On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses

We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model where spikes are effective at times multiple of a characteristic time scale $\delta$, where $\delta$ can be \textit{arbitrary} small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and Integrate-and-Fire models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.Comment: 36 pages, 9 figure

Dense reconstruction methods for active vision

This paper aims to analyse how to introduce 3D information into an active vision system . In order to do so, we propose to realiz e a dense reconstruction from a monocular sequence in an active vision application . We first present existing algorithms for dens e reconstruction . After having compared their drawbacks and advantages, we describe the chosen algorithm . Finally, we show th e results obtained from synthetic images and images acquired when using an artificial robotic head .Ce papier cherche à analyser comment introduire des données tridimensionnelles au sein d'un système de vision active. En effet, nous nous sommes proposés de réaliser une reconstruction dense 3D à partir de l'analyse d'une séquence monoculaire, dans un paradigme de vision active. Nous présentons tout d'abord les différents algorithmes déjà existants dans le domaine de la reconstruction dense, en faisant ressortir leurs avantages et leurs inconvénients. Nous décrivons, ensuite, l'algorithme choisi pour pallier à certains de ces inconvénients. Enfin, nous montrons quelques résultats à partir d'images synthétiques ou de vues réelles acquises par la tête artificielle

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

A three-parameter affine approximation of focus and zoom variations

This work aims to develop a dynamic approximation to the variation in a lens' intrinsic parameters when the zoom and focus parameters are modified . This approximation is built by tracking two generic points in a monocular image sequence. Our preliminary analysis demonstrates that a particular three-parameter affine model is sufficient to describe these modifications . The general affine model is not acceptable on a mathematical or physical level : the mathematical transformation to be used has only five parameters, instead of six, and an analysis of the physics reveals that three parameters are sufficient . Experimentally, this approximation is entirely valid, with the precision being better than 1 .5 pixels in almost every case . Using a least-squares method, we obtain very simple equations in which the precision of the estimate increases with the number of available correspondences .Dans ce travail, on approxime dynamiquement le changement de focale et de la mise au point en suivant deux points quelconques entre deux images prises par la même caméra. Plus précisément, on étudie la variation des paramètes intrinsèques lors d'un changement de la mise au point et du zoom. On démontre grâce à cette analyse, qu'un modèle de transformation affine à 3 paramètres est tout à fait suffisant, et qu'un modèle de transformation affine général ne se justifie pas, car la transformation à utiliser n'a - mathématiquement - que 5 paramètres et non 6 tandis que l'analyse physique du système montre que 3 paramètres suffisent. Expérimentalement, le modèle est justifié, car la précision est meilleure que 1.5 pixel pour des variations de la mise au point et dans tous les cas meilleure que si l'on utilise le modèle général. Par une méthode des moindres carrés on accède à des équations très simples qui nous permettent d'obtenir une précision dépendant du nombre des points suivi

Simulation of networks of spiking neurons: A review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of Computational Neuroscience, in press (2007

A New Solution to the Relative Orientation Problem using only 3 Points and the Vertical Direction

This paper presents a new method to recover the relative pose between two images, using three points and the vertical direction information. The vertical direction can be determined in two ways: 1- using direct physical measurement like IMU (inertial measurement unit), 2- using vertical vanishing point. This knowledge of the vertical direction solves 2 unknowns among the 3 parameters of the relative rotation, so that only 3 homologous points are requested to position a couple of images. Rewriting the coplanarity equations leads to a simpler solution. The remaining unknowns resolution is performed by an algebraic method using Grobner bases. The elements necessary to build a specific algebraic solver are given in this paper, allowing for a real-time implementation. The results on real and synthetic data show the efficiency of this method

Multiscale simulation of the interlaminar failure of graphene nanoplatelets reinforced fibers laminate composite materials

This article presents a multiscale approach to derive the interlaminar properties of graphene nanoplatelets (GNPs)‐based polymeric composites reinforced by short glass fibers (SGFs) and unidirectional carbon fibers (UCFs). The approach accounts for the debonding at the interface of a 2‐phases GNPs/polymer matrix using a cohesive model. The resulting composite is used within a 3‐phases nanocomposite consisting either of a GNPs/polyamide/SGFs or a GNPs/epoxy/UCFs nanocomposite. Experiments are performed for determining the interlaminar fracture toughness in mode I for the GNPs/epoxy/UCFs. Results show that the aspect ratio (AR) of GNPs influences the effective Young modulus which increases until a threshold. Also, the addition of the GNPs increases up to 10% the transverse Young modulus and up to 11% the shear modulus as well as up to 16% the transverse tensile strength useful in crashworthiness performance. However, the nanocomposite behavior remains fiber dominant in the longitudinal direction. This leads to a weak variation of the mechanical properties in that direction. Due to the well‐known uniform dispersion issues of GNPs, the interlaminar fracture toughness GIC has decreased up to 8.5% for simulation and up to 2.4% for experiments while no significant variation of the interlaminar stress distribution is obtained compared to a nanocomposite without GNPs