

plains 98% of the original variance. at odds with the results of the first three sessions,in which we observe an almost complete absence ofavoidance. Moreover, this hypothesis implies a de-points of Fig. 3 incorporate the large scale learningcreasing value of CORRSS along the sessions andas a systematic effect. This feature is recorded by

the time-independent parameter (A) which is lowerthan the corresponding parameter on the large scale.

These results confirm that the animals learnthrough the trials, but this learning is completelyunrelated to the large scale one. The large scalelearning is far more efficient than the small scaleone because, although being slower, it works for amuch longer time than the small scale one.

Experiment B was analyzed using the same proce-dure as that for experiment A and gave coincidentresults, as evidenced by Tables 2b–4b confirmingthe independence between small and large scalesand the consistency between the small and the inter-mediate scales.

The low individual level of correlation on the smallscale and the independence between the small andlarge scales made evident by the renormalizationapproach make the kinetic analysis of this experi-ment unnecessary.

DISCUSSION

Our data highlight the existence of two separateand independent dynamics for learning on small andlarge time scales. The derived intermediate scalesproved to be linearly consistent with the small scale,while learning through the sessions evidenced quali-tatively different features. From a descriptive pointof view this implies a consolidation of learning dur-ing the intersession intervals. This consolidation

FIG. 1. Individual learning through trials and sessions. Theprocess introduces a strong nonlinearity in the pas- latency times (0.1-s units) observed in animals 3 and 4 throughoutsage from the trials to the sessions scale. From a the whole experiment is reported as a function of the session

number. Within each session the points representing single trialsquantitative point of view, large scale learning isare chronologically ordered on an arbitrary scale. The full linesmore efficient than small scale, and the value of theindicate linear regressions carried out over the latencies in eachperformance reached is driven by the large scale or-session and their slope reflects the rate of small scale learning.der. The substantial difference between the time It is worth noting (1) the random distribution of positive and

constants referring to the two processes is consistent negative slopes on the small scale and (2) the overall decreasingof latency throughout the sessions (large scale learning).with the lack of correlation between them.

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89A QUANTITATIVE APPROACH TO ACTIVE AVOIDANCE

we did not observe any such trend. Last, we did notobserve any significant trend to concentrate theavoidance responses in more advanced trials (datanot shown).

From a purely theoretical perspective it is worthnoting that the coexistence of a small scale chaoticdynamics with an ordered large scale structure wasfound to ameliorate the learning efficiency of artifi-cial neural networks (Basti & Perrone, 1989;Mpitsos & Burton, 1992; Tsuda, 1992) and examplesof chaotic dynamics came from the analysis of EEGtracks (Skarda & Freeman, 1987; Basar, 1990).

The existence of two separate scales of learningin a different but related experimental context wasclearly evidenced by Karni and Sagi (1993).

A system which learns by maintaining a basiclevel of variability together with the progressive

FIG. 3. Dynamics of small scale learning. The latency re-large scale ordering necessary to solve the task corded in each of the 40 trials included in each session has beenproved better at generalizing than a globally ordered averaged over the animals and over the sessions and plotted as

a function of the trial number. The full line represents the bestsystem (Mpitsos & Burton, 1992; Tsuda, 1992; Abra-fit of the data obtained by a simple exponential function Y Å Aham & Shaw, 1984). Moreover, the existence of an∗ exp(0B ∗ X) with A Å 49.74 latency units (0.1 s) and B Å 0.005irreducible level of variability is linked to the extinc-trials01 correspondent to 5 ∗ 1003 min01.

tion of learned behaviors (Tsuda, 1992; Basti & Per-rone, 1989; Amit, 1989).

to extinguish the learned response (Isaacson et al.,In the Active Avoidance frame there is evidence1961).(Isaacson, Douglas, & Moore, 1961) that hippocam-

Therefore, it is plausible to postulate a functionalpus-ablated rats show a clear improvement of learn-role of the small scale noise in terms of extinction ofing ability with respect to sham-operated animals.learned responses.The hippocampus-ablated animals show a clear

In terms of molecular correlates of learning, ourlearning dynamics at the trials scale, too, but faildata imply the need for conjecturing dynamicallyindependent mechanisms for the different aspectsof learning (Selz & Mandell, 1992), thus ruling outsimplistic hypotheses of the existence of a single ba-sic molecular correlate of learning (Nicoll, Kauer, &Malenka, 1988).

From an applications point of view, the lack ofdependence between large and small scale learningcasts doubt on the validity of many pharmacologicaltesting strategies making use of Active Avoidance.Methodologies based on daily sessions measure dif-ferent events with respect to the single session-basedexperiments, thus providing different informationon the possible effects of a drug.

Some preliminary data regarding the Morris Wa-ter Maze we obtained in our laboratory confirm theexistence of two dynamically independent scales forlearning at trials (minutes) and sessions (days) lev-els. These preliminary results point to a generalvalue of this finding not restricted to the ActiveFIG. 2. Dynamics of large scale learning. The latency re-Avoidance paradigm.corded in each session averaged for all the animals has been

reported as function of sessions. The full line represents the bestREFERENCESfit to the data obtained by a simple exponential function Y Å A

∗ exp(0B ∗ X), where A Å 63.19 latency units (0.1 s) and B Å Abraham, R. H., & Shaw, C. D. (1984). The geometry of behavior,Part 2: Chaotic behavior. Santa Cruz, CA: Aerial Press.0.102 sessions01 correspondent to 6.94 ∗ 1005 min01.

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90 GIULIANI ET AL.

