Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow

Leaving a few exceptions aside, cellular automata (CA) and the intimately related coupled-map lattices (CML), commonly known as continuous cellular automata (CCA), as well as models that are based upon one of these paradigms, employ a regular tessellation of an Euclidean space in spite of the various drawbacks this kind of tessellation entails such as its inability to cover surfaces with an intricate geometry, or the anisotropy it causes in the simulation results. Recently, a CCA-based model describing steady-state heat flow has been proposed as an alternative to Laplace's equation that is, among other things, commonly used to describe this process, yet, also this model suffers from the aforementioned drawbacks since it is based on the classical CCA paradigm. To overcome these problems, we first conceive CCA on irregular tessellations of an Euclidean space after which we show how the presented approach allows a straightforward simulation of steady-state heat flow on surfaces with an intricate geometry, and, as such, constitutes an full-fledged alternative for the commonly used and easy-to-implement finite difference method, and the more intricate finite element method

Convergence analysis of hybrid cellular automata for topology optimization

The hybrid cellular automaton (HCA) algorithm was inspired by the structural adaptation of bones to their ever changing mechanical environment. This methodology has been shown to be an effective topology synthesis tool. In previous work, it has been observed that the convergence of the HCA methodology is affected by parameters of the algorithm. As a result, questions have been raised regarding the conditions by which HCA converges to an optimal design. The objective of this investigation is to examine the conditions that guarantee convergence to a Karush-Kuhn-Tucker (KKT) point. In this paper, it is shown that the HCA algorithm is a fixed point iterative scheme and the previously reported KKT optimality conditions are corrected. To demonstrate the convergence properties of the HCA algorithm, a simple cantilevered beam example is utilized. Plots of the spectral radius for projections of the design space are used to show regions of guaranteed convergence

Data-driven and Model-based Verification: a Bayesian Identification Approach

This work develops a measurement-driven and model-based formal verification approach, applicable to systems with partly unknown dynamics. We provide a principled method, grounded on reachability analysis and on Bayesian inference, to compute the confidence that a physical system driven by external inputs and accessed under noisy measurements, verifies a temporal logic property. A case study is discussed, where we investigate the bounded- and unbounded-time safety of a partly unknown linear time invariant system

KKT conditions satisfied using adaptive neighboring in hybrid cellular automata for topology optimization

The hybrid cellular automaton (HCA) method is a biologically inspired algorithm capable of topology synthesis that was developed to simulate the behavior of the bone functional adaptation process. In this algorithm, the design domain is divided into cells with some communication property among neighbors. Local evolutionary rules, obtained from classical control theory, iteratively establish the value of the design variables in order to minimize the local error between a field variable and a corresponding target value. Karush-Kuhn-Tucker (KKT) optimality conditions have been derived to determine the expression for the field variable and its target. While averaging techniques mimicking intercellular communication have been used to mitigate numerical instabilities such as checkerboard patterns and mesh dependency, some questions have been raised whether KKT conditions are fully satisfied in the final topologies. Furthermore, the averaging procedure might result in cancellation or attenuation of the error between the field variable and its target. Several examples are presented showing that HCA converges to different final designs for different neighborhood configurations or averaging schemes. Although it has been claimed that these final designs are optimal, this might not be true in a precise mathematical sense—the use of the averaging procedure induces a mathematical incorrectness that has to be addressed. In this work, a new adaptive neighboring scheme will be employed that utilizes a weighting function for the influence of a cell’s neighbors that decreases to zero over time. When the weighting function reaches zero, the algorithm satisfies the aforementioned optimality criterion. Thus, the HCA algorithm will retain the benefits that result from utilizing neighborhood information, as well as obtain an optimal solution

A framework for the local information dynamics of distributed computation in complex systems

The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of these individual information dynamics on a local scale within a system, and describes the manner in which they interact to create non-trivial computation where "the whole is greater than the sum of the parts". We describe the application of the framework to cellular automata, a simple yet powerful model of distributed computation. This is an important application, because the framework is the first to provide quantitative evidence for several important conjectures about distributed computation in cellular automata: that blinkers embody information storage, particles are information transfer agents, and particle collisions are information modification events. The framework is also shown to contrast the computations conducted by several well-known cellular automata, highlighting the importance of information coherence in complex computation. The results reviewed here provide important quantitative insights into the fundamental nature of distributed computation and the dynamics of complex systems, as well as impetus for the framework to be applied to the analysis and design of other systems.Comment: 44 pages, 8 figure

Statistical Physics of Vehicular Traffic and Some Related Systems

In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the way the vehicles influence each others' movement. Therefore, vehicular traffic, modeled as a system of interacting "particles" driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called "particle-hopping" models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.Comment: 170 pages, Latex, figures include

Synthesis methods for manual aerospace control systems with applications to SST design

Synthesis methods for manual aerospace control systems using digital programming and man machine performance data with application to supersonic transport desig

The Study of Correlation Structures of DNA Sequences: A Critical Review

The study of correlation structure in the primary sequences of DNA is reviewed. The issues reviewed include: symmetries among 16 base-base correlation functions, accurate estimation of correlation measures, the relationship between $1/f$ and Lorentzian spectra, heterogeneity in DNA sequences, different modeling strategies of the correlation structure of DNA sequences, the difference of correlation structure between coding and non-coding regions (besides the period-3 pattern), and source of broad distribution of domain sizes. Although some of the results remain controversial, a body of work on this topic constitutes a good starting point for future studies.Comment: LaTeX, two figures, postscript is expected to be 46 pages. To appear in the special issue of Computer & Chemistry (1997