The Slice Algorithm For Irreducible Decomposition of Monomial Ideals

Irreducible decomposition of monomial ideals has an increasing number of applications from biology to pure math. This paper presents the Slice Algorithm for computing irreducible decompositions, Alexander duals and socles of monomial ideals. The paper includes experiments showing good performance in practice.Comment: 25 pages, 8 figures. See http://www.broune.com/ for the data use

Tropical types and associated cellular resolutions

An arrangement of finitely many tropical hyperplanes in the tropical torus leads to a notion of `type' data for points, with the underlying unlabeled arrangement giving rise to `coarse type'. It is shown that the decomposition of the tropical torus induced by types gives rise to minimal cocellular resolutions of certain associated monomial ideals. Via the Cayley trick from geometric combinatorics this also yields cellular resolutions supported on mixed subdivisions of dilated simplices, extending previously known constructions. Moreover, the methods developed lead to an algebraic algorithm for computing the facial structure of arbitrary tropical complexes from point data.Comment: minor correction

Interacting errors in large-eddy simulation: a review of recent developments

The accuracy of large-eddy simulations is limited, among others, by the quality of the subgrid parameterisation and the numerical contamination of the smaller retained flow structures. We review the effects of discretisation and modelling errors from two different perspectives. We first show that spatial discretisation induces its own filter and compare the dynamic importance of this numerical filter to the basic large-eddy filter. The spatial discretisation modifies the large-eddy closure problem as is expressed by the difference between the discrete 'numerical stress tensor' and the continuous 'turbulent stress tensor'. This difference consists of a high-pass contribution associated with the specific numerical filter. Several central differencing methods are analysed and the importance of the subgrid resolution is established. Second, we review a database approach to assess the total simulation error and its numerical and modelling contributions. The interaction between the different sources of error is shown to lead to their partial cancellation. From this analysis one may identify an 'optimal refinement strategy' for a given subgrid model, discretisation method and flow conditions, leading to minimal total simulation error at a given computational cost. We provide full detail for homogeneous decaying turbulence in a 'Smagorinsky fluid'. The optimal refinement strategy is compared with the error reduction that arises from grid refinement of the dynamic eddy-viscosity model. The main trends of the optimal refinement strategy as a function of resolution and Reynolds number are found to be adequately followed by the dynamic model. This yields significant error reduction upon grid refinement although at coarse resolutions significant error levels remain. To address this deficiency, a new successive inverse polynomial interpolation procedure is proposed with which the optimal Smagorinsky constant may be efficiently approximated at a given resolution. The computational overhead of this optimisation procedure is shown to be well justified in view of the achieved reduction of the error level relative to the 'no-model' and dynamic model predictions

New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions

We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the truncation error on the boundary points, the spectral radius, or a combination of these. We examine in detail a set of operators that are up to tenth order accurate in the interior, and we surprisingly find that a combination of these optimizations can improve the operators' spectral radius and accuracy by orders of magnitude in certain cases. We also construct high-order dissipation operators that are compatible with these new finite difference operators and which are semi-definite with respect to the appropriate summation by parts scalar product. We test the stability and accuracy of these new difference and dissipation operators by evolving a three-dimensional scalar wave equation on a spherical domain consisting of seven blocks, each discretized with a structured grid, and connected through penalty boundary conditions.Comment: 16 pages, 9 figures. The files with the coefficients for the derivative and dissipation operators can be accessed by downloading the source code for the document. The files are located in the "coeffs" subdirector

Cloud-based desktop services for thin clients

Cloud computing and ubiquitous network availability have renewed people's interest in the thin client concept. By executing applications in virtual desktops on cloud servers, users can access any application from any location with any device. For this to be a successful alternative to traditional offline applications, however, researchers must overcome important challenges. The thin client protocol must display audiovisual output fluidly, and the server executing the virtual desktop should have sufficient resources and ideally be close to the user's current location to limit network delay. From a service provider viewpoint, cost reduction is also an important issue

Efficient Regularization of Squared Curvature

Curvature has received increased attention as an important alternative to length based regularization in computer vision. In contrast to length, it preserves elongated structures and fine details. Existing approaches are either inefficient, or have low angular resolution and yield results with strong block artifacts. We derive a new model for computing squared curvature based on integral geometry. The model counts responses of straight line triple cliques. The corresponding energy decomposes into submodular and supermodular pairwise potentials. We show that this energy can be efficiently minimized even for high angular resolutions using the trust region framework. Our results confirm that we obtain accurate and visually pleasing solutions without strong artifacts at reasonable run times.Comment: 8 pages, 12 figures, to appear at IEEE conference on Computer Vision and Pattern Recognition (CVPR), June 201