This paper investigates the problem of robust passivity of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Lyapunov functional method, the Itô differential rule, and matrix analysis techniques, we establish a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the stochastic neural network is robustly passive in the sense of expectation. A delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be less than 1 is removed. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.

Ongoing advances in experimental technique are making commonplace simultaneous recordings of the activity of tens to hundreds of cortical neurons at high temporal resolution. Latent population models, including Gaussian-process factor analysis and hidden linear dynamical system (LDS) models, have proven effective at capturing the statistical structure of such data sets. They can be estimated efficiently, yield useful visualisations of population activity, and are also integral building-blocks of decoding algorithms for brain-machine interfaces (BMI). One practical challenge, particularly to LDS models, is that when parameters are learned using realistic volumes of data the resulting models often fail to reflect the true temporal continuity of the dynamics; and indeed may describe a biologically-implausible unstable population dynamic that is, it may predict neural activity that grows without bound. We propose a method for learning LDS models based on expectation maximisation that constrains parameters to yield stable systems and at the same time promotes capture of temporal structure by appropriate regularisation. We show that when only little training data is available our method yields LDS parameter estimates which provide a substantially better statistical description of the data than alternatives, whilst guaranteeing stable dynamics. We demonstrate our methods using both synthetic data and extracellular multi-electrode recordings from motor cortex.

Neuronal inter-spike intervals (ISIs) have previously been described as Poisson, Gamma, inverse Gaussian or other unimodal distributions. We analyzed ISIs of rhythmic and arrhythmic neuronal spike trains in cerebellum recorded from freely behaving rats, and found that their distributions can be described as the summation or integration of multiple Gaussian distributions. The ISIs of rhythmic cerebellar Purkinje cells have a main Gaussian peak at a basic firing interval and exponentially reduced peaks at multiples of this firing period. ISIs of arrhythmic Purkinje cells can be modeled as the integration of multiple Gaussian distributions centered at continuous intervals with exponentially reduced peak amplitudes. The sources of variability are directly related to the relative timing of action potentials between neighboring cells since we show that irregularities of discharge in one cell are associated with the previous history of its discharge in time relative to another cell. Through relative phase analyses, we demonstrate that the shape and the mathematical form of the ISI distributions in cerebellum are direct result of dynamic interactions in the nearby neuronal network, in addition to intrinsic firing properties. The analysis in this paper provides a unified description of cerebellar inter-spike interval distributions which deviate from the usual Poisson assumptions. Our results suggest the existence of an intrinsic rhythmicity in cells exhibiting arrhythmic spike trains in cerebellum, and may identify an important source of variability in neuronal firing patterns that is relevant to the mechanism of neural computation in cerebellum.

Neural networks have been a much publicized topic of research in recent years and are now beginning to be used in a wide range of subject areas. One of the strands of interest in neural networks is...

Neural networks show a progressive increase in complexity during the time course of evolution. From diffuse nerve nets in Cnidaria to modular, hierarchical systems in macaque and humans, there is a gradual shift from simple processes involving a limited amount of tasks and modalities to complex functional and behavioral processing integrating different kinds of information from highly specialized tissue. However, studies in a range of species suggest that fundamental similarities, in spatial and topological features as well as in developmental mechanisms for network formation, are retained across evolution. ‘Small-world’ topology and highly connected regions (hubs) are prevalent across the evolutionary scale, ensuring efficient processing and resilience to internal (e.g. lesions) and external (e.g. environment) changes. Furthermore, in most species, even the establishment of hubs, long-range connections linking distant components, and a modular organization, relies on similar mechanisms. In conclusion, evolutionary divergence leads to greater complexity while following essential developmental constraints.

Early in life, visual experience influences the refinement of the preferential response for specific stimulus features exhibited by neurons in the primary visual cortex. A striking example of this influence is the reduction in cortical direction selectivity observed in cats reared under high-frequency stroboscopic illumination. Although various mechanisms have been proposed to explain the maturation of individual properties of neuronal responses, a unified account of the joint development of the multiple response features of cortical neurons has remained elusive. In this study, we show that Hebbian synaptic plasticity accounts for the simultaneous refinement of orientation and direction selectivity under both normal and stroboscopic rearing, if one takes into account the spatiotemporal input to the retina during oculomotor activity. In a computational model of the LGN and V1, eye movements are sufficient to establish the patterns of thalamocortical activity required for a Hebbian refinement of both direction- and orientation-selective responses during exposure to natural stimuli. Furthermore, we show that consideration of fixational eye movements explains the simultaneous loss of direction selectivity and preservation of orientation selectivity observed as a consequence of stroboscopic rearing. These results further support a role for oculomotor activity in the refinement of the response properties of V1 neurons.

Aversive processing plays a central role in human phobic fears and may also be important in some symptoms of psychosis. We developed a temporal-difference model of the conditioned avoidance response, an important experimental model for aversive learning which is also a central pharmacological model of psychosis. In the model, dopamine neurons reported outcomes that were better than the learner expected, typically coming from reaching safety states, and thus controlled the acquisition of a suitable policy. The model accounts for normal conditioned avoidance learning, the persistence of responding in extinction, and critical effects of dopamine blockade, notably that subjects experiencing shocks under dopamine blockade, and hence failing to avoid them, nevertheless develop avoidance responses when both shocks and dopamine blockade are subsequently removed. These postulated roles of dopamine in aversive learning can thus account for many of the effects of dopaminergic modulation seen in laboratory models of psychopathological processes.

We present an approach to obtain nonlinear information about neuronal response by computing multiple linear approximations. By calculating local linear approximations centered around particular stimuli, one can obtain insight into stimulus features that drive the response of highly nonlinear neurons, such as neurons highly selective to a small set of stimuli. We implement this approach based on stimulus–spike correlation (i.e., reverse correlation or spike-triggered average) methods. We illustrate the benefits of these linear approximations with a simplified two-dimensional model and a model of an auditory neuron that is highly selective to particular features of a song.

The increasing number of books that provide overviews and reviews of various aspects of computational neuroscience is a welcome signpost in the maturation of this field. Indeed, the relatively rece...