Related papers: The combinatorics of the colliding bullets problem
A problem of optimally allocating partially effective ammunition $x$ to be used on randomly arriving enemies in order to maximize an aircraft's probability of surviving for time~$t$, known as the Bomber Problem, was first posed by…
We analyze combinatorial optimization problems over a pair of random point sets of equal cardinal. Typical examples include the matching of minimal length, the traveling salesperson tour constrained to alternate between points of each set,…
The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear…
Keller proposed a combinatorial conjecture on construction of an n-by-infinite matrix, which comes from showing the existence of many orbits of different sizes in certain linear group actions. He proved it for the case n=4, and we show that…
In this survey, we discuss volumetric and combinatorial results concerning (mostly finite) intersections or unions of balls (mostly of equal radii) in the $d$-dimensional real vector space, mostly equipped with the Euclidean norm. Our first…
We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strategy for this game, we give another proof of the existence of…
The algebraic intersection type unification problem is an important component in proof search related to several natural decision problems in intersection type systems. It is unknown and remains open whether the algebraic intersection type…
This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of…
The Generalized Discretizable Molecular Distance Geometry Problem is a distance geometry problems that can be solved by a combinatorial algorithm called ``Branch-and-Prune''. It was observed empirically that the number of solutions of YES…
In the last twenty years, there have been significant advances in the study of the blow-up phenomenon for the critical generalized Korteweg-de Vries equation, including the determination of sufficient conditions for blowup, the stability of…
Inspired by the Japanese game Pachinko, we study simple (perfectly "inelastic" collisions) dynamics of a unit ball falling amidst point obstacles (pins) in the plane. A classic example is that a checkerboard grid of pins produces the…
An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This…
In this paper the problem of maximizing the distance to a given fixed point over an intersection of balls is considered. It is known that this problem is NP complete in the general case, since any subset sum problem can be solved upon…
Consider two balls with radius $r>0$ whose centers are at a distance $2$, positioned symmetrically with respect to the origin in ${\mathbb{R}}^d$. Suppose that the initial velocities are independent standard normal vectors. When $r\to0$,…
Solution of the scattering problem turns to be very difficult task both from the formal as well as from the computational point of view. If the last two decades have witnessed decisive progress in ab initio bound state calculations,…
We consider bandit problems involving a large (possibly infinite) collection of arms, in which the expected reward of each arm is a linear function of an $r$-dimensional random vector $\mathbf{Z} \in \mathbb{R}^r$, where $r \geq 2$. The…
We establish a connection between capillary floating in neutral equilibrium and the billiard ball problem. This allows us to reduce the question of floating in neutral equilibrium at any orientation with a prescribed contact angle for…
Consider the following process whereby $n$ balls are distributed into $k$ bins. Repeatedly, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. Will Ma…
We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the first n balls is asymptotically normal if its…
We consider a large class of bullet models that contains, in particular, the colliding bullet model with creations and a new loop model. For this large class of bullet models, we give sufficient conditions on their parameter to be…