42776203
Fixed-Point Attractor Analysis for a Class of Neurodynamics
Nearly all models in neural networks start from the assumption that the input-output characteristic is a sigmoidal function. On parameter space, we present a systematic and feasible method for analyzing the whole spectrum of attractorsall-saturated, all-but-one-saturated, all-but-twosaturated, and so onof a neurodynamical system with a saturated sigmoidal function as its input-output characteristic. We present an argument that claims, under a mild condition, that only all-saturated or all but-one-saturated attractors are observable for the neurodynamics. For any given all-saturated configuration (all-but-one-saturated configuration ) the article shows how to construct an exact parameter region R()(()) such that if and only if the parameters fall within R()(()), then () is an attractor (a fixed point) of the dynamics. The parameter region for an all-saturated fixed-point attractor is independent of the specific choice of a saturated sigmoidal function, whereas for an all-but-one-saturated fixed point, it is sensitive to the input-output characteristic. Based on a similar idea, the role of weight normalization realized by a saturated sigmoidal function in competitive learning is discussed. A necessary and sufficient condition is provided to distinguish two kinds of competitive learning: stable competitive learning with the weight vectors representing extremes of input space and being fixed-point attractors, and unstable competitive learning. We apply our results to Linsker's model and (using extreme value theory in statistics) the Hopfield model and obtain some novel results on these two models.
26554848
What is observable in a class of neurodynamics?
7897839
Effects of Correlation and Degree of Balance in Random Synaptic Inputs on the Output of the Hodgkin-Huxley Model
We examine the effects of degree of balance between inhibitory and excitatory random synaptic inputs, and of positive correlation between the inputs on the mean and variability of the output of the classical Hodgkin-Huxley (HH) model for squid giant axon, using computer simulation. The mean interspike interval (ISI) and the coefficient of variation of ISI change little as the degree of balance changes, unlike the leaky integrate-and-fire model, frequently used in stochastic network modelling as an approximation to more biophysically based models. Low correlations (up to about 0.1) between 100 excitatory inputs each firing at 100 Hz reduce the mean(ISI) to below a third of its value when the inputs are independent, and CV by a factor of 5 from a near-Poisson range to one associated with regular firing.
652273
Decoding Input Signals in Time Domain—A Model Approach
From an observation of efferent interspike intervals of a neuron, we consider how to decode the input temporal information. It is found that the integrate-and-fire model is blind in the temporal domain due to the fact that its efferent firing rate is independent of the input temporal frequency. The conclusion is then confirmed for the integrate-and-fire model with correlated inputs, with reversal potentials, with a nonlinear leakage and with a subthreshold oscillation. For the Hodgkin-Huxley model, however, in terms of efferent firing rates alone, it is possible to read out the input temporal information.
39095130
Output jitter diverges to infinity, converges to zero or remains constant
877766
Inhibitory inputs increase a neurons's firing rate
Abstract Neurons are typically thought of as receiving information primarily through excitatory inputs, with inhibitory inputs playing a gating or regulating role. In this paper we demonstrate that increasing the strength of inhibitory inputs to the Hodgkin–Huxley and FitzHugh–Nagumo models can induce them to fire faster. This result is counter-intuitive and important in neural network modelling where inhibitory inputs are often neglected.
36256315
Visual-Based View-Invariant Human Motion Analysis: A Review
This paper provides a comprehensive survey of research on view-invariant human motion analysis. Recent research has shown that view-invariant related issues has been one of the bottlenecks for human motion understanding. The priority in this paper has been given to view-invariant pose representation and estimation, behaviour understanding. Research challenges and future directions are discussed in the end.
863031
Component Selection to Optimize Distance Function Learning in Complex Scientific Data Sets
Analyzing complex scientific data, e.g., graphs and images, often requires comparison of features: regions on graphs, visual aspects of images and related metadata, some features being relatively more important. The notion of similarity for comparison is typically distance between data objects which could be expressed as distance between features. We refer to distance based on each feature as a component. Weights of components representing relative importance of features could be learned using distance function learning algorithms. However, it is seldom known which components optimize learning, given criteria such as accuracy, efficiency and simplicity. This is the problem we address. We propose and theoretically compare four component selection approaches: Maximal Path Traversal, Minimal Path Traversal, Maximal Path Traversal with Pruning and Minimal Path Traversal with Pruning. Experimental evaluation is conducted using real data from Materials Science, Nanotechnology and Bioinformatics. A trademarked software tool is developed as a highlight of this work.
1438319
Identities and Parseval type relations for the L2-transform
Abstract In the present paper, the authors introduce identities for the L 2 -transform which yield a Parseval type relationship for the L 2 -transform. The Parseval type relationship proven in this paper give rise to useful corollaries for evaluating indefinite integrals of special functions. Some examples are also given as illustrations of the results presented here.
78402
Composed products and module polynomials over finite fields
Abstract A general notion of composition of polynomials over a finite field was introduced by Brawley and Carlitz (1987). In their paper they developed a unique decomposition theory in two special cases of the composed product, but they left open the question of uniqueness in the general case. This paper settles this open question by proving that irreducibles do indeed decompose uniquely with respect to the general notion and, in doing so, unifies the two separate treatments of Brawley and Carlitz into a single, more general theory. The paper also offers a generalization which unifies into a single theory the notions of ‘belonging to an exponent’ and ‘belonging to a q -polynomial’, which are basic in the theory of finite fields.
17110258
An ontology for scientific information in a Grid environment: the earth system Grid
In the emerging world of Grid Computing, shared computational, data, other distributed resources are becoming available to enable scientific advancement through collaborative research and collaboratories. This paper describes the increasing role of ontologies in the context of Grid Computing for obtaining, comparing and analyzing data. We present ontology entities and a declarative model that provide the outline for an ontology of scientific information. Relationships between concepts are also given. The implementation of some concepts described in this ontology is discussed within the context of the Earth System Grid II (ESG)[1].