Dynamical Mass Generation in a Finite-Temperature Abelian Gauge Theory

We write down the gap equation for the fermion self-energy in a finite-temperature abelian gauge theory in three dimensions. The instantaneous approximation is relaxed, momentum-dependent fermion and photon self-energies are considered, and the corresponding Schwinger-Dyson equation is solved numerically. The relation between the zero-momentum and zero-temperature fermion self-energy and the critical temperature T_c, above which there is no dynamical mass generation, is then studied. We also investigate the effect which the number of fermion flavours N_f has on the results, and we give the phase diagram of the theory with respect to T and N_f.Comment: 20 LaTeX pages, 4 postscript figures in a single file, version to appear in Physical Review

Network Tomography: Identifiability and Fourier Domain Estimation

The statistical problem for network tomography is to infer the distribution of $\mathbf{X}$, with mutually independent components, from a measurement model $\mathbf{Y}=A\mathbf{X}$, where $A$ is a given binary matrix representing the routing topology of a network under consideration. The challenge is that the dimension of $\mathbf{X}$ is much larger than that of $\mathbf{Y}$ and thus the problem is often called ill-posed. This paper studies some statistical aspects of network tomography. We first address the identifiability issue and prove that the $\mathbf{X}$ distribution is identifiable up to a shift parameter under mild conditions. We then use a mixture model of characteristic functions to derive a fast algorithm for estimating the distribution of $\mathbf{X}$ based on the General method of Moments. Through extensive model simulation and real Internet trace driven simulation, the proposed approach is shown to be favorable comparing to previous methods using simple discretization for inferring link delays in a heterogeneous network.Comment: 21 page

Pragmatic meta analytic studies: learning the lessons from naturalistic evaluations of multiple cases

This paper explores the concept of pragmatic meta‐analytic studies in eLearning. Much educational technology literature focuses on developers and teachers describing and reflecting on their experiences. Few connections are made between these experiential ‘stories’. The data set is fragmented and offers few generalisable lessons. The field needs guidelines about what can be learnt from such single‐case reports. The pragmatic meta‐analytic studies described in this paper have two common aspects: (1) the cases are related in some way, and (2) the data are authentic, that is, the evaluations have followed a naturalistic approach. We suggest that examining a number of such cases is best done by a mixed‐methods approach with an emphasis on qualitative strategies. In the paper, we overview 63 eLearning cases. Three main meta‐analytic strategies were used: (1) meta‐analysis of the perception of usefulness across all cases, (2) meta‐analysis of recorded benefits and challenges across all cases, and (3) meta‐analysis of smaller groups of cases where the learning design and/or use of technology are similar. This study indicated that in Hong Kong the basic and non‐interactive eLearning strategies are often valued by students, while their perceptions of interactive strategies that are potentially more beneficial fluctuate. One possible explanation relates to the level of risk that teachers and students are willing to take in venturing into more innovative teaching and learning strategies

Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping

A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the Gaussian Mat\'{e}rn fields and a wide family of fields with oscillating covariance functions. Nonstationary covariance models are obtained by spatially varying the parameters in the SPDEs, and the model parameters are estimated using direct numerical optimization, which is more efficient than standard Markov Chain Monte Carlo procedures. The model class is used to estimate daily ozone maps using a large data set of spatially irregular global total column ozone data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS383 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org