Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schrödinger's equation, which is half of the defining equations of Bohmian mechanics. I try ...

Given two integers n and k, n ≥ k > 1, a k-hypertournament T on n vertices is a pair (V, A), where V is a set of vertices, |V | = n and A is a set of k-tuples of vertices, called arcs, so that for any k-subset S of V , A contains exactly one of the k! k-tuples whose entries belong to S. A 2-hypertournament is merely an (ordinary) tournament. A path is a sequence v1a1v2a2v3...vt−1at−1vt of disti...

A Langevin equation with multiplicative noise is an equation schematically of the form dq/dt=-F(q)+e(q)xi, where e(q)xi is Gaussian white noise whose amplitude e(q) depends on q itself. I show how to convert such equations into path integrals. The definition of the path integral depends crucially on the convention used for discretizing time, and I specifically derive the correct path integral w...

A tournament T,, consists of a set of n vertices and a single directed edge joining every pair of distinct vertices. We denote the vertices of T’. by {l, . . . , n). A permutation aI, . . . , a, of the vertices is a generalized path. The type af the path is characterized by the sequence a,_1 = e3 l l l E~__~ where si = i-1 if e -+ ai+1 and 6 = -1 if a, -+ ai tl. We also say that mn_l is realize...

We show that the following variation of the single-source shortest path problem is NP-complete. Let a weighted, directed, acyclic graph G = (V, E, w) with source and sink vertices s and t be given. Let in addition a mapping f on E be given that associate information with the edges (e.g., a pointer), such that f (e) = f (e ′) means that edges e and e ′ carry the same information; for such edges ...

We consider the problem of a robot inside an unknown polygon that has to nd a path from a starting point s to a target point t. We assume that it is equipped with an on-board vision system through which it can get the visibility map of its surroundings. Furthermore, we assume that the robot is contained in a simple polygon that belongs to the class of generalized streets. We consider three prob...

| We show that HMM word recognition using Deller and Snider's \any path" procedure makes an assumption of independence that is not made by either the forward or Viterbi algorithms. We also point out that additional savings in execution time can be achieved by precomputation. I N 1], hidden Markov model (HMM) recognition is considered using a state-space-like formulation: x(t + 1) = Ax(t) + u(t)...