On the properties of discrete spatial filters for CFD

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The spatial filtering of variables in the context of Computational Fluid Dynamics (CFD) is a common practice. Most of the discrete filters used in CFD simulations are locally accurate models of continuous operators. However, when filters are adaptative, i.e. the filter width is not constant, or meshes are irregular, discrete filters sometimes break relevant global properties of the continuous models they are based on. For example, the principle of maxima and minima reduction or conservation are eventually infringed. In this paper, we analyze the properties of analytic continuous convolution filters and extract those we consider to define filtering. Then, we impose the accomplishment of these properties on explicit discrete filters by means of constraints. Three filters satisfying the derived conditions are deduced and compared to common differential discrete CFD filters on synthetic fields. Tests on the developed discrete filters show the fulfillment of the imposed properties. In particular, the problem of maxima and minima generation is resolved for physically relevant cases. The tests are conducted on the basis of the eigenvectors of graph Laplacian matrices of meshes. Thus, insight into the relations between filtering and oscillation growth on general meshes is provided. Further tests on singularity fields and on isentropic vortices have also been conducted to evaluate the performance of filters on basic CFD fields. Results confirm that imposing the proposed conditions makes discrete filters properties consistent with those of the continuous ones.Peer ReviewedPostprint (author's final draft

Structure in the 3D Galaxy Distribution: I. Methods and Example Results

Three methods for detecting and characterizing structure in point data, such as that generated by redshift surveys, are described: classification using self-organizing maps, segmentation using Bayesian blocks, and density estimation using adaptive kernels. The first two methods are new, and allow detection and characterization of structures of arbitrary shape and at a wide range of spatial scales. These methods should elucidate not only clusters, but also the more distributed, wide-ranging filaments and sheets, and further allow the possibility of detecting and characterizing an even broader class of shapes. The methods are demonstrated and compared in application to three data sets: a carefully selected volume-limited sample from the Sloan Digital Sky Survey redshift data, a similarly selected sample from the Millennium Simulation, and a set of points independently drawn from a uniform probability distribution -- a so-called Poisson distribution. We demonstrate a few of the many ways in which these methods elucidate large scale structure in the distribution of galaxies in the nearby Universe.Comment: Re-posted after referee corrections along with partially re-written introduction. 80 pages, 31 figures, ApJ in Press. For full sized figures please download from: http://astrophysics.arc.nasa.gov/~mway/lss1.pd

KR3^3: An Architecture for Knowledge Representation and Reasoning in Robotics

This paper describes an architecture that combines the complementary strengths of declarative programming and probabilistic graphical models to enable robots to represent, reason with, and learn from, qualitative and quantitative descriptions of uncertainty and knowledge. An action language is used for the low-level (LL) and high-level (HL) system descriptions in the architecture, and the definition of recorded histories in the HL is expanded to allow prioritized defaults. For any given goal, tentative plans created in the HL using default knowledge and commonsense reasoning are implemented in the LL using probabilistic algorithms, with the corresponding observations used to update the HL history. Tight coupling between the two levels enables automatic selection of relevant variables and generation of suitable action policies in the LL for each HL action, and supports reasoning with violation of defaults, noisy observations and unreliable actions in large and complex domains. The architecture is evaluated in simulation and on physical robots transporting objects in indoor domains; the benefit on robots is a reduction in task execution time of 39% compared with a purely probabilistic, but still hierarchical, approach.Comment: The paper appears in the Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

Theory of Raman response in three-dimensional Kitaev spin liquids: application to β−\beta- and γ−\gamma-Li2_2IrO3_3 compounds

We calculate the Raman response for the Kitaev spin model on the $\mathcal{H}$-$0$, $\mathcal{H}$-$1$, and $\mathcal{H}$-$\infty$ harmonic honeycomb lattices. We identify several quantitative features in the Raman spectrum that are characteristic of the spin liquid phase. Unlike the dynamical structure factor, which probes both the Majorana spinons and flux excitations that emerge from spin fractionalization, the Raman spectrum in the Kitaev models directly probes a density of states of pairs of fractional, dispersing Majorana spinons. As a consequence, the Raman spectrum in all these models is gapless for sufficiently isotropic couplings, with a low-energy power law that results from the Fermi lines (or points) of the dispersing Majorana spinons. We show that the polarization dependence of the Raman spectrum contains crucial information about the symmetry of the ground state. We also discuss to what extent the features of the Raman response that we find reflect generic properties of the spin liquid phase, and comment on their possible relevance to $\alpha-$, $\beta-$ and $\gamma-$Li$_2$IrO$_3$ compounds.Comment: 19 pages, 10 figures. VERSION 2: Corrected Figure 5 and fixed inconsistencies between A and B chain-labelings. Also- a few typos and two new ref

Building Program Vector Representations for Deep Learning

Deep learning has made significant breakthroughs in various fields of artificial intelligence. Advantages of deep learning include the ability to capture highly complicated features, weak involvement of human engineering, etc. However, it is still virtually impossible to use deep learning to analyze programs since deep architectures cannot be trained effectively with pure back propagation. In this pioneering paper, we propose the "coding criterion" to build program vector representations, which are the premise of deep learning for program analysis. Our representation learning approach directly makes deep learning a reality in this new field. We evaluate the learned vector representations both qualitatively and quantitatively. We conclude, based on the experiments, the coding criterion is successful in building program representations. To evaluate whether deep learning is beneficial for program analysis, we feed the representations to deep neural networks, and achieve higher accuracy in the program classification task than "shallow" methods, such as logistic regression and the support vector machine. This result confirms the feasibility of deep learning to analyze programs. It also gives primary evidence of its success in this new field. We believe deep learning will become an outstanding technique for program analysis in the near future.Comment: This paper was submitted to ICSE'1

Quantum phases and phase transitions of Mott insulators

This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. The simplest class of Mott insulators have an even number of S=1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S=1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S=1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories (T. Senthil et al., cond-mat/0312617) of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations.Comment: 51 pages, 13 figure