Amit, D. (1989). Modelling brain function: The world of attractor Isaacson, R. L., Douglas, R. J., & Moore, R. Y. (1961). The effectof radical hippocampal ablation on acquisition of avoidanceneural networks. Cambridge, MA: Cambridge Univ. Press.response. Journal of Comparative Physiology and Psychol-Anderson, J. A., Silverstein, J. W., Ritz, S. A., & Randall, S. J.ogy, 54, 625–628.(1977). Distinctive features, categorial perception, and proba-

bility learning: Some applications of a neural model. Psycho- Lebart, L., Morineau, A., & Warwick, K. M. (1984). Multivariatelogical Review, 5(84), 413–451. descriptive statistical analysis. New York: Wiley.

Aon, M. A., & Cortassa, S. (1993). An allometric interpretation Linsker, R. (1988). Self organization in a perceptual network.of the spatio-temporal organization of molecular and cellular Computer, March, 105–117.processes. Molecular and Cellular Biochemistry, 1(120), 1– McNamara, M. C., Benignus, G., Benignus, V. A., & Miller, A. T.,13. Jr. (1977). Active and passive avoidance learning in rats as

Babloyantz, A., & Destexhe, A. (1986). Low-dimensional chaos in a function of age. Experimental Aging Research, 3, 3–16.an instance of epilepsy. Proceedings of the National Academy Mpitsos, G. J., & Burton, R. M., Jr. (1992). Convergence andof Science USA, 83, 3513–3517. divergence in neural networks: Processing of chaos and bio-

Banerjee, S., Sibbald, P., & Maze, J. (1990). Quantifying the dy- logical analogy. Neural Networks, 5, 605–625.namics of order and organization in biological systems. Jour- Nicoll, R. A., Kauer, J. A., & Malenka, R. C. (1988). The currentnal of Theoretical Biology, 143, 91–111. excitement in long term potentiation. Neuron, 1, 2.

Bartholomew, D. J. (1984). The foundation of factor analysis. Bio- Paulus, M. P., & Geyer, M. A. (1993). Three independent factorsmetrika, 71, 221–232. characterize spontaneous rat motor activity. Behavioral

Basar, E. (1983). Toward a physical approach to integrative physi- Brain Research, 53, 11–20.ology. I. Brain dynamics and physical causality. American Preisendorfer, R. W. (1988). Principal component analysis in me-Journal of Physiology, 245, R510–R533. teorology and oceanography. Development in atmospheric sci-

Basar, E. (1990). Chaos in brain function. Heidelberg: Springer- ence, 17. Amsterdam: Elsevier.Verlag.

Savageau, M. A. (1991). Reconstructionist molecular biology. TheBasti, G., & Perrone, A. (1989). On the cognitive function of deter- New Biologist 3(2), 190–197.

ministic chaos in neural networks. Proceedings of IEEE/Selz, K. A., & Mandell, A. J. (1992). Critical coherence and charac-INNS ISCNN.

teristic times in brain stem neuronal discharge patterns. InBenigni, R., & Giuliani, A. (1986). A new insight into chemical Single neuron computation. Neural nets: Foundations to ap-

mutagenesis by multivariate data analysis. Journal of Theo- plications. (Chap. 20, pp. 525–560). New York: Academicretical Biology, 121(4), 477–486. Press.

Benzecri, J. P. (1980). La pratique del l’ analyse des donnes. Paris: Shepard, R. N. (1987). Toward a universal law of generalizationDunod. for psychological science. Science 237, 1317–1323.

Boyer, P. D. (1970). The enzyme, Vol. II, Kinetics and mechanism Skarda, C. A., & Freeman, W. J. (1987). How brains make chaos3rd. ed. New York: Academic Press. in order to make sense of the world. Behavior and Brain

Frauenfelder, H., Sligar, S. G., & Wolynes, P. G. (1991). The en- Science, 10(2), 161–190.ergy landscapes and motions of proteins. Science, 254, 1598–

Softky, W. R., & Kammen, D. M. (1991). Correlations in high1603.dimensional or asymmetric data sets: Hebbian neuronal pro-

Ghirardi, O., Caprioli, A., Milano, S., Giuliani, A., Ramacci, cessing. Neural Networks, 4, 337–347.M. T., & Angelucci, L. (1992). Active avoidance learning in old

Stein, D. L. (1989). Spin glasses. Scientific American, July, 36–rats chronically treated with levocarnitine acetyl. Physiology42.and Behavior, 52, 185–187.

Tsuda, I. (1992). Dynamic link of memory—Chaotic memory mapGiuliani, A., Capuani, G., Miccheli, A., Aureli, T., Ramacci,in nonequilibrium neural networks. Neural Networks, 5,M. T., & Conti, F. (1991). Multivariate data analysis in bio-313–326.chemistry: A new integrative approach to metabolic control

Vautard, R., Yiou, P., & Ghil, M. (1992). Singular-spectrum analy-in brain aging. Cellular and Molecular Biology, 37(6), 631–sis: A toolkit for short, noisy chaotic signals. Physica 58D,638.95–126.Giuliani, A., Ghirardi, O., Caprioli, A., Di Serio, S., Ramacci,

West, B. J. (1985). An essay on the importance of being non linear.M. T., & Angelucci, L. (1994). Multivariate analysis of behav-In Lecture notes in biomathematics, 62. Heidelberg: Springer-ioral aging highlights some unexpected features of complexVerlag.systems organization. Behavioral and Neural Biology, 61,

110–122. Wilson, K. G. (1979). Problems in physics with many scales oflength. Scientific American, August, 140–157.Karni, A., & Sagi, D. (1993). The time course of learning a visual

skill. Nature, 365(16), 250–252. Yates, F. E. (1982). The 10th J. A. F. Stevenson memorial lectureoutline of a physical theory of physiological systems. Cana-Killeen, P. R. (1992). Mechanics of the animate. Journal of the

Experimental Analysis of Behavior, 57, 429–463. dian Journal of Physiology and Pharmacology, 60, 217–248.

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