Related papers: Curvature Correction in the Strutinsky's Method
In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial…
We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and…
In this paper, we consider stochastic second-order methods for minimizing a finite summation of nonconvex functions. One important key is to find an ingenious but cheap scheme to incorporate local curvature information. Since the true…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
Smoothing is an estimation technique that takes into account both past and future observations, and can be more accurate than filtering alone. In this Letter, a quantum theory of smoothing is constructed using a time-symmetric formalism,…
In this paper we introduce two new notions of sectional curvature for Riemannian manifolds with density. Under both notions of curvature we classify the constant curvature manifolds. We also prove generalizations of the theorems of…
A class of smoothing methods is proposed for solving mathematical programs with equimibrium constraints. We introduce new and very simple regularizations of the complementarity constraints. Some estimate distance to optimal solution and…
In this paper we introduce new symmetrization with respect to mixed volume or anisotropic curvature integral, which generalizes the one with respect to quermassintegral due to Talenti and Tso. We show a P\'olya-Szego type principle for such…
Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…
Surface and curvature properties of asymmetric nuclear matter are studied beyond the proton drip. Using the semiclassical extended Thomas-Fermi method, the calculations are performed in the non-relativistic and relativistic meson field…
N-Body simulations are a very important tool in the study of formation of large scale structures. Much of the progress in understanding the physics of galaxy formation and comparison with observations would not have been possible without…
In this article, we give a complete and self--contained account of Chernysh's strengthening of the Gromov--Lawson surgery theorem for metrics of positive scalar curvature. No claim of originality is made.
The main issues of the original Symmetrical smoothing method consists of approximation of the extremal volume of the set by the smooth symmetric function (sum of step functions) and then solve the optimization problem. when making…
Efficient processing of particulate products across various manufacturing steps requires that particles possess desired attributes such as size and shape. Controlling the particle production process to obtain required attributes will be…
In this paper we study the curvature flow of a curve in a plane endowed with a minkowskian norm whose unit ball is smooth. We show that many of the properties known in the euclidean case can be extended (with due adaptations) to this new…
Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider…
We reconstruct the shape of the primordial power spectrum (PPS) using a smoothing spline. Our adapted smoothing spline technique provides a complementary method to existing efforts to search for smooth features in the PPS, such as a running…
We present a detailed analysis of three models predicting the properties of non-uniform matter in the crust of neutron stars: the compressible liquid-drop model, the fourth order Extended Thomas Fermi (ETF) method, and ETF plus Strutinsky…
Particle smoothing enables state estimation in nonlinear and non-Gaussian state-space models, but its practical use is often limited by high computational cost. Backward smoothing methods such as the Forward Filter Backward Smoother (FFBS)…