Approximations of Shannon Mutual Information for Discrete Variables with Applications to Neural Population Coding

Although Shannon mutual information has been widely used, its effective calculation is often difficult for many practical problems, including those in neural population coding. Asymptotic formulas based on Fisher information sometimes provide accurate approximations to the mutual information but this approach is restricted to continuous variables because the calculation of Fisher information requires derivatives with respect to the encoded variables. In this paper, we consider information-theoretic bounds and approximations of the mutual information based on Kullback--Leibler divergence and R\'{e}nyi divergence. We propose several information metrics to approximate Shannon mutual information in the context of neural population coding. While our asymptotic formulas all work for discrete variables, one of them has consistent performance and high accuracy regardless of whether the encoded variables are discrete or continuous. We performed numerical simulations and confirmed that our approximation formulas were highly accurate for approximating the mutual information between the stimuli and the responses of a large neural population. These approximation formulas may potentially bring convenience to the applications of information theory to many practical and theoretical problems.Comment: 31 pages, 6 figure

IQGAP1 knockdown enhances the endothelial barrier in vitro

IQGAP1 overexpression inhibits E-cadherin-mediated epithelial cell-cell adhesion by distabilizing the adherens junctions, and activated Rac1 and Cdc42 may prevent these effects by removing IQGAP1 from the adherens junction complex. In the present study, we determined if IQGAP1 associates with the adherens junction of endothelial cells and affects endothelial barrier function. In human umbilical vein endothelial cells (HUVECs), IQGAP1 associated with VE-cadherin, the catenins, beta, gamma, alpha, and p120, but not with N-cadherin or the tight junction proteins, occludin, claudin-5, and ZO-1. Detergent extracted most of the IQGAP1 associated with VE-cadherin. Treatment of endothelial cells with sphingosine-1-phosphate (S1P), which increases the activity of Rac1, increased the association of IQGAP1 with Rac1, and the amount of insoluble VE-cadherin and beta-catenin at intercellular junctions. To determine if the increased localization of junctional VE-cadherin induced by S1P occurred via the removal of IQGAP1, the protein level of IQGAP1 was reduced with small interfering RNA or siRNA. Reduction of IQGAP1 by transfection of siRNA resulted in a higher endothelial electrical resistance in HUVECs as compared to transfection of a scrambled siRNA. Reduction of IQGAP1 also induced an increase and a decrease, respectively, in the protein levels of VE-cadherin and N-cadherin. Also, more VE-cadherin and less N-cadherin were associated with p120 and beta-catenin. Furthermore, more insoluble (cytoskeletal-associated) VE-cadherin was localized at intercellular junctions and less insoluble N-cadherin was present in HUVECs. Overexpression of a VE-cadherin-alpha-catenin fusion protein, which lacked the binding sites for beta-catenin on VE-cadherin and alpha-catenin, diminished the localization of junctional IQGAP1. These findings suggest that IQGAP1 knockdown positively influences the endothelial barrier by increasing the protein level of VE-cadherin and the interaction of VE-cadherin with the cytoskeleton, possibly by enhancing the p120-VE-cadherin association

A comprehensive study on the role of hormones, seed coat and genes during the germination of canola (Brassica napus) seed under adverse environmental conditions

Seed vigor, although not well understood, is a key critical component for yield and is in part due to a well establishment and vigorous stand of canola (Brassica napus) seedling under less than ideal conditions in Western Canada. My objective was to determine what constitutes vigor by studying the response of a black seed line and a yellow seed line imbibed at 8 ºC in either water, saline or osmotic solutions, abscisic acid (ABA), ABA biosynthesis inhibitor, gibberellin (GA4+7), inhibitor of GA biosynthesis and a germination promoter, fusicoccin. Also tested was the effect of seed coat (testa) on seed germination rate and percent germination. Previous studies have established that seed vigor is in part hormonal controlled and genetically controlled. In our study, gene expression was investigated by using transcriptome analysis and hormonal analysis was used to quantitate the changes in hormones and their metabolites during germination. Both the black and the yellow canola seed lines were very sensitive to increasing concentrations of saline and osmotic solutions; however, at the same osmotic potential, osmotic solutions were more inhibitory. The yellow seed line was more sensitive to these conditions than the black seed line. As expected, ABA delayed seed germination, whereas GA4+7 enhanced seed germination and GA4+7 partially overcame the inhibitory effect of ABA. The seed coat was a major factor affecting the germination rate of the yellow seed line; however, GA4+7 overcame the inhibitory effect of the seed coat, whereas ABA exacerbated it. Fusicoccin was more stimulatory to germination than GA4+7; however, unlike GA4+7, it was unable to overcome the inhibitory effect of paclobutrazol, a GA biosynthesis inhibitor. Fluridone, an ABA biosynthesis inhibitor, was unable to overcome the inhibitory effects of a saline solution suggesting that the inhibitory effect was not due to elevated ABA levels. Ethylene, a stimulator of germination, did not appear to be involved in the germination of these two lines. Controlled deterioration at 35 ºC, 85% RH was either partially or completely overcome by exogenous GA4+7. This study demonstrates that the role of hormones, salinity and seed coat on the germination of canola seed under low temperature environmental conditions. During germination, ABA declined while GA4 increased. Higher ABA was found in un-germinated seeds compared to germinated seeds. GA4+7 was lower in seeds imbibed in the saline solution compared to seeds imbibed in water. Un-germinated seeds imbibed in ABA had lower GA4+7 compared to un-germinated seeds imbibed in water; however, the contents of GA4+7 were similar for germinated seeds imbibed in either water or ABA. Phaseic acid (PA) and dihydrophaseic acid (DPA) increased in seeds imbibed in either water, the saline solution or ABA, while they decreased in seeds imbibed in GA4+7. In addition, we found that ABA inhibited GA4 biosynthesis, whereas, GA had no effect on ABA biosynthesis, but altered the ABA catabolic pathway. Gene expression profiles revealed that there are significant differences between un-germinated and germinated seeds. Seeds imbibed in water, GA4+7, a saline solution or ABA had different gene profiles. LEA genes, hormone-related genes, hydrolase-related genes and specific seed germination-related genes were identified and their expression profiles were finely associated with seed germination performance

Convergence Analysis of Deep Residual Networks

Various powerful deep neural network architectures have made great contribution to the exciting successes of deep learning in the past two decades. Among them, deep Residual Networks (ResNets) are of particular importance because they demonstrated great usefulness in computer vision by winning the first place in many deep learning competitions. Also, ResNets were the first class of neural networks in the development history of deep learning that are really deep. It is of mathematical interest and practical meaning to understand the convergence of deep ResNets. We aim at characterizing the convergence of deep ResNets as the depth tends to infinity in terms of the parameters of the networks. Toward this purpose, we first give a matrix-vector description of general deep neural networks with shortcut connections and formulate an explicit expression for the networks by using the notions of activation domains and activation matrices. The convergence is then reduced to the convergence of two series involving infinite products of non-square matrices. By studying the two series, we establish a sufficient condition for pointwise convergence of ResNets. Our result is able to give justification for the design of ResNets. We also conduct experiments on benchmark machine learning data to verify our results