Related papers: Stochastic comparisons, differential entropy and v…
Context: Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF). In order to successfully exploit such observables, a detailed…
Two identities in statistical mechanics involving entropy differences (or ratios of density of states) at constant energy are derived. The first provides a nontrivial extension of the Jarzynski equality to the microcanonical ensemble [C.…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This…
The recently developed "Data Set Diagonalization" method (DSD) is applied to measure compatibility of the data sets that are used to determine parton distribution functions (PDFs). Discrepancies among the experiments are found to be…
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with…
Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…
Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, optimal first-passage…
We have discovered analytical expressions for the probability density function (PDF) of photons that are multiply scattered in relativistic flows, under the assumption of isotropic and inelastic scattering. These expressions characterize…
The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a…
Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences -- no…
Experimental data in Particle and Nuclear physics, Particle Astrophysics and Radiation Protection Dosimetry are obtained from experimental facilities comprising a complex array of sensors, electronics and software. Computer simulation is…
We report a joint experimental and theoretical investigation of the probability distribution functions (pdf's) of the normal and tangential (frictional) forces in amorphous frictional media. We consider both the joint pdf of normal and…