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Structured Decompositions and Efficient Algorithms 2008

作者： Dahlke, Stephan Daubechies, Ingrid Elad, M. Kutyniok, Gitta Teschke, Gerd Philipps-Universität Marburg FB12 Mathematik und Informatik Hans-Meerwein Straße Lahnberge Marburg35032 Germany Princeton University Program in Applied and Computational Mathematics Fine Hall Washington Road PrincetonNJ08544-1000 United States Technion Computer Science Department Haifa Technion City32000 Israel Universität Osnabrück Institute of Mathematics Osnabrück49069 Germany Hochschule Neubrandenburg University of Applied Sciences Institute for Computational Mathematics in Science and Technology Brodaer Str. 2 Neubrandenburg17033 Germany

New emerging technologies such as high-precision sensors or new MRI machines drive us towards a challenging quest for new, more effective, and more daring mathematical models and algorithms. Therefore, in the last few years researchers have started to investigate different methods to efficiently represent or extract relevant information from complex, high dimensional and/or multimodal data. Efficiently in this context means a representation that is linked to the features or characteristics of interest, thereby typically providing a sparse expansion of such. Besides the construction of new and advanced ansatz systems the central question is how to design algorithms that are able to treat complex and high dimensional data and that efficiently perform a suitable approximation of the signal. One of the main challenges is to design new sparse approximation algorithms that would ideally combine, with an adjustable tradeoff, two properties: a provably good 'quality' of the resulting decomposition under mild assumptions on the analyzed sparse signal, and numerically efficient design. The topic is driven by applications as well as by theoretical questions. Therefore, the aim of this seminar was to bring together a good mixture of scientists with different backgrounds in order to discuss recent progress as well as new challenging perspectives. In particular, it was intended to strengthen the interaction of mathematicians and computer scientists. © 2009 Dagstuhl Seminar Proceedings. All Rights Reserved.

关键词： Clustering algorithms

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Analysis of hyperspectral data with diffusion maps and Fuzzy ART

Analysis of hyperspectral data with diffusion maps and Fuzzy...

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International Joint Conference on Neural Networks (IJCNN)

作者： Rui Xu Louis du Plessis Steven Damelin Michael Sears Donald C. Wunsch Applied Computational Intelligence Laboratory Department of Electrical & Computer Engineering Missouri University of Science and Technology MO USA School of Computational and Applied Mathematics University of the Witwatersrand Johannesburg South Africa Department of Mathematical Sciences Georgia Southern University Statesboro GA USA School of Computer Science University of the Witwatersrand Johannesburg South Africa Department of Electrical & Computer Engineering Missouri University of Science and Technology Rolla MO USA

The presence of large amounts of data in hyperspectral images makes it very difficult to perform further tractable analyses. Here, we present a method of analyzing real hyperspectral data by dimensionality reduction using diffusion maps. Diffusion maps interpret the eigenfunctions of Markov matrices as a system of coordinates on the original data set in order to obtain an efficient representation of data geometric descriptions. A neural network clustering theory, Fuzzy ART, is further applied to the reduced data to form clusters of the potential minerals. Experimental results on a subset of hyperspectral core imager data show that the proposed methods are promising in addressing the complicated hyperspectral data and identifying the minerals in core samples.

关键词： Data analysis Hyperspectral imaging Subspace constraints Frequency Minerals Optical imaging Multispectral imaging Pixel Africa Neural networks

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Target detection in hyperspectral mineral data using wavelet analysis

Target detection in hyperspectral mineral data using wavelet...

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IEEE International Symposium on Geoscience and Remote Sensing (IGARSS)

作者： Michael Mitchley Michael Sears Steven Damelin School of Computer Science University of the Witwatersrand Johannesburg South Africa School of Computational and Applied Mathematics University of the Witwatersrand Johannesburg South Africa Department of Mathematical Science Georgia Southern University Statesboro GA USA

A method for the automatic supervised detection of multiple mineral targets in hyperspectral mineral data is presented in this paper. The method makes use of wavelet analysis, wavelet-based denoising using thresholding of wavelet detail coefficients, and feature reduction based on sequential forward selection, which utilises an extension of receiver operating characteristic curves to fuzzy set membership in order to measure discriminating capability. The method is shown to run in time linear to the number of hyperspectral bands, per pixel. Furthermore, an extension of this method to linear unmixing is presented, based on minimising the least-squares error between abundance estimates and actual spectra by varying a thresholding parameter to eliminate outliers and imposing a sum-to-one constraint on the abundances.

关键词： Object detection Hyperspectral imaging Minerals Wavelet analysis Data analysis Hyperspectral sensors Feature extraction Human computer interaction Wavelet domain Africa

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Reducing the dimensionality of hyperspectral data using diffusion maps

Reducing the dimensionality of hyperspectral data using diff...

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IEEE International Symposium on Geoscience and Remote Sensing (IGARSS)

作者： Louis du Plessis Steven Damelin Michael Sears School of Computational and Applied Mathematics University of the Witwatersrand South Africa Department of Mathematical Sciences Georgia Southern University Statesboro GA USA School of Computer Science University of the Witwatersrand Johannesburg South Africa

We examine the analysis of hyperspectral data produced by the Hy-perspectral Core Imager of AngloGold Ashanti. The dimension of the data is reduced using diffusion maps and the data is then clustered using three divisive clustering strategies. Divisive k-means, PDDP and the NCut algorithm are used. It is shown that the clusterings produced are reasonably accurate compared to a reference clustering, but superior with respect to an internal quality evaluation. Moreover, using a divisive algorithm makes it possible to keep track of inter-cluster similarities. It is also shown that by embedding sample spectra in a dataset it is possible to identify particular minerals within the cluster.

