Celulární automat a CML systémy

The main aim of this thesis is the study of cellular automata and discrete dynamical systems on a lattice. Both tools, cellular automata as well as dynamical systems on a lattice are introduced and elementary properties described. The relation between cellular automata and dynamical system on lattice is derived. The main goal of the thesis is also the use of the cellular automata as that mathematical tool of evolution visualization of discrete dynamical systems. The theory of cellular automata is applied to the discrete dynamical systems on a lattice Laplacian type and implemented in Java language.Hlavním cílem práce je studium vztahu celulárních automatů a diskrétních dynamických systémů na mřížce. Oba nástroje, jak celulární automat tak dynamický systém na mřížce, jsou zavedeny a jejich základní vlastnosti popsány. Vztah mezi celulárními automaty a dynamickými systémy na mřížce je podrobně popsán. Hlavním cílem práce je dále použití nástroje celulárního automatu jako matematického vizualizačního prostředku evoluce diskrétních dynamických systémů. Teorie celulárních automatů je použita na dynamické systémy na mřížce Lamplaceova typu a implementována v prostředí Java.470 - Katedra aplikované matematikyvelmi dobř

Limit shape and height fluctuations of random perfect matchings on square-hexagon lattices

We study asymptotics of perfect matchings on a large class of graphs called the contracting square-hexagon lattice, which is constructed row by row from either a row of a square grid or a row of a hexagonal lattice. We assign the graph periodic edge weights with period $1\times n$, and consider the probability measure of perfect matchings in which the probability of each configuration is proportional to the product of edge weights. We show that the partition function of perfect matchings on such a graph can be computed explicitly by a Schur function depending on the edge weights. By analyzing the asymptotics of the Schur function, we then prove the Law of Large Numbers (limit shape) and the Central Limit Theorem (convergence to the Gaussian free field) for the corresponding height functions. We also show that the distribution of certain type of dimers near the turning corner is the same as the eigenvalues of Gaussian Unitary Ensemble, and that in the scaling limit under the boundary condition that each segment of the bottom boundary grows linearly with respect the dimension of the graph, the frozen boundary is a cloud curve whose number of tangent points to the bottom boundary of the domain depends on the size of the period, as well as the number of segments along the bottom boundary

A Neuromorphic Model for Achromatic and Chromatic Surface Representation of Natural Images

This study develops a neuromorphic model of human lightness perception that is inspired by how the mammalian visual system is designed for this function. It is known that biological visual representations can adapt to a billion-fold change in luminance. How such a system determines absolute lightness under varying illumination conditions to generate a consistent interpretation of surface lightness remains an unsolved problem. Such a process, called "anchoring" of lightness, has properties including articulation, insulation, configuration, and area effects. The model quantitatively simulates such psychophysical lightness data, as well as other data such as discounting the illuminant, the double brilliant illusion, and lightness constancy and contrast effects. The model retina embodies gain control at retinal photoreceptors, and spatial contrast adaptation at the negative feedback circuit between mechanisms that model the inner segment of photoreceptors and interacting horizontal cells. The model can thereby adjust its sensitivity to input intensities ranging from dim moonlight to dazzling sunlight. A new anchoring mechanism, called the Blurred-Highest-Luminance-As-White (BHLAW) rule, helps simulate how surface lightness becomes sensitive to the spatial scale of objects in a scene. The model is also able to process natural color images under variable lighting conditions, and is compared with the popular RETINEX model.Air Force Office of Scientific Research (F496201-01-1-0397); Defense Advanced Research Project and the Office of Naval Research (N00014-95-0409, N00014-01-1-0624

Constructing Synchronously Rotating Double White Dwarf Binaries

We have developed a self-consistent-field technique similar to the one described by Hachisu, Eriguchi, & Nomoto (1986b) that can be used to construct detailed force-balanced models of synchronously rotating, double white dwarf (DWD) binaries that have a wide range of total masses, mass ratios, and separations. In addition to providing a computational tool that can be used to provide quiet initial starts for dynamical studies of the onset of mass transfer in DWD systems, we show that this SCF technique can be used to construct model sequences that mimic the last portion of the detached inspiral phase of DWD binary evolutions, and semi-detached model sequences that mimic a phase of conservative mass transfer.Comment: 51 pages, 10 figures, submitted for publication in Astrophysical Journal Supplement Serie