Related papers: Toward a dynamical model for prime numbers
This article studies the dynamics of a finite chain with infinite components. The equation which permits us to find the probability distribution of the chain length is constructed and analysed. This research is a continuation of paper…
Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…
To analyse a very large data set containing lengthy variables, we adopt a sequential estimation idea and propose a parallel divide-and-conquer method. We conduct several conventional sequential estimation procedures separately, and properly…
We study odd numbers through a straightforward indexing. We focus in particular on odd prime and composite numbers and their distribution. With a counting argument, we calculate the limit of two sums and compare their convergence rate.
In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…
We discuss the role of information entropy on the behaviour of random processes, and how this might take effect in the dynamics of financial market prices. We then go on to show how the Open Quantum Systems approach can be used as a more…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
Discrete and Continuous Dynamics is the first in a series of articles on Network Models for Epidemiology. This project began in the Fall quarter of 2014 in my continuous modeling course. Since then, it has taken off and turned into a series…
In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In…
We investigate the distribution of the digits of quotients of randomly chosen positive integers taken from the interval $[1,T]$, improving the previously known error term for the counting function as $T\to+\infty$. We also resolve some…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
We study pairs of consecutive odd numbers through a straightforward indexing. We focus in particular on twin primes and their distribution. With a counting argument, we calculate the limit of an alternating sum that is equal to 1 which…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
We consider the computability of entropy and information in classical Hamiltonian systems. We define the information part and total information capacity part of entropy in classical Hamiltonian systems using relative information under a…
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…
We studied two probabilistic models of the distribution of primes in the natural number [1].The paper considers the third probabilistic model of the distribution of primes in the natural number. The author proved that the results obtained…
We discuss the differential equation method for establishing dynamic concentration of discrete random processes. We present several relatively simple examples of it and aim to make the method understandable to the unfamiliar reader who has…
We study the behavior of a nonlinear semiclassical system using Shannon entropy and two approaches to statistical complexity. These systems involve the interaction between classical variables (representing the environment) and quantum ones.…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite…