Related papers: A new algorithm to search for small nonzero |x^3 -…
We present an algorithm aimed to recognize if a given tensor is a non-identifiable rank-3 tensor.
For a given nonnegative matrix $A=(A_{ij})$, the matrix scaling problem asks whether $A$ can be scaled to a doubly stochastic matrix $D_1AD_2$ for some positive diagonal matrices $D_1,D_2$.The Sinkhorn algorithm is a simple iterative…
We prove two basic conjectures on the distribution of the smallest singular value of random n times n matrices with independent entries. Under minimal moment assumptions, we show that the smallest singular value is of order n^{-1/2}, which…
We design and analyze an algorithm for computing solutions with coefficients in a finite field $\mathbb{F}_q$ of underdetermined systems defined over $\mathbb{F}_q$. The algorithm is based on reductions to zero-dimensional searches. The…
Three algorithms looking for pretty large partial Hadamard matrices are described. Here "large" means that hopefully about a third of a Hadamard matrix (which is the best asymptotic result known so far, [dLa00]) is achieved. The first one…
The Hamming oracle returns the Hamming distance between an unknown binary $n$-vector $x$ and a binary query $n$-vector y. The objective is to determine $x$ uniquely using a sequence of $m$ queries. What are the minimum number of queries…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
New methods for finding submatrices of (locally) maximal volume and large projective volume are proposed and studied. Detailed analysis is also carried out for existing methods. The effectiveness of the new methods is shown in the…
The LHC experiments have great potential in discovering many possible new particles up to the TeV scale. The significance calculation of an observation of a physics signal with known location and shape is no longer valid when either the…
Using the action of the Yang-Baxter elements of the Hecke algebra on polynomials, we define two bases of polynomials in n variables. The Hall-Littlewood polynomials are a subfamily of one of them. For q=0, these bases specialize into the…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…
We prove a conjecture about the minimal nonnegative solutions of algebraic Riccati equations associated with reducible singular M-matrices. The result enhances our understanding of the behaviour of doubling algorithms for finding the…
There is a recent surge of interest in developing algorithms for finding sparse solutions of underdetermined systems of linear equations $y = \Phi x$. In many applications, extremely large problem sizes are envisioned, with at least tens of…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…
We present a new algorithm for finding isolated zeros of a system of real-valued functions in a bounded interval in $\mathbb{R}^n$. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and…
This paper develops an efficient iterative method for computing all zeros of solutions of second order ordinary differential equations. A third order Halleys method is first derived by approximating the solution of an associated Riccati…
We survey recent results on Calderon's inverse problem with partial data, focusing on three and higher dimensions.
We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes…
A new algebraic object is introduced - recurrent fractions, which is an n-dimensional generalization of continued fractions. It is used to describe an algorithm for rational approximations of algebraic irrational numbers. Some…