Using a new notion of path-derivative, we study the well-posedness backward stochastic differential equation driven by continuous martingale M when f(s,?,y,z) is locally Lipschitz in (y,z): Yt=?(M[0,T])+?tTf(s,M[0,s],Ys?,Zsms)dtr[M,M]s??tTZsdMs?NT+Nt.Here, M[0,t] path from 0 to t and m defined [M,M]t=?0tmsms?dtr[M,M]s. When BSDE one-dimensional, show existence uniqueness solution. On contrary, ...

(1) Suppose that w belongs to a C d , d r. The total number of leaves in C 0 ; : : :; C d?1 is P d?1 j=0 2 j = 2 d ? 1. Therefore, 2 d ? 1 < i. Since w belongs to C d , i P d j=0 2 j = 2 d+1 ? 1. Thus, 2 d i < 2 d+1 , implying that d = blog ic. Consider the path from the root of T r to w. The path has length 2d + 1: d edges on the path from the root of T r to v d , one edge connecting v d and t...

We present a significantly faster algorithm for the restricted shortest path problem, in which we are given two vertices s, t, and the goal is to find the shortest path that is subject to a side constraint. More formally, rather than just having a single weight, each edge has two weights: a cost-weight, and a delay-weight. We are given a threshold T which corresponds to the maximum delay we can...

Let T be a tree. Given x, y ∈ V (T ), x →T y denotes the unique path from x to y in T . We denote by distT (x, y) the number of edges on the path x →T y; note that if x = y then distT (x, y) = 0. Definition S1 (Gene-Losses). Given a DGS-reconciliation α = 〈MD,MG , Σ, ΣG ,∆D,∆G , Θ,Ξ, τ〉 for D,G and S, let g ∈ I(G) and {g′, g′′} = Ch(d). The number of gene-losses GeneLossα(g) at node g, is defin...

Given an undirected graph G = (V,E), two distinguished vertices s and t of G, and a diameter bound D, a D-s, t-path is a path between s and t composed of at most D edges. An edge e is called D-irrelevant if does not belong to any D-s, t-path of G. In this paper we study the problem of efficiently detecting D-irrelevant edges and also study the computational complexity of diameter-related proble...

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....

If x is a vertex of a tree T of radius r, if k and 1 are integers, if 0 < k < r, 0 < I < r, and if P is an L-path with one end at x, then define /3(x; k,P) to be the number of vertices of T that are reachable from x via the l-path P and that are outside of the k-ball about x. That is, fl(x; k, P) = 1 (y E V( T ): y is reachable from x via P, d(x, y) > k} I. Define the k-ball l-path branch weigh...

Major issue arising in mobile ad hoc networks (MANETs) is the selection of the optimal path between any two nodes. A method that has been advocated to improve routing efficiency is to select the most stable path so as to reduce the latency and the overhead due to re-routing instability problem. We study both the availability and the duration probability of a routing path that is subject to link...

Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum mechanics. 1. It is well known that dynamical evolution of any one-dimensional quantum-mechanical system, described by a wave function Ψ(x, t), is given by Ψ(x ′′ , t...

Dynamic time warping is not suitable for on-line applications because it requires complete knowledge of both series before the alignment of the first elements can be computed. We present a novel online time warping algorithm which has linear time and space costs, and performs incremental alignment of two series as one is received in real time. This algorithm is applied to the alignment of audio...