Geometric Verification of Features in Flow Fields

title: Spatial domain wavelet design for feature preservation in computational data sets
abstract: High-fidelity wavelet transforms can facilitate visualization and analysis of large scientific data sets. However, it is important that salient characteristics of the original features be preserved under the transformation. We present a set of filter design axioms in the spatial domain which ensure that certain feature characteristics are preserved from scale to scale and that the resulting filters correspond to wavelet transforms admitting in-place implementation. We demonstrate how the axioms can be used to design linear feature-preserving filters that are optimal in the sense that they are closest in L2 to the ideal low pass filter. We are particularly interested in linear wavelet transforms for large data sets generated by computational fluid dynamics simulations. Our effort is different from classical filter design approaches which focus solely on performance in the frequency domain. Results are included that demonstrate the feature-preservation characteristics of our filters

title: Vortex Visualization for Practical Engineering Applications
abstract: In order to understand complex vortical flows in large data sets, we must be able to detect and visualize vortices in an automated fashion. In this paper, we present a feature-based vortex detection and visualization technique that is appropriate for large computational fluid dynamics data sets computed on unstructured meshes. In particular, we focus on the application of this technique to visualization of the flow over a serrated wing and the flow field around a spinning missile with dithering canards. We have developed a core line extraction technique based on the observation that vortex cores coincide with local extrema in certain scalar fields. We also have developed a novel technique to handle complex vortex topology that is based on k-means clustering. These techniques facilitate visualization of vortices in simulation data that may not be optimally resolved or sampled. Results are included that highlight the strengths and weaknesses of our approach. We conclude by describing how our approach can be improved to enhance robustness and expand its range of applicability

title: Feature Mining Paradigms for Scientific Data
abstract: Numerical simulation is replacing experimentation as a means to gain insight into complex physical phenomena. Analyzing the data produced by such simulations is extremely challenging, given the enormous sizes of the datasets involved. In order to make efficient progress, analyzing such data must advance from current techniques that only visualize static images of the data, to novel techniques that can mine, track, and visualize the important features in the data. In this paper, we present our research on a unified framework that addresses this critical challenge in two science domains: computational fluid dynamics and molecular dynamics. We offer a systematic approach to detect the significant features in both domains, characterize and track them, and formulate hypotheses with regard to their complex evolution. Our framework includes two paradigms for feature mining, and the choice of one over the other, for a given application, can be determined based on local or global influence of relevant features in the data.

title: Convergence of the simultaneous algebraic reconstruction technique (SART)
abstract: In 1984, the simultaneous algebraic reconstruction technique (SART) was developed as a major refinement of the algebraic construction technique (ART). Since then, the SART approach remains a powerful tool for iterative image reconstruction. However, the convergence of the SART has never been established. This long-standing conjecture is proven under the condition that coefficients of the linear imaging system are non-negative. It is shown that from any initial value the sequence generated by the SART converges to a weighted least square solution. The importance of the SART and several relevant issues are also discussed.

title: A Surface Reconstruction Method for Highly Noisy Point Clouds
abstract: In this paper we propose a surface reconstruction method for highly noisy and non-uniform data based on minimal surface model and tensor voting method. To deal with ill-posedness, noise and/or other uncertainties in the data we processes the raw data first using tensor voting before we do surface reconstruction. The tensor voting procedure allows more global and robust communications among the data to extract coherent geometric features and saliency independent of the surface reconstruction. These extracted information will be used to preprocess the data and to guide the final surface reconstruction. Numerically the level set method is used for surface reconstruction. Our method can handle complicated topology as well as highly noisy and/or non-uniform data set. Moreover, improvements of efficiency in implementing the tensor voting method are also proposed. We demonstrate the ability of our method using synthetic and real data.

title: Updating Views Over Recursive XML
abstract: We study the problem of updating XML views defined over XML documents. A view update is performed by finding the base updates over the underlying data sources that achieve the desired view update. If such base updates do not exist, the view update is said to be untranslatable and rejected. In SQL, determining whether a view update is translatable is performed using schema level analysis, where the view definition and the base schema are used. XML schemas are more complex than SQL schemas, and can specify recursive types and cardinality constraints. In this paper, we propose a solution based on schema level analysis for determining whether an update over XML views is translatable and for finding the translation if one exists, while considering the features of XML schemas.

title: The Hamiltonicity of Directed sigma - tao Cayley Graphs (or: A Tale of Backtracking)
abstract: Let τ be the 2-cycle (1 2) and σ the n-cycle (12 … n). These two cycles generate the symmetric group Sn. Let Gn denote the directed Cayley graph Cay(τ, σ: Sn). Based on erroneous computer calculations, Nijenhuis and Wilf (1975, p. 238; 1978, p. 288) give as an exercise to show that G5 does not have a Hamiltonian path. To the contrary, we show that G5 is Hamiltonian. Furthermore, we show that G6 has a Hamilton path. Our results illustrate how a little theory and some good luck can save a lot of time in backtracking searches.

title: Global Exponential Stability and Periodicity of CNNs with Time-Varying Discrete and Distributed Delays
abstract: In this paper, based on the Lyapunov stability analysis for functional differential equations, the problems of global exponential stability and periodic solutions for a class of cellular neural networks with time-varying delays and distributed delays are investigated. By constructing a new suitable Lyapunov functional, some simple sufficient conditions ensuring existence, uniqueness, global exponential stability of the equilibrium point and periodic oscillation of the networks are obtained, which are easy to check and apply in practice. In addition, an example is also given to illustrate the effectiveness of the theory.