The ability of neuronal networks to generalize using an induction method

Inductive generalization means the ability of a neural network to learn a given algorithm using incomplete information about it. A consideration based on the information theory leads to a simple equation connecting characteristics of the network with those of the algorithm to be learned. The main conclusion is that the most efficient generalization is achieved on the networks with minimal complexity sufficient for realization of the algorithm under consideration. The obtained equation is compared with the results of computer simulations for a universal neural network obtained in the present paper as well as by other workers. A good agreement is observed between theoretical predictions for generalization efficacy and results of computer simulations.     

Oblique dipole layer potentials applied to electrocardiology

We study the properties of the potential field generated by an oblique dipole layer. This field arises, for instance, in describing the potential elicited by a depolarization wavefront spreading in the myocardium when a dependence of the potential on the cardiac fiber orientation is introduced. The representation of cardiac bioelectric sources by means of an oblique dipole layer leads to a mathematical structure which generalizes the classical solid angle theory used in electrocardiology, which has been challenged by recent experimental evidence, and links models previously proposed with a view to adequately reproduce the potential observed in experiments. We investigate also the relationship between our model and an intracellular current model and we derive potential jump formulae for some models which account for the anisotropic structure of the myocardium. The potential generated by an oblique dipole layer is considered both for unbounded and bounded domains. In the latter case an integral boundary equation is derived and we study its solvability. A numerical procedure for solving this integral equation by means of the finite element method with collocation is outlined.     

Oscillations in a refractory neural net

A functional differential equation that arises from the classic theory of neural networks is considered. As the length of the absolute refractory period is varied, there is, as shown here, a super-critical Hopf bifurcation. As the ratio of the refractory period to the time constant of the network increases, a novel relaxation oscillation occurs. Some approximations are made and the period of this oscillation is computed.     

Multiple Tests for Different Sets of Variables Using a Data‐Driven Ordering of Hypotheses,with an Application to Gene Expression Data

A multiple parametric test procedure is proposed, which considers tests of means of several variables. The single variables or subsets of variables are ordered according to a data‐dependent criterion and tested in this succession without alpha‐adjustment until the first non‐significant test. The test procedure needs the assumption of a multivariate normal distribution and utilizes the theory of spherical distributions. The basic version is particularly suited for variables with approximately equal variances. As a typical example, the procedure is applied to gene expression data from a commercial array.     

The structural error-in-equation model to evaluate individual bioequivalence

Individual bioequivalence is assessed using an extension of the classical structural equation model, known as the error-in-equation model. This procedure estimates the relationship between individual means, as well as the variance-covariance parameters, of the bioavailabilities measurement model, by considering individual means related through a straight line with a random term, whereas the classical structural equation considers a deterministic linear relationship. We discuss the implications of this approach in terms of the bioavailabilities measurement model and how to test the overall hypothesis of individual bioequivalence. Both models are compared in a simulation study and a case example is presented.     

An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series

In this paper, the extended Kalman filter (EKF) algorithm is applied to model the gene regulatory network from gene time series data. The gene regulatory network is considered as a nonlinear dynamic stochastic model that consists of the gene measurement equation and the gene regulation equation. After specifying the model structure, we apply the EKF algorithm for identifying both the model parameters and the actual value of gene expression levels. It is shown that the EKF algorithm is an online estimation algorithm that can identify a large number of parameters (including parameters of nonlinear functions) through iterative procedure by using a small number of observations. Four real-world gene expression data sets are employed to demonstrate the effectiveness of the EKF algorithm, and the obtained models are evaluated from the viewpoint of bioinformatics.     

