相关论文: Beyond the Rosenfeld Functional: Loop Contribution…

Algorithms in machine learning and AI do critically depend on at least three key components: (i) the risk function, which is the expectation of the loss function, (ii) the function space, which is often called the hypothesis space, and…

This expository article explores the vital role of interpolation theory and Lorentz spaces in the rigorous analysis of partial differential equations (PDEs). While classical Lebesgue spaces ($L_{p}$) successfully measure the magnitude of…

Logconcave functions represent the current frontier of efficient algorithms for sampling, optimization and integration in R^n. Efficient sampling algorithms to sample according to a probability density (to which the other two problems can…

In discussing the phase transition of the three-dimensional complex |psi|^4 theory, we study the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using…

A central question in rough path theory is characterising the law of stochastic processes on path spaces. It is established in [I. Chevyrev & T. Lyons, Characteristic functions of measures on geometric rough paths, Ann. Probab. 44 (2016),…

Reduced density-matrix functional theory (RDMFT) has become an appealing alternative to density-functional theory to describe electronic properties of highly-correlated systems. Here we derive exact conditions for the suitability of RDMFT…

We extend the Rate-Distortion-Perception (RDP) framework to the R\'enyi information-theoretic regime, utilizing Sibson's $\alpha$-mutual information to characterize the fundamental limits under distortion and perception constraints. For…

The precision of quantum metrology is widely believed to be restricted by the Heisenberg limit, corresponding to a root mean square error that is inversely proportional to the number of independent processes probed in an experiment, N. In…

In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological…

This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…

We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…

We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an…

We propose an anisotropic generalisation of the line correlation function (ALCF) to separate and quantify phase information in the large-scale structure of galaxies. The line correlation function probes the strictly non-linear regime of…

We extend to strongly correlated molecular systems the recently introduced basis-set incompleteness correction based on density-functional theory (DFT) [E. Giner et al., J. Chem. Phys. 149, 194301 (2018)]. This basis-set correction relies…

The properties of a hard-sphere fluid in contact with hard spherical and cylindrical walls are studied. Rosenfeld's density functional theory (DFT) is applied to determine the density profile and surface tension $\gamma$ for wide ranges of…

The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase…

In a recent paper [M. G\"ul et al., Phys. Rev. E, 110 (6), 064115] we showed that test particle sum rules, which address the excess chemical potential and isothermal compressibility, could be used to develop new and accurate classical…

The result of performing integrations over connection type variables in the path integral for the discrete field theory may be poorly defined in the case of non-compact gauge group with the Haar measure exponentially growing in some…

Multivariate Bessel processes $(X_{t,k})_{t\ge0}$ describe interacting particle systems of Calogero-Moser-Sutherland type and are related with $\beta$-Hermite and $\beta$-Laguerre ensembles. They depend on a root system and a multiplicity…

We have generalized the network approach to include the effects of short-range imperfections in order to analyze recent experiments on mesoscopic superconducting double loops. The presence of weakly scattering imperfections causes gaps in…