Related papers: Computation of Analytic Capacity and applications …
A boundary integral equation method is presented for fast computation of the analytic capacities of compact sets in the complex plane. The method is based on using the Kerzman--Stein integral equation to compute the Szeg\"o kernel and then…
Our main result marks progress on an old conjecture of Vitushkin. We show that a compact set in the plane with plenty of big projections (PBP) has positive analytic capacity, along with a quantitative lower bound. A higher dimensional…
In this work we provide a way to introduce a probability measure on the space of minimal fillings of finite additive metric spaces as well as an algorithm for its computation. The values of probability, got from the analytical solution,…
We present a numerical method for computing the logarithmic capacity of compact subsets of $\mathbb{C}$, which are bounded by Jordan curves and have finitely connected complement. The subsets may have several components and need not have…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our…
Compactness is one of the core notions of analysis: it connects local properties to global ones and makes limits well-behaved. We study the computational properties of the compactness of Cantor space $2^{\mathbb{N}}$ for uncountable covers.…
Using complex methods combined with Baire's Theorem we show that one-sided extendability, extendability and real analyticity are rare phenomena on various spaces of functions in the topological sense. These considerations led us to…
An analytic center cutting plane method is an iterative algorithm based on the computation of analytic centers. In this paper, we propose some analytic center cutting plane methods for solving quasimonotone or pseudomonotone variational…
We give a new criterion for a classical gas with a repulsive pair potential to exhibit uniqueness of the infinite volume Gibbs measure and analyticity of the pressure. Our improvement on the bound for analyticity is by a factor $e^2$ over…
We obtain a series of lower bounds for the product set of combinatorial cubes, as well as some non--trivial upper estimates for the multiplicative energy of such sets.
We consider the problem of maximizing a fractionally subadditive function under a knapsack constraint that grows over time. An incremental solution to this problem is given by an order in which to include the elements of the ground set, and…
Criteria for approximability of functions by solutions of homogeneous second order elliptic equations (with constant complex coefficients) in the norms of the Whitney $C^1$-spaces on compact sets in $\mathbb R^2$ are obtained in terms of…
Using Chebyshev polynomials combined with some mild combinatorics, we provide a new formula for the analytical planar limit of a random matrix model with a one-cut potential $V$. For potentials $V(x)=x^{2}/2-\sum_{n\ge1}a_{n}x^{n}/n$, as a…
We consider a network design problem with random arc capacities and give a formulation with a probabilistic capacity constraint on each cut of the network. To handle the exponentially-many probabilistic constraints a separation procedure…
We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed…
Potential theory on the complement of a subset of the real axis attracts a lot of attention both in function theory and applied sciences. The paper discusses one aspect of the theory - the logarithmic capacity of closed subsets of the real…
In this note we take a new look at the local convergence of alternating optimization methods for low-rank matrices and tensors. Our abstract interpretation as sequential optimization on moving subspaces yields insightful reformulations of…
The algorithm of modified wavelet analysis is discussed. It is based on the weighted least squares approximation. Contrary to the Gaussian as a weight function, we propose to use a compact weight function. The accuracy estimates using the…
A method for the analytical evaluation of layer potentials arising in the collocation boundary element method for the Laplace and Helmholtz equation is developed for piecewise flat boundary elements with polynomial shape functions. The…