Robust filtering circuit design for stochastic gene networks under intrinsic and extrinsic molecular noises

How to design a robust gene network to tolerate more intrinsic kinetic parameter variations and to attenuate more extrinsic environmental noises to achieve a desired filtering level will be an important topic for systems biology and synthetic biology. At present, there is no good systematic design method to achieve robust gene network design. In this study, a gene network suffering from intrinsic kinetic parameter fluctuations and extrinsic environmental noises is modeled as a Langevin equation with state-dependent stochastic noises. Based on the nonlinear stochastic filtering theory, a systematic gene circuit design method is proposed to make gene networks improve their robustness to tolerate more intrinsic noises and to attenuate extrinsic noises to a prescribed filtering level. The robust gene network design principles have not only yielded a comprehensive design theory of robust gene networks, but also gained valuable insights into the molecular noise filtering of gene networks from the systematic perspective.     

A new simplified method for constructing Wagner networks and the cladistics of Pentachaeta (Compositae,Astereae)

The new procedure for constructing a Wagner network presented differs from Farris’s (1970) method in that the amount of computation required is reduced. The usefulness of this procedure was examined by applying it to the 20 characters considered in a recent monograph of the seven OTUs of the genusPentachaeta. A single network was derived from some 945 or more networks possible for this group. A comparison of the network constructed by this simplified method to that constructed by Farris’ procedure revealed no differences. An attempt to reconstruct the cladistic history of this group by generating a Wagner tree based on the network resulted in four equally possible trees, suggesting that further data are needed before cladogenesis in this group is resolved.     

L-Leucinamide hydrogensquarate: spectroscopic and structural elucidation

The hydrogensquarate [LeuNH(2)] (HSq) of L-leucinamide has been synthesized and its structure has been determined by single crystal X-ray diffraction. A three dimensional network is formed by hydrogen bonds with participation of the O=C-NH(2) function, the hydrogensquarate ion and the N(+)H(3) group [NH(2)...O=C((Sq)) (2.840 and 2.749 A), ((Sq))OH...O=C(NH(2)) (2.618 A), NH(3) (+)...O=C((Sq)) (3.246, 2.804 and 2.823 A)], respectively. A theoretical approximation of the electronic structure was carried out by means of ab initio UMP2 and MP2 level of theory at the 6-311++G** basis set. The IR-spectroscopic assignment in the solid-phase was obtained by linear-polarized IR-spectroscopy of oriented samples as colloid suspensions in a nematic host and application of the reducing-difference procedure for the interpretation of polarized IR-spectra.     

A zonal model of cortical functions

A model of cortical functions is developed with the object of simulating the observed behavior of individual neurons organized in unit circuits and functional systems of the cerebellum, the cerebrum and the hippocampal formation. The neuronal model is capable of representing refractory and potentiated states, as well as the firing and lowest resting states. The unit circuits of each system consist of all common types of cells with known synaptic connections. In the cerebral system these unit circuits are interconnected to form columns as well as zones. A new discrete neural network equation, which takes account of interactions with the extracellular field, is proposed to simulate electrical activity in these circuits. A coherent theory of cortical activity and functions is derived that accounts for many of the observed phenomena, including those associated with the development of long-term potentiation and sequential memory. Three appendices are devoted to the theory of extracellular interactions, the derivation of non-linear network equations, and a computer program to simulate learning in the cortex.     

Dynamic neural field with local inhibition

A lateral-inhibition type neural field model with restricted connections is presented here and represents an experimental extension of the continuum neural field theory (CNFT) by suppression of the global inhibition. A modified CNFT equation is introduced and allows for a locally defined inhibition to spatially expand within the network and results in a global competition extending far beyond the range of local connections by virtue of diffusion of inhibition. The resulting model is able to attend to a moving stimulus in the presence of a very high level of noise, several distractors or a mixture of both.     

