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In the CA1 area of the hippocampus, the magnitude of long-term potentiation (LTP) depends not only on the frequency of applied stimuli, but also on their number. With a slice preparation using extracellu- lar recording in the hippocampus CA1 of a guinea pig, we investigate the magnitude of LTP induced by electrical stimuli with a range of frequencies and the number of applied stimuli. We find that the magnitude of the saturated potentiation obtained with periodic stimuli largely depends on the frequency and is insensitive to the number of stimuli, once the saturation level has been obtained. Furthermore, we investigated nonperi- odic stimuli and found that the magnitude of the saturated potentiation is also sensitive to the statistical correlation between successive interstimu- lus intervals, even when their average frequency is held constant. In order to explain the LTP dependence on these various experimental parameters, we propose a simple mathematical model for the induction of LTP. In the model, an exponentially decaying element released as a result of previous stimuli is coupled with a new stimulus to act as thepotentiation force, and the magnitude of potentiation is determined by this potentiation force. We can determine the decaying time constant of this hypothetical element as a model parameter by fitting the model to the experimental data. The time scale is found to be of the order of 200 msc. A molecular or cellular factor with this decaying time constant is likely to be induced in LTP induction. Hippocampus 7:416-426, 1997. r 1997 Wiley-Liss, Inc.

It has been emphasized that the temporal occurrence of earthquakes in various spatial areas and over ranges of magnitude may be described by a unique distribution of inter-earthquake intervals under suitable rescaling, implying the presence of a universal mechanism governing seismicity. Nevertheless, it is possible that some features in the fine temporal patterns of event occurrences differ between spatial regions, reflecting different conditions that cause earthquakes, such as relative motion of tectonic plates sharing a boundary. By abstracting the non-Poissonian feature from non-stationary sequences using a metric of local variation of event intervals Lv, we find a wide range of non-Poissonian burstiness present in the temporal event occurrences in different spatial areas. Firstly, the degree of bursty features in the occurrence of earthquakes depends on spatial location; earthquakes tend to be bursty in areas where they are less frequent. Secondly, systematic regional differences remain even if the overall correlation between burstiness and the rate of event occurrence is eliminated. Thirdly, the degree of burstiness is particularly high on divergent tectonic boundaries compared to convergent and transform boundaries. In this way, temporal patterns of event occurrences bear witness to the circumstances underlying event generation.

It has been empirically established that the cerebral cortical areas defined by Brodmann one hundred years ago solely on the basis of cellular organization are closely correlated to their function, such as sensation, association, and motion. Cytoarchitectonically distinct cortical areas have different densities and types of neurons. Thus, signaling patterns may also vary among cytoarchitectonically unique cortical areas. To examine how neuronal signaling patterns are related to innate cortical functions, we detected intrinsic features of cortical firing by devising a metric that efficiently isolates non-Poisson irregular characteristics, independent of spike rate fluctuations that are caused extrinsically by ever-changing behavioral conditions. Using the new metric, we analyzed spike trains from over 1,000 neurons in 15 cortical areas sampled by eight independent neurophysiological laboratories. Analysis of firing-pattern dissimilarities across cortical areas revealed a gradient of firing regularity that corresponded closely to the functional category of the cortical area; neuronal spiking patterns are regular in motor areas, random in the visual areas, and bursty in the prefrontal area. Thus, signaling patterns may play an important role in function-specific cerebral cortical computation., Author Summary Neurons, or nerve cells in the brain, communicate with each other using stereotyped electric pulses, called spikes. It is believed that neurons convey information mainly through the frequency of the transmitted spikes, called the firing rate. In addition, neurons may communicate some information through the finer temporal patterns of the spikes. Neuronal firing patterns may depend on cellular organization, which varies among the regions of the brain, according to the roles they play, such as sensation, association, and motion. In order to examine the relationship among signals, structure, and function, we devised a metric to detect firing irregularity intrinsic and specific to individual neurons and analyzed spike sequences from over 1,000 neurons in 15 different cortical areas. Here we report two results of this study. First, we found that neurons exhibit stable firing patterns that can be characterized as “regular”, “random”, and “bursty”. Second, we observed a strong correlation between the type of signaling pattern exhibited by neurons in a given area and the function of that area. This suggests that, in addition to reflecting the cellular organization of the brain, neuronal signaling patterns may also play a role in specific types of neuronal computations.

