Related papers: Optimal Bounds for Integrals with Respect to Copul…
Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin…
In this paper, we construct a bound copula, which can reach both Frechet's lower and upper bounds for perfect positive and negative dependence cases. Since it covers a wide range of dependency and simple for computational purposes, it can…
Approximating integrals is a fundamental task in probability theory and statistical inference, and their applied fields of signal processing, and Bayesian learning, as soon as expectations over probability distributions must be computed…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
We study the problem of deriving compressibility measures for Piecewise Linear Approximations (PLAs), i.e., error-bounded approximations of a set of two-dimensional increasing data points using a sequence of segments. Such approximations…
The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient…
We design a Quasi-Polynomial time deterministic approximation algorithm for computing the integral of a multi-dimensional separable function, supported by some underlying hyper-graph structure, appropriately defined. Equivalently, our…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…
Approximating solutions of ordinary and partial differential equations constitutes a significant challenge. Based on functional expressions that inherently depend on neural networks, neural forms are specifically designed to precisely…
In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…
Extreme-value copulas arise as the limiting dependence structure of component-wise maxima. Defined in terms of a functional parameter, they are one of the most widespread copula families due to their flexibility and ability to capture…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…
A representation of the sharp constant in a pointwise estimate of the gradient of a harmonic function in a multidimensional half-space is obtained under the assumption that function's boundary values belong to $L^p$. This representation is…