Neural modeling with dynamically adjustable threshold and refractory period.

A variant of the FitzHugh-Nagumo model is proposed in order to fully make use of the computational properties of intraneuronal dynamics. The mechanisms of threshold and refractory periods resulting from the double dynamical processes are qualitatively studied through computer simulation. The results show that the variant neuron model has the property that its threshold, refractory period and response amplitude are dynamically adjustable. This paper has also discussed some problems relating to collective property, learning and implementation of the neural network based on the neuron model proposed. It is noted that the implicit way to describe threshold and refractory period is advantageous to adaptive learning in neural networks and that molecular electronics probably provides an effective approach to implementing the above neuron model.     

A model cortical circuit for the storage of temporal sequences

Despite the fact that temporal information processing is of particular significance in biological memory systems, not much has yet been explored about how these systems manage to store temporal information involved in sequences of stimuli. A neural network model capable of learning and recalling temporal sequences is proposed, based on a neural mechanism in which the sequences are expanded into a series of periodic rectangular oscillations. Thus, the mathematical framework underlying the model, to some extent, is concerned with the Walsh function series. The oscillatory activities generated by the interplay between excitatory and inhibitory neuron pools are transmitted to another neuron pool whose role in learning and retrieval is to modify the rhythms and phases of the rectangular oscillations. Thus, a basic functional neural circuit involves three different neuron pools. The modifiability of rhythms and phases is incorporated into the model with the aim of improving the quality of the retrieval. Numerical simulations were conducted to show the characteristic features of the learning as well as the performance of the model in memory recall.     

Simplified neuron model as a principal component analyzer

A simple linear neuron model with constrained Hebbian-type synaptic modification is analyzed and a new class of unconstrained learning rules is derived. It is shown that the model neuron tends to extract the principal component from a stationary input vector sequence.     

One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death II: transition state metastability

This is the second of two papers in which we study a mathematical model of cytoskeleton-induced neuron death. Recent evidence indicates that aggravated assembly or destruction of the cytoskeleton can trigger programmed death in neurons, by mechanisms as yet poorly understood. In our model, assembly control of the neuronal cytoskeleton interacts with both cellular stress levels and cytosolic free radical concentrations to trigger neurodegeneration. This trigger mechanism is further modulated by a diffusible toxic factor released from dying neurons. In the companion report we established that the model relates the observed general patterns of neuron decline to specific scales of cytoskeleton reorganization and cell-cell interaction strength. In this paper we study the transit of neurons through states intermediate between initial viability and cell death in our model. We find that the stochastic flow of neuron fate, from viability to cell death, self-organizes into two distinct temporal phases. There is a rapid relaxation of the initial neuron population to a more disordered phase that is long-lived, or metastable, with respect to the time scales of change in single cells. Strikingly, cellular egress from this metastable phase follows the one-hit kinetic pattern of exponential decline now established as a principal hallmark of cell death in neurodegenerative disorders. Intermediate state metastability may therefore be an important element in the systems biology of one-hit neurodegeneration.     

Addition of song-related neurons in swamp sparrows coincides with memorization, not production, of learned songs

During song learning in birds, neurons are added to some song nuclei and lost from others. Previous studies have been unable to distinguish whether these neural changes are uniquely associated with memorizing a song model (sensory acquisition) or vocal practice (sensorimotor learning). In this study we measured changes in neuron number within song nuclei of swamp sparrows, a species in which the two phases of song learning are nonoverlapping. Male swamp sparrows were collected as hatchlings and tape-tutored from approximately 22 to 62 days of age. Swamp sparrows memorize about 60% of their song material during this period, but do not begin practicing this learned material until approximately 275 days of age. Birds were sacrificed at 23, 41, 61, 71, 274, or 340 days of age. During sensory acquisition, neuron number increased drastically in both the caudal nucleus of the ventral hyperstriatum (HVc) and Area X. The period of sensorimotor learning was not associated with any further changes in neuron number within these regions. We were unable to detect any significant changes in neuron number within the magnocellular nucleus of the neostriatum or the robust nucleus of the archistriatum during either stage of song learning. These results raise the possibility that ongoing addition of HVc and Area X neurons may encourage, and thereby temporally restrict, song acquisition.     

