We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect to its singular support.

We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect to its singular support.

this paper presents a comparison study between the multilayer perceptron (mlp) and radial basis function (rbf) neural networks with supervised learning and back propagation algorithm to track hand gestures. both networks have two output classes which are hand and face. skin is detected by a regional based algorithm in the image, and then networks are applied on video sequences frame by frame in...

Networks have been used to describe and model a wide range of complex systems, both natural as well as man-made. One particularly interesting application in the earth sciences is the use of complex networks to represent and study the global climate system. In this paper, we motivate this general approach, explain the basic methodology, report on the state of the art (including our contributions...

Singular spectrum analysis (SSA), a linear univariate and multivariate time series technique , is essentially principal component analysis (PCA) applied to the time series and additional copies of the time series lagged by 1 to K time steps. Neural network theory has meanwhile allowed PCA to be generalized to nonlinear PCA (NLPCA). In this paper, NLPCA is further extended to perform nonlinear S...

Currently, there does not seem to exist a commonly agreed definition of the robustness of a network, nor a framework to modify a network in order to meet some desired level of robustness. The goal of this article is to present a definition and a framework to compute topological network robustness.

The vanishing and exploding gradient problems are well-studied obstacles that make it difficult for recurrent neural networks to learn long-term time dependencies. We propose a reparameterization of standard recurrent neural networks to update linear transformations in a provably norm-preserving way through Givens rotations. Additionally, we use the absolute value function as an element-wise no...

The paper provides a condition for differentiability as well as an equivalent criterion for Lipschitz continuity of singular normal distributions. Such distributions are of interest, for instance, in stochastic optimization problems with probabilistic constraints, where a comparatively small (nondegenerate-) normally distributed random vector induces a large number of linear inequality constrai...