Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces

In this paper we associate a new geometric invariant to the space of fiat connections on a G (= SU(2))-bundle on a compact Riemann surface M and relate it tcr the symplectic structure on the space Hom(pi(1)(M), G)/G consisting of representations of the fundamental group pi(1)(M) Of M into G module the conjugate action of G on representations.

Multi-Agent Rendezvous Algorithm with Rectilinear Decision Domain

The aim of this paper is to develop a computationally efficient decentralized rendezvous algorithm for a group of autonomous agents. The algorithm generalizes the notion of sensor domain and decision domain of agents to enable implementation of simple computational algorithms. Specifically, the algorithm proposed in this paper uses a rectilinear decision domain (RDD) as against the circular decision domain assumed in earlier work. Because of this, the computational complexity of the algorithm reduces considerably and, when compared to the standard Ando's algorithm available in the literature, the RDD algorithm shows very significant improvement in convergence time performance. Analytical results to prove convergence and supporting simulation results are presented in the paper.

A model for heat transfer in a honey bee swarm

A swarm is a temporary structure formed when several thousand honey bees leave their hive and settle on some object such as the branch of a tree. They remain in this position until a suitable site for a new home is located by the scout bees. A continuum model based on heat conduction and heat generation is used to predict temperature profiles in swarms. Since internal convection is neglected, the model is applicable only at low values of the ambient temperature T-a. Guided by the experimental observations of Heinrich (1981a-c, J. Exp. Biol. 91, 25-55; Science 212, 565-566; Sci. Am. 244, 147-160), the analysis is carried out mainly for non-spherical swarms. The effective thermal conductivity is estimated using the data of Heinrich (1981a, J. Exp. Biol. 91, 25-55) for dead bees. For T-a = 5 and 9 degrees C, results based on a modified version of the heat generation function due to Southwick (1991, The Behaviour and Physiology of Bees, PP 28-47. C.A.B. International, London) are in reasonable agreement with measurements. Results obtained with the heat generation function of Myerscough (1993, J. Theor. Biol. 162, 381-393) are qualitatively similar to those obtained with Southwick's function, but the error is more in the former case. The results suggest that the bees near the periphery generate more heat than those near the core, in accord with the conjecture of Heinrich (1981c, Sci. Am. 244, 147-160). On the other hand, for T-a = 5 degrees C, the heat generation function of Omholt and Lonvik (1986, J. Theor. Biol. 120, 447-456) leads to a trivial steady state where the entire swarm is at the ambient temperature. Therefore an acceptable heat generation function must result in a steady state which is both non-trivial and stable with respect to small perturbations. Omholt and Lonvik's function satisfies the first requirement, but not the second. For T-a = 15 degrees C, there is a considerable difference between predicted and measured values, probably due to the neglect of internal convection in the model.

Cascades of Selective Pulses on Connected Single-Quantum Transitions Leading to the Selective Excitation of Multiple-Quantum Coherences

A symmetric cascade of selective pulses applied on connected transitions leads to the excitation of a selected multiple-quantum coherence by a well-defined angle. This cascade selectively operates on the subspace of the multiple-quantum coherence and acts as a generator of rotation selectively on the multiple-quantum subspace. Single-transition operator algebra has been used to explain these experiments. Experiments have been performed on two- and three-spin systems. It is shown that such experiments can be utilized to measure the relaxation times of selected multiple-quantum coherences or of a specifically prepared initial longitudinal state of the spin system.