Related papers: The Calibration Method for Free Discontinuity Prob…
We establish a new monotonicity formula for minimizers of the Mumford-Shah functional in planar domains. Our formula follows the spirit of Bucur-Luckhaus, but works with the David-L\'eger entropy instead of the energy. Interestingly, this…
The one of the most interesting problem of discrete mathematics is the SAT (satisfiability) problem. Good way in SAT solver developing is to transform the SAT problem to the problem of continuous search of global minimums of the functional…
In this paper we explore the use of an equation of motion decoupling method as an impurity solver to be used in conjunction with the dynamical mean field self-consistency condition for the solution of lattice models. We benchmark the…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
In survey sampling, calibration is a very popular tool used to make total estimators consistent with known totals of auxiliary variables and to reduce variance. When the number of auxiliary variables is large, calibration on all the…
In this paper, we study local minimizers of a degenerate version of the Alt-Caffarelli functional. Specifically, we consider local minimizers of the functional $J_{Q}(u, \Omega):= \int_{\Omega} |\nabla u|^2 + Q(x)^2\chi_{\{u>0\}}dx$ where…
Calibration$\unicode{x2014}$the problem of ensuring that predicted probabilities align with observed class frequencies$\unicode{x2014}$is a basic desideratum for reliable prediction with machine learning systems. Calibration error is…
Calibration of fixtures in robotic work cells is essential but also time consuming and error-prone, and poor calibration can easily lead to wasted debugging time in downstream tasks. Contact-based calibration methods let the user measure…
We consider the inverse conductivity problem with discontinuous conductivities. We show in a rigorous way, by a convergence analysis, that one can construct a completely discrete minimization problem whose solution is a good approximation…
We start by taking the analytical approach to discuss how the minimizer of Yamabe functional provides constant scalar curvature and its relationship with the Sobolev Space $W^{1,2}.$ Then, after demonstrating the importance of the sphere…
In this paper we refine the process of computing calibration functions for a number of multiclass classification surrogate losses. Calibration functions are a powerful tool for easily converting bounds for the surrogate risk (which can be…
This paper is the first part of an ongoing project aimed at providing a local minimality criterion, based on a second variation approach, for the triple point configurations of the Mumford-Shah functional.
We propose a controllability method for the numerical solution of time-harmonic Maxwell's equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the…
We prove the uniform rectifiability of brittle fractures in arbitrary dimension. The existing approach for the Mumford-Shah functional, which relies on separation-type properties of the singular set, faces serious obstacles in the Griffith…
Multiple lidars are prevalently used on mobile vehicles for rendering a broad view to enhance the performance of localization and perception systems. However, precise calibration of multiple lidars is challenging since the feature…
This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…
The Multilevel Monte Carlo (MLMC) approach usually works well when estimating the expected value of a quantity which is a Lipschitz function of intermediate quantities, but if it is a discontinuous function it can lead to a much slower…
Free-discontinuity problems describe situations where the solution of interest is defined by a function and a lower dimensional set consisting of the discontinuities of the function. Hence, the derivative of the solution is assumed to be a…
While widely used as a general method for uncertainty quantification, the bootstrap method encounters difficulties that raise concerns about its validity in practical applications. This paper introduces a new resampling-based method, termed…
A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…