Related papers: Simple CVM-based approximations for the configurat…
We present a Bethe approximation to study lattice models of linear polymers. The approach is variational in nature and based on the cluster variation method (CVM). We focus on a model with $(i)$ a nearest neighbor attractive energy…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
Order-disorder effects on equation of state (EOS) properties of substitutional binary alloys are investigated with the cluster variation method (CVM) based on ab initio effective cluster interactions (ECI). Calculations are applied to the…
We bound the number of nearly orthogonal vectors with fixed VC-dimension over $\setpm^n$. Our bounds are of interest in machine learning and empirical process theory and improve previous bounds by Haussler. The bounds are based on a simple…
A method to simulate local properties and processes in crystals with impurities via constructing cluster models within the frame of the compound-tunable embedding potential (CTEP) and highly-accurate {\it ab initio} relativistic…
The nonconforming virtual element method (NCVEM) for the approximation of the weak solution to a general linear second-order non-selfadjoint indefinite elliptic PDE in a polygonal domain is analyzed under reduced elliptic regularity. The…
A novel method to determine the density and temperature of a system based on quantum Fermionic fluctuations is generalized to the limit where the reached temperature T is large compared to the Fermi energy {\epsilon}f . Quadrupole and…
The predictions of the geometric collective model (GCM) for different sets of Hamiltonian parameter values are related by analytic scaling relations. For the quartic truncated form of the GCM -- which describes harmonic oscillator, rotor,…
This paper presents the notion of a variation entropy. This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself. It appears that all semi-norms are admissible variation…
The conditional mutual information quantifies the conditional dependence of two random variables. It has numerous applications; it forms, for example, part of the definition of transfer entropy, a common measure of the causal relationship…
A new DC thermal model of Carbon Nanotube Field Effect Transistors (CNTFETs) is proposed. The model is based on a number of fitting parameters depending on bias conditions by third order polynomials. The model includes three thermal…
In this paper, we propose a new adaptive cross algorithm for computing a low tubal rank approximation of third-order tensors, with less memory and lower computational complexity than the truncated tensor SVD (t-SVD). This makes it…
The description of chemical processes at the molecular level is often facilitated by use of reaction coordinates, or collective variables (CVs). The CV measures the progress of the reaction and allows the construction of profiles that track…
The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
The Thomas - Fermi equation describing the screening of the Coulomb potential inside heavy neutral atoms is reconsidered. An accurate representation for its numerical solution was obtained by means of the variational principle. The proposed…
Finite temperature disordered solid solutions and magnetic materials are difficult to study directly using first principles calculations, due to the large unit cells and many independent samples that are required. In this work, we develop a…
The Variation After Projection approach is applied for the first time to the pairing hamiltonian to describe the thermodynamics of small systems with fixed particle number. The minimization of the free energy is made by a direct…
The constant-volume heat capacity, C_V(T, rho), of the restricted primitive model (RPM) electrolyte is considered in the vicinity of its critical point. It is demonstrated that, despite claims, recent simulations for finite systems do not…
The virial expansion characterizes the high-temperature approach to the quantum-classical crossover in any quantum many-body system. Here, we calculate the virial coefficients up to the fifth-order of Fermi gases in 1D, 2D, and 3D, with…