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Many stellar systems exhibit a finite spatial extent, yet constructing self-consistent spherical models with a prescribed outer boundary is non-trivial because sharp density cutoffs introduce discontinuities that lead to inconsistencies in…
The exact Kohn-Sham iteration of generalized density-functional theory in finite dimensions witha Moreau-Yosida regularized universal Lieb functional and an adaptive damping step is shown toconverge to the correct ground-state density.
This work presents a theory to unify the two independent theoretical frameworks of Kohn-Sham (KS) density functional theory (DFT) and reduced density matrix functional theory (RDMFT). The generalization of the KS orbitals to hypercomplex…
We prove the existence of a $(d-2)$-dimensional purely unrectifiable set upon which a family of \emph{even} singular integral operators is bounded.
We investigate properties of the set of discrete Morse functions on a simplicial complex as defined by Forman. It is not difficult to see that the pairings of discrete Morse functions of a finite simplicial complex again form a simplicial…
Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When…
In this paper, we investigate the behavior of the bounds of the composition for rough singular integral operators on the weighted space. More precisely, we obtain the quantitative weighted bounds of the composite operator for two singular…
We consider the class of weakly porous sets in Euclidean spaces. As our main goal, we give a precise characterization in terms of dyadic covering of these sets. Also, we obtain the Carleson embedding inequality for porous sets.
We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…
Continuous conformal transformation minimizes the conformal energy. The convergence of minimizing discrete conformal energy when the discrete mesh size tends to zero is an open problem. This paper addresses this problem via a careful error…
Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size and help interpretability. However enforcing these shape…
Many deep learning architectures for semantic segmentation involve a Fully Convolutional Neural Network (FCN) followed by a Conditional Random Field (CRF) to carry out inference over an image. These models typically involve unary potentials…
We investigate a quasi-one-dimensional (Q1D) system of hard spheres confined within a cylindrical pore so narrow that only nearest-neighbor interactions occur. By mapping this Q1D system onto a one-dimensional polydisperse mixture of…
In this paper we analyse and improve integer discrete flows for lossless compression. Integer discrete flows are a recently proposed class of models that learn invertible transformations for integer-valued random variables. Their discrete…
In this article we consider the classical singular integral operator over a local field with rough kernels. We study the boundedness of such an operator on different function spaces by relaxing the smoothness condition on kernels.
We study contraction conditions for an iterated function system of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space,…
We consider generalisations of the elliptic Calogero--Moser systems associated to complex crystallographic groups in accordance to [1]. In our previous work [2], we proposed these systems as candidates for Seiberg--Witten integrable systems…
Training materials through periodic drive allows to endow materials and structures with complex elastic functions. As a result of the driving, the system explores the high dimensional space of structures, ultimately converging to a…
We have studied the color dipole picture for the description of the deep inelastic process, mainly the structure functions which are driven directly by the gluon distribution. Estimates for those functions are obtained using the effective…
Resonance coupling in non-Hermitian systems can lead to exotic features, such as bound states in the continuum (BICs) and exceptional points (EPs), which have been widely employed to control the propagation and scattering of light. Yet,…