Entry times in automata with simple defect dynamics

In this paper, we consider a simple cellular automaton with two particles of different speeds that annihilate on contact. Following a previous work by K\r urka et al., we study the asymptotic distribution, starting from a random configuration, of the waiting time before a particle crosses the central column after time n. Drawing a parallel between the behaviour of this automata on a random initial configuration and a certain random walk, we approximate this walk using a Brownian motion, and we obtain explicit results for a wide class of initial measures and other automata with similar dynamics.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

The asymmetric exclusion process: Comparison of update procedures

The asymmetric exclusion process (ASEP) has attracted a lot of interest not only because its many applications, e.g. in the context of the kinetics of biopolymerization and traffic flow theory, but also because it is a paradigmatic model for nonequilibrium systems. Here we study the ASEP for different types of updates, namely random-sequential, sequential, sublattice-parallel and parallel. In order to compare the effects of the different update procedures on the properties of the stationary state, we use large-scale Monte Carlo simulations and analytical methods, especially the so-called matrix-product Ansatz (MPA). We present in detail the exact solution for the model with sublattice-parallel and sequential updates using the MPA. For the case of parallel update, which is important for applications like traffic flow theory, we determine the phase diagram, the current, and density profiles based on Monte Carlo simulations. We furthermore suggest a MPA for that case and derive the corresponding matrix algebra.Comment: 47 pages (11 PostScript figures included), LATEX, Two misprints in equations correcte

Self-Healing Cellular Automata to Correct Soft Errors in Defective Embedded Program Memories

Static Random Access Memory (SRAM) cells in ultra-low power Integrated Circuits (ICs) based on nanoscale Complementary Metal Oxide Semiconductor (CMOS) devices are likely to be the most vulnerable to large-scale soft errors. Conventional error correction circuits may not be able to handle the distributed nature of such errors and are susceptible to soft errors themselves. In this thesis, a distributed error correction circuit called Self-Healing Cellular Automata (SHCA) that can repair itself is presented. A possible way to deploy a SHCA in a system of SRAM-based embedded program memories (ePM) for one type of chip multi-processors is also discussed. The SHCA is compared with conventional error correction approaches and its strengths and limitations are analyzed

The Role of Opportunistic Punishment in the Evolution of Cooperation: An application of stochastic dynamics to public good game

This paper discusses the role of opportunistic punisher who may act selfishly to free-ride cooperators or not to be exploited by defectors. To consider opportunistic punisher, we make a change to the sequence of one-shot public good game; instead of putting action choice first before punishment, the commitment of punishment is declared first before choosing the action of each participant. In this commitment-first setting, punisher may use information about her team, and may defect to increase her fitness in the team. Reversing sequence of public good game can induce different behavior of punisher, which cannot be considered in standard setting where punisher always chooses cooperation. Based on stochastic dynamics developed by evolutionary economists and biologists, we show that opportunistic punisher can make cooperation evolve where cooperative punisher fails. This alternative route for the evolution of cooperation relies paradoxically on the players' selfishness to profit from others' unconditional cooperation and defection.Comment: 30 page, 9 figure

Physics of Transport and Traffic Phenomena in Biology: from molecular motors and cells to organisms

Traffic-like collective movements are observed at almost all levels of biological systems. Molecular motor proteins like, for example, kinesin and dynein, which are the vehicles of almost all intra-cellular transport in eukayotic cells, sometimes encounter traffic jam that manifests as a disease of the organism. Similarly, traffic jam of collagenase MMP-1, which moves on the collagen fibrils of the extracellular matrix of vertebrates, has also been observed in recent experiments. Traffic-like movements of social insects like ants and termites on trails are, perhaps, more familiar in our everyday life. Experimental, theoretical and computational investigations in the last few years have led to a deeper understanding of the generic or common physical principles involved in these phenomena. In particular, some of the methods of non-equilibrium statistical mechanics, pioneered almost a hundred years ago by Einstein, Langevin and others, turned out to be powerful theoretical tools for quantitaive analysis of models of these traffic-like collective phenomena as these systems are intrinsically far from equilibrium. In this review we critically examine the current status of our understanding, expose the limitations of the existing methods, mention open challenging questions and speculate on the possible future directions of research in this interdisciplinary area where physics meets not only chemistry and biology but also (nano-)technology.Comment: 33 page Review article, REVTEX text, 29 EPS and PS figure

A model-based approach to automated test generation and error localization for Simulink/Stateflow

Simulink/Stateflow is a popular commercial model-based development tool for many industrial domains. For safety and security concerns, verification and testing must be performed on the Simulink/Stateflow designs and the generated code. We present an automatic test generation approach for Simulink/Stateflow based on its translation to a formal model, called Input/Output Extended Finite Automata (I/O-EFA), that is amenable to formal analysis such as test generation. The approach automatically identifies a set of input-output sequences to activate all executable computations in the Simulink/Stateflow diagram by applying three different techniques, model checking, constraint solving and reachability reduction & resolution. These tests (input-output sequences) are then used for validation purposes, and the failed versus passed tests are used to localize the fault to plausible Simulink/Stateflow blocks. The translation and test generation approaches are automated and implemented in a toolbox that can be executed in Matlab that interfaces with NuSMV