Given a set P n of n points on the plane labeled with the integers f1; : : : ; ng, an increasing path of P n is a sequence of points i 1 < : : : < i k such that the polygonal path ob-1 is non-self intersecting. We show that any point set on the plane admits an increasing path of length at least p 2n. We also study the problem of nding the longest common increasing path of two convex point sets ...

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path from s to t in a polyhedral terrain. We give some properties of such paths. In the case where the face sequence is specified, we show that the shortest descending path is unique, and giv...

We describe an Eulerian path approach to the DNA fragment assembly that was originated by Idury and Waterman 1995, and then advanced by Pevzner et al. 2001b. This combinatorial approach bypasses the traditional “overlap-layout-consensus” approach and successfully resolved some of the troublesome repeats in practical assembly projects. The assembly results by the Eulerian path approach are accur...

In this paper, we first establish a version of the central limit theorem for double sequence {pi(n)} that satisfies linear recurrence relation. Then find and prove under some commonly observed conditions, embedding distributions an H-linear family graphs with spiders is asymptotic to normal distribution. Applications are given well-known path-like ring-like sequences graphs. We also Euler-genus...

Abstract. In this paper we review some applications of the path integral methodology of quantum mechanics to financial modeling and options pricing. A path integral is defined as a limit of the sequence of finite-dimensional integrals, in a much the same way as the Riemannian integral is defined as a limit of the sequence of finite sums. The risk-neutral valuation formula for path-dependent opt...

In this paper, we present an efficient visibility-based algorithm for determining a locally exact shortest path (LESP) from a source point to a destination point on a (triangulated) polyhedral surface. Our algorithm, of a finitely-iterative scheme, evolves an initial approximately shortest path into a LESP. During each iteration, we first compute the exact shortest path restricted on the curren...

Abstract. In this paper we review some applications of the path integral methodology of quantum mechanics to financial modeling and options pricing. A path integral is defined as a limit of the sequence of finite-dimensional integrals, in a much the same way as the Riemannian integral is defined as a limit of the sequence of finite sums. The risk-neutral valuation formula for path-dependent opt...

The problem of determining a collision free path within a region is an important area of research in robotics. One significant aspect of this problem is coverage path planning, which is a process to find a path that passes through each reachable position in the desired area. This task is fundamental to many robotic applications such as cleaning, painting, underwater operations, mine sweeping, l...

Let η = (η1, η2, . . . , ηt) and ν = (ν1, ν2, . . . , νt) be two sequences of nonnegative integers. (Append zeros if necessary to the end of the shorter sequence so that they are the same length.) We say that ν is majorized by η if ∑j l=1 νl ≤ ∑j l=1 ηl for all 1 ≤ j ≤ t and tl=1 νl = ∑t l=1 ηl. We write ν 1 η. Let Γ = (V,E) be a graph where V is a finite vertex set and E ⊆ V ×V is an edge set....