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We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
This paper is concerned with numerical approximation of some two-dimensional Keller-Segel chemotaxis models, especially those generating pattern formations. The numerical resolution of such nonlinear parabolic-parabolic or…
We study a new flexible method to extend linearly the graph of a non-linear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography…
It is known that chaotic systems have widely been used in cryptography. Generally, floating point simulations are used to generate pseudo-random sequence of numbers. Although, it is possible to find some works on the degradation of chaotic…
Parallel algorithms for solving any image processing task is a highly demanded approach in the modern world. Cellular Automata (CA) are the most common and simple models of parallel computation. So, CA has been successfully used in the…
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid.…
In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the…
We study a two-dimensional semi-totalistic binary cell-state cellular automaton, which imitates a reversible precipitation in an abstract chemical medium. The systems exhibits a non-trivial growth and nucleation. We demonstrate how basic…
Binary machines are a generalization of Feedback Shift Registers (FSRs) in which both, feedback and feedforward, connections are allowed and no chain connection between the register stages is required. In this paper, we present an algorithm…
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…
We present a new Life-like cellular automaton (CA) capable of logic universality -- the X-rule. The CA is 2D, binary, with a Moore neighborhood and $\lambda$ parameter similar to the game-of-Life, but is not based on birth/survival and is…
In quasi-Monte Carlo methods, generating high-dimensional low discrepancy sequences by generator matrices is a popular and efficient approach. Historically, constructing or finding such generator matrices has been a hard problem. In…
A comparative algebraic framework for elementary cellular automata is developed, centered on the role of spatial symmetry. The primary object of study is Rule~22, the elementary cellular automaton with algebraic normal form…
This paper reports on the application of sequence analysis algorithms for agents in robotic soccer and a suitable representation is proposed to achieve this mapping. The objective of this research is to generate novel better in-game…
In the paper I sketch a theory of massively parallel proofs using cellular automata presentation of deduction. In this presentation inference rules play the role of cellular-automatic local transition functions. In this approach we…
An equidistribution is a theoretical quality criteria that measures the uniformity of a linear pseudo-random number generator (PRNG). In this work, we first show that all existing linear cellular automaton (CA) based pseudo-random number…
We introduce a new framework for constructing topological quantum memories, by recasting error recovery as a dynamical process on a field generating cellular automaton. We envisage quantum systems controlled by a classical hardware composed…
We present a new method for nonlinear prediction of discrete random sequences under minimal structural assumptions. We give a mathematical construction for optimal predictors of such processes, in the form of hidden Markov models. We then…
Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have…
A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…