Related papers: Triangle Inscribed-Triangle Picking
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We…
Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
We give a linear-time algorithm to decide 3-colorability (and find a 3-coloring, if it exists) of quadrangulations of a fixed surface. The algorithm also allows to prescribe the coloring for a bounded number of vertices.
We give a linear-time algorithm to decide 3-colorability of a triangle-free graph embedded in a fixed surface, and a quadratic-time algorithm to output a 3-coloring in the affirmative case. The algorithms also allow to prescribe the…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
Stochastic finite automata arise naturally in many language and speech processing tasks. They include stochastic acceptors, which represent certain probability distributions over random strings. We consider the problem of efficient…
We study the problem of finding maximum-area triangles that can be inscribed in a polygon in the plane. We consider eight versions of the problem: we use either convex polygons or simple polygons as the container; we require the triangles…
A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not cross the circles. The tripartite-circle crossing number of…
This paper deals with the typical cell in a Poisson line tessellation in the plane whose directional distribution is concentrated on three equally spread values with possibly different weights. Such a random polygon can only be a triangle,…
Starting from any given rational-sided, right triangle, for example the $(3,4,5)$-triangle with area $6$, we use Euclidean geometry to show that there are infinitely many other rational-sided, right triangles of the same area. We show…
We perform Monte Carlo simulations to determine the average excluded area $<A_{ex}>$ of randomly oriented squares, randomly oriented widthless sticks and aligned squares in two dimensions. We find significant differences between our results…
A non trivial problem that arises in several applications is the estimation of the mean of a truncated normal distribution. In this paper, an iterative deterministic scheme for approximating this mean is proposed. It has been inspired from…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
This paper explores and proves the one-seventh area triangle using a purely algebraic approach as opposed to a geometric one. A triangle set purely in the complex plane is used so that we can utilise features of the complex number system to…
We establish a relationship between the two important central lines of the triangle, the Euler line and the Brocard axis, in a configuration with an arbitrary rectangle and a random point. The classical Cartesian coordinate system method…
We measure the geometry of a crumpled sheet of paper with laser-aided topography and discuss its statistical properties. The curvature of an elasto-plastic fold scales linearly with applied force. The curvature distribution follows an…