Related papers: Numerical analytic continuation: Answers to well-p…

This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…

- In this paper we introduce a new method to solve fixed-delay optimal control problems which exploits numerical homotopy procedures. It is known that solving this kind of problems via indirect methods is complex and computationally…

The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible…

We consider the spectral definition of the fractional Laplace operator and study a basic linear problem involving this operator and singular forcing. In two dimensions, we introduce an appropriate weak formulation in fractional Sobolev…

We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and…

This paper investigates the problem of estimating the spectral power parameters of random analog sources using numerical measurements acquired with minimum digitization complexity. Therefore, spectral analysis has to be performed with…

Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…

The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates…

We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…

Spectral estimation can be preformed using the so called THREE-like approach. Such method leads to a convex optimization problem whose solution is characterized through its dual problem. In this paper, we show that the dual problem can be…

In this paper, we discuss a class of spectral partition problems with a measure constraint, for partitions of a given bounded connected open set. We establish the existence of an optimal open partition, showing that the corresponding…

In this paper, we investigate the problem of mining numerical data in the framework of Formal Concept Analysis. The usual way is to use a scaling procedure --transforming numerical attributes into binary ones-- leading either to a loss of…

In this thesis, the numerical solution of three different classes of problems have been studied. Specifically, new techniques have been proposed and their theoretical analysis has been performed, accompanied by a wide set of numerical…

An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically…

We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…

We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…

In this article we perform a critical assessment of different known methods for the analytical continuation of bosonic functions, namely the maximum entropy method, the non-negative least-square method, the non-negative Tikhonov method, the…

Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…