The structure of receptive elds in the visual cortex is believed to be shaped by unsupervised learning. A simple variant of unsupervised learning is the extraction of principal components. In this paper, we derived analytically the form of the principal components of natural images. An assumption is made that only small circular regions of the images are being used as training patterns. The der...

The properties of a classical simple liquid are strongly affected by the application of an external potential that supports inhomogeneity. To understand the nature of these property changes, the equilibrium particle distribution functions of the liquid have, typically, been calculated directly using either integral equation or density functional based analyses. In this study, we develop a diffe...

We consider the existence of analytic solutions of a certain class of iterative second-order functional differential equation of the form x (x [r] (z)) = c 0 z 2 + c 1 (x(z)) 2 + (c 2 x [2] (z)) 2 + ··· + c m (x [m] (z)) 2 , m,r ≥ 0.

Let us consider the Analytic Hierarchy Process in which the labels are structured as graded numbers. To obtain the scoring that corresponds to the best alternative, or the ranking of the alternatives, we need to use a total order for the graded numbers involved in the problem. In this article, we consider a definition of such a total order, which is based upon two subjective aspects: the degree...

Nonuniform elastic strain is known to induce pseudo-Landau levels in Dirac materials. But these are hardly resolvable an analytic fashion when the strong, because of emerging complicated space dependence both strain-modulated Fermi velocity and strain-induced pseudomagnetic field. We analytically characterize solution experimentally accessible strongly bent graphene nanoribbons, by treating eff...

Abstract. The Fourier analytic approach to sections of convex bodies has recently been developed and has led to several results, including a complete analytic solution to the BusemannPetty problem, characterizations of intersection bodies, extremal sections of lp-balls. In this article, we extend this approach to projections of convex bodies and show that the projection counterparts of the resu...