Elka Korutcheva

Origins of scaling relations in nonequilibrium growth

Scaling and hyperscaling laws provide exact relations among critical exponents describing the behavior of a system at criticality. For nonequilibrium growth models with a conserved drift there exist few of them. One such relation is

Random field effects in classical and quantum critical phenomena

alpha +z=4

Detecting the most unusual part of a digital image

, found to be inexact in a renormalization group calculation for several classical models in this field. Herein we focus on the two-dimensional case and show that it is possible to construct conserved surface growth equations for which the relation

On the phase transitions in superconductors with quenched impurities

alpha +z=4

Finite-size effects in a field-theoretic model with long-range exchange interaction

is exact in the renormalization group sense. We explain the presence of this scaling law in terms of the existence of geometric principles dominating the dynamics.

Intelligence and embodiment: A statistical mechanics approach

The effect of quenched random fields on classical and quantum critical behaviour is studied by means of the ϵ-analysis for a number of systems. The investigation is performed in terms of a generalized random-field correlation function. The interplay of short-range correlations as well as of a parameter-dependent variety of long-range correlations with thermal and quantum fluctuations is revealed.

On the quantum finite-size sealing

The purpose of this paper is to introduce an algorithm that can detect the most unusual part of a digital image. The most unusual part of a given shape is defined as a part of the image that has the maximal distance to all non intersecting shapes with the same form. n nThe method can be used to scan image databases with no clear model of the interesting part or large image databases, as for example medical databases.

Spatial asymmetric retrieval states in binary attractor neural network

The question whether the Halperin-Lubensky-Ma result for a fluctuation-induced weakly first-order phase transition in superconductors holds in the presence of quenched impurities is considered. The renormalisation-group recursion relations have a new stable fixed point for 1<n<or=366, which describes a real critical behaviour in the range 2<Dc(n)<d<4 of space dimensionalities d (n/2 is the number of components of the complex order parameter). Some features of the new fixed point are discussed. The critical exponents are presented for 1<n<or=366.

Influence of long-range correlated impurities upon the phase transition in model superconductors

We present a systematic approach to the calculation of finite-size (FS) effects for anO(n) field-theoretic model with both short-range (SR) and long-range (LR) exchange interactions. The LR exchange interaction decays at large distances as 1/rd+2−2α,α→0+,α→0+. Renormalization group calculations ind=du−ε are performed for a system with a fully finite (block) geometry under periodic boundary conditions. We calculate the FS shift of the critical temperature and the FS renormalized coupling constant of the model to one-loop order. The universal scaling variable is obtained and the FS scaling hypothesis is verified.

Random-Field Correlations and Quantum Critical Phenomena

Evolutionary neuroscience has been mainly dominated by the principle of phylogenetic conservation, specifically, by the search for similarities in brain organization. This principle states that closely related species tend to be similar because they have a common ancestor. However, explaining, for instance, behavioral differences between humans and chimpanzees, has been revealed to be notoriously difficult. In this paper, the hypothesis of a common information-processing principle exploited by the brains evolved through natural evolution is explored. A model combining recent advances in cognitive psychology and evolutionary neuroscience is presented. The macroscopic effects associated with the intelligence-like structures postulated by the model are analyzed from a statistical mechanics point of view. As a result of this analysis, some plausible explanations are put forward concerning the disparities and similarities in cognitive capacities which are observed in nature across species. Furthermore, an interpretation on the efficiency of brains computations is also provided. These theoretical results and their implications against modern theories of intelligence are shown to be consistent with the formulated hypothesis.