Several papers have appeared recently establishing the analyticity of the central path at the boundary point for both linear programming (LP) and linear complementarity problems (LCP). While the proofs for LP are long, proceeding from limiting properties of the corresponding derivatives, the proofs for LCP are very simple, consisting of an application of the implicit function theorem to a certa...

This is a brief and informal introduction to cluster algebras. It roughly follows the historical path of their discovery, made jointly with A. Zelevinsky. Total positivity serves as the main motivation. Mathematics Subject Classification (2000). Primary 13F60, Secondary 05E10, 05E15, 14M15, 15A23, 15B48, 20F55, 22E46.

Let G be a complete graph with n+ 1 vertices. In a recent paper of the authors, it is shown that the path trees of the graph play a special role in the structure of the truncated powers and partition functions that are associated with the graph. Motivated by the above, we take here a closer look at the geometry of the simplicial cones associated with the graph, and the role played by those simp...

The secondary back-iron plays important role in performance of single-sided linear induction motors (SLIMs). On one hand, it provides a return path for the primary flux; on the other hand, it is employed as a mechanical support for the secondary sheet. The conductivity of the iron used in the back-iron as well as its magnetic permeability influence the outputs of the machine, while the magnetic...

Ad hoc routing protocols that use broadcast for route discovery may be inefficient if the path between any source-destination pair is frequently broken. We propose and evaluate a simple mechanism that allows fast route repair in on demand ad hoc routing protocols. We apply our proposal to the Ad hoc On-demand Distance Vector (AODV) routing protocol. The proposed system is based on the Controlle...

A new and simple algorithm for finding shortest paths in a directed graph is proposed. In the single origin-single destination case, the algorithm maintains a single path starting at the origin, which is extended or contracted by a single node at each iteration. Simultaneously, at most one dual variable is adjusted at each iteration so as to either improve or maintain the value of a dual functi...

Cognitive radio is an emerging technology, which aims to upgrade the spectrum utilization by allowing the secondary users to operate at the spectrum bands vacated by the primary users. A cognitive radio system model was simulated and the performance of the energy detector was evaluated by using different wireless channel models. These models include Additive White Gaussian Noise (AWGN) model, R...

In this paper we investigate the cluster behavior of linearly interacting Brownian motions indexed by Z. We show that (on a logarithmic scale) the block average process converges in path space to Brownian motion. c © 2000 Elsevier Science B.V. All rights reserved. MSC: primary 60K35; secondary 60G15; 60F17

We study a semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. Key results are semiboundedness theorem of the Schrödinger operator, Laplace-type asymptotic formula and IMS localization formula. We also make a remark on semiclassical problem of a Schrödinger operator on a path space over a Riemannian manifold. MSC: Primary 81Q20, Secondary 60H07, 35J10.