How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation

This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks ? and; (ii) what are the effects of synaptic plasticity on these statistics ? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure

Cerebral Autosomal Dominant Arteriopathy with Subcortical Infarcts and Leukoencephalopathy (CADASIL) as a model of small vessel disease: update on clinical, diagnostic, and management aspects.

Cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL) is the most common and best known monogenic small vessel disease. Here, we review the clinical, neuroimaging, neuropathological, genetic, and therapeutic aspects based on the most relevant articles published between 1994 and 2016 and on the personal experience of the authors, all directly involved in CADASIL research and care. We conclude with some suggestions that may help in the clinical practice and management of these patients

Performance of quadrature amplitude modulation orthogonal frequency division multiplexing-based free space optical links with non-linear clipping effect over gamma-gamma modelled turbulence channels

The free space optical (FSO) communication systems have attracted significant research and commercial interest in the last few years because of their low installation and operational cost along with their very high performance characteristics. However, for terrestrial FSO links, the optical signal propagates through the atmosphere which exhibits time-varying behaviour that implies variations in the links' performance. In this study, the authors estimate the performance metrics for terrestrial FSO links which are using the orthogonal frequency division multiplexing (OFDM) technique with a quadrature amplitude modulation scheme over turbulence channels. More specifically, the authors investigate the influence of the non-linear clipping effect of the OFDM scheme, along with the atmospheric turbulence modelled using the gamma-gamma distribution. Both effects significantly influence the performance of the link and here the authors derive closed form mathematical expressions for the estimation of the average signal to noise ratio, the outage probability and the average bit error rate that are vital for FSO system performance characterisation. Finally, using these expressions, the authors present the corresponding numerical results for common parameter values of the FSO links and investigate the accuracy of the expressions for marginal cases with nearly negligible turbulence effect. © 2015 The Institution of Engineering and Technology

Measures of trajectory ensemble disparity in nonequilibrium statistical dynamics

Many interesting divergence measures between conjugate ensembles of nonequilibrium trajectories can be experimentally determined from the work distribution of the process. Herein, we review the statistical and physical significance of several of these measures, in particular the relative entropy (dissipation), Jeffreys divergence (hysteresis), Jensen-Shannon divergence (time-asymmetry), Chernoff divergence (work cumulant generating function), and Renyi divergence

Discriminative extended canonical correlation analysis for pattern set matching

In this paper we address the problem of matching sets of vectors embedded in the same input space. We propose an approach which is motivated by canonical correlation analysis (CCA), a statistical technique which has proven successful in a wide variety of pattern recognition problems. Like CCA when applied to the matching of sets, our extended canonical correlation analysis (E-CCA) aims to extract the most similar modes of variability within two sets. Our first major contribution is the formulation of a principled framework for robust inference of such modes from data in the presence of uncertainty associated with noise and sampling randomness. E-CCA retains the efficiency and closed form computability of CCA, but unlike it, does not possess free parameters which cannot be inferred directly from data (inherent data dimensionality, and the number of canonical correlations used for set similarity computation). Our second major contribution is to show that in contrast to CCA, E-CCA is readily adapted to match sets in a discriminative learning scheme which we call discriminative extended canonical correlation analysis (DE-CCA). Theoretical contributions of this paper are followed by an empirical evaluation of its premises on the task of face recognition from sets of rasterized appearance images. The results demonstrate that our approach, E-CCA, already outperforms both CCA and its quasi-discriminative counterpart constrained CCA (C-CCA), for all values of their free parameters. An even greater improvement is achieved with the discriminative variant, DE-CCA.Comment: Machine Learning, 201