A low-order model of biological neural networks

A biologically plausible low-order model (LOM) of biological neural networks is proposed. LOM is a recurrent hierarchical network of models of dendritic nodes and trees; spiking and nonspiking neurons; unsupervised, supervised covariance and accumulative learning mechanisms; feedback connections; and a scheme for maximal generalization. These component models are motivated and necessitated by making LOM learn and retrieve easily without differentiation, optimization, or iteration, and cluster, detect, and recognize multiple and hierarchical corrupted, distorted, and occluded temporal and spatial patterns. Four models of dendritic nodes are given that are all described as a hyperbolic polynomial that acts like an exclusive-OR logic gate when the model dendritic nodes input two binary digits. A model dendritic encoder that is a network of model dendritic nodes encodes its inputs such that the resultant codes have an orthogonality property. Such codes are stored in synapses by unsupervised covariance learning, supervised covariance learning, or unsupervised accumulative learning, depending on the type of postsynaptic neuron. A masking matrix for a dendritic tree, whose upper part comprises model dendritic encoders, enables maximal generalization on corrupted, distorted, and occluded data. It is a mathematical organization and idealization of dendritic trees with overlapped and nested input vectors. A model nonspiking neuron transmits inhibitory graded signals to modulate its neighboring model spiking neurons. Model spiking neurons evaluate the subjective probability distribution (SPD) of the labels of the inputs to model dendritic encoders and generate spike trains with such SPDs as firing rates. Feedback connections from the same or higher layers with different numbers of unit-delay devices reflect different signal traveling times, enabling LOM to fully utilize temporally and spatially associated information. Biological plausibility of the component models is discussed. Numerical examples are given to demonstrate how LOM operates in retrieving, generalizing, and unsupervised and supervised learning.     

The impact of network topology on the performance of MAP selection algorithms

The performance of the Hierarchical Mobile IPv6 (HMIPv6) protocol is affected by the Mobility Anchor Point (MAP) selection. Many MAP selection algorithms have been proposed. Researchers have based their algorithms on different operating principles, movement patterns and evaluation metrics, while the network topology model has remained essentially the same – a simple tree. Our study abolishes this restriction by expanding the research to different types of topologies. They are compared both analytically and by simulation. The results show that trees differ from other topologies in an important aspect. They do not allow the simultaneous reduction of average distance from Mobile Node (MN) to MAP and frequency of MAP changes. As a consequence, widely accepted cost functions can only be reduced by careful consideration of user-specific parameters such as speed and communication activity. We show that in other topologies, including internet models, there is no such limitation. The paper also analyses the topology characteristics that are beneficial to MAP selection, leading to simultaneous reduction of MAP distances and frequency of MAP changes. The demonstrated characteristics are verified by simulations of topology evolution.     

Recoding patterns of sensory input: higher-order features and the function of nonlinear dendritic trees

Here analytical and simulation results are presented characterizing the recoding arising when overlapping patterns of sensor input impinge on an array of model neurons with branched thresholded dendritic trees. Thus, the neural units employed are intended to capture the integrative behavior of pyramidal cells that sustain isolated Na(+) or NMDA spikes in their branches. Given a defined set of sensor vectors, equations were derived for the probability of firing of both branches and neurons and for the expected overlap between the neural firing patterns triggered by two afferent patterns of given overlap. Thus, both the sparseness of the neural representation and the orthogonalization of overlapping vectors were computed. Simulations were then performed with an array of 1000 neurons comprising 30,000 branches to verify the analytical results and confirm their applicability to systems (which include any practicable artificial system) in which the combinatorically possible branches and neurons are severely subsampled. A means of readout and a measure of discrimination performance were provided so that the accuracy of discrimination among overlapping sensor vectors could be optimized as a function of neuron structure parameters. Good performance required both orthogonalization of the afferent patterns, so that discrimination was accurate and free of interference, and maintenance of a minimum level of neural activity, so that some neurons fired in response to each sensor pattern. It is shown that the discrimination performance achieved by arrays of neurons with branched dendritic trees could not be reached with single-compartment units, regardless of how many of the latter are used. The analytical results furnish a benchmark against which to measure further enhancements in the performance of subsequent simulated systems incorporating local neural mechanisms which, while often less amenable to closed-form analysis, are ubiquitous in biological neural circuitry.     

Mean instantaneous firing frequency is always higher than the firing rate

Frequency coding is considered one of the most common coding strategies employed by neural systems. This fact leads, in experiments as well as theoretical studies, to construction of so-called transfer functions, where the output firing frequency is plotted against the input intensity. The term "firing frequency" can be understood differently in different contexts. Basically, it means that the number of spikes over an interval of preselected length is counted and then divided by the length of the interval, but due to the obvious limitations, the length of observation cannot be arbitrarily long. Then firing frequency is defined as reciprocal to the mean interspike interval. In parallel, an instantaneous firing frequency can be defined as reciprocal to the length of current interspike interval, and by taking a mean of these, the definition can be extended to introduce the mean instantaneous firing frequency. All of these definitions of firing frequency are compared in an effort to contribute to a better understanding of the input-output properties of a neuron.     

