相关论文: Solving the Parity Problem with Rule 60 in Array S…

We studied the rule 150 elementary cellular automaton in terms of the distribution of the spacings of the singular values of the matieces obtained from proper time evolutions patterns. The distribution has strong resembrance to that of the…

We study a class of nonlinear elliptic problems driven by a double-phase operator with variable exponents, arising in the modeling of heterogeneous materials undergoing phase transitions. The associated Poisson problem features a…

When a system which contains a dipole, and whose dimensionality is less than three, is studied in a code which imposes periodic boundary conditions in all three dimensions, an artificial electric field arises which keeps the potential…

We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power…

Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…

We define a new strict and computable hierarchy for the family of automaton semigroups, which reflects the various asymptotic behaviors of the state-activity growth. This hierarchy extends that given by Sidki for automaton groups, and also…

We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…

Complexity Theory is highly interdisciplinary, therefore any regularities must hold on all levels of organization, independent on the nature of the system. An open question in science is how complex systems self-organize to produce emergent…

We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms…

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…

Evolving one-dimensional cellular automata (CAs) with genetic algorithms has provided insight into how improved performance on a task requiring global coordination emerges when only local interactions are possible. Two approaches that can…

Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type…

We study cellular automata with randomly selected rules. Our setting are two-neighbor rules with a large number $n$ of states. The main quantity we analyze is the asymptotic probability, as $n \to \infty$, that the random rule has a…

So-called separation automata are in the core of several recently invented quasi-polynomial time algorithms for parity games. An explicit $q$-state separation automaton implies an algorithm for parity games with running time polynomial in…

How coperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model…

The Satisfactory Partition problem consists in deciding if the set of vertices of a given undirected graph can be partitioned into two nonempty parts such that each vertex has at least as many neighbours in its part as in the other part.…

This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…

Two cases of evolutionary stable strategy with periodic payoffs are studied. The first is a generalization of Uyttendaele et al. The second is prisoner's dilemma with periodic payoff. It is shown that reducing the defection payoff by a…

As a means to solve optimization problems using quantum computers, the problem is typically recast into a Ising spin model whose ground-state is the solution of the optimization problem. An alternative to the Ising formulation is the…

Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…