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The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. Begin with a complete graph on $n$ vertices and proceed to remove the edges of triangles one at a time, where each triangle removed is…
Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…
Linear stability analysis of an elastically anchored wing in a uniform flow is investigated both analytically and numerically. The analytical formulation explicitly takes into account the effect of the wake on the wing by means of…
Given an edge-weighted metric complete graph with $n$ vertices, the maximum weight metric triangle packing problem is to find a set of $n/3$ vertex-disjoint triangles with the total weight of all triangles in the packing maximized. Several…
The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity…
Billiard systems offer a simple setting to study regular and chaotic dynamics. Gravitational billiards are generalizations of these classical billiards which are amenable to both analytical and experimental investigations. Most previous…
Inverted landing is a challenging feat to perform in aerial robots, especially without external positioning. However, it is routinely performed by biological fliers such as bees, flies, and bats. Our previous observations of landing…
Classical countably additive real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the same probability value -- namely, zero -- to cases that are impossible as well as to cases that are possible.…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
We present an approach to analyzing the safety of asynchronous, independent, non-deterministic, turn-to-bearing horizontal maneuvers for two vehicles. Future turn rates, final bearings, and continuously varying ground speeds throughout the…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
Getting an unbiased result is a remarkably long standing problem of collective observation/measurement. It is pointed out that quantum coin tossing can generate unbiased result defeating dishonesty.
Online bipartite matching with edge arrivals remained a major open question for a long time until a recent negative result by [Gamlath et al. FOCS 2019], who showed that no online policy is better than the straightforward greedy algorithm,…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
We investigate the collapse of three inelastic particles in dimension $d \geq 2$. We obtain general results of convergence and asymptotics concerning the variables of the dynamical system describing a collapsing system of particles. We…
The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For non-spherical particles, the distance of closest approach depends on orientation,…
We present numerical simulations of the gravitational three-body problem, in which three particles lie at rest close to the vertices of an equilateral triangle. In the unperturbed problem, the three particles fall towards the center of mass…
We consider the maximum bipartite matching problem in stochastic settings, namely the query-commit and price-of-information models. In the query-commit model, an edge e independently exists with probability $p_e$. We can query whether an…
Tightness is a generalisation of the notion of convexity: a space is tight if and only if it is "as convex as possible", given its topological constraints. For a simplicial complex, deciding tightness has a straightforward exponential time…
We study a simple model of a bouncing ball that takes explicitely into account the elastic deformability of the body and the energy dissipation due to internal friction. We show that this model is not subject to the problem of inelastic…