Related papers: The Use of Minimal Spanning Trees in Particle Phys…
We give a complete proof that in any finite-dimensional normed linear space a finite set of points has a minimal spanning tree in which the maximum degree is bounded above by the strict Hadwiger number of the unit ball, i.e., the largest…
A rectilinear Steiner tree for a set $P$ of points in $\mathbb{R}^2$ is a tree that connects the points in $P$ using horizontal and vertical line segments. The goal of Minimal Rectilinear Steiner Tree is to find a rectilinear Steiner tree…
LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to…
A {\em tree cover} of a metric space $(X,d)$ is a collection of trees, so that every pair $x,y\in X$ has a low distortion path in one of the trees. If it has the stronger property that every point $x\in X$ has a single tree with low…
The concept of Space-Time Crystals (STC), i.e. translational symmetry breaking in time and space, was recently proposed and experimentally demonstrated for quantum systems. Here, we transfer this concept to magnons and experimentally…
We consider finite point subsets (distributions) in compact metric spaces. Non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in metric balls are given in the case of general…
We discuss the prospect of studying physics at short distances, such as Planck length or GUT scale, using supersymmetry as a probe. Supersymmetry breaking parameters contain information on all physics below the scale where they are induced.…
We investigate blob-trees, a new way of connecting a set of points, by a mixture of enclosing them by cycles (as in the convex hull) and connecting them by edges (as in a spanning tree). We show that a minimum-cost blob-tree for $n$ points…
We calculate the low-lying spectrum of new particles expected in a minimal model wherein supersymmetry breaking at < 100 TeV is indirectly transmitted to the Standard Model. We calculate the couplings of these particles relevant to their…
We lay out the phenomenological behavior of event-shape observables evaluated by solving optimal transport problems between collider events and reference geometries -- which we name 'manifold distances' -- to provide guidance regarding…
We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain…
Euclidean Steiner trees are relevant to model minimal networks in real-world applications ubiquitously. In this paper, we study the feasibility of a hierarchical approach embedded with bundling operations to compute multiple and mutually…
From theoretical point of view and not being in contradiction with current observational data, the cosmic strings should have fundamentally different origin and are characterized by wide range of energies. The paper is devoted to search for…
This paper introduces a novel stability measure for edit distances between merge trees of piecewise linear scalar fields. We apply the new measure to various metrics introduced recently in the field of scalar field comparison in scientific…
The concept of $n$-distance was recently introduced to generalize the classical definition of distance to functions of $n$ arguments. In this paper we investigate this concept through a number of examples based on certain geometrical…
The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.
In the first part of the paper, we present an (1+\mu)-approximation algorithm to the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings between the spanning tree and the lines. The…
Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been…
Targeted color-dots with varying shapes and sizes in images are first exhaustively identified, and then their multiscale 2D geometric patterns are extracted for testing spatial uniformness in a progressive fashion. Based on color theory in…
We review some collider phenomenology of unparticle physics, including real emissions and virtual exchanges of unparticle. Existing experimental constraints from collider physics as well as astrophysics are briefly discussed.