A new stochastic STDP Rule in a neural Network Model

Thought to be responsible for memory, synaptic plasticity has been widely studied in the past few decades. One example of plasticity models is the popular Spike Timing Dependent Plasticity (STDP). The huge litterature of STDP models are mainly based deterministic rules whereas the biological mechanisms involved are mainly stochastic ones. Moreover, there exist only few mathematical studies on plasticity taking into account the precise spikes timings. In this article, we aim at proposing a new stochastic STDP rule with discrete synaptic weights which allows a mathematical analysis of the full network dynamics under the hypothesis of separation of timescales. This model attempts to answer the need for understanding the interplay between the weights dynamics and the neurons ones

A lower bound in Nehari's theorem on the polydisc

By theorems of Ferguson and Lacey (d=2) and Lacey and Terwilleger (d>2), Nehari's theorem is known to hold on the polydisc D^d for d>1, i.e., if H_\psi is a bounded Hankel form on H^2(D^d) with analytic symbol \psi, then there is a function \phi in L^\infty(\T^d) such that \psi is the Riesz projection of \phi. A method proposed in Helson's last paper is used to show that the constant C_d in the estimate \|\phi\|_\infty\le C_d \|H_\psi\| grows at least exponentially with d; it follows that there is no analogue of Nehari's theorem on the infinite-dimensional polydisc

A Mathematical Analysis of Memory Lifetime in a simple Network Model of Memory

We study the learning of an external signal by a neural network and the time to forget it when this network is submitted to other signals considered as noise. The presentation of an external stimulus changes the state of the synapses in a network of binary neurons. Multiple presentations of a unique signal leads to its learning. Then, the presentation of other signals also changes the synaptic weight (during the forgetting time). We study the number of external signals to which the network can be submitted until the initial signal is considered as forgotten. We construct an estimator of the initial signal thanks to the synaptic currents. In our model, these synaptic currents evolve as Markov chains. We study mathematically these Markov chains and obtain a lower bound on the number of external stimulus that the network can receive before the initial signal is forgotten. We finally present numerical illustrations of our results

Comparison and contrast in perceptual categorization

People categorized pairs of perceptual stimuli that varied in both category membership and pairwise similarity. Experiments 1 and 2 showed categorization of 1 color of a pair to be reliably contrasted from that of the other. This similarity-based contrast effect occurred only when the context stimulus was relevant for the categorization of the target (Experiment 3). The effect was not simply owing to perceptual color contrast (Experiment 4), and it extended to pictures from common semantic categories (Experiment 5). Results were consistent with a sign-and-magnitude version of N. Stewart and G. D. A. Brown's (2005) similarity-dissimilarity generalized context model, in which categorization is affected by both similarity to and difference from target categories. The data are also modeled with criterion setting theory (M. Treisman & T. C. Williams, 1984), in which the decision criterion is systematically shifted toward the mean of the current stimuli

Structural constraints on the emergence of oscillations in multi-population neural networks

Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.Comment: Main text: 30 pages, 5 Figures. Supplementary information: 20 pages, 9 Figures. Supplementary Information is integrated in the main fil

Kajian Penambahan Gambir sebagai Bahan Penyamak Nabati terhadap Mutu Kimiawi Kulit Kambing

Gambier contains tannin which functions as vegetable tanning material. This study aimed to determine, the gambier addition to produces the best chemical quality leather according to Indonesian National Standard chemical quality goatleather (SNI 06-0463-1989). The method was used experimental method randomized block design, which consists of 5 treatments with 4 replications. Treatment of this study was added the gambier percentage (%), each treatment consisting of: treatment A: 15%, B: 20%, C: 25%, D: 30%, and E: 35%. The variables were measured water content, oil/fat content, water-soluble substances content, levels of substances rawhide, levels of insoluble ash in the water, levels of tanning substances (tannins) bound and the tanning degree. The results showed a significantly different effect (P 0.05) oil/fat content, ash content and levels of tanning substances (tannins) bound. The conclusion of this study was the addition of 25% was the best gambier percentage, with 17.06±0.15% water content, the fat/oil 7.69±1.24%, the levels of water-soluble substances 4.16±0.99%, levels of substances rawhide 42.47±6.39%, 0.99±0.03% levels of insoluble ash in the water, levels of tanning substances (tannins) bound 27.63±2.75% and 65.46% tanning degree, which all meet the quality standard ISO test 06-0994-1989 and SNI No.0253-2009

Von Bezold assimilation effect reverses in stereoscopic conditions

Lightness contrast and lightness assimilation are opposite phenomena: in contrast, grey targets appear darker when bordering bright surfaces (inducers) rather than dark ones; in assimilation, the opposite occurs. The question is: which visual process favours the occurrence of one phenomenon over the other? Researchers provided three answers to this question. The first asserts that both phenomena are caused by peripheral processes; the second attributes their occurrence to central processes; and the third claims that contrast involves central processes, whilst assimilation involves peripheral ones. To test these hypotheses, an experiment on an IT system equipped with goggles for stereo vision was run. Observers were asked to evaluate the lightness of a grey target, and two variables were systematically manipulated: (i) the apparent distance of the inducers; and (ii) brightness of the inducers. The retinal stimulation was kept constant throughout, so that the peripheral processes remained the same. The results show that the lightness of the target depends on both variables. As the retinal stimulation was kept constant, we conclude that central mechanisms are involved in both lightness contrast and lightness assimilation

A mathematical approach on memory capacity of a simple synapses model

International audienceNetwork models of Memory: Capacity of neural networks in memorising external inputs is a complex problem which has given rise to numerous research. It is widely accepted that memory sits where communication between two neurons takes place, in synapses. It involves a huge number of chemical reactions, cascades, ion flows, protein states and even more mechanisms, which makes it really complex. Such a complexity stresses the need of simplifying models: this is done in network models of memory. Problem: Most of these models don't take into account both synaptic plasticity and neural dynamic. Adding dynamics on the weights makes the analysis more difficult which explains that most models consider either a neural or a synaptic weight dynamic. We decided to study the binary synapses model of Amit and Fusi (1994), model we wish to complete with a neural network afterwards in order to get closer to biology. Purpose: Propose a rigorous mathematical approach of the model of Amit and Fusi (1994) as part of a more ambitious aim which is to have a general mathematical framework adapted to many models of memory