In a self-organization process of a neural network, each neuron becomes responsive to one of the input signals frequently presented. Prominent response of a neuron has been considered as a feature detecting signal. It is found that the activity pattern of the set of neurons shows a structurized information classification scheme rather than a mere ability in feature detection. Kinship among the pieces of information is emphasized by the mapping of the activity pattern.

By introducing a physiological constraint in the auto-correlation matrix memory, the system is found to acquire an ability in cognition i.e. the ability to identify and input pattern by its proximity to any one of the stored memories. The physiological constraint here is that the attribute of a given synapse (i.e. excitatory or inhibitory) is uniquely determined by the neuron it belongs. Thus the synaptic coupling is generally not symmetric. Analytical and numerical analyses revealed that the present model retrieves a memory if an input pattern is close to the pattern of the stored memories; if not, it gives a clear response by going into a special mode where almost all neurons are in the same state in each time step. This uniform mode may be stationary or periodic, depending on whether or not the number of the excitatory neurons exceeds the number of inhibitory neurons.

Phase transitions of active rotator systems with short-range coupling are discussed. The constituents of the system which we call active rotators are represented by a phase model of a limit-cycle oscillator or an excitable element, i.e., dt/J/dt = w-bsint/J, (Iw/bl

On etudie un systeme modele pour des oscillateurs cycle limite distribues sur un reseau cubique a d dimensions

We present a method to derive the H -theorem directly from the (two-body) Bogolubov-Green- Cohen equation. With this method, we can investigate the circumstances under which the equation exhibits monotonous approach to equilibrium. This method suggests also that further coarsegraining in time in some sense is needed for this equation as far as the H -theorem is concerned.

On etudie le modele de phase d'un oscillateur aleatoirement module en frequence cycle limite avec une force externe periodique

By computer simulations of an active rotator model, it is found that 1-, 2and 3-dimensional oscillator lattices with distributed natural frequencies exhibit peculiar clustering patterns due to local entrainment. A simple theory suggests that some of such self-entrained clusters mayor may not develop into macroscopic size depending on system dimension, and this fact consistently explains our numerically obtained order parameter curves.

A rule of synaptic modification in neural networks is proposed under a principle which minimises 'free energy' with synaptic strength roughly bounded. The rule does not allow the overloading of memories which can be a cause of failure in the memory process and it stabilises the synaptic connection, provided that memories are properly stored.

La variation non lineaire du logarithme du volume libre avec le nombre de plus proches voisins, prise en compte dans l'approximation de Bragg-Williams permet de prevoir l'existence d'une fusion. L'equation d'etat qui en resulte est une courbe du type de van der Waals et presente une transition de phase du premier ordre

We present an intuitive method to calculate the pair distribution function and the equation of state for the hard sphere system by an elementary kinetic theory. The resulting equation of state not only reproduces exactly the second and the third virial coefficients, but also exhibits a remarkable agreement with molecular-dynamics results.

Free 'volume' of the one dimensional hard rod and the two dimensional hard disk systems is obtained analytically and compared to that of the three dimensional hard sphere system obtained numerically. The logarithm of the free volume plotted against the number of holes makes an S-shape in cases of hard sphere and hard disk systems, in contrast with the hard rod system in which case it is a monotonical convex function. Similarity between these dependences of hard sphere and hard disk systems is shown to be closely connected not only with the melting transition, but also with the existence of three phases in the case of hard core systems with attractive potentials.

On introduit un modele de rotateur actif afin d'etudier la dynamique statistique d'une grande population d'oscillateurs a cycle limite ou d'elements excitables. Ceci se definit dynamiquement comme une version stochastique d'un modele planaire relaxationnel modifiee par une force constante additionnelle

It is found that the density expansion in the argument of the exponential function gives a fine convergence on the equation of state of the hard-sphere system. The pair distribution function and the equation of state is constructed by an intuitive kinetic theoretical method. The equation of state of the hard-core system with attractive potential is constructed semiempirically with the aid of this simple analytical result, and Kamerling-Onnes' constant of the critical point is obtained analytically.

