We consider the open string vacuum amplitude determining the interaction between a stack of N D3-branes and a single probe brane. When using light cone gauge, it is clear that the sum of planar diagrams (relevant in the large-N limit) is described by the free propagation of a closed string. A naive calculation suggests that the Hamiltonian of the closed string is of the form H = H0 − gsNP̂ . The...

Several constructions on directed graphs originating in the study of flow equivalence symbolic dynamics (e.g., splittings and delays) are known to preserve Morita class Leavitt path algebras over any coefficient field F. We prove that many these results not only independent F, but largely linear algebra altogether. do this by formulating proving generalisations theorems which category F-vector ...

We are given a transportation line where displacements happen at a bigger speed than in the rest of the plane. A shortest time path is a path between two points which takes less than or equal time to any other. We consider the time to follow a shortest time path to be the time distance between the two points. In this paper, we give a simple algorithm for computing the Time Voronoi Diagram, that...

Robotic systems are usually built as independent agents that collaborate to accomplish a specific task. Analysis of robot path planning consists of route planning and path generation. We will show how to apply the Cell-DEVS formalism and the CD++ toolkit for these tasks. We present a Cell-DEVS model for route planning, which, based on the obstacles, finds different paths available and creates a...

We introduce two new related metrics, the geodesic width and the link width, for measuring the “distance” between two non-intersecting polylines in the plane. If the two polylines have n vertices in total, we present algorithms to compute the geodesic width of the two polylines in O(n2 log n) time using O(n2) space and the link width in O(n3 log n) time using O(n2) working space where n is the ...

Given k disjoint regions in the plane or space, the bridge problem asks for k − 1 line segments (optimal bridges) which connect these regions so as to minimize the length of the longest path between two points in the final connected region. We present O(n) and O(n2) time algorithms for finding an optimal bridge between two convex regions in the plane and space, respectively. An important proper...

The size of a Reduced Ordered Binary Decision Diagram (ROBDD) is directly influenced by the variables ordering technique used to build the ROBDD. Therefore various variables ordering techniques have been proposed to minimize the size of BDDs. Unfortunately there is no unique method that can be used to obtain the least number of nodes for all BDDs. In this paper we propose two new methods based ...

Most of the emphasis in path planning, a topic of much interest in several domains, has been on finding the optimal path or at most k optimal paths, but in domains such as adversarial planning, one of the agents might deliberately take less optimal paths to confuse the opponent, and by the same token an agent, for inferring opponent’s intent, has to consider all possible paths that the opponent...

In this paper, we consider the minimization of the longest path length (LPL) for binary decision diagrams (BDDs) and heterogeneous multi-valued decision diagrams (MDDs). Experimental results show that: (1) For many logic functions, node minimization of BDDs also minimizes the LPLs of BDDs. (2) When we use heterogeneous MDDs for representing logic functions and minimize the memory sizes of heter...