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

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 high-resolution pointing system for fast scanning platforms: The EBEX example

The E and B experiment (EBEX) is a balloon-borne telescope designed to measure the polarization of the cosmic microwave background with 8' resolution employing a gondola scanning with speeds of order degree per second. In January 2013, EBEX completed 11 days of observations in a flight over Antarctica covering $\sim$ 6000 square degrees of the sky. The payload is equipped with two redundant star cameras and two sets of three orthogonal gyroscopes to reconstruct the telescope attitude. The EBEX science goals require the pointing to be reconstructed to approximately 10" in the map domain, and in-flight attitude control requires the real time pointing to be accurate to $\sim$ 0.5$^{\circ}$ . The high velocity scan strategy of EBEX coupled to its float altitude only permits the star cameras to take images at scan turnarounds, every $\sim$ 40 seconds, and thus requires the development of a pointing system with low noise gyroscopes and carefully controlled systematic errors. Here we report on the design of the pointing system and on a simulation pipeline developed to understand and minimize the effects of systematic errors. The performance of the system is evaluated using the 2012/2013 flight data, and we show that we achieve a pointing error with RMS=25" on 40 seconds azimuth throws, corresponding to an error of $\sim$ 4.6" in the map domain.Comment: 14 pages, Proceedings of the 2015 IEEE Aerospace Conferenc

Rigidity and Non-recurrence along Sequences

Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main focus in this article is to characterize explicitly the structural properties of sequences which can be rigidity sequences or non-recurrent sequences for some weakly mixing dynamical system. For ergodic transformations generally and for weakly mixing transformations in particular there are both parallels and distinctions between the class of rigid sequences and the class of non-recurrent sequences. A variety of classes of sequences with various properties are considered showing the complicated and rich structure of rigid and non-recurrent sequences

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

Composition Operators and Endomorphisms

If $b$ is an inner function, then composition with $b$ induces an endomorphism, $\beta$, of $L^\infty(\mathbb{T})$ that leaves $H^\infty(\mathbb{T})$ invariant. We investigate the structure of the endomorphisms of $B(L^2(\mathbb{T}))$ and $B(H^2(\mathbb{T}))$ that implement $\beta$ through the representations of $L^\infty(\mathbb{T})$ and $H^\infty(\mathbb{T})$ in terms of multiplication operators on $L^2(\mathbb{T})$ and $H^2(\mathbb{T})$. Our analysis, which is based on work of R. Rochberg and J. McDonald, will wind its way through the theory of composition operators on spaces of analytic functions to recent work on Cuntz families of isometries and Hilbert $C^*$-modules

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