Time-varying contour topology

The contour tree has been used to compute the topology of isosurfaces, generate a minimal seed set for accelerated isosurface extraction, and provide a user interface to segment individual contour components in a scalar field. In this paper, we extend the benefits of the contour tree to time-varying data visualization. We define temporal correspondence of contour components and describe an algorithm to compute the correspondence information in time-dependent contour trees. A graph representing the topology changes of time-varying isosurfaces is constructed in real-time for any selected isovalue using the precomputed correspondence information. Quantitative properties, such as surface area and volume of contour components, are computed and labeled on the graph. This topology change graph helps users to detect significant topological and geometric changes in time-varying isosurfaces. The graph is also used as an interactive user interface to segment, track, and visualize the evolution of any selected contour components over time.     

Canonical Forms and Algorithms for Steiner Trees in Uniform Orientation Metrics

We present some fundamental structural properties for minimum length networks (known as Steiner minimum trees) interconnecting a given set of points in an environment in which edge segments are restricted to λ uniformly oriented directions. We show that the edge segments of any full component of such a tree contain a total of at most four directions if λ is not a multiple of 3, or six directions if λ is a multiple of 3. This result allows us to develop useful canonical forms for these full components. The structural properties of these Steiner minimum trees are then used to resolve an important open problem in the area: does there exist a polynomial time algorithm for constructing a Steiner minimum tree if the topology of the tree is known? We obtain a simple linear time algorithm for constructing a Steiner minimum tree for any given set of points and a given Steiner topology.     

The dynamics of integrate-and-fire: mean versus variance modulations and dependence on baseline parameters

The leaky integrate-and-fire (LIF) is the simplest neuron model that captures the essential properties of neuronal signaling. Yet common intuitions are inadequate to explain basic properties of LIF responses to sinusoidal modulations of the input. Here we examine responses to low and moderate frequency modulations of both the mean and variance of the input current and quantify how these responses depend on baseline parameters. Across parameters, responses to modulations in the mean current are low pass, approaching zero in the limit of high frequencies. For very low baseline firing rates, the response cutoff frequency matches that expected from membrane integration. However, the cutoff shows a rapid, supralinear increase with firing rate, with a steeper increase in the case of lower noise. For modulations of the input variance, the gain at high frequency remains finite. Here, we show that the low-frequency responses depend strongly on baseline parameters and derive an analytic condition specifying the parameters at which responses switch from being dominated by low versus high frequencies. Additionally, we show that the resonant responses for variance modulations have properties not expected for common oscillatory resonances: they peak at frequencies higher than the baseline firing rate and persist when oscillatory spiking is disrupted by high noise. Finally, the responses to mean and variance modulations are shown to have a complementary dependence on baseline parameters at higher frequencies, resulting in responses to modulations of Poisson input rates that are independent of baseline input statistics.     

Stability of Dissipation Elements: A Case Study in Combustion

Recently, dissipation elements have been gaining popularity as a mechanism for measurement of fundamental properties of turbulent flow, such as turbulence length scales and zonal partitioning. Dissipation elements segment a domain according to the source and destination of streamlines in the gradient flow field of a scalar function f : → ?. They have traditionally been computed by numerically integrating streamlines from the center of each voxel in the positive and negative gradient directions, and grouping those voxels whose streamlines terminate at the same extremal pair. We show that the same structures map well to combinatorial topology concepts developed recently in the visualization community. Namely, dissipation elements correspond to sets of cells of the Morse‐Smale complex. The topology‐based formulation enables a more exploratory analysis of the nature of dissipation elements, in particular, in understanding their stability with respect to small scale variations. We present two examples from combustion science that raise significant questions about the role of small scale perturbation and indeed the definition of dissipation elements themselves.     

Graph topology and gap topology for unstable systems

A reformation is provided of the graph topology and the gap topology for a general setting (including lumped linear time-invariant systems and distributed linear time-invariant systems) in the frequency domain. Some essential properties and their comparisons are clearly presented in the reformulation. It is shown that the gap topology is suitable for general systems rather than square systems with unity feedback. It is shown that whenever an unstable plant can be stabilized by feedback, it is a closed operator, mapping a subspace of the input space to the output space. Hence, the gap topology can always be applied whenever the unstable plant can be stabilized. The graph topology and the gap topology are suitable for different subsets of systems and have many similar characteristics. If one confines them to the same subset, they will be identical. The definitions of the graph metric and the gap metric are discussed     

