Related papers: On the basis-set extrapolation
Stochastic programming can be applied to consider uncertainties in energy system optimization models for capacity expansion planning. However, these models become increasingly large and time-consuming to solve, even without considering…
In Paper I, the effective one-electron potentials (OEP) method was introduced and demonstrated as an efficient approach to reduce the computational cost of evaluation of the charge-transfer interaction energy within the effective fragment…
We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of basic semialgebraic sets which works in weak exponential time. That is, out of a set of exponentially small measure in the space of…
Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which…
The main purpose of this work is the one of providing an efficient scheme for constructing reduced interpolation models for kernel bases. In literature such problem is mainly addressed via the well-established knot insertion or knot removal…
In this paper, we give new sparse interpolation algorithms for black box univariate and multivariate rational functions h=f/g whose coefficients are integers with an upper bound. The main idea is as follows: choose a proper integer beta and…
quest for processing speed potential. In fact, we always get a fraction of the technically available computing power (so-called {\em theoretical peak}), and the gap is likely to go hand-to-hand with the hardware complexity of the target…
We have investigated the title question for the W4-08 thermochemical benchmark using partial-wave truncations of a large reference (REF) basis set, as well as for standard F12-optimized basis sets. With the REF basis set, the root mean…
We develop a model based on the fractional exclusion statistics (FES) applicable to non-homogeneous interacting particle systems. Here the species represent elementary volumes in an (s+1)-dimensional space, formed by the direct product…
Only a few numerical methods can treat boundary value problems on polygonal and polyhedral meshes. The BEM-based Finite Element Method is one of the new discretization strategies, which make use of and benefits from the flexibility of these…
We study the properties of memory of a financial time series adopting two different methods of analysis, the detrended fluctuation analysis (DFA) and the analysis of the power spectrum (PSA). The methods are applied on three time series:…
Inspired by the AdS/CFT correspondence, we study the pseudoscalar mesons of QCD through a dual embedding in a strongly curved extra dimensional spacetime. This model incorporates the consequences of symmetry and has very few free…
We consider the problem of extrapolating treatment effects across heterogeneous populations (``sites"/``contexts"). We consider an idealized scenario in which the researcher observes cross-sectional data for a large number of units across…
Handling long-context sequences efficiently remains a significant challenge in large language models (LLMs). Existing methods for token selection in sequence extrapolation either employ a permanent eviction strategy or select tokens by…
The Bethe-Salpeter equation plays a crucial role in understanding the physics of correlated fermions, relating to optical excitations in solids as well as resonances in high-energy physics. Yet, it is notoriously difficult to control…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…
The exponential stability, in both mean square and almost sure senses, for energy solutions to a class of nonlinear and non-autonomous stochastic PDEs with finite memory is investigated. Various criteria for stability are obtained. An…
We consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to…
We have developed and benchmarked a new extended basis set for explicitly correlated calculations, namely cc-pV5Z-F12. It is offered in two variants, cc-pV5Z-F12 and cc- pV5Z-F12(rev2), the latter of which has additional basis functions on…
Memory is a complex phenomenon that involves several distinct mechanisms. These mechanisms operate at different spatial and temporal levels. This chapter focuses on the theoretical framework and the mathematical models that have been…