Related papers: A functional approach to the numerical conformal b…

Feedforward neural networks offer a promising approach for solving differential equations. However, the reliability and accuracy of the approximation still represent delicate issues that are not fully resolved in the current literature.…

We use the numerical bootstrap to study conformal line defects with $O(2)$ global symmetry. Our results are very general and capture in particular conformal line defects originating from bulk CFTs with a continuous global symmetry, which…

We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional…

Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science.…

We describe an efficient method for the approximation of functions using radial basis functions (RBFs), and extend this to a solver for boundary value problems on irregular domains. The method is based on RBFs with centers on a regular grid…

This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…

Genus two partition functions of 2d chiral conformal field theories are given by Siegel modular forms. We compute their conformal blocks and use them to perform the conformal bootstrap. The advantage of this approach is that it imposes…

First-principles density functional theory (DFT) codes which employ a localized basis offer advantages over those which use plane-wave bases, such as better scaling with system size and better suitability to low-dimensional systems. The…

In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…

This is the first in a series of articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here, we introduce spaces of…

In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…

Despite recent advances in multi-scale deep representations, their limitations are attributed to expensive parameters and weak fusion modules. Hence, we propose an efficient approach to fuse multi-scale deep representations, called…

Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…

In this paper, we give a geometric interpretation of optimal functionals in the context of intersection of symmetry planes and cyclic polytopes. For 1D CFTs, we demonstrate that at given derivative order, the functional is given by a…

We discuss an idea of how 3D critical exponents can be determined by Conformal Field Theory techniques.

We present a comprehensive study of radial basis function (RBF) approximations for elliptic and obstacle-type boundary value problems under a variational formulation. Our focus is on practical accuracy, robustness and efficiency. To address…

A program of wide interest in modern conformal bootstrap studies is to numerically solve general conformal field theories, based on a critical assumption that the dynamics is encoded in the conformal four-point crossing equations and…

We use analytic (super-)conformal bootstrap methods to derive explicit expressions for the structure constants of $\mathcal{N}=1$ Liouville CFT in the `timelike' regime of the superconformal central charge. The obtained expressions take the…

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion…