Covariant hamiltonian dynamics

We discuss the covariant formulation of the dynamics of particles with abelian and non-abelian gauge charges in external fields. Using this formulation we develop an algorithm for the construction of constants of motion, which makes use of a generalization of the concept of Killing vectors and tensors in differential geometry. We apply the formalism to the motion of classical charges in abelian and non-abelian monopole fieldsComment: 15 pages, no figure

Universal Behavior in Large-scale Aggregation of Independent Noisy Observations

Aggregation of noisy observations involves a difficult tradeoff between observation quality, which can be increased by increasing the number of observations, and aggregation quality which decreases if the number of observations is too large. We clarify this behavior for a protypical system in which arbitrarily large numbers of observations exceeding the system capacity can be aggregated using lossy data compression. We show the existence of a scaling relation between the collective error and the system capacity, and show that large scale lossy aggregation can outperform lossless aggregation above a critical level of observation noise. Further, we show that universal results for scaling and critical value of noise which are independent of system capacity can be obtained by considering asymptotic behavior when the system capacity increases toward infinity.Comment: 10 pages, 3 figure

Chemical equilibration and thermal dilepton production from the quark gluon plasma at finite baryon density

The chemical equilibration of a highly unsaturated quark-gluon plasma has been studied at finite baryon density. It is found that in the presence of small amount of baryon density, the chemical equilibration for gluon becomes slower and the temperature decreases less steeply as compared to the baryon free plasma. As a result, the space time integrated yield of dilepton is enhanced if the initial temperature of the plasma is held fixed. Even at a fixed initial energy density, the suppression of the dilepton yields at higher baryo-chemical potential is compensated, to a large extent, by the slow cooling of the plasma.Comment: Latex, 19 pages, 8 postscript figures. To appear in Phys. Rev.

Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding

A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks

Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to elucidate brain functions. This study investigates the tracking dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of neuronal recurrent interactions, CANNs can hold a continuous family of stationary states. They form a continuous manifold in which the neural system is neutrally stable. We systematically explore how this property facilitates the tracking performance of a CANN, which is believed to have clear correspondence with brain functions. By using the wave functions of the quantum harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is decomposed into different motion modes, corresponding to distortions in the amplitude, position, width or skewness of the network state. We then develop a perturbative approach that utilizes the dominating movement of the network's stationary states in the state space. This method allows us to approximate the network dynamics up to an arbitrary accuracy depending on the order of perturbation used. We quantify the distortions of a Gaussian bump during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable and the reaction time for the network to catch up with an abrupt change in the stimulus.Comment: 43 pages, 10 figure

Health effects of gasoline exposure. I. Exposure assessment for U.S. distribution workers.

Personal exposures were estimated for a large cohort of workers in the U.S. domestic system for distributing gasoline by trucks and marine vessels. This assessment included development of a rationale and methodology for extrapolating vapor exposures prior to the availability of measurement data, analysis of existing measurement data to estimate task and job exposures during 1975-1985, and extrapolation of truck and marine job exposures before 1975. A worker's vapor exposure was extrapolated from three sets of factors: the tasks in his or her job associated with vapor sources, the characteristics of vapor sources (equipment and other facilities) at the work site, and the composition of petroleum products producing vapors. Historical data were collected on the tasks in job definitions, on work-site facilities, and on product composition. These data were used in a model to estimate the overall time-weighted-average vapor exposure for jobs based on estimates of task exposures and their duration. Task exposures were highest during tank filling in trucks and marine vessels. Measured average annual, full-shift exposures during 1975-1985 ranged from 9 to 14 ppm of total hydrocarbon vapor for truck drivers and 2 to 35 ppm for marine workers on inland waterways. Extrapolated past average exposures in truck operations were highest for truck drivers before 1965 (range 140-220 ppm). Other jobs in truck operations resulted in much lower exposures. Because there were few changes in marine operations before 1979, exposures were assumed to be the same as those measured during 1975-1985. Well-defined exposure gradients were found across jobs within time periods, which were suitable for epidemiologic analyses

Minimizing Unsatisfaction in Colourful Neighbourhoods

Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods, given a predetermined number of colours. In the analytical framework of a tree approximation, carried out at both zero and finite temperatures, solutions obtained by population dynamics give rise to estimates of the threshold connectivity for the incomplete to complete transition, which are consistent with those of existing algorithms. The nature of the transition as well as the validity of the tree approximation are investigated.Comment: 28 pages, 12 figures, substantially revised with additional explanatio