Structure and reversibility of 2D hexagonal cellular automata

Cellular automata are used to model dynamical phenomena by focusing on their local behavior which depends on the neighboring cells in order to express their global behavior. The geometrical structure of the models suggests the algebraic structure of cellular automata. After modeling the dynamical phenomena, it is sometimes an important problem to be able to move backwards in order to understand it better. This is only possible if cellular automata is reversible. In this paper, 2D finite cellular automata defined by local rules based on hexagonal cell structure are studied. Rule matrix of the hexagonal finite cellular automaton is obtained. The rank of rule matrices representing the 2D hexagonal finite cellular automata via an algorithm is computed. It is a well known fact that determining the reversibility of a 2D cellular automata is a very difficult problem in general. Here, the reversibility problem of this family of 2D hexagonal cellular automata is also resolved completely.     

State estimation for fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays

This paper deals with the problem of state estimation for fuzzy cellular neural networks (FCNNs) with time delay in the leakage term, discrete and unbounded distributed delays. In this paper, leakage delay in the leakage term is used to unstable the neuron states. It is challenging to develop a delay dependent condition to estimate the unstable neuron states through available output measurements such that the error-state system is globally asymptotically stable. By constructing the Lyapunov-Krasovskii functional which contains a triple-integral term, an improved delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). However, by using the free-weighting matrices method, a simple and efficient criterion is derived in terms of LMIs for estimation. The restriction such as the time-varying delay which was required to be differentiable or even its time-derivative which was assumed to be smaller than one, are removed. Instead, the time-varying delay is only assumed to be bounded. Finally, numerical examples and its simulations are given to demonstrate the effectiveness of the derived results.     

Colon segmentation and colonic polyp detection using cellular neural networks and three-dimensional template matching

Abstract: In this study, an automatic three-dimensional computer-aided detection system for colonic polyps was developed. Computer-aided detection for computed tomography colonography aims at facilitating the detection of colonic polyps. First, the colon regions of whole computed tomography images were carefully segmented to reduce computational burden and prevent false positive detection. In this process, the colon regions were extracted by using a cellular neural network and then the regions of interest were determined. In order to improve the segmentation performance of the study, weights in the cellular neural network were calculated by three heuristic optimization techniques, namely genetic algorithm, differential evaluation and artificial immune system. Afterwards, a three-dimensional polyp template model was constructed to detect polyps on the segmented regions of interest. At the end of the template matching process, the volumes geometrically similar to the template were emhanced.     

Recognition and analysis of cell nuclear phases for high-content screening based on morphological features

Automated analysis of molecular images has increasingly become an important research in computational life science. In this paper some new and efficient algorithms for recognizing and analyzing cell phases of high-content screening are presented. The conceptual frameworks are based on the morphological features of cell nuclei. The useful preprocessing includes: smooth following and linearization; extraction of morphological structural points; shape recognition based morphological structure; issue of touching cells for cell separation and reconstruction. Furthermore, the novel detecting and analyzing strategies of feed-forward and feed-back of cell phases are proposed based on gray feature, cell shape, geometrical features and difference information of corresponding neighbor frames. Experiment results tested the efficiency of the new method.     

Robust synchronization in an array of fuzzy delayed cellular neural networks with stochastically hybrid coupling

In this paper, the robust synchronization control problem of an array of fuzzy cellular neural networks with uncertain stochastically coupling is investigated, which involves constant coupling, discrete time-varying delay coupling and distributed time-varying delay coupling. By using adaptive feedback control scheme and exploiting some stochastic analysis techniques, several sufficient conditions are developed to ensure the synchronization of stochastically hybrid coupled fuzzy neural networks with all admissible uncertainties in mean square. Finally, a numerical example illustrated by scale-free complex networks is provided to show the effectiveness and the applicability of the proposed method.     

Generalized Besicovitch and Weyl spaces: Topology, patterns, and sliding block codes

The Besicovitch and Weyl topologies on the space of configurations take a point of view completely different from the usual product topology; as such, the properties of the former are much different from that of the latter. The one-dimensional case has already been the subject of thorough studies; we extend it to greater dimensions, and also to more general groups.     

化学混沌与BZ反应的细观元胞自动机模拟

将所提出的细观元胞自动要应用于化学混沌与ＢＺ反应的计算机模拟,分别制定了８组分和５组分系统中粒子随机运动和反应碰撞的演化规则,建立了Ｗｉｌｌａｍｏｗｓｋｉ－Ｒｏｓｓｌｅｒ化学混沌与Ｂｅｌｏｕｓｏｖ－Ｚｈａｌｂｏｔｉｎｓｋｉ反应的二维元胞自动机模型,并在计算机上对它们进行了成功地动态模拟。     

On the use of energy minimization for CA based analysis in elasticity

There has been recent interest in exploring alternative computational models for structural analysis that are better suited for a design environment requiring repetitive analysis. The need for such models is brought about by significant increases in computer processing speeds, realized primarily through parallel processing. To take full advantage of such parallel machines, however, the computational approach itself must be revisited from a totally different perspective; parallelization of inherently serial paradigms is subject to limitations introduced by a requirement of information coordination. The cellular automata (CA) model of decentralized computations provides one such approach which is ideally tailored for parallel computers. The proposed paper examines the applicability of the cellular automata model in problems of 2-D elasticity. The focus of the paper is in the use of a genetic algorithm based optimization process to derive the rules for local interaction required in evolving the cellular automata. Received August 28, 2000     

Analyzing the structure of a class of linear automata over a ring $$ Z_{p^k } $$

Basic finite-automaton characteristics are established for the class of all linear automata and information-lossless automata over a ring. The complexities of solving problems of parametric identification and initial-state identification are analyzed. The sets of fixed points for mappings realized by initial automata are characterized. Canonical forms are proposed for linear automata over the ring. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 60–74, May–June 2008.