Back-engineering of spiking neural networks parameters

We consider the deterministic evolution of a time-discretized spiking network of neurons with connection weights having delays, modeled as a discretized neural network of the generalized integrate and fire (gIF) type. The purpose is to study a class of algorithmic methods allowing to calculate the proper parameters to reproduce exactly a given spike train generated by an hidden (unknown) neural network. This standard problem is known as NP-hard when delays are to be calculated. We propose here a reformulation, now expressed as a Linear-Programming (LP) problem, thus allowing to provide an efficient resolution. This allows us to "back-engineer" a neural network, i.e. to find out, given a set of initial conditions, which parameters (i.e., connection weights in this case), allow to simulate the network spike dynamics. More precisely we make explicit the fact that the back-engineering of a spike train, is a Linear (L) problem if the membrane potentials are observed and a LP problem if only spike times are observed, with a gIF model. Numerical robustness is discussed. We also explain how it is the use of a generalized IF neuron model instead of a leaky IF model that allows us to derive this algorithm. Furthermore, we point out how the L or LP adjustment mechanism is local to each unit and has the same structure as an "Hebbian" rule. A step further, this paradigm is easily generalizable to the design of input-output spike train transformations. This means that we have a practical method to "program" a spiking network, i.e. find a set of parameters allowing us to exactly reproduce the network output, given an input. Numerical verifications and illustrations are provided.Comment: 30 pages, 17 figures, submitte

Nerve injury increases native CaV2.2 trafficking in dorsal root ganglion mechanoreceptors

Neuronal N-type (CaV2.2) voltage-gated calcium channels are essential for neurotransmission from primary afferent terminals in the dorsal horn. In this study we have utilized a knock-in mouse expressing CaV2.2 with an inserted extracellular hemagglutinin-tag (CaV2.2_HA), to visualise the distribution of endogenous CaV2.2 in dorsal root ganglion (DRG) neurons and their primary afferents in the dorsal horn. We examined the effect of partial sciatic nerve ligation (PSNL) and found an increase in CaV2.2_HA only in large and medium dorsal root ganglion neurons, and also in deep dorsal-horn synaptic terminals. Furthermore, there is a parallel increase in co-expression with GFRα1, present in a population of low threshold mechanoreceptors, both in large DRG neurons and in their terminals. The increased expression of CaV2.2_HA in these DRG neurons and their terminals is dependent on the presence of the auxiliary subunit α2δ-1, which is required for channel trafficking to the cell surface and to synaptic terminals, and likely contributes to enhanced synaptic transmission at these synapses following PSNL. In contrast the increase of GFRα1 is not altered in α2δ-1 knockout mice. We also found following PSNL there is patchy loss of glomerular synapses immunoreactive for CaV2.2_HA and CGRP or IB4, restricted to the superficial layers of the dorsal horn. This reduction is not dependent on α2δ-1, and likely reflects partial deafferentation of C-nociceptor presynaptic terminals. Therefore, we can distinguish in this pain model two different events affecting specific DRG terminals, with opposite consequences for CaV2.2_HA expression and function in the dorsal horn

Supervised Learning in Multilayer Spiking Neural Networks

The current article introduces a supervised learning algorithm for multilayer spiking neural networks. The algorithm presented here overcomes some limitations of existing learning algorithms as it can be applied to neurons firing multiple spikes and it can in principle be applied to any linearisable neuron model. The algorithm is applied successfully to various benchmarks, such as the XOR problem and the Iris data set, as well as complex classifications problems. The simulations also show the flexibility of this supervised learning algorithm which permits different encodings of the spike timing patterns, including precise spike trains encoding.Comment: 38 pages, 4 figure

Automatic Curve Fitting Based on Radial Basis Functions and a Hierarchical Genetic Algorithm

Curve fitting is a very challenging problem that arises in a wide variety of scientific and engineering applications. Given a set of data points, possibly noisy, the goal is to build a compact representation of the curve that corresponds to the best estimate of the unknown underlying relationship between two variables. Despite the large number of methods available to tackle this problem, it remains challenging and elusive. In this paper, a new method to tackle such problem using strictly a linear combination of radial basis functions (RBFs) is proposed. To be more specific, we divide the parameter search space into linear and nonlinear parameter subspaces. We use a hierarchical genetic algorithm (HGA) to minimize a model selection criterion, which allows us to automatically and simultaneously determine the nonlinear parameters and then, by the least-squares method through Singular Value Decomposition method, to compute the linear parameters. The method is fully automatic and does not require subjective parameters, for example, smooth factor or centre locations, to perform the solution. In order to validate the efficacy of our approach, we perform an experimental study with several tests on benchmarks smooth functions. A comparative analysis with two successful methods based on RBF networks has been included

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

Historical biogeography of the leopard (Panthera pardus) and its extinct Eurasian populations

Background: Resolving the historical biogeography of the leopard (Panthera pardus) is a complex issue, because patterns inferred from fossils and from molecular data lack congruence. Fossil evidence supports an African origin, and suggests that leopards were already present in Eurasia during the Early Pleistocene. Analysis of DNA sequences however, suggests a more recent, Middle Pleistocene shared ancestry of Asian and African leopards. These contrasting patterns led researchers to propose a two-stage hypothesis of leopard dispersal out of Africa: an initial Early Pleistocene colonisation of Asia and a subsequent replacement by a second colonisation wave during the Middle Pleistocene. The status of Late Pleistocene European leopards within this scenario is unclear: were these populations remnants of the first dispersal, or do the last surviving European leopards share more recent ancestry with their African counterparts? Results: In this study, we generate and analyse mitogenome sequences from historical samples that span the entire modern leopard distribution, as well as from Late Pleistocene remains. We find a deep bifurcation between African and Eurasian mitochondrial lineages (~ 710 Ka), with the European ancient samples as sister to all Asian lineages (~ 483 Ka). The modern and historical mainland Asian lineages share a relatively recent common ancestor (~ 122 Ka), and we find one Javan sample nested within these. Conclusions: The phylogenetic placement of the ancient European leopard as sister group to Asian leopards suggests that these populations originate from the same out-of-Africa dispersal which founded the Asian lineages. The coalescence time found for the mitochondrial lineages aligns well with the earliest undisputed fossils in Eurasia, and thus encourages a re-evaluation of the identification of the much older putative leopard fossils from the region. The relatively recent ancestry of all mainland Asian leopard lineages suggests that these populations underwent a severe population bottleneck during the Pleistocene. Finally, although only based on a single sample, the unexpected phylogenetic placement of the Javan leopard could be interpreted as evidence for exchange of mitochondrial lineages between Java and mainland Asia, calling for further investigation into the evolutionary history of this subspecies

Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data

B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approximation of smooth explicit data. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots for each surface dimension and the B-spline coefficients simultaneously. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth surfaces and comparison with a successful method have been included