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So far, various techniques have been implemented for generating discrete distributions based on continuous distributions. The characteristics and properties of this kind of probability distributions have been studied. Furthermore, the…
We show that fractional exclusion statistics is manifested in general in interacting systems and we discuss the conjecture recently introduced (J. Phys. A: Math. Theor. 40, F1013, 2007), according to which if in a thermodynamic system the…
Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…
We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions,…
For configurational space of arbitrary dimension a strict form of the uncertainty principle has been obtained, which takes into account the dependence of inequality limit on the effective number of pure states present in given statistical…
Local similarity theory is suggested based on the Brunt-Vaisala frequency and the dissipation rate of turbulent kinetic energy instead the turbulent fluxes used in the traditional Monin-Obukhov similarity theory. Based on dimensional…
The behavior of a family of dissipative dynamical systems representing transformations of two-dimensional torus is studied on a discrete lattice and compared with that of conservative hyperbolic automorphisms of the torus. Applying…
We study the presence of abelian discrete symmetries in globally consistent orientifold compactifications based on rational conformal field theory. We extend previous work [1] by allowing the discrete symmetries to be a linear combination…
We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to…
We investigate the systematic mechanism for designing fast mixing Markov chain Monte Carlo algorithms to sample from discrete point processes under the Dobrushin uniqueness condition for Gibbs measures. Discrete point processes are defined…
We begin by investigating relationships between two forms of Hilbert-Schmidt two-re[al]bit and two-qubit "separability functions"--those recently advanced by Lovas and Andai (J. Phys. A 50 [2017] 295303), and those earlier presented by…
We study a version of the Lebesgue differentiation theorem in which the integral averages are replaced with medians over Busemann--Feller differentiation bases. Our main result gives several characterizations for the differentiation…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We construct random Morse functions on surfaces by random walk and compute related distributions. We study the space of Morse functions through these random variables. We consider subspaces characterized by the surfaces with boundary…
The Poisson bipolar model considers user-base station pairs distributed at random on a flat domain, similar to matchsticks scattered onto a table. Though this is a simple and tractable setting in which to study dense networks, it doesn't…
We consider elastic reflection and transmission of electrons by a disordered system characterized by a $2N\!\times\!2N$ scattering matrix $S$. Expressing $S$ in terms of the $N$ radial parameters and of the four $N\!\times\!N$ unitary…
Cosine similarity is an established similarity metric for computing associations on vectors, and it is commonly used to identify related samples from biological perturbational data. The distribution of cosine similarity changes with the…
This article presents a theoretical study of the scaling properties of the kinetic energy spectrum in compressible turbulence. From the fundamental symmetries and linear transformations of the microscopic action, we derive exact relations…
We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs…
We have integrated density functional theory (DFT) into quantitative convergent-beam electron diffraction (QCBED) to create a synergy between experiment and theory called QCBED-DFT. This synergy resides entirely in the electron density…