Lie algebra cohomology and group structure of gauge theories

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincar\'e duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator $Q^{\dagger}$ for the Lie algebra cohomology induced by BRST generator $Q$. We also point out an interesting duality relation - Poincar\'e duality - with respect to gauge anomalies and Wess-Zumino-Witten topological terms. We consider the consistent embedding of the BRST adjoint generator $Q^{\dagger}$ into the relativistic phase space and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint N\"other charge $Q^{\dagger}$.Comment: 24 pages, RevTex, Revised version submitted to J. Math. Phy

Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models

Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing recent work we compare various periodic and quasiperiodic models, where the couplings and/or the lattice may be aperiodic, and where the Ising couplings may be either ferromagnetic, or antiferromagnetic, or of mixed sign. We present some of our results on the square-lattice fully-frustrated Ising model. Finally, we make a few remarks on our recent works on the pentagrid Ising model and on overlapping unit cells in three dimensions and how these works can be utilized once more detailed results for pair correlations in, e.g., the eight-vertex model or the chiral Potts model or even three-dimensional Yang-Baxter integrable models become available.Comment: LaTeX2e using iopart.cls, 10 pages, 5 figures (5 eps files), Dunk Island conference in honor of 60th birthday of A.J. Guttman

Multiple Timescale Energy Scheduling for Wireless Communication with Energy Harvesting Devices

The primary challenge in wireless communication with energy harvesting devices is to efficiently utilize the harvesting energy such that the data packet transmission could be supported. This challenge stems from not only QoS requirement imposed by the wireless communication application, but also the energy harvesting dynamics and the limited battery capacity. Traditional solar predictable energy harvesting models are perturbed by prediction errors, which could deteriorate the energy management algorithms based on this models. To cope with these issues, we first propose in this paper a non-homogenous Markov chain model based on experimental data, which can accurately describe the solar energy harvesting process in contrast to traditional predictable energy models. Due to different timescale between the energy harvesting process and the wireless data transmission process, we propose a general framework of multiple timescale Markov decision process (MMDP) model to formulate the joint energy scheduling and transmission control problem under different timescales. We then derive the optimal control policies via a joint dynamic programming and value iteration approach. Extensive simulations are carried out to study the performances of the proposed schemes

Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices

It has been shown in earlier works that for Q=0 and L a multiple of N, the ground state sector eigenspace of the superintegrable tau_2(t_q) model is highly degenerate and is generated by a quantum loop algebra L(sl_2). Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2 algebras. For Q not equal 0, we shall show here that the corresponding eigenspace of tau_2(t_q) is still highly degenerate, but splits into two spaces, each containing 2^{r-1} independent eigenvectors. The generators for the sl_2 subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q=0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q not equal 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages, uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added, improvements and minor corrections made, erratum to paper 2 included. Version 3: Small paragraph added in introductio

Identified Particle Production in d+Au and p+p collisions at RHIC

The BRAHMS experiment at RHIC has measured the transverse momentum spectra of charged pions, kaons and (anti-)protons over a wide range of rapidity in d+Au and p+p collisions at $\sqrt{s_{NN}}=200$GeV. The nuclear modification factor $R_{dAu}$ at forward rapidities shows a clear suppression for $\pi^{+}$. The measured net-proton yields in p+p collisions are compared to PYTHIA and HIJING/B and seem to be better described by the latter.Comment: 4 pages, 3 figures, presented at the 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions, "Quark Matter 2006", Shanghai, China, November 14-20, 2006. to appear in the proceedings of Quark Matter 2006 as a special issue of Journal of Physics G: Nuclear and Particle Physic

Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths

We compute the correlation functions of the three state superintegrable chiral Potts spin chain for chains of length 3,4,5. From these results we present conjectures for the form of the nearest neighbor correlation function.Comment: 10 pages; references update

Genetic algorithms with elitism-based immigrants for dynamic shortest path problem in mobile ad hoc networks

This article is posted here with permission from the IEEE - Copyright @ 2009 IEEEIn recent years, the static shortest path (SP) problem has been well addressed using intelligent optimization techniques, e.g., artificial neural networks (ANNs), genetic algorithms (GAs), particle swarm optimization (PSO), etc. However, with the advancement in wireless communications, more and more mobile wireless networks appear, e.g., mobile ad hoc network (MANET), wireless sensor network (WSN), etc. One of the most important characteristics in mobile wireless networks is the topology dynamics, that is, the network topology changes over time due to energy conservation or node mobility. Therefore, the SP problem turns out to be a dynamic optimization problem (DOP) in MANETs. In this paper, we propose to use elitism-based immigrants GA (EIGA) to solve the dynamic SP problem in MANETs. We consider MANETs as target systems because they represent new generation wireless networks. The experimental results show that the EIGA can quickly adapt to the environmental changes (i.e., the network topology change) and produce good solutions after each change.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1

Learning in abstract memory schemes for dynamic optimization

We investigate an abstraction based memory scheme for evolutionary algorithms in dynamic environments. In this scheme, the abstraction of good solutions (i.e., their approximate location in the search space) is stored in the memory instead of good solutions themselves and is employed to improve future problem solving. In particular, this paper shows how learning takes place in the abstract memory scheme and how the performance in problem solving changes over time for different kinds of dynamics in the fitness landscape. The experiments show that the abstract memory enables learning processes and efficiently improves the performance of evolutionary algorithms in dynamic environments