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Classical density functional theory (cDFT) and dynamical density functional theory (DDFT) are modern statistical mechanical theories for modeling many-body colloidal systems at the one-body density level. The theories hinge on knowing the…
We discuss the problem for detecting long-range correlations in sequences of values obtained by generators of pseudo-random numbers. The basic idea is that the H{\"o}lder exponent for a sufficiently long sequence of uncorrelated random…
In the exact Kohn-Sham density-functional theory (DFT), the total energy versus the number of electrons is a series of linear segments between integer points. However, commonly used approximate density functionals produce total energies…
We scrutinize the accuracy of the pseudopotential approximation in density-functional theory (DFT) calculations of surfaces by systematically comparing to results obtained within a full-potential setup. As model system we choose the CO…
It is well-known that the Bhattacharyya, Hellinger, Kullback-Leibler, $\alpha$-divergences, and Jeffreys' divergences between densities belonging to a same exponential family have generic closed-form formulas relying on the strictly convex…
We first extend the result of Ali and Silvey [Journal of the Royal Statistical Society: Series B, 28.1 (1966), 131-142] who first reported that any $f$-divergence between two isotropic multivariate Gaussian distributions amounts to a…
At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, $\xi_{Z}$, is associated with…
Recently, S. Li and A. Pott\cite{LP} proposed a new concept of intersection distribution concerning the interaction between the graph $\{(x,f(x))~|~x\in\F_{q}\}$ of $f$ and the lines in the classical affine plane $AG(2,q)$. Later, G.…
The recently proposed Householder transformed density-matrix functional embedding theory (Ht-DMFET) [Sekaran et al., Phys. Rev. B 104, 035121 (2021)], which is equivalent to (but formally simpler than) density matrix embedding theory (DMET)…
The standard deviations of the energy and Poynting power densities for an isotropic random field near a perfectly conducting planar boundary are characterized, based on quartic plane-wave expansions. For normal and transverse components,…
In this paper, we hypothesize that internal function sharing is one of the reasons to weaken o.o.d. or systematic generalization in deep learning for classification tasks. Under equivalent prediction, a model partitions an input space into…
We decompose the energy error of any variational DFT calculation into a contribution due to the approximate functional and that due to the approximate density. Typically, the functional error dominates, but in many interesting situations,…
In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…
The novel functional dimensional regularization (FDR) scheme has proven capable of yielding results that are competitive with the state-of-the-art in the computation of critical exponents in $d=3$, while also reproducing those from the…
We discuss several approaches to defining power in studies designed around the Benjamini-Hochberg (BH) false discovery rate (FDR) procedure. We focus primarily on the \textit{average power} and the $\lambda$-\textit{power}, which are the…
Density functional theory is discussed in the context of one-particle systems. We show that the ground state density $\rho_0(x)$ and energy $E_0$ are simply related to a family of external potential energy functions with ground state wave…
The accuracy of density-functional theory (DFT) is determined by the quality of the approximate functionals, such as exchange-correlation in electronic DFT and the excess functional in the classical DFT formalism of fluids. The exact…
The recently proposed universal relations between the moments of the polydispersity distributions of a phase-separated weakly polydisperse system are analyzed in detail using the numerical results obtained by solving a simple density…
We present an accurate local density-functional for electronic-structure calculations within the density functional theory (DFT). The functional is derived by analyzing the structure of the standard perturbative expansion of the correlation…
Dynamical Mean-Field Theory (DMFT) has opened new perspectives for the investigation of strongly correlated electron systems and greatly improved our understanding of correlation effects in models and materials. In contrast to…