Instantons in Four-Fermi Term Broken SUSY with General Potential

It is shown how to solve the Euclidean equations of motion of a point particle in a general potential and in the presence of a four-Fermi term. The classical action in this theory depends explicitly on a set of four fermionic collective coordinates. The corrections to the classical action due to the presence of fermions are of topological nature in the sense that they depend only on the values of the fields at the boundary points $\tau \to \pm \infty$. As an application, the Sine-Gordon model with a four-Fermi term is solved explicitly and the corrections to the classical action are computed.Comment: 8 page

Boundary States, Extended Symmetry Algebra and Module Structure for certain Rational Torus Models

The massless bosonic field compactified on the circle of rational $R^2$ is reexamined in the presense of boundaries. A particular class of models corresponding to $R^2=\frac{1}{2k}$ is distinguished by demanding the existence of a consistent set of Newmann boundary states. The boundary states are constructed explicitly for these models and the fusion rules are derived from them. These are the ones prescribed by the Verlinde formula from the S-matrix of the theory. In addition, the extended symmetry algebra of these theories is constructed which is responsible for the rationality of these theories. Finally, the chiral space of these models is shown to split into a direct sum of irreducible modules of the extended symmetry algebra.Comment: 12 page

A Verification Framework for Fictitious Play Based Learning Algorithms

Distributed optimisation techniques have gained increasing attention due to fast development of autonomous robots. Many algorithms have been proposed to make optimisation more efficient. In this paper we propose a framework, which is based on probabilistic verification techniques, in order to compare the performance of various game-theoretic algorithms, in particular, fictitious play and its variants, after a finite number of iterations. To demonstrate the effectiveness of the framework, we apply the framework to a game which is inspired by wireless communication network problems, on five variations of fictitious play algorithms

Distributed selection of flight formation in UAV missions

Recent advances in sensor, processor and airframe technologies allow coordination of large groups of autonomous unmanned aerial vehicles (UAV) today. Reconfiguration of the formation is sometimes necessary in order to accomplish a mission’s objectives. A centralised solution to optimal reconfiguration may often be either impossible or intractable due to sensor, communication, physical, computational restrictions. Thus a distributed approach may be more appropriate to accommodate real-world scenarios. In this article we propose a novel distributed control method, which is divided into two modules: a leaderfollower module, which allows UAVs to keep a pre-specified formation, and a decision making module that allows UAVs to choose among various available formations in an optimum sense. UAVs choose the best formation to accomplish each part of the mission and retain this formation till the next way-point. The simulation presented uses a 5-leg mission and Parrot AR-drones are used as test-beds to demonstrate the usefulness of the proposed distributed controller