Explicit Determination of the Picard Group of Moduli Spaces of Semi-Stable G-Bundles on Curves

Let $\mathcal C$ be a smooth irreducible projective curve over the complex numbers and let $G$ be a simple simply-connected complex algebraic group. Let $\mathfrak M=\mathfrak M(G,\mathcal C)$ be the moduli space of semistable principal $G$-bundles on $\mathcal C$. By an earlier result of Kumar-Narasimhan, the Picard group of $\mathfrak M$ is isomorphic with the group of integers. However, in their work the generator of the Picard group was not determined explicitly. The aim of this paper to give the generator `explicitly.' The proof involves an interesting mix of geometry and topology.Comment: 22 pages; final versio

Testing Game Theory in the Field: Swedish LUPI Lottery Games

Game theory is usually difficult to test precisely in the field because predictions typically depend sensitively on features that are not controlled or observed. We conduct one such test using field data from the Swedish lowest unique positive integer (LUPI) game. In the LUPI game, players pick positive integers and whoever chose the lowest unique number wins a fixed prize. Theoretical equilibrium predictions are derived assuming Poisson- distributed uncertainty about the number of players, and tested using both field and laboratory data. The field and lab data show similar patterns. Despite various deviations from equilibrium, there is a surprising degree of convergence toward equilibrium. Some of the deviations from equilibrium can be rationalized by a cognitive hierarchy model

Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for 4 and 5 Dimensions

We develop a method of constructing percolation clusters that allows us to build very large clusters using very little computer memory by limiting the maximum number of sites for which we maintain state information to a number of the order of the number of sites in the largest chemical shell of the cluster being created. The memory required to grow a cluster of mass s is of the order of $s^\theta$ bytes where $\theta$ ranges from 0.4 for 2-dimensional lattices to 0.5 for 6- (or higher)-dimensional lattices. We use this method to estimate $d_{\scriptsize min}$, the exponent relating the minimum path $\ell$ to the Euclidean distance r, for 4D and 5D hypercubic lattices. Analyzing both site and bond percolation, we find $d_{\scriptsize min}=1.607\pm 0.005$ (4D) and $d_{\scriptsize min}=1.812\pm 0.006$ (5D). In order to determine $d_{\scriptsize min}$ to high precision, and without bias, it was necessary to first find precise values for the percolation threshold, $p_c$: $p_c=0.196889\pm 0.000003$ (4D) and $p_c=0.14081\pm 0.00001$ (5D) for site and $p_c=0.160130\pm 0.000003$ (4D) and $p_c=0.118174\pm 0.000004$ (5D) for bond percolation. We also calculate the Fisher exponent, $\tau$, determined in the course of calculating the values of $p_c$: $\tau=2.313\pm 0.003$ (4D) and $\tau=2.412\pm 0.004$ (5D)

GR@PPA 2.7 event generator for pppp/ppˉp\bar{p} collisions

The GR@PPA event generator has been updated to version 2.7. This distribution provides event generators for $V$ ($W$ or $Z$) + jets ($\leq$ 4 jets), $VV$ + jets ($\leq$ 2 jets) and QCD multi-jet ($\leq$ 4 jets) production processes at $pp$ and $p\bar{p}$ collisions, in addition to the four bottom quark productions implemented in our previous work (GR@PPA\_4b). Also included are the top-pair and top-pair + jet production processes, where the correlation between the decay products are fully reproduced at the tree level. Namely, processes up to seven-body productions can be simulated, based on ordinary Feynman diagram calculations at the tree level. In this version, the GR@PPA framework and the process dependent matrix-element routines are separately provided. This makes it easier to add further new processes, and allows users to make a choice of processes to implement. This version also has several new features to handle complicated multi-body production processes. A systematic way to combine many subprocesses to a single base-subprocess has been introduced, and a new method has been adopted to calculate the color factors of complicated QCD processes. They speed up the calculation significantly.Comment: 21 pages, no figur

Famas-NewCon: A generator program for stacking in the reference case

The FAMAS-Newcon project aims at developing new logistic control structures for a containerterminal capable of handling jumbo container ships within 24 hours. In one of the subprojectsstacking aspects is studied. This report describes a generator model in which on the basis of a global description arrival and departure moments of individual containers are generated for a medium term (15 weeks). The global description consists of a specification of the modal split in terms of containers handled by jumbo's, deepsea, shortsea, rail, barge and trucks, next a specification of the number and type of containers transported by an individual jumbo and deepsea and finally a specification of the dwell time. The output of the generator program is a file with the following container information: arrival and departure times,import/export modality and the import/export ship in case that is a deepsea or jumbo. This file serves as the input of a stacking program which is described in a sequel report. The advantage of this construction is that several stacking strategies can be compared with the same arrival and departures of containers.generator program;stacking;logistic control structures