相关论文: Motzkin numbers out of Random Domino Automaton

Krawtchouk's polynomials occur classically as orthogonal polynomials with respect to the binomial distribution. They may be also expressed in the form of matrices, that emerge as arrays of the values that the polynomials take. The algebraic…

In the prediction of oscillating time series, the interest is in the turning points of successive oscillations rather than the samples themselves. For this purpose a scheme has been proposed; the state space reconstruction is limited to the…

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly…

Event-by-event intermittency analysis of Toy Monte Carlo events is performed in the scenario of high multiplicity events as is the case at recent colliders RHIC and LHC for AA collisions. A power law behaviour of Normalized Factorial…

In this paper, we perform an arithmetization of well-formed parenthesis strings with zeros (Motzkin words) and of corresponding Motzkin paths. The transformations used are reminiscent of G\"odel numbering for mathematical objects of some…

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…

The concept of proper time, which is different from universal time, has been introduced into the physics of earthquakes. The global activity of strong earthquakes was chosen as the object of study. We consider the sequence of earthquakes as…

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a…

We continue to consider the ordered lexicographic sequence, which is constructed according to the formal characteristics of a series of natural numbers. For analysis, we selected balanced parentheses with zeros, Motzkin words. As you know,…

For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities…

The results of numerical simulation of the interaction of topological solitons (2+1)-dimensional O(3) non-linear sigma model in reversed time are presented. At the first stage, models of interactions of topological vortices are developed,…

This paper concerns the inverse random source problem of the stochastic Maxwell equations driven by white noise in an inhomogeneous background medium. The well-posedness is established for the direct source problem, and the estimates and…

Laboratory earthquakes exhibit characteristics of a low dimensional random attractor with a dimension similar to that of natural slow earthquakes. A model of stochastic differential equations based on rate and state-dependent friction…

Boltzmann machines are physics informed generative models with wide applications in machine learning. They can learn the probability distribution from an input dataset and generate new samples accordingly. Applying them back to physics, the…

We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and…

We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one…

The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…

We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…

In this paper, we redesign and simplify an algorithm due to Remy et al. for the generation of rooted planar trees that satisfies a given partition of degrees. This new version is now optimal in terms of random bit complexity, up to a…

In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…