Two-point heterogeneous connections in a continuum neural field model

We examine a novel heterogeneous connection scheme in a 1D continuum neural field model. Multiple two-point connections are added to a local connection function in order to model the “patchy” connections seen in, for example visual cortex. We use a numerical approach to solve the equations, choosing the locations of the two-point connections stochastically. We observe self-sustained persistent fluctuations of activity which can be classified into two types (one of which is similar to that seen in network models of discrete excitable neurons, the other being particular to this model). We study the effect of parameters such as system size and the range, number and strength of connections, on the probability that a particular realisation of the connections is able to exhibit persistent fluctuations.     

Waves in a simple,excitable or oscillatory,reaction-diffusion model

A simple one variable caricature for oscillating and excitable reaction-diffusion systems is introduced. It is shown that as a parameter, , varies the system dynamics change from oscillatory ( > ₀) to excitable ( < ₀) and the frequency of the oscillation vanishes as for ₀. When such dynamics are coupled by continuous diffusion in a ring geometry (1-space dimension), propagating wave trains may be found. On an infinite ring excitable devices lead to unique solitary waves which are analogous to pulse waves. A solvable example is presented, illustrating properties of dispersion, excitability, and waves. Finally it is shown that the caricature arises in a natural way from more general excitable/oscillatory systems.     

Derivation of a field equation of brain activity

We present a nonlinear field theory of the brain under realistic anatomical connectivity conditions describing the interaction between functional units within the brain. This macroscopic field theory is derived from the quasi-microscopic conversion properties of neural populations occurring at synapses and somas. Functional units are treated as inhomogeneities within a nonlinear neural tissue.     

Stability switches,oscillatory multistability,and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks

A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss computational properties of the system due to the delay when an external drive of the network mimicks external sensory input.     

Relative longevity and field metabolic rate in birds

Metabolism is a defining feature of all living organisms, with the metabolic process resulting in the production of free radicals that can cause permanent damage to DNA and other molecules. Surprisingly, birds, bats and other organisms with high metabolic rates have some of the slowest rates of senescence begging the question whether species with high metabolic rates also have evolved mechanisms to cope with damage induced by metabolism. To test whether species with the highest metabolic rates also lived the longest I determined the relationship between relative longevity (maximum lifespan), after adjusting for annual adult survival rate, body mass and sampling effort, and mass-specific field metabolic rate (FMR) in 35 species of birds. There was a strongly positive relationship between relative longevity and FMR, consistent with the hypothesis. This conclusion was robust to statistical control for effects of potentially confounding variables such as age at first reproduction, latitude and migration distance, and similarity in phenotype among species because of common phylogenetic descent. Therefore, species of birds with high metabolic rates senesce more slowly than species with low metabolic rates.     

Induced electric field and current density patterns in bone fractures

We have used the low frequency solver of the computer program SEMCAD‐X to model the induced electric field and current density patterns in simple models of a fractured femur embedded off‐center in cylindrical muscle tissue; a 1 cm fracture gap is filled with callus. The model is exposed to a 1 kHz, 1 mT sinusoidal magnetic field. The frequency chosen is typical of the major Fourier components of many waveforms used to stimulate fracture healing using pulsed magnetic fields; the intensity is also a typical level. Models include fractures perpendicular to the bone and at an angle from the perpendicular, each exposed to a field applied parallel to the bone or parallel to either of the two axes perpendicular to it. We find that all directions of applied magnetic fields produce essentially parallel induced electric fields and current densities through the plane of the callus, but that a magnetic field applied parallel to the bone induces considerably higher fields and currents than the same strength field applied in either perpendicular direction. Because investigations of pulsed‐field devices, including modeling of induced fields and currents, peaked more than a decade ago, this is the first application to our knowledge of the current capabilities of computer modeling systems to biological systems at low frequencies. Bioelectromagnetics 33:585–593, 2012. © 2012 Wiley Periodicals, Inc.     

