Statistical Mechanics and Entropy

This paper presents a random set based approach to tracking of an unknown number of extended targets, in the presence of clutter measurements and missed detections, where the targets' extensions are modeled as random matrices. For this purpose, the random matrix framework developed recently by Koch is adapted into the…

• UMUT ORGUNER

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• ATİLLA GÜLEÇ

In this study, we investigate the infection system of the novel coronavirus (2019-nCoV) with a nonlocal operator defined in the Caputo sense. With the help of the fractional natural decomposition method (FNDM), which is based on the Adomian decomposition and natural transform methods, numerical results were obtained t…

• HACI MEHMET BAŞKONUŞ

As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide class of such systems,…

• UĞUR TIRNAKLI

We investigate the probability density of rescaled sums of iterates of deterministic dynamical systems, a problem relevant for many complex physical systems consisting of dependent random variables. A central limit theorem (CLT) is valid only if the dynamical system under consideration is sufficiently mixing. For the…

• UĞUR TIRNAKLI

Using the existing collected data from European and African countries, we present a statistical analysis of forecast of the future number of daily deaths and infections up to 10 September 2020. We presented numerous statistical analyses of collected data from both continents using numerous existing statistical theorie…

• SEDA İĞRET ARAZ

The probability distribution of sums of iterates of the logistic map at the edge of chaos has been recently shown [U. Tirnakli, Phys. Rev. E 75, 040106(R) (2007)] to be numerically consistent with a q-Gaussian, the distribution which-under appropriate constraints-maximizes the nonadditive entropy Sq, which is the basi…

• UĞUR TIRNAKLI

This paper presents a new prediction update for extended targets whose extensions are modeled as random matrices. The prediction is based on several minimizations of the Kullback-Leibler divergence (KL-div) and allows for a kinematic state dependent transformation of the target extension. The results show that the ext…

• UMUT ORGUNER

In extended/group target tracking, where the extensions of the targets are estimated, target spawning and combination events might have significant implications on the extensions. This paper investigates target spawning and combination events for the case that the target extensions are modeled in a random matrix frame…

• UMUT ORGUNER

For a family of logisticlike maps, we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space. We found that the phase-space volume occupied by the ensemble W(t) depicts a power-law decay with log-periodic oscillations reflect…

• UĞUR TIRNAKLI

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• ERDAL BAŞ

Numerous expressions exist in the scientific literature purporting to represent entropy. Are they all acceptable? To answer this question, we review the thermodynamic definition of entropy, and establish eight criteria that must be satisfied by it. The definition and criteria are obtained by using solely the general,…

• EROL ÇUBUKÇU