Related papers: Self Organizing Map algorithm and distortion measu…
Analyses based on quantum metrology have shown that the ability to localize the positions of two incoherent point sources can be significantly enhanced through the use of mode sorting. Here we theoretically and experimentally investigate…
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come.…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
The objective of this study is improving the location estimate of a mobile robot capable of motion on a plane and mounted with a conventional 2D LIDAR sensor, given an initial guess for its location on a 2D map of its surroundings.…
We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by…
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
This paper discusses lowest-order nonstandard finite element methods for space discretization and explicit and implicit schemes for time discretization of the biharmonic wave equation with clamped boundary conditions. A modified Ritz…
This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…
The main challenge of nonconvex optimization is to find a global optimum, or at least to avoid ``bad'' local minima and meaningless stationary points. We study here the extent to which algorithms, as opposed to optimization models and…
In this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.
The paper deals with a Batch Self Organizing Map algorithm (DBSOM) for data described by distributional-valued variables. This kind of variables is characterized to take as values one-dimensional probability or frequency distributions on a…
A popular class of algorithms to optimize the dual LP relaxation of the discrete energy minimization problem (a.k.a.\ MAP inference in graphical models or valued constraint satisfaction) are convergent message-passing algorithms, such as…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
We numerically benchmark methods for computing harmonic maps into the unit sphere, with particular focus on harmonic maps with singularities. For the discretization we compare two different approaches, both based on Lagrange finite…
In the general theory of quantum measurement, one associates a positive semidefinite operator on a $d$-dimensional Hilbert space to each of the $n$ possible outcomes of an arbitrary measurement. In the special case of a projective…
We introduce a minor variant of the approximate D-optimal design of experiments with a more general information matrix that takes into account the representation of the design space S. The main motivation (and result) is that if S in R^d is…
We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to $\mathbb{R}^d$ containing a distorted reflection symmetry pattern. We pose the problem of detecting…
We present an algorithm for creating contiguous cartograms using meshes. We use numerical optimization to minimize cartographic error and distortion by transforming the mesh vertices. The vertices can either be optimized in the plane or…
Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…