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Electronic structure calculations based on Density Functional Theory have successfully predicted numerous ground state properties of a variety of molecules and materials. However, exchange and correlation functionals currently used in the…

We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the…

We investigate fractional-charge and fractional-spin errors in range-separated density-functional theory. Specifically, we consider the range-separated hybrid (RSH) method which combines long-range Hartree-Fock (HF) exchange with a…

Perception is crucial for robots that act in real-world environments, as autonomous systems need to see and understand the world around them to act properly. Panoptic segmentation provides an interpretation of the scene by computing a…

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…

We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/over-parameterized regime. In this work, we derive precise non-asymptotic error bounds of RF…

A two-parameter extension of the density-scaled double hybrid approach of Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)] is presented. It is based on the explicit treatment of a fraction of multideterminantal exact exchange. The…

This study emphasizes the significance of exploring distance-based source separation (DSS) in outdoor environments. Unlike existing studies that primarily focus on indoor settings, the proposed model is designed to capture the unique…

Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…

Double hybrid (DH) density functionals are amongst the most accurate density functional approximations developed so far, largely due to incorporation of correlation effects from unoccupied orbitals via second order perturbation theory…

We analyze Local SGD (aka parallel or federated SGD) and Minibatch SGD in the heterogeneous distributed setting, where each machine has access to stochastic gradient estimates for a different, machine-specific, convex objective; the goal is…

We develop a non-linear and non-empirical (nlane) double hybrid density functional derived from an accurate interpolation of the adiabatic connection in density functional theory, incorporating the correct asymptotic expansions. By bridging…

We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…

We show that the DCSD (distinguishable clusters with all singles and doubles) correlation method permits the calculation of vibrational spectra at near-CCSD(T) quality but at no more than CCSD cost, and with comparatively inexpensive…

In this work we address the Multiscale Spectral Generalized Finite Element Method (MS-GFEM) developed in [I. Babu\v{s}ka and R. Lipton, Multiscale Modeling and Simulation 9 (2011), pp. 373--406]. We outline the numerical implementation of…

In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the…

The density functional theory (DFT) approximations that are the most accurate for the calculation of band gap of bulk materials are hybrid functionals like HSE06, the MBJ potential, and the GLLB-SC potential. More recently, generalized…

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms…

An alternative separation of short-range exchange and correlation energies is used in the framework of second-order range-separated density-functional perturbation theory. This alternative separation was initially proposed by Toulouse et…

Diverse decoding of large language models is crucial for applications requiring multiple semantically distinct responses, yet existing methods primarily achieve lexical rather than semantic diversity. This limitation significantly…