Neuron loss and addition in developing zebra finch song nuclei are independent of auditory experience during song learning

In zebra finches early auditory experience is critical for normal song development. Young males first listen to and memorize a suitable song model and then use auditory feedback from their own vocalizations to mimic that model. During these two phases of vocal learning, song-related brain regions exhibit large, hormone-induced changes in volume and neuron number. Overlap between these neural changes and auditory-based vocal learning suggests that processing and acquiring auditory input may influence cellular processes that determine neuron number in the song system. We addressed this hypothesis by measuring neuron density, nuclear volume, and neuron number within the song system of normal male zebra finches and males deafened prior to song learning (10 days of age). Measures were obtained at 25, 50, 65, and 120 days of age, and included four song nuclei: the hyperstriatum ventralis pars caudalis or higher vocal center (HVc), Area X, the robust nucleus of the archistriatum (RA), and the lateral magnocellular nucleus of the anterior neostriatum (IMAN). In both HVc and Area X, nuclear volume and neuron number increased markedly with age in both normal and deafened birds. The volume of RA also increased with age and was not affected by early deafening. In IMAN, deafening also did not affect the overall age-related loss of neurons, although at 25 days neuron number was slightly less in deafened than in normal birds. We conclude that while the addition and loss of neurons in the developing song system may provide plasticity essential for song learning, these changes do not reflect learning.(ABSTRACT TRUNCATED AT 250 WORDS)     

Context codes and the effect of noisy learning on a simplified hippocampal CA3 model

This paper investigates how noise affects a minimal computational model of the hippocampus and, in particular, region CA3. The architecture and physiology employed are consistent with the known anatomy and physiology of this region. Here, we use computer simulations to demonstrate and quantify the ability of this model to create context codes in sequential learning problems. These context codes are mediated by local context neurons which are analogous to hippocampal place-coding cells. These local context neurons endow the network with many of its problem-solving abilities. Our results show that the network encodes context on its own and then uses context to solve sequence prediction under ambiguous conditions. Noise during learning affects performance, and it also affects the development of context codes. The relationship between noise and performance in a sequence prediction is simple and corresponds to a disruption of local context neuron firing. As noise exceeds the signal, sequence completion and local context neuron firing are both lost. For the parameters investigated, extra learning trials and slower learning rates do not overcome either of the effects of noise. The results are consistent with the important role played, in this hippocampal model, by local context neurons in sequence prediction and for disambiguation across time.     

How synapses in the auditory system wax and wane: theoretical perspectives

Spike-timing-dependent synaptic plasticity has recently provided an account of both the acuity of sound localization and the development of temporal-feature maps in the avian auditory system. The dynamics of the resulting learning equation, which describes the evolution of the synaptic weights, is governed by an unstable fixed point. We outline the derivation of the learning equation for both the Poisson neuron model and the leaky integrate-and-fire neuron with conductance synapses. The asymptotic solutions of the learning equation can be described by a spectral representation based on a biorthogonal expansion.     

Towards a general theory of neural computation based on prediction by single neurons

Although there has been tremendous progress in understanding the mechanics of the nervous system, there has not been a general theory of its computational function. Here I present a theory that relates the established biophysical properties of single generic neurons to principles of Bayesian probability theory, reinforcement learning and efficient coding. I suggest that this theory addresses the general computational problem facing the nervous system. Each neuron is proposed to mirror the function of the whole system in learning to predict aspects of the world related to future reward. According to the model, a typical neuron receives current information about the state of the world from a subset of its excitatory synaptic inputs, and prior information from its other inputs. Prior information would be contributed by synaptic inputs representing distinct regions of space, and by different types of non-synaptic, voltage-regulated channels representing distinct periods of the past. The neuron's membrane voltage is proposed to signal the difference between current and prior information ("prediction error" or "surprise"). A neuron would apply a Hebbian plasticity rule to select those excitatory inputs that are the most closely correlated with reward but are the least predictable, since unpredictable inputs provide the neuron with the most "new" information about future reward. To minimize the error in its predictions and to respond only when excitation is "new and surprising," the neuron selects amongst its prior information sources through an anti-Hebbian rule. The unique inputs of a mature neuron would therefore result from learning about spatial and temporal patterns in its local environment, and by extension, the external world. Thus the theory describes how the structure of the mature nervous system could reflect the structure of the external world, and how the complexity and intelligence of the system might develop from a population of undifferentiated neurons, each implementing similar learning algorithms.     