节点移动性对MANETs网络拓扑特征的影响

在影响MANETs网络性能的众多因素之中,动态变化的网络拓扑结构是不可忽视的一个重要方面,而节点的移动特性是导致MANET网络拓扑变化的主要原因之一,因此研究节点的移动性对网络拓扑结构特性的影响具有重要的意义。采用复杂网络理论研究节点移动性对MANET网络拓扑结构统计特性的影响。介绍复杂网络的基本统计特性参数,通过仿真实验,详细分析了几种经典节点移动模型下,节点移动速度、信号辐射半径、节点密度等参数对MANET网络的平均度、聚类系数和调和平均最短路径长度的影响。结果表明节点的移动方式对MANET网络拓扑结构统计特性产生不同的影响。     

神经元膜电位对信息的编码

神经元膜电位的放电活动是神经编码的基础。然而,目前对于神经元电活动对神经信息的编码方式,至今尚未形成一个完整的认识。传统的编码理论认为神经系统以离散的动作电位放电序列进行信息的表达和传递,主要研究动作电位的发放频率和放电活动的时间模式。基于该理论,对神经元放电序列所携带的信息已经出现了一些定量的计算方法,但这些方法还很难应用到大规模神经元网络的计算当中。本研究以神经元的膜电位为研究对象,展示了如何量化膜电位序列所携带的信息,并将该计算结果与传统放电序列方沣的计算结果进行了对比分析,其结果取得了很好的一致性。本研究为神经活动信息量的定量计算提供了一种新的思路和方法。     

Convergence of topological patterns of optimal periodic structures under multiple scales

The current techniques for topology optimization of material microstructure are typically based on infinitely small and periodically repeating base cells. These base cells have no actual size. It is uncertain whether the topology of the microstructure obtained from such a material design approach could be translated into real structures of macroscale. In this work we have carried out a first systematic study on the convergence of topological patterns of optimal periodic structures, the extreme case of which is a material microstructure with infinitesimal base cells. In a series of numerical experiments, periodic structures under various loading and boundary conditions are optimized for stiffness and frequency. By increasing the number of unit cells, we have found that the topologies of the unit cells converge rapidly to certain patterns. It is envisaged that if we continue to increase the number of unit cells and thus reduce the size of each unit cell until it becomes the infinitesimal material base cell, the optimal topology of the unit cell would remain the same. The finding from this work is of significant practical importance and theoretical implication because the same topological pattern designed for given loading and boundary conditions could be used as the optimal solution for the periodic structure of vastly different scales, from a structure with a few (e.g. 20) repetitive modules to a material microstructure with an infinite number of base cells.     

Switched-capacitor neuromorphs with wide-range variable dynamics.

The use of switched capacitors as wide-range, programmable resistive elements in spatially extensive artificial dendritic trees (ADT's) is described. We show that silicon neuro-morphs with ADT's can produce impulse responses that last millions of times longer than the initiating impulse and that dynamical responses are tunable in both shape and duration over a wide range. The switched-capacitor resistors forming a dendritic tree are shown indirectly to have a useful programmable resistance range between 500 KOmega and 1000 GOmega. Experimental results are presented that show variable impulse response functions, tunable frequency selectivity, and rate-invariance of spatiotemporal pattern responses.     

Modeling Dormant Fruit Trees for Agricultural Automation

Dormant pruning of fruit trees is one of the most costly and labor‐intensive activities in specialty crop production. We present a system that solves the first step in the process of automated pruning: accurately measuring and modeling the fruit trees. Our system employs a laser sensor to collect observations of fruit trees from multiple perspectives, and it uses these observations to measure parameters needed for pruning. A split‐and‐merge clustering algorithm divides the collected data into three sets of points: trunk candidates, junction point candidates, and branches. The trunk candidates and junction point candidates are then further refined by a robust fitting algorithm that models as cylinders each segment of the trunk and primary branches. In this work, we focus on measuring the diameters of the primary branches and the trunk, which are important factors in dormant pruning and can be obtained directly from the cylindrical models. We show that the results are qualitatively satisfactory using synthetic and real data. Our experiments with three synthetic and three real apple trees of two different varieties showed that the system is able to identify the primary branches with an average accuracy of 98% and estimate their diameters with an average error of 0.6 cm. Although the current implementation of the system is too slow for large‐scale practical applications (it can measure approximately two trees per hour), our study shows that the proposed approach may serve as a fundamental building block of robotic pruners in the near future.     

Ergodicity of spike trains: when does trial averaging make sense?

