Related papers: Pick Up Sticks
The construction of a universal static quantum computer actually provides another proof of the NP-hardness of spin-glass problems.
Theory of Inventive Problem Solving (TRIZ) is a powerful tool widely used in engineering community. It is based on identification of a physical contradiction in a problem, and based on the corresponding pair of contradicting parameters…
Spiking networks that perform probabilistic inference have been proposed both as models of cortical computation and as candidates for solving problems in machine learning. However, the evidence for spike-based computation being in any way…
We add another brick to the large building comprising proofs of Pick's theorem. Although our proof is not the most elementary, it is short and reveals a connection between Pick's theorem and the pointwise convergence of multiple Fourier…
A picture-hanging puzzle is the task of hanging a framed picture with a wire around a set of nails in such a way that it can remain hanging on certain specified sets of nails, but will fall if any more are removed. The classical brain…
We show that the higher-order matching problem is decidable using a game-theoretic argument.
We obtain exact solutions of a problem arising from queueing theory using properties of Kapteyn series.
There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy…
In this paper, we study the two dimensional Peskin problem with general elasticity law. Specifically, we prove global regularity for small perturbations, in suitable critical spaces, of the circle solution, possibly containing corners. For…
The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this work, we show that, remarkably,…
This talk describes how techniques developed by Computer Scientists have helped our understanding of certain problems in statistical physics which involve randomness and ``frustration''. Examples will be given from two problems that have…
Artificial spike-based computation, inspired by models of computations in the central nervous system, may present significant performance advantages over traditional methods for specific types of large scale problems. In this paper, we…
We solve the classical "Game of Pure Strategy" using linear programming. We notice an intricate even-odd behavior in the results of our computations, that seems to encourage odd or maximal bids.
We prove Union-Closed sets conjecture.
In this paper we study regularity estimates for the solution to an obstacle problem arising in stochastic impulse control theory. We prove using elementary methods the known sharp $C_{loc}^{1,1}$ estimate for the solution. The new proof is…
We study collections of point masses which move freely along the real line and stick together when they collide via perfectly inelastic collisions. We quantify the way particles stick together and explain how to associate a probability…
The motivation for this paper comes out of our experience with teaching natural deduction (ND) and with the way this formal system is implemented by the \textsc{Coq} proof assistant, namely by means of so-called tactics, which are…
Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…
The sticky particle system is a system of partial differential equations which assert the conservation of mass and momentum of a collection of particles that interact only via inelastic collisions. These equations arise in Zel'dovich's…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.