One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death I: cell-fate arrival times

Much experimental evidence shows that the cytoskeleton is a downstream target and effector during cell death in numerous neurodegenerative diseases, including Parkinson's, Huntington's, and Alzheimer's diseases. However, recent evidence indicates that cytoskeletal dysfunction can also trigger neuronal death, by mechanisms as yet poorly understood. This is the first of two papers in which we study a mathematical model of cytoskeleton-induced neuron death. In our model, assembly control of the neuronal cytoskeleton interacts with both cellular stress levels and cytosolic free radical concentrations to trigger neurodegeneration. This trigger mechanism is further modulated by the presence of cell interactions in the form of a diffusible toxic factor released by dying neurons. We find that, consistent with empirical observations, our model produces one-hit exponential and sigmoid patterns of cell dropout. In all cases, cell dropout is exponential-tailed and described accurately by a gamma distribution. The transition between exponential and sigmoidal is gradual, and determined by a synergetic interaction between the magnitude of fluctuations in cytoskeleton assembly control and by the degree of cell coupling. We conclude that a single mechanism involving neuron interactions and fluctuations in cytoskeleton assembly control is compatible with the experimentally observed range of neuronal attrition kinetics.     

Probability density function learning by unsupervised neurons.

In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation methods, with special emphasis to the universal approximation ability. The paper also provides a survey of PDF learning from incomplete data, as well as results of several experiments performed on real-world problems and signals.     

避暗反应测定大鼠学习记忆功能方法的探讨

目的 为了提高避暗反应测定动物学习记忆功能的敏感性,本实验对三种实验及统计方法进行了评价。方法 采用IBO致基底前脑胆碱能神经元损伤模型和东莨菪碱所致的记忆障碍模型,对单次简单测试法、多次简单测试法和多次记分测试法的敏感性进行了比较。结果 对于基底前脑损伤模型,单次简单测试法的潜伏期学习记忆指标无法显示出模型组与对照组之间的差异。多次简单测试法两种指标均能显示出显著性差异,且较多次记分测试法的指标差异的显著性高。对于东莨菪碱致痴呆模型,也有同样的效果。结论 多次简单测试法更能敏感地反映动物的学习记忆功能。     

A neural circuit model of emotional learning using two pathways with different granularity and speed of information processing

We propose a neural circuit model of emotional learning using two pathways with different granularity and speed of information processing. In order to derive a precise time process, we utilized a spiking model neuron proposed by Izhikevich and spike-timing-dependent synaptic plasticity (STDP) of both excitatory and inhibitory synapses. We conducted computer simulations to evaluate the proposed model. We demonstrate some aspects of emotional learning from the perspective of the time process. The agreement of the results with the previous behavioral experiments suggests that the structure and learning process of the proposed model are appropriate.     

A neural network model based on the analogy with the immune system

The similarities between the immune system and the central nervous system lead to the formulation of an unorthodox neural network model. The similarities between the two systems are strong at the system level, but do not seem to be so striking at the level of the components. A new model of a neuron is therefore formulated, in order that the analogy can be used. The essential feature of the hypothetical neuron is that it exhibits hysteresis at the single neuron level. A network of N such neurons is modelled by an N-dimensional system of ordinary differential equations, which exhibits almost 2N attractors. The model has a property that resembles free will. A conjecture concerning how the network might learn stimulus-response behaviour is described. According to the conjecture, learning does not involve modifications of the strengths of synaptic connections. Instead, stimuli ("questions") selectively applied to the network by a "teacher" can be used to take the system to a region of the N-dimensional phase space where the network gives the desired stimulus-response behaviour. A key role for sleep in the learning process is suggested. The model for sleep leads to prediction that the variance in the rates of firing of the neurons associated with memory should increase during waking hours, and decrease during sleep.     

Real neuron assemblies forming during screen structure activities of the brain

The assembly organization of neuron reactions is a specific peculiarity of the screen structures of which the projection fields of the higher parts of the brain are composed. Such an organization is characterized by the local synergism of the responses of neuron groups in-teracting antagonistically, in contrast to the global neuron synergism of the nuclear segmental structures and the individual neuron antagonism of diffuse unspecific structures. Another characteristic feature of assembly organization is the presumable participation of neurons in the reaction of the assembly which warrants the flexibility and reliability of the realization of central functions. Of interest is the phylogenetic decrease in size and increase in number of working assemblies per unit area of projection field which enhances the resolving power of the analyzer. In different analyzer fields under the action of different stimuli a constant relationship of the reactions is found, i.e., two excited neurons to one inhibited neuron. Apparently, this proportion underlies the organization of balanced assemblies. The inadequacy of the stimuli and the deterioration of the functional state of the brain favor the "spreading" of assemblies; they increase in size, but at the same time the close correlation is lost between the impulse currents of the incoming neurons.Rostov-on-DonState University. Translated from Neirofiziologiya, Vol. 1, No. 2, pp. 123–129, September–October, 1969.     

