Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time ...

1. Examples 1.1. Poisson Process 1.2. Markov Chain 1.3. Martingale 1.4. Brownian Motion 2. Definition of the Stochastic Process 3. Poisson Process 3.1. The Distribution 3.2. A Construction of the Poisson Process 3.3. Generalizations 4. Brownian Motion 4.1. Random Walk 4.2. Distributions 4.3. Path Properties 4.4. Local Time 4.5. Fourier Series Representation Glossary Bibliography Boigraphical Sk...

Exact evaluation of (TrS(p)) is here performed for real symmetric matrices S of arbitrary order n , up to some integer p , where the matrix entries are independent identically distributed random variables, with an arbitrary probability distribution. These expectations are polynomials in the moments of the matrix entries; they provide useful information on the spectral density of the ensemble in...

We consider graph optimization problems where the cost of a solution depends only on the shortest-path metric in the graph, such as Steiner Tree or Traveling Salesman. We study a scenario where such a problem needs to be solved repeatedly on random subgraphs of a given graph G. With the goal of speeding up the repeated queries and saving space, we describe the construction of a sparse subgraph ...

Recommendation has become an increasingly important research area because of the abundance of online documents and shopping opportunities. The readily available context information for these tasks posts challenges to recommendation systems to deal with heterogeneous and inter-connected problem spaces. In this study, we use a graph representation for publication databases with rich meta-data. Wi...

Mobile robot navigation is to find an optimal path to guide the movement of the robot, so path planning is guaranteed to find a feasible optimal path. However, the path planning problem must be solve two problems, i.e., the path must be kept away from obstacles or avoid the collision with obstacles and the length of path should be minimized. In this paper, a path planning algorithm based on ran...

This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed deterministic path-dependent cases, value function turns out be a random field on path space it characterized by Hamilton–Jacobi (SPHJ) equation. A notion viscosity solution proposed proved unique associated SPHJ

Consider the random hypercube H 2 (pn) obtained from the hypercube H n 2 by deleting any given edge with probabilty 1− pn, independently of all the other edges. A diameter path in H 2 is a longest geodesic path in H n 2 . Consider the following two ways of tampering with the random graph H 2 (pn): (i) choose a diameter path at random and adjoin all of its edges to H 2 (pn); (ii) choose a diamet...

Due to business and environmental issues, the efficient design of an integrated forward/reverse logistics network has recently attracted more attention from researchers. The significance of transportation cost and customer satisfaction spurs an interest in developing a flexible network design model with different delivery paths. This paper proposes a flexible mixed-integer programming model to ...

We show that the notoriously difficult problem of finding and reporting the smallest number of vertex-disjoint paths that cover the vertices of a graph can be solved timeand work-optimally for cographs. Our algorithm solves this problem in O(log n) time using n log n processors on the EREW-PRAM for an n-vertex cograph G represented by its cotree.