Neuronal information processing is often studied on the basis of spiking patterns. The relevant statistics such as firing rates calculated with the peri-stimulus time histogram are obtained by averaging spiking patterns over many experimental runs. However, animals should respond to one experimental stimulation in real situations, and what is available to the brain is not the trial statistics but the population statistics. Consequently, physiological ergodicity, namely, the consistency between trial averaging and population averaging, is implicitly assumed in the data analyses, although it does not trivially hold true. In this letter, we investigate how characteristics of noisy neural network models, such as single neuron properties, external stimuli, and synaptic inputs, affect the statistics of firing patterns. In particular, we show that how high membrane potential sensitivity to input fluctuations, inability of neurons to remember past inputs, external stimuli with large variability and temporally separated peaks, and relatively few contributions of synaptic inputs result in spike trains that are reproducible over many trials. The reproducibility of spike trains and synchronous firing are contrasted and related to the ergodicity issue. Several numerical calculations with neural network examples are carried out to support the theoretical results.     

Information and topology in attractor neural networks

A wide range of networks, including those with small-world topology, can be modeled by the connectivity ratio and randomness of the links. Both learning and attractor abilities of a neural network can be measured by the mutual information (MI) as a function of the load and the overlap between patterns and retrieval states. In this letter, we use MI to search for the optimal topology with regard to the storage and attractor properties of the network in an Amari-Hopfield model. We find that while an optimal storage implies an extremely diluted topology, a large basin of attraction leads to moderate levels of connectivity. This optimal topology is related to the clustering and path length of the network. We also build a diagram for the dynamical phases with random or local initial overlap and show that very diluted networks lose their attractor ability.     

Explicit level set and density methods for topology optimization with equivalent minimum length scale constraints

The goal of this paper is to introduce local length scale control in an explicit level set method for topology optimization. The level set function is parametrized explicitly by filtering a set of nodal optimization variables. The extended finite element method (XFEM) is used to represent the non-conforming material interface on a fixed mesh of the design domain. In this framework, a minimum length scale is imposed by adopting geometric constraints that have been recently proposed for density-based topology optimization with projections filters. Besides providing local length scale control, the advantages of the modified constraints are twofold. First, the constraints provide a computationally inexpensive solution for the instabilities which often appear in level set XFEM topology optimization. Second, utilizing the same geometric constraints in both the density-based topology optimization and the level set optimization enables to perform a more unbiased comparison between both methods. These different features are illustrated in a number of well-known benchmark problems for topology optimization.

     

Effects of synaptic synchrony on the neuronal input-output relationship

The firing rate of individual neurons depends on the firing frequency of their distributed synaptic inputs, with linear and nonlinear relations subserving different computational functions. This letter explores the relationship between the degree of synchrony among excitatory synapses and the linearity of the response using detailed compartmental models of cortical pyramidal cells. Synchronous input resulted in a linear input-output relationship, while asynchronous stimulation yielded sub- and supraproportional outputs at low and high frequencies, respectively. The dependence of input-output linearity on synchrony was sigmoidal and considerably robust with respect to dendritic location, stimulus irregularity, and alteration of active and synaptic properties. Moreover, synchrony affected firing rate differently at lower and higher input frequencies. A reduced integrate-and-fire model suggested a mechanism explaining these results based on spatiotemporal integration, with fundamental implications relating synchrony to memory encoding.     

Heuristic algorithms for designing self-repairing protection trees in mesh networks

Protection trees have been used in the past for restoring multicast and unicast traffic in networks in various failure scenarios. In this paper we focus on shared self-repairing trees for link protection in unicast mesh networks. Shared protection trees have been proposed as a relatively simple approach that is easy to reconfigure and could provide sub-second restoration times with sub-optimal redundancy requirement. The self-repairing nature of this class of protection trees may make them an attractive option for cases where dynamic changes in network topology or demand may occur. In this paper, we present heuristic algorithms to design a self-repairing protection tree for a given network. We study the restorability performance of shared trees and examine the limitations of such schemes in specific topologies, such as cases where long node chains exist. Using extensive simulations with thousands of randomly generated network graphs. We compare redundancy and average backup path length of shared protection trees with optimal tree designs and non-tree designs. We also apply our algorithms to the problem of designing the protection tree in a pre-designed fixed-capacity network, and study the performance of shared protection trees in this scenario under different network loads and link utilization levels.     

Comparison properties of stochastic decision free Petri nets

Stochastic comparison problems arising in the analysis of stochastic decision free Petri nets are treated. The analysis is based on the evolution equations satisfied by firing times. Various structural properties are obtained, including the association of the firing times and their stochastic and convex monotonicity with respect to the holding time sequences, the initial marking, and the topology. The association and the stochastic monotonicity properties are extended to the counters using an inversion relation. It is also proven that the counters and the throughput are stochastically concave in the initial marking, provided that the holding times are independent, identically distributed, and belong to a subclass of the log-concave distribution functions that are introduced. Various bounds for the asymptotic cycle time and the throughput are then derived from these stochastic ordering results. Comparative results are presented for the marking and response times