An extended model for a spiking neuron class

This paper proposes an extension to the model of a spiking neuron for information processing in artificial neural networks, developing a new approach for the dynamic threshold of the integrate-and-fire neuron. This new approach invokes characteristics of biological neurons such as the behavior of chemical synapses and the receptor field. We demonstrate how such a digital model of spiking neurons can solve complex nonlinear classification with a single neuron, performing experiments for the classical XOR problem. Compared with rate-coded networks and the classical integrate-and-fire model, the trained network demonstrated faster information processing, requiring fewer neurons and shorter learning periods. The extended model validates all the logic functions of biological neurons when such functions are necessary for the proper flow of binary codes through a neural network.     

The enzymatic neuron as a reaction-diffusion network of cyclic nucleotides

Recent evidence suggests that the cyclic nucleotides play a central role in the intracellular processing of neural signals. The dynamics of this system may be seen as a realization of the enzymatic neuron model. Enzymatic neurons are formal neurons which map binary afferent signals into patterns of excitation across an abstract membrane. The distribution of enzyme-like elements called excitases enables a set of local threshold functions to determine the firing activity of the neuron. This paper analyzes the basic properties of enzymatic neurons in a simple continuous-time framework, and shows how they may be presented as reaction-diffusion networks which model the cyclic nucleotide system. We present the results of computer simulations of this neuron and discuss its implications for selectional learning and its relation to conventional two-factor systems. One fundamental property of the reaction-diffusion neuron is its so-called “double-dynamics” property; examination of this property and its contribution to the computing power of the neuron provides some insight into the obscure relation between microscopic and macroscopic models of computation.     

Spike-timing-dependent plasticity for neurons with recurrent connections

The dynamics of the learning equation, which describes the evolution of the synaptic weights, is derived in the situation where the network contains recurrent connections. The derivation is carried out for the Poisson neuron model. The spiking-rates of the recurrently connected neurons and their cross-correlations are determined self- consistently as a function of the external synaptic inputs. The solution of the learning equation is illustrated by the analysis of the particular case in which there is no external synaptic input. The general learning equation and the fixed-point structure of its solutions is discussed.     

Neural circuits underlying imitation learning of hand actions: an event-related fMRI study

The neural bases of imitation learning are virtually unknown. In the present study, we addressed this issue using an event-related fMRI paradigm. Musically naive participants were scanned during four events: (1) observation of guitar chords played by a guitarist, (2) a pause following model observation, (3) execution of the observed chords, and (4) rest. The results showed that the basic circuit underlying imitation learning consists of the inferior parietal lobule and the posterior part of the inferior frontal gyrus plus the adjacent premotor cortex (mirror neuron circuit). This circuit, known to be involved in action understanding, starts to be active during the observation of the guitar chords. During pause, the middle frontal gyrus (area 46) plus structures involved in motor preparation (dorsal premotor cortex, superior parietal lobule, rostral mesial areas) also become active. Given the functional properties of area 46, a model of imitation learning is proposed based on interactions between this area and the mirror neuron system.     

Computational Consequences of Temporally Asymmetric Learning Rules: I. Differential Hebbian Learning

Temporally asymetric learning rules governing plastic changes in synaptic efficacy have recently been identified in physiological studies. In these rules, the exact timing of pre- and postsynaptic spikes is critical to the induced change of synaptic efficacy. The temporal learning rules treated in this article are approximately antisymmetric; the synaptic efficacy is enhanced if the postsynaptic spike follows the presynaptic spike by a few milliseconds, but the efficacy is depressed if the postsynaptic spike precedes the presynaptic spike. The learning dynamics of this rule are studied using a stochastic model neuron receiving a set of serially delayed inputs. The average change of synaptic efficacy due to the temporally antisymmetric learning rule is shown to yield differential Hebbian learning. These results are demonstrated with both mathematical analyses and computer simulations, and connections with theories of classical conditioning are discussed.