We construct a chaotic discrete-time continuous-state Hopfield networkwith piecewise-affine nonnegative activation functions and weight matrix with small positive entries. More precisely, there exists Cantor set $ C in the state space such that network has sensitive dependence on initial conditions at states orbit of each as its \omega $-limit set. The approach we use is based tools developed e...

This paper presents an efficient approach to the classification of the affine equivalence classes of cosets of the first order ReedMuller code with respect to cryptographic properties such as correlationimmunity, resiliency and propagation characteristics. First, we apply the method to completely classify all the 48 classes into which the general affine group AGL(2, 5) partitions the cosets of ...

This paper considers least squares estimators for regression problems over convex, uniformly bounded, uniformly Lipschitz function classes minimizing the empirical risk over max-affine functions (the maximum of finitely many affine functions). Based on new results on nonlinear nonparametric regression and on the approximation accuracy of maxaffine functions, these estimators are proved to achie...

We continue our study of intermediate sums over polyhedra, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasipolynomial of a rational simplex, Math. Comp. 75 (2006), 1449– 1466]. By well-known decompositions, it is sufficient to consider the case of affine cones s+c, where s is an arbitrary real vertex and c is a rational polyhed...

We continue our study of intermediate sums over polyhedra, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasipolynomial of a rational simplex, Math. Comp. 75 (2006), 1449– 1466]. By well-known decompositions, it is sufficient to consider the case of affine cones s+c, where s is an arbitrary real vertex and c is a rational polyhed...

The paper is devoted to the local classification of generic control-affine systems on an n-dimensional manifold with scalar input for any n ≥ 4 or with two inputs for n = 4 and n = 5, up to state-feedback transformations, preserving the affine structure (in C∞ category for n = 4 and Cω category for n ≥ 5). First using the Poincare series of moduli numbers we introduce the intrinsic numbers of f...

A family of polynomial τ -functions for the NLS-Toda hierarchy is constructed. The hierarchy is associated with the homogeneous vertex operator representation of the affine algebra g of type A (1) 1 . These τ -functions are given explicitly in terms of Schur functions that correspond to rectangular Young diagrams. It is shown that an arbitrary polynomial τ -function which is an eigenvector of d...

self-affine maps were successfully used for edge detection, image segmentation, and contour extraction. they belong to the general category of patch-based methods. particularly, each self-affine map is defined by one pair of patches in the image domain. by minimizing the difference between these patches, the optimal translation vector of the self-affine map is obtained. almost all image process...