A stochastic analysis of first-order reaction networks

A stochastic model for a general system of first-order reactions in which each reaction may be either a conversion reaction or a catalytic reaction is derived. The governing master equation is formulated in a manner that explicitly separates the effects of network topology from other aspects, and the evolution equations for the first two moments are derived. We find the surprising, and apparently unknown, result that the time evolution of the second moments can be represented explicitly in terms of the eigenvalues and projections of the matrix that governs the evolution of the means. The model is used to analyze the effects of network topology and the reaction type on the moments of the probability distribution. In particular, it is shown that for an open system of first-order conversion reactions, the distribution of all the system components is a Poisson distribution at steady state. Two different measures of the noise have been used previously, and it is shown that different qualitative and quantitative conclusions can result, depending on which measure is used. The effect of catalytic reactions on the variance of the system components is also analyzed, and the master equation for a coupled system of first-order reactions and diffusion is derived. All authors contributed equally to this work.     

Control analysis of metabolic networks. 2. Total differentials and general formulation of the connectivity relations

The mathematical background of the connectivity relations of metabolic control theory is analysed. The connectivity relations are shown to reflect general properties of total differentials of reaction rate vi, flux J, and metabolite concentration Xj. Connectivity relations hold for any metabolic network in which all vi are homogeneous functions of enzyme concentration Ei. This notion allows established algebraic methods to be used for the formulation of connectivity relations for metabolic systems in which numerous constraints are imposed on metabolite concentrations. A general procedure to derive connectivity relations for such metabolic systems is given. To encourage a broader audience to apply control theory to physiological systems, an easy-to-use graphical procedure is derived for formulating connectivity relations for biochemical systems in which no metabolite is involved in more than one constraint.     

Estimation of Infiltration Parameters and the Irrigation Coefficients with the Surface Irrigation Advance Distance

A theory based on Manning roughness equation, Philip equation and water balance equation was developed which only employed the advance distance in the calculation of the infiltration parameters and irrigation coefficients in both the border irrigation and the surge irrigation. The improved procedure was validated with both the border irrigation and surge irrigation experiments. The main results are shown as follows. Infiltration parameters of the Philip equation could be calculated accurately only using water advance distance in the irrigation process comparing to the experimental data. With the calculated parameters and the water balance equation, the irrigation coefficients were also estimated. The water advance velocity should be measured at about 0.5 m to 1.0 m far from the water advance in the experimental corn fields.     

基于视觉编码的图象处理研究──Ⅰ．原理、算法及实现

提出Ｇａｂｏｒ小波表达的概念及其在图象处理中实现的数学模型和算法框架,主要解决了运算中非正交性问题、收敛性问题,使得该算法及模型可以实现图象的分析和重建,并且可以应用于对视觉编码理论的解释。     

时滞BAM神经网络模型的稳定性分析

本文研究了一个含有n+1个神经元的多时滞BAM型神经网络模型.利用儒歇定理及其推论分析了该动力特征方程根的分布情况,进而得到动力系统稳定和Hopf分支存在的条件,画出了分支图.研究了该动力系统的Pitchfork分支,得到了Pitchfork分支曲线,讨论了在分支曲线的不同区域里平衡点的稳定性.     

基于视觉编码的图象处理研究──Ⅰ．原理、算法及实现

提出Ｇａｂｏｒ小波表达的概念及其在图象处理中实现的数学模型和算法框架,主要解决了运算中非正交性问题、收敛性问题,使得该算法及模型可以实现图象的分解和重建,并且可以应用于对视觉编码理论的解释。     

Quantitative evaluation of the allometric transformation of of biological structures

Detection and quantification of allometry is a crucial problem in understanding morphological changes, both for systematic and morphogenetic purposes. A section of S.A.M. (Shape Analytical Morphometry) software system was used for this attempt. It consists of the following steps: a) boundary detection; b) starting point detection; c) size normalization; d) extraction of the fundamental shape by Kth order polynomials; e) finding of symmetry evaluator (S.A.E.) by means of a second degree equation. This last procedure gives an arc-chord complex that expresses a vector for allometry where intercept value was for application point, first degree coefficient was for direction and second degree coefficient was for modulus and versus. The main parameters, isometry fraction and allometry fraction may be understood referring them to morphogenetic models.