7,430 research outputs found

    Codimension-two bifurcations in animal aggregation models with symmetry

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    Report on the Second Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE2)

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    This technical report records and discusses the Second Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE2). The report includes a description of the alternative, experimental submission and review process, two workshop keynote presentations, a series of lightning talks, a discussion on sustainability, and five discussions from the topic areas of exploring sustainability; software development experiences; credit & incentives; reproducibility & reuse & sharing; and code testing & code review. For each topic, the report includes a list of tangible actions that were proposed and that would lead to potential change. The workshop recognized that reliance on scientific software is pervasive in all areas of world-leading research today. The workshop participants then proceeded to explore different perspectives on the concept of sustainability. Key enablers and barriers of sustainable scientific software were identified from their experiences. In addition, recommendations with new requirements such as software credit files and software prize frameworks were outlined for improving practices in sustainable software engineering. There was also broad consensus that formal training in software development or engineering was rare among the practitioners. Significant strides need to be made in building a sense of community via training in software and technical practices, on increasing their size and scope, and on better integrating them directly into graduate education programs. Finally, journals can define and publish policies to improve reproducibility, whereas reviewers can insist that authors provide sufficient information and access to data and software to allow them reproduce the results in the paper. Hence a list of criteria is compiled for journals to provide to reviewers so as to make it easier to review software submitted for publication as a “Software Paper.

    Lattice symmetry breaking perturbations for spiral waves

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    Spiral waves in two-dimensional excitable media have been observed experimentally and studied extensively. It is now well-known that the symmetry properties of the medium of propagation drives many of the dynamics and bifurcations which are experimentally observed for these waves. Also, symmetry-breaking induced by boundaries, inhomogeneities and anisotropy have all been shown to lead to different dynamical regimes as to that which is predicted for mathematical models which assume infinite homogeneous and isotropic planar geometry. Recent mathematical analyses incorporating the concept of forced symmetry-breaking from the Euclidean group of all planar translations and rotations have given model-independent descriptions of the effects of media imperfections on spiral wave dynamics. In this paper, we continue this program by considering rotating waves in dynamical systems which are small perturbations of a Euclidean-equivariant dynamical system, but for which the perturbation preserves only the symmetry of a regular square lattice

    Computing CMB Anisotropy in Compact Hyperbolic Spaces

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    The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. For compact topologies, the two main effects on the CMB are: (1) the breaking of statistical isotropy in characteristic patterns determined by the photon geodesic structure of the manifold and (2) an infrared cutoff in the power spectrum of perturbations imposed by the finite spatial extent. We present a completely general scheme using the regularized method of images for calculating CMB anisotropy in models with nontrivial topology, and apply it to the computationally challenging compact hyperbolic topologies. This new technique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. We estimate a Bayesian probability for a selection of models by confronting the theoretical pixel-pixel temperature correlation function with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations. If the universe is of comparable size, the likelihood function is very dependent upon orientation of the manifold wrt the sky. While most orientations may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over the conventional infinite models.Comment: 15 pages, LaTeX (IOP style included), 3 color figures (GIF) in separate files. Minor revision to match the version accepted in Class. Quantum Grav.: Proc. of Topology and Cosmology, Cleveland, 1997. The paper can be also downloaded from http://www.cita.utoronto.ca/~pogosyan/cwru_proc.ps.g

    Self-scaled barriers for irreducible symmetric cones

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    Self-scaled barrier functions are fundamental objects in the theory of interior-point methods for linear optimization over symmetric cones, of which linear and semidefinite programming are special cases. We are classifying all self-scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with a decomposition theorem for self-scaled barriers this concludes the algebraic classification theory of these functions. After introducing the reader to the concepts relevant to the problem and tracing the history of the subject, we start by deriving our result from first principles in the important special case of semidefinite programming. We then generalise these arguments to irreducible symmetric cones by invoking results from the theory of Euclidean Jordan algebras.Comment: 12 page
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