Clocks and patterns in myxobacteria: a remembrance of Art Winfree

At the beginning of their aggregation phase waves of cell density sweep across the surface of myxobacteria colonies. These waves are unlike any other in biology. Waves can be linear, concentric or spiral and when they collide, instead of annihilating one another they appear to pass through each other unchanged. Moreover, the wavelength determines the spacing and pattern of fruiting bodies that will rise up presaging sporulation. The explanation for these waves was suggested by the work of Art Winfree on cellular clocks, and confirmed by a mathematical model that explains all of the observed wave behavior. The story of how this model evolved illustrates the roles of chance and scientific networking in the search for the explanation of a new phenomenon.     

Dynamical correlation patterns and corresponding community structure in neural spontaneous activity at criticality

It has been considered that the state in the vicinity of a critical point, which is the point between ordered and disordered states, can underlie and facilitate information processing of the brain in various aspects. In this research, we numerically study the influence of criticality on one aspect of brain information processing, i.e., the community structure, which is an important characteristic of complex networks. We examine community structure of the functional connectivity in simulated brain spontaneous activity, which is based on dynamical correlations between neural activity patterns at different positions. The brain spontaneous activity is simulated by a neural field model whose parameter covers subcritical, critical, and supercritical regions. Then, the corresponding dynamical correlation patterns and community structure are compared. In the critical region, we found some distinctive properties, namely high correlation and correlation switching, high modularity and a low number of modules, high stability of the dynamical functional connectivity, and moderate flexibility of the community structure across temporal scales. We also discuss how these characteristics might improve information processing of the brain.     

Influence of Various Feeding Conditions,the Migrating Myoelectric Complex and Cholinergic Drugs on Antral Slow Waves in Sheep

The presented study was designed to elucidate whether the cholinergic mechanisms control ovine antral slow waves in various physiological conditions, including feeding and various phases of migrating myoelectric complex (MMC). The investigations were carried out on six adult sheep of Polish Merino breed with seven bipolar electrodes surgically implanted onto the antral and small intestinal wall. In the course of chronic experiments, the myoelectric activity was recorded from these regions using the multichannel electroencephalograph. Experiments were performed on 48h fasted and non-fasted animals. During some of these experiments, sheep were fed with standard fodder. During control experiments 0.15M NaCl was slowly administered i.v. through the indwelling catheter and during other experiment, hexamethonium bromide (2.0 and 5.0mg/kg), atropine sulfate (0.02; 0.1; 0.5 and 1.5mg/kg) and pirenzepine dihydrochloride (0.02; 0.5 and 2.0mg/kg) were administered i.v. during phase 1-2a or 2b MMC. The drugs were also given in combinations. The recordings were analysed and the antral slow wave amplitudes and frequencies were calculated. Unlike the slow wave amplitude, either feeding or the anticholinergic drugs significantly increased slow wave frequency, especially when the given procedure was started during phase 2b MMC. The most pronounced effects were observed after hexamethonium given alone or in combinations. Thus, the cholinergic system modulates antral slow wave frequency in sheep.     

Existence and stability of local excitations in homogeneous neural fields

Summary Dynamics of excitation patterns is studied in one-dimensional homogeneous lateral-inhibition type neural fields. The existence of a local excitation pattern solution as well as its waveform stability is proved by the use of the Schauder fixed-point theorem and a generalized version of the Perron-Frobenius theorem of positive matrices to the function space. The dynamics of the field is in general multi-stable so that the field can keep short-term memory.     

