Recall that part of motivation for studying Boolean product polynomials was to understand the matroid Mn spanned by nonzero n-vectors with components 0 or 1. We should note here that understanding the real linear algebra of these vectors can go much…

We study a family of symmetric polynomials that we refer to as the Boolean product polynomials. The motivation for studying these polynomials stems f…

In this paper we address the basic geometric question of when a given convex set is the image under a linear map of an affine slice of a given closed…

Consider the sum of $d$ many i.i.d. random permutation matrices on $n$ labels along with their transposes. The resulting matrix is the adjacency matr…

We introduce a class of quadratic support (QS) functions, many of which play a crucial role in a variety of applications, including machine learning,…

(i) This part is a special case of [25, Thm. 2.6].

We construct obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains, with general reflecti…

We prove a stability result in the hybrid inverse problem of recovering the electrical conductivity from partial knowledge of one current density fie…

Suppose X is a topologically contractible smooth complex variety of dimension ≤2, then every vector bundle on X is isomorphic to a trivial bundle.4

We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A^1-homotopy theory; when k = C, the smooth manifolds X…

A single permutation, seen as union of disjoint cycles, represents a regular graph of degree two. Consider $d$ many independent random permutations and superimpose their graph structures. It is a common model of a random regular (multi-) graph of de…

A single permutation, seen as union of disjoint cycles, represents a regular graph of degree two. Consider $d$ many independent random permutations a…

In this paper, we consider two regularized transformation-optics cloaking schemes for electromagnetic (EM) waves. Both schemes are based on the blowu…

We study the Einstein equations coupled with the scalar field equations, $\hbox{Ein}(g)=T$, $T=T(g,\phi)+F^1$, and $\square_g\phi^\ell-m^2\phi^\ell= …

The analysis in this case is similar to the analysis is Section 3. Instead of appealing to Lamperti’s results we appeal to classical results on convergence for martingale problems, in particular we use (JS03, , Theorem IX.4.21). We will provide deta…

We investigate the random flight process that arises as the Boltzmann-Grad limit of a random scatterer Lorentz gas with variable scatterer density in…

In this section we study the dynamical systems on stationary Bratteli diagrams B from the ergodic-theoretic point of view. Our results extend the work of A. Livshits [L2] on minimal Vershik maps and substitution systems, and our methods are rather s…

We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodi…

The study of actions of countable groups by automorphisms of compact abelian groups has recently undergone intensive development, revealing deep conn…

Exceptional sequences are certain ordered sequences of quiver representations. We introduce a class of objects called strand diagrams and use this mo…

We study two inverse problems on a globally hyperbolic Lorentzian manifold $(M,g)$. The problems are: 1. Passive observations in spacetime: Conside…

We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. B…

We evaluate the probabilities of various events under the uniform distribution on the set of 312-avoiding permutations of 1,...,N. We derive exact fo…

We study a graph-theoretic model of interface dynamics called $Competitive\, Erosion$. Each vertex of the graph is occupied by a particle, which can …

The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model.…

In this paper, we study the alternating direction method for finding the Dantzig selectors, which are first introduced in [8]. In particular, at each…

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