Adaptive Multigrid Algorithm for Lattice QCD

We present a new multigrid solver that is suitable for the Dirac operator in the presence of disordered gauge fields. The key behind the success of the algorithm is an adaptive projection onto the coarse grids that preserves the near null space. The resulting algorithm has weak dependence on the gauge coupling and exhibits very little critical slowing down in the chiral limit. Results are presented for the Wilson Dirac operator of the 2d U(1) Schwinger model.Comment: 4 pages, 2 figure

Adaptive multigrid algorithm for the lattice Wilson-Dirac operator

We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called gamma_5-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume

What is Method Variance and How Can We Cope With It? A Panel Discussion

A panel of experts describes the nature of, and remedies for, method variance. In an attempt to help the reader understand the nature of method variance, the authors describe their experiences with method variance both on the giving and the receiving ends of the editorial review process, as well as their interpretation of other reviewers’ comments. They then describe methods of data analysis and research design, which have been used for detecting and eliminating the effects of method variance. Most methods have some utility, but none prevent the researcher from making faulty inferences. The authors conclude with suggestions for resolving disputes about method variance

Extending the applicability of multigrid methods

Multigrid methods are ideal for solving the increasingly large-scale problems that arise in numerical simulations of physical phenomena because of their potential for computational costs and memory requirements that scale linearly with the degrees of freedom. Unfortunately, they have been historically limited by their applicability to elliptic-type problems and the need for special handling in their implementation. In this paper, we present an overview of several recent theoretical and algorithmic advances made by the TOPS multigrid partners and their collaborators in extending applicability of multigrid methods. Specific examples that are presented include quantum chromodynamics, radiation transport, and electromagnetics

Team sports performance analysed through the lens of social network theory: implications for research and practice

This paper discusses how social network analyses and graph theory can be implemented in team sports performance analyses to evaluate individual (micro) and collective (macro) performance data, and how to use this information for designing practice tasks. Moreover, we briefly outline possible limitations of social network studies and provide suggestions for future research. Instead of cataloguing discrete events or player actions, it has been argued that researchers need to consider the synergistic interpersonal processes emerging between teammates in competitive performance environments. Theoretical assumptions on team coordination prompted the emergence of innovative, theoretically-driven methods for assessing collective team sport behaviours. Here, we contribute to this theoretical and practical debate by conceptualising sports teams as complex social networks. From this perspective, players are viewed as network nodes, connected through relevant information variables (e.g., a ball passing action), sustaining complex patterns of interaction between teammates (e.g., a ball passing network). Specialized tools and metrics related to graph theory could be applied to evaluate structural and topological properties of interpersonal interactions of teammates, complementing more traditional analysis methods. This innovative methodology moves beyond use of common notation analysis methods, providing a richer understanding of the complexity of interpersonal interactions sustaining collective team sports performance. The proposed approach provides practical applications for coaches, performance analysts, practitioners and researchers by establishing social network analyses as a useful approach for capturing the emergent properties of interactions between players in sports teams