Related papers: Partition Parameters for Girth Maximum (m, r) BTUs

We study the height of the maximal particle at time $t$ of a one dimensional branching Brownian motion with a space-dependent branching rate. The branching rate is set to zero in finitely many intervals (obstacles) of order $t$. We obtain…

We characterize all maximally entangling bipartite unitary operators, acting on systems $A,B$ of arbitrary finite dimensions $d_A\le d_B$, when use of ancillary systems by both parties is allowed. Several useful and interesting consequences…

For integers $m_1,...,m_d>0$ and a cuboid $M=[0,m_1]\times ... \times [0,m_d]\subset \mathbb{R}^d$, a brick of $M$ is a closed cuboid whose vertices have integer coordinates. A set $H$ of bricks in $M$ is a system of brick islands if for…

We provide a two-sided inequality for the alpha-optimal partition value of a measurable space according to n nonatomic finite measures. The result extends and often improves Legut (1988) since the bounds are obtained considering several…

We consider the problem of optimally insulating a given domain $\Omega$ of ${\mathbb{R}}^d$; this amounts to solve a nonlinear variational problem, where the optimal thickness of the insulator is obtained as the boundary trace of the…

Geometrical objects with integral side lengths have fascinated mathematicians through the ages. We call a set $P=\{p_1,...,p_n\}\subset\mathbb{Z}^2$ a maximal integral point set over $\mathbb{Z}^2$ if all pairwise distances are integral and…

In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…

We propose a sufficient and necessary separability criterion for pure states in multipartite and high dimensional systems. Its main advantage is operational and computable. The obvious expressions of this criterion can be given out by the…

Muon colliders are expected to naturally have a small spread in beam energy making them an ideal place to study the excitation curve. We present the parameter determinations that are possible from measuring the total cross section near…

Let $S$ be a set of $n$ points in $\mathbb{R}^d$. A Steiner convex partition is a tiling of ${\rm conv}(S)$ with empty convex bodies. For every integer $d$, we show that $S$ admits a Steiner convex partition with at most $\lceil…

The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…

Consider a system consisting of n d-dimensional quantum particles (qudits), and suppose that we want to optimize the entanglement between each pair. One can ask the following basic question regarding the sharing of entanglement: what is the…

A graph has a perfect partition if all its perfect matchings can be partitioned so that each part is a 1-factorization of the graph. Let $L_{rm, r}=K_{rm,rm}-mK_{r,r}$. We first give a formula to count the number of perfect matchings of…

This paper is concerned with determining the number of generators in each degree for minimal sets of homogeneous generators for saturated ideals defining fat point subschemes $Z=m_1p_1+ ... +m_rp_r$ for general sets of points $p_i$ of…

A balanced partition is a clustering of a graph into a given number of equal-sized parts. For instance, the Bisection problem asks to remove at most k edges in order to partition the vertices into two equal-sized parts. We prove that…

This paper presents an information-theoretic approach to address the phasor measurement unit (PMU) placement problem in electric power systems. Different from the conventional 'topological observability' based approaches, this paper…

A new method for calculation of goodness of multidimensional fits in particle physics experiments is proposed. This method finds the smallest and largest clusters of nearest neighbors for observed data points. The cluster size is used to…

We consider min-max $r$-gather clustering problem and min-max $r$-gathering problem. In the min-max $r$-gather clustering problem, we are given a set of users and divide them into clusters with size at least $r$; the goal is to minimize the…

We deal with the boundedness of the multilinear fractional integral operator $I_{\gamma,m}$ from a product of weighted Lebesgue spaces into adequate weighted Lipschitz spaces. Our results generalize some previous estimates not only for the…

An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement…