Related papers: Universal Spatiotemporal Sampling Sets for Discret…

Let $A_1$ and $A_2$ be randomly chosen subsets of the first $n$ integers of cardinalities $s_2\geq s_1 = \Omega(s_2)$, such that their sumset $A_1+A_2$ has size $m$. We show that asymptotically almost surely $A_1$ and $A_2$ are almost fully…

In this paper, we consider the optimization problem for the first Dirichlet eigenvalue $\lambda_1(\Omega)$ of the $p$-Laplacian $\Delta_p$, $1< p< \infty$, over a family of doubly connected planar domains $\Omega= B \setminus \overline{P}$,…

Dictionary learning for sparse representations has been successful in many reconstruction tasks. Simplicial learning is an adaptation of dictionary learning, where subspaces become clipped and acquire arbitrary offsets, taking the form of…

We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the space and the reproducing kernel. If the volume of shells is…

We consider $L^2$-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear…

Massive volumes of high-dimensional data that evolves over time is continuously collected by contemporary information processing systems, which brings up the problem of organizing this data into clusters, i.e. achieve the purpose of…

We study the geometry and dynamics of discrete subgroups $\Gamma$ of $\PSL(3,\mathbb{C})$ with an open invariant set $\Omega \subset \PC^2$ where the action is properly discontinuous and the quotient $\Omega/\Gamma$ contains a connected…

We consider a heat-type operator L structured on the left invariant 1-homogeneous vector fields which are generators of a Carnot group, multiplied by a uniformly positive matrix of bounded measurable coefficients depending only on time. We…

The present phase of Machine Learning is characterized by supervised learning algorithms relying on large sets of labeled examples ($n \to \infty$). The next phase is likely to focus on algorithms capable of learning from very few labeled…

Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization…

Sampling of a spatiotemporal field for environmental sensing is of interest. Traditionally, a few fixed stations or sampling locations aid in the reconstruction of the spatial field. Recently, there has been an interest in mobile sensing…

The Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied from a Hamiltonian point of view. The complexified Ashtekar canonical variables are used, and the symmetry reduction is performed…

We consider the following eigenvalue optimization in the composite membrane problem with fractional Laplacian: given a bounded domain $\Omega\subset \mathbb{R}^n$, $\alpha>0$ and $0<A<|\Omega|$, find a subset $D\subset \Omega$ of area $A$…

Satellite image time series, bolstered by their growing availability, are at the forefront of an extensive effort towards automated Earth monitoring by international institutions. In particular, large-scale control of agricultural parcels…

This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…

Short-and-sparse deconvolution (SaSD) is the problem of extracting localized, recurring motifs in signals with spatial or temporal structure. Variants of this problem arise in applications such as image deblurring, microscopy, neural spike…

We study $L^2$-maximal regularity for non-autonomous evolution equations of the form \begin{equation}\label{Abstract equation} \dot u(t)+\mathcal A(t)u(t)=f(t)\ \ t\in[0,T],\ \ u(0)=u_0. \end{equation} where $\mathcal A(t),\ t\in [0,T]$…

This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$ norm…

With a densely defined symmetric semi-bounded operator of nonzero defect indexes $L_0$ in a separable Hilbert space ${\cal H}$ we associate a topological space $\Omega_{L_0}$ ({\it wave spectrum}) constructed from the reachable sets of a…

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…