On the trace formula for Hecke operators on congruence subgroups, II

In a previous paper, we obtained a general trace formula for double coset operators acting on modular forms for congruence subgroups, expressed as a sum over conjugacy classes. Here we specialize it to the congruence subgroups $\Gamma_0(N)$ and $\Gamma_1(N)$, obtaining explicit formulas in terms of class numbers for the trace of a composition of Hecke and Atkin-Lehner operators. The formulas are among the simplest in the literature, and hold without any restriction on the index of the operators. We give two applications of the trace formula for $\Gamma_1(N)$: we determine explicit trace forms for $\Gamma_0(4)$ with Nebentypus, and we compute the limit of the trace of a fixed Hecke operator as the level $N$ tends to infinity

Vortices in SO(3)xZ(2) simulations

We study the configuration space of the Tomboulis $SO(3) \times Z(2)$ formulation with periodic boundary conditions. The dynamical variables are constrained by the required coincidence of Z(2) and SO(3) monopoles. We propose an update algorithm that satisfies the constraints and is straightforward to implement. We further prove that this it reaches all configurations. We show how the boundary conditions put constraints on the configuration space. We measure gauge invariant vortex counters for "thin", "thick" and "hybrid" vortex sheets. For comparison we also measure projection vortex counters defined in the maximal center gauge.Comment: LaTe

Efficient coalition formation and stable coalition structures in a supply chain environment

We study a real supply chain environment from which specific information and knowledge can be extrapolated for other similar environments. We focus our research on the analysis of the interactions between members forming different teams (and between the teams themselves), and on the leader’s management of the supply chain. We note that there are many elements that contribute to the profitability of the network, which is dependent on the actions of the actors involved. We analyze certain characteristics that the actors have, such as their behavior, adaptation and learning levels, effort and willingness. Based on these components, we examine the performance of our actors and of the teams that the actors form. We provide specific calculations that take into account most of the components determining the added value to the system. One of the advantages of our main formula is that it can be used to monitor the progress of the actors, as well as it can help in the identification of problematic aspects impeding in the creation of value for the system. Our formula is very flexible and a modeler is able to adapt it to similar environments, providing him with great insight in the structures that he investigates. We study certain theoretical games from which we uncover certain information and characteristics of similar environments and settings. Moreover, we provide a real life example in order to truly understand the mechanism of the network, and validate our theoretical assessments. Moreover, we provide certain recommendations for a leader that is responsible for the supervision of actors (which have specific responsibilities) and the administration of a supply chain environment.coalition, supply chain management, core, value of the game, Coalition Factor Estimation

Improving the Partial-Global Stochastic Metropolis Update for Dynamical Smeared Link Fermions

We discuss several methods that improve the partial-global stochastic Metropolis (PGSM) algorithm for smeared link staggered fermions. We present autocorrelation time measurements and argue that this update is feasible even on reasonably large lattices.Comment: 3 pages, 3 figures, Lattice2002(algor