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A sender holds a word x consisting of n blocks x_i, each of t bits, and wishes to broadcast a codeword to m receivers, R_1,...,R_m. Each receiver R_i is interested in one block, and has prior side information consisting of some subset of…
We classify modules and rings with some specific properties of their intersection graphs. In particular, we describe rings with infinite intersection graphs containing maximal left ideals of finite degree. This answers a question raised in…
We study embedding a subset $K$ of the unit sphere to the Hamming cube $\{-1,+1\}^m$. We characterize the tradeoff between distortion and sample complexity $m$ in terms of the Gaussian width $\omega(K)$ of the set. For subspaces and several…
In this paper we consider two pointsets in $\mathrm{PG}(2,q^n)$ arising from a linear set $L$ of rank $n$ contained in a line of $\mathrm{PG}(2,q^n)$: the first one is a linear blocking set of R\'edei type, the second one extends the…
This paper studies problems related to visibility among points in the plane. A point $x$ \emph{blocks} two points $v$ and $w$ if $x$ is in the interior of the line segment $\bar{vw}$. A set of points $P$ is \emph{$k$-blocked} if each point…
A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper subsets (called blocks) of a point-set with $v$ points satisfying (i) every two blocks intersect each other in $\lambda$ points for a fixed $\lambda < v$ (ii) there…
Closed form expressions are given for computing the parameters and vectors that identify and define the $n-1$ dimensional conic section that results from the intersection of a hyperplane with an $n$-dimensional conic section: cone,…
Paul Erd\H{o}s and L\'aszl\'o Lov\'asz established that any \emph{maximal intersecting family of $k-$sets} has at most $k^{k}$ blocks. They introduced the problem of finding the maximum possible number of blocks in such a family. They also…
In this note, we investigate the maximal number of intersection points of a line with the contour of hypersurface amoebas in $\mathbb{R}^n$. We define the latter number to be the $\mathbb{R}$-degree of the contour. We also investigate the…
We study the metric dimension and optimal split-resolving sets of the point-circle incidence graph of a M\"obius plane. We prove that the metric dimension of a M\"obius plane of order $q$ is around $2q$, and that an optimal split-resolving…
This paper considers joint beamformer design towards maximizing the mutual information in a coherent wireless sensor network with noisy observation and multiple antennae. Leveraging the weighted minimum mean square error and block…
Matrix factorizations of a hypersurface yield a description of the asymptotic structure of minimal free resolutions over the hypersurface. We introduce a new concept of matrix factorizations for complete intersections that allows us to…
We use the two-alpha cluster model to describe the properties of $^{8}$Be. The $E2$-transitions in a two-body continuum can be described as bremsstrahlung in an inelastic scattering process. We compute cross sections as functions of initial…
We consider the problem of finding the minimal number of points required to intersect all lines in an affine space over the finite field of order 3. We also consider the problem of finding the minimal number of points required to intersect…
We consider Jacobi matrices $J$ whose parameters have the power asymptotics $\rho_n=n^{\beta_1} \left( x_0 + \frac{x_1}{n} + {\rm O}(n^{-1-\epsilon})\right)$ and $q_n=n^{\beta_2} \left( y_0 + \frac{y_1}{n} + {\rm O}(n^{-1-\epsilon})\right)$…
Intersecting codes are linear codes where every two nonzero codewords have non-trivially intersecting support. In this article we expand on the theory of this family of codes, by showing that nondegenerate intersecting codes correspond to…
In this paper we study an one-dimensional two-species exclusion model with open boundaries. The model consists of two types of particles moving in opposite directions on an open lattice. Two adjacent particles swap their positions with rate…
In this article we construct a new family of semifields, containing and extending two well-known families, namely Albert's generalised twisted fields and Petit's cyclic semifields (also known as Johnson-Jha semifields). The construction…
Suppose $\mathcal{X}$ is an $n$-correct set of nodes in the plane, that is, it admits a unisolvent interpolation with bivariate polynomials of total degree less than or equal to $n.$ Then an algebraic curve $q$ of degree $k\le n$ can pass…
Designing the phase behavior of multicomponent mixtures is a rich area with many potential applications. One key question is how more than $M+1$ phases, as would normally be allowed by Gibbs' phase rule at generic temperature in a mixture…