The pair approximation of the cluster variation method is applied to the hole theory of classical fluids and the melting transition of the hard-sphere system is discussed. The exact free volume of the hard-sphere molecule is used to make up an effective ‘interaction’ assigned to a cluster which consists of an occupied site by a molecule and its nearest neighbour sites occupied by molecules and holes. This method supplies much improved results compared with those of the molecular-field approximation which corresponds to the site approximation in the cluster variation method.

The cognition is based on classification processes. In every stage of computation or information processing, a sub-unit in each site of the brain will also classify whether or not the input signal to that unit is identifiable in its part.

Receptive properties of neurons in visual pathways of mammalian brains have become clarified as a result of physiological and anatomical research. There are a number of neurons with rather simple receptive functions, which respond to different types of spatial differentiation of the lightness field. The significance of each function, however, is not yet understood in terms of visual perception. For instance, although the neurons for early stage visual processing participate in spatial differentiation, we are not particularly conscious of the spatial derivatives of images, but are able to recover the general images.

The purpose of the present paper is to demonstrate the utility of what we call an active rotator model. We will study some dynamical processes for which the interaction of infinitely many degrees of freedom is essential. The processes with which we are concerned take place in a spatially distributed system that is more or less homogeneous in its constitution; the system consists of many similar units, and each unit is assumed to be functionally active in some sense. More specifically, it is assumed that each element (which will ordinarily be called a cell) represents either a limit-cycle oscillator or an excitable functional unit. Since, as is well known, oscillation and excitability are dynamical modes commonly shared by cellular membrane and biochemical reactions, the present subject is relevant to many physiological processes in living organisms. Examples of what are considered to be populations of such active elements include the population of pacemaker cells in the sino-atrial node of a mammal’s heart and neural nets in the cerebral cortex. Our system need not be restricted to discrete populations of well-defined units; even continuous or almost continuous tissues such as the smooth muscle of the small intestine or other digestive organs may also comprise possible examples.

We consider a binary choice problem represented by a conditional probability p(s|x), where input x/spl isin/[0,1] and output s/spl isin/{-1,+1}. The function p(s|x) is assumed to be monotonically increasing with respect to x. For the best prediction, the learner must fix the optimal boundary /spl theta//sub o/ determined by p(s=+1|/spl theta//sub o/)=p(s=-1|/spl theta//sub o/)=1/2 without precise knowledge of the function. Learning algorithms should work incrementally for practicality, if possible. We present incremental algorithms which ensure that the learner fixes the optimal parameter /spl theta//sub o/ in the limit that the number of examples t becomes infinite. We further investigate the rate of convergence in the following two typical cases. When the learner can specify the position of input x by queries in the course of learning, the mean square deviation decreases as O(t/sup -1/). On the other hand, if x is chosen independently from some distribution p(x), the learner cannot attain convergence as O(t/sup -1/), but rather as O(t/sup -4/5/). This rate can be accelerated by an elaborate technique up to O((In t)/sup 2/t/sup -1/), as t/spl rarr//spl infin/.

The set of firing rates of the presynaptic excitatory and inhibitory neurons constitutes the input signal to the postsynaptic neuron. Estimation of the time-varying input rates from intracellularly recorded membrane potential is investigated here. For that purpose, the membrane potential dynamics must be specified. We consider the Ornstein-Uhlenbeck stochastic process, one of the most common single-neuron models, with time-dependent mean and variance. Assuming the slow variation of these two moments, it is possible to formulate the estimation problem by using a state-space model. We develop an algorithm that estimates the paths of the mean and variance of the input current by using the empirical Bayes approach. Then the input firing rates are directly available from the moments. The proposed method is applied to three simulated data examples: constant signal, sinusoidally modulated signal, and constant signal with a jump. For the constant signal, the estimation performance of the method is comparable to that of the traditionally applied maximum likelihood method. Further, the proposed method accurately estimates both continuous and discontinuous time-variable signals. In the case of the signal with a jump, which does not satisfy the assumption of slow variability, the robustness of the method is verified. It can be concluded that the method provides reliable estimates of the total input firing rates, which are not experimentally measurable.

http://ptp.ipap.jp/link?PTPS/161/244/; International audience; We numerically demonstrate that collective bifurcations in two-dimensional lattices of locally coupled logistic maps share most of the defining features of equilibrium second-order phase transitions. Our simulations suggest that these transitions between distinct collective dynamical regimes belong to the universality class of Miller and Huse model with synchronous update.