Travelling waves and EEG patterns during epileptic seizure: analysis with an integrate-and-fire neural network

Epilepsy is characterized by paradoxical patterns of neural activity. They may cause different types of electroencephalogram (EEG), which dynamically change in shape and frequency content during the temporal evolution of seizure. It is generally assumed that these epileptic patterns may originate in a network of strongly interconnected neurons, when excitation dominates over inhibition. The aim of this work is to use a neural network composed of 50 x 50 integrate-and-fire neurons to analyse which parameter alterations, at the level of synapse topology, may induce network instability and epileptic-like discharges, and to study the corresponding spatio-temporal characteristics of electrical activity in the network. We assume that a small group of central neurons is stimulated by a depolarizing current (epileptic focus) and that neurons are connected via a Mexican-hat topology of synapses. A signal representative of cortical EEG (ECoG) is simulated by summing the membrane potential changes of all neurons. A sensitivity analysis on the parameters describing the synapse topology shows that an increase in the strength and in spatial extension of excitatory vs. inhibitory synapses may cause the occurrence of travelling waves, which propagate along the network. These propagating waves may cause EEG patterns with different shape and frequency, depending on the particular parameter set used during the simulations. The resulting model EEG signals include irregular rhythms with large amplitude and a wide frequency content, low-amplitude high-frequency rapid discharges, isolated or repeated bursts, and low-frequency quasi-sinusoidal patterns. A slow progressive temporal variation in a single parameter may cause the transition from one pattern to another, thus generating a highly non-stationary signal which resembles that observed during ECoG measurements. These results may help to elucidate the mechanisms at the basis of some epileptic discharges, and to relate rapid changes in EEG patterns with the underlying alterations at the network level.     

带时滞互惠模型的稳定性和行波解的存在性

本文建立了一类空间非局部带时滞影响的互惠生物种群系统模型.前部分利用线性化方法证明了该模型的简单动力学行为,即证明了零平衡点和两个边界平衡点都是不稳定的,唯一的正平衡点是稳定的,同时还用Redlinger上下解方法得出了该模型的初边值问题存在唯一的正则解;后部分则证明了该反应扩散系统连接零平衡点和正平衡点的行波解的存在性.     

Short period oscillations in wintertime atmospheric vortidty patterns and the geomagnetic field

Abstract

An oscillation is reported to exist in an index which measures the atmospheric vorticity over most of the northern hemisphere. This oscillation has a period very close to nine days and it is more prominent during the colder part of the year. Possible relationships between the atmospheric vorticity index and the geomagnetic field are discussed.     

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.     

赣榆县厉庄地埂利用型式试验

在赣榆县厉庄以大金鸡菊、紫穗槐和红柳三种经济植物进行了地埂利用型式试验,取得了比较明显的水土保持效果和改善农田小环境的生态效益。栽植后第三年植物覆盖率达90％或100％;地面蒸发量减少15.2～17.7％;截留降水量为0.5～0.7mm;大气相对湿度提高3.7～5.4％;土壤养分也有不同程度的增加。经济效益估测每亩地埂可收到300～600元,比种黄豆高5～9倍。效益最好的是红柳,大金鸡菊次之,紫穗槐较低。     

Learning and coding of concepts in neural networks

Our environment consists of virtually an infinite number of scenarios in which we have to function. In order to respond properly to an incoming stimulus, the brain has first to analyze it, and to find out the basic familiar elements that are part of it. In other words, by using a library which contains a relatively small number of basic concepts, the brain analyzes the multitude of incoming events. Some of those basic concepts are innate, but many of them must be learned, in order to accommodate for the arbitrary environment around us. A classifying box is defined as the neural network that finds out the familiar concepts that are present in an incoming stimulus. Models for classifying boxes are introduced, and possible mechanisms by which they may establish their libraries of concepts are suggested, and then compared and evaluated by computer simulations.     

