A new cooperative search algorithm that introduces a GA-like selection mechanism is developed. In this algorithm, a state-space search problem is solved concurrently by multiple agents, each of which executes the Real-Time-A* algorithm. These agents compete for existence, i.e., each agent periodically reproduces o spring stochastically based on its tness de ned by the heuristic estimation value...

Multimodal multiobjective optimization problems (MMOPs) widely exist in real-world applications, which have multiple equivalent Pareto-optimal solutions that are similar the objective space but totally different decision space. While some evolutionary algorithms (EAs) been developed to find recent years, they ineffective handle large-scale MMOPs having a large number of variables. This article ...

1. Non-commutative probability spaces In general, a non-commutative probability space is a pair (A, τ), where A is a unital algebra (over the field of complex numbers C) and τ a linear functional with τ(I) = 1, where I is the identity of A. Elements of A are called random variables. Since positivity is a key concept in (classical) probability theory, this can be captured by assuming that A is a...

We provide a simple proof that the kth gap, A *, for the Mathieu operator-dz/dxs + 2~ cos (2x) is A& = 8(~/4)* [(k-l)!]-* (1 + o(k-s)), a result obtained (up to the value of an integral) by Harrell. The key observation is that what is involved is tunneling in momentum space.

The paper describes an application of the A* algorithm for flight path planning for airplanes with defined motion dynamics operating in a continuous three-dimensional space constrained by existing physical obstacles. The presented A* algorithm modification provides significant acceleration (reduction of the state space) of the path planning process. The described algorithm is able to find a pat...

Efficient methods for storing and querying language models are critical for scaling to large corpora and high Markov orders. In this paper we propose methods for modeling extremely large corpora without imposing a Markov condition. At its core, our approach uses a succinct index – a compressed suffix tree – which provides near optimal compression while supporting efficient search. We present al...

If A and B are compact operators on a Hilbert space, with singular values satisfying s j (A) = s j (B) = s j ((A + B)/2) Let A be a compact linear operator from a Hilbert space H into a Hilbert space K. The singular values s 1 (A) ≥ s 2 (A) ≥. .. are the eigenvalues of |A| := (A * A) 1/2. We refer to [3] for other equivalent definitions and basic properties. In this note we offer two proofs, ge...