On directed information theory and Granger causality graphs

Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks can be used to assess Granger causality graphs of stochastic processes. We show that directed information theory includes measures such as the transfer entropy, and that it is the adequate information theoretic framework needed for neuroscience applications, such as connectivity inference problems.Comment: accepted for publications, Journal of Computational Neuroscienc

Welcome to the new open access NeuroSci

With sincere satisfaction and pride, I present to you the new journal, NeuroSci, for which I am pleased to serve as editor-in-chief. To date, the world of neurology has been rapidly advancing, NeuroSci is a cross-disciplinary, open-access journal that offers an opportunity for presentation of novel data in the field of neurology and covers a broad spectrum of areas including neuroanatomy, neurophysiology, neuropharmacology, clinical research and clinical trials, molecular and cellular neuroscience, neuropsychology, cognitive and behavioral neuroscience, and computational neuroscience. Members of our editorial board will welcome the contributions in this wide field of neurosciences. The following are welcome messages from some editorial board members

A Mathematical model for Astrocytes mediated LTP at Single Hippocampal Synapses

Many contemporary studies have shown that astrocytes play a significant role in modulating both short and long form of synaptic plasticity. There are very few experimental models which elucidate the role of astrocyte over Long-term Potentiation (LTP). Recently, Perea & Araque (2007) demonstrated a role of astrocytes in induction of LTP at single hippocampal synapses. They suggested a purely pre-synaptic basis for induction of this N-methyl-D- Aspartate (NMDA) Receptor-independent LTP. Also, the mechanisms underlying this pre-synaptic induction were not investigated. Here, in this article, we propose a mathematical model for astrocyte modulated LTP which successfully emulates the experimental findings of Perea & Araque (2007). Our study suggests the role of retrograde messengers, possibly Nitric Oxide (NO), for this pre-synaptically modulated LTP.Comment: 51 pages, 15 figures, Journal of Computational Neuroscience (to appear

Evolving structure-function mappings in cognitive neuroscience using genetic programming

A challenging goal of psychology and neuroscience is to map cognitive functions onto neuroanatomical structures. This paper shows how computational methods based upon evolutionary algorithms can facilitate the search for satisfactory mappings by efficiently combining constraints from neuroanatomy and physiology (the structures) with constraints from behavioural experiments (the functions). This methodology involves creation of a database coding for known neuroanatomical and physiological constraints, for mental programs made of primitive cognitive functions, and for typical experiments with their behavioural results. The evolutionary algorithms evolve theories mapping structures to functions in order to optimize the fit with the actual data. These theories lead to new, empirically testable predictions. The role of the prefrontal cortex in humans is discussed as an example. This methodology can be applied to the study of structures or functions alone, and can also be used to study other complex systems. (This article does not exactly replicate the final version published in the Journal of Swiss Psychology. It is not a copy of the original published article and is not suitable for citation.

Efficient simulations of tubulin-driven axonal growth

This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman--Rachford splitting scheme combined with temporal and spatial scalings of the model. Simulations based on this scheme have shown to be efficient, accurate, and reliable which makes it possible to evaluate the model, e.g.\ its dependency on biological and physical model parameters. These evaluations show among other things that the initial axon growth is very fast, that the active transport is the dominant reason over diffusion for the growth velocity, and that the polymerization rate in the growth cone does not affect the final axon length.Comment: Authors' accepted version, (post refereeing). The final publication (in Journal of Computational Neuroscience) is available at Springer via http://dx.doi.org/10.1007/s10827-016-0604-

A discrete time neural network model with spiking neurons II. Dynamics with noise

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky integrate and fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.Comment: 43 pages - revised version - to appear il Journal of Mathematical Biolog

Flexible resonance in prefrontal networks with strong feedback inhibition

[EN] Oscillations are ubiquitous features of brain dynamics that undergo task-related changes in synchrony, power, and frequency. The impact of those changes on target networks is poorly understood. In this work, we used a biophysically detailed model of prefrontal cortex (PFC) to explore the effects of varying the spike rate, synchrony, and waveform of strong oscillatory inputs on the behavior of cortical networks driven by them. Interacting populations of excitatory and inhibitory neurons with strong feedback inhibition are inhibition-based network oscillators that exhibit resonance (i.e., larger responses to preferred input frequencies). We quantified network responses in terms of mean firing rates and the population frequency of network oscillation; and characterized their behavior in terms of the natural response to asynchronous input and the resonant response to oscillatory inputs. We show that strong feedback inhibition causes the PFC to generate internal (natural) oscillations in the beta/gamma frequency range (>15 Hz) and to maximize principal cell spiking in response to external oscillations at slightly higher frequencies. Importantly, we found that the fastest oscillation frequency that can be relayed by the network maximizes local inhibition and is equal to a frequency even higher than that which maximizes the firing rate of excitatory cells; we call this phenomenon population frequency resonance. This form of resonance is shown to determine the optimal driving frequency for suppressing responses to asynchronous activity. Lastly, we demonstrate that the natural and resonant frequencies can be tuned by changes in neuronal excitability, the duration of feedback inhibition, and dynamic properties of the input. Our results predict that PFC networks are tuned for generating and selectively responding to beta- and gamma-rhythmic signals due to the natural and resonant properties of inhibition-based oscillators. They also suggest strategies for optimizing transcranial stimulation and using oscillatory networks in neuromorphic engineering.This material is based upon research supported by the U. S. Army Research Office under award number ARO W911NF-12-R-0012-02 to N. K., the U. S. Office of Naval Research under award number ONR MURI N00014-16-1-2832 to M. H., and the National Science Foundation under award number NSF DMS-1042134 (Cognitive Rhythms Collaborative: A Discovery Network) to N. K. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Sherfey, JS.; Ardid-Ramírez, JS.; Hass, J.; Hasselmo, ME.; Kopell, NJ. (2018). Flexible resonance in prefrontal networks with strong feedback inhibition. 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