Smad signaling in the neural crest regulates cardiac outflow tract remodeling through cell autonomous and non-cell autonomous effects

Neural crest cells (NCCs) are indispensable for the development of the cardiac outflow tract (OFT). Here, we show that mice lacking Smad4 in NCCs have persistent truncus arteriosus (PTA), severe OFT cushion hypoplasia, defective OFT elongation, and mispositioning of the OFT. Cardiac NCCs lacking Smad4 have increased apoptosis, apparently due to decreased Msx1/2 expression. This contributes to the reduction of NCCs in the OFT. Unexpectedly, mutants have MF20-expressing cardiomyocytes in the splanchnic mesoderm within the second heart field (SHF). This may result from abnormal differentiation or defective recruitment of differentiating SHF cells into OFT. Alterations in Bmp4, Sema3C, and PlexinA2 signals in the mutant OFT, SHF, and NCCs, disrupt the communications among different cell populations. Such disruptions can further affect the recruitment of NCCs into the OFT mesenchyme, causing severe OFT cushion hypoplasia and OFT septation failure. Furthermore, these NCCs have drastically reduced levels of Ids and MT1-MMP, affecting the positioning and remodeling of the OFT. Thus, Smad-signaling in cardiac NCCs has cell autonomous effects on their survival and non-cell autonomous effects on coordinating the movement of multiple cell lineages in the positioning and the remodeling of the OFT.     

典型河谷型城市春季温湿场特征及其生态环境效应

快速的城市化对城市气候要素产生了重要的影响,城市温度场、湿度场的分布格局和结构特征强烈的影响着城市生态系统的物流、能流,产生了一系列生态环境效应.应用城市气候流动观测、定点观测、GIS空间分析和遥感反演等方法,模拟分析了典型河谷型城市——兰州市的春季温湿场特征和演变规律,结果表明:一日中14:30和20:30温度场的分布格局较为类似,高值区主要位于火车站、第二热电厂、五里铺十字、盘旋路围成的高惯高耗区域;8:30温度场的热中心位于西关十字至胜利宾馆开发程度较高的商贸区附近;一日中8:30和20:30的湿度场分布格局较为相似,湿度场强度较大的区域主要位于城区北部的徐家山森林公园、雁滩村、高滩村等开发程度较弱的绿地区和低惯低耗区,高湿度区分布与高植被覆盖率区域基本一致.利用景观生态学理论,热场空间分布结合NDVI分布,进行了热力景观空间格局分析和热力景观类型的划分,城区不同热力景观格局的形成与能耗、人口、建筑、下垫面类型之间存在显著的因果关系,NDVI＞0.5的区域对应湿度场强度高值区、热场强度低值区.利用城、郊气象站观测数据,分析了近50年城区热岛效应和干岛效应强度的变化规律,近50年城区热岛强度和干岛强度呈现逐渐增强的趋势,热岛强度的线性趋势达到0.31℃/10a,干岛强度的线性趋势达到-2.1％/10a,20世纪70年代之后急剧增强.城市热岛强度和干岛强度作为人类活动对城市生态系统影响的一种量度,与各时段城市化发展水平、城市建设规模、城市下垫面性质的改变等因素是密切联系的.     

Rac1 deficiency in the forebrain results in neural progenitor reduction and microcephaly

The Rho family of small GTPases has been implicated in many neurological disorders including mental retardation, but whether they are involved in primary microcephaly (microcephalia vera) is unknown. Here, we examine the role of Rac1 in mammalian neural progenitors and forebrain development by a conditional gene-targeting strategy using the Foxg1-Cre line to delete floxed-Rac1 alleles in the telencephalic ventricular zone (VZ) of mouse embryos. We found that Rac1 deletion in the telencephalic VZ progenitors resulted in reduced sizes of both the striatum and cerebral cortex. Analyses further indicated that this abnormality was caused by accelerated cell-cycle exit and increased apoptosis during early corticogenesis (approximately E14.5), leading to a decrease of the neural progenitor pool in mid-to-late telencephalic development (E16.5 to E18.5). Moreover, the formation of patch-matrix compartments in the striatum was impaired by Rac1-deficiency. Together, these results suggest that Rac1 regulates self-renewal, survival, and differentiation of telencephalic neural progenitors, and that dysfunctions of Rac1 may lead to primary microcephaly.