关键词： Hyperspectral imaging Hyperspectral sensors Human computer interaction Minerals Clustering algorithms mathematics computer science Spatial resolution Subspace constraints Africa

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Default network and intelligence difference

Default network and intelligence difference

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Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

作者： Ming Song Yong Liu Yuan Zhou Kun Wang Chunshui Yu Tianzi Jiang Research Center of Computational Medicine Sino-French Laboratory in Computer Science Automation and Applied Mathematics Institution of Automation Chinese Academy and Sciences Beijing China Department of Radiology Xuanwu Hospital of Capital Medical University Beijing China

In the last few years, many studies in the cognitive and system neuroscience found that a consistent network of brain regions, referred to as the default network, showed high levels of activity when no explicit task was performed. Some scientists believed that the resting state activity might reflect some neural functions that consolidate the past, stabilize brain ensembles and prepare us for the future. Here, we modeled default network as undirected weighted graph and then used graph theory to investigate the topological properties of the default network of the two groups of people with different intelligence levels. We found that, in both groups, the posterior cingulate cortex showed the greatest degree in comparison to the other brain regions in the default network, and that the medial temporal lobes and cerebellar tonsils were topologically separations from the other brain regions in the default network. More importantly, we found that the strength of some functional connectivities and the global efficiency of default network were significantly different between the superior intelligence group and the average intelligence group, which indicates that the functional integration of the default network might be related to the individual intelligent performance.

关键词： Intelligent networks Humans Artificial intelligence Neuroscience Graph theory Temporal lobe Intelligent sensors Automation Hospitals Alzheimer's disease

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Block Ignition Inertial Confinement Fusion (ICF) with Condensed Matter Cluster Type Targets for p‐B11 Powered Space Propulsion

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AIP Conference Proceedings 2009年第1期1103卷 656-672页

作者： George H. Miley H. Hora J. Badziak J. Wolowski Zheng‐Ming Sheng Jie Zhang F. Osman Weiyan Zhang Xia tu He aUniversity of Illinois Urbana‐Champaign NPL Associates 216 Talbot Laboratory 104 S. Wright St. Urbana IL 61801 217‐333‐3772 bDepartment of Theoretical Physics University of New South Wales Sydney Australia cInstitute of Plasma Physics and Laser Microfusion Warsaw Poland dBeijing National Laboratory for CondensedMatter Physics Institute of Physics Chinese Academy of ScienceBeijing 100080 China eSchool of Computer Sciences University of Western Sydney Penrith Australia fChina Academy of Engineering Physics Mianyang China gInstitute of Applied Physics and Computational Mathematics Beijing China hInstitute of Physics Academy of Science Prague Czech Republic

The use of laser‐driven Inertial Confinement Fusion (ICF) for space propulsion has been the subject of several earlier conceptual design studies, (see: Orth, 1998; and other references therein). However, these studies were based on older ICF technology using either “direct “or “in‐direct x‐ray driven” type target irradiation. Important new directions have opened for laser ICF in recent years following the development of “chirped” lasers capable of ultra short pulses with powers of TW up to few PW which leads to the concept of “fast ignition (FI)” to achieve higher energy gains from target implosions. In a recent publication the authors showed that use of a modified type of FI, termed “block ignition” (Miley et al., 2008), could meet many of the requirements anticipated (but not then available) by the designs of the Vehicle for Interplanetary Space Transport Applications (VISTA) ICF fusion propulsion ship (Orth, 2008) for deep space missions. Subsequently the first author devised and presented concepts for imbedding high density condensed matter “clusters” of deuterium into the target to obtain ultra high local fusion reaction rates (Miley, 2008). Such rates are possible due to the high density of the clusters (over an order of magnitude above cryogenic deuterium). Once compressed by the implosion, the yet higher density gives an ultra high reaction rate over the cluster volume since the fusion rate is proportional to the square of the fuel density. Most recently, a new discovery discussed here indicates that the target matrix could be composed of B11 with proton clusters imbedded. This then makes p‐B11 fusion practical, assuming all of the physics issues such as stability of the clusters during compression are resolved. Indeed, p‐B11 power is ideal for fusion propulsion since it has a minimum of unwanted side products while giving most of the reaction energy to energetic alpha particles which can be directed into an exhaust (propulsion) nozzle. Power plants using p‐

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A multi-level genetic algorithm for a multi-stage space allocation problem 7

A multi-level genetic algorithm for a multi-stage space allo...

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7th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2008

作者： Adewumi, Aderemi O. Montaz Ali, M. Ayeni, Joshua O. School of Computational and Applied Mathematics University of Witwatersrand Johannesburg South Africa Department of Computer Sciences Faculty of Science University of Lagos Lagos Nigeria

We considered the case of a multi-stage hostel space allocation problem based on data set obtained from a tertiary institution. Genetic Algorithm was applied at different levels of the allocation. We studied the effects of parameter change on solutions obtained. The rate of feasibility of the solutions was also determined. © Practice and Theory of Automated Timetabling, PATAT *** right reserved.

关键词： Genetic algorithms

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Diffusion maps - A probabilistic interpretation for spectral embedding and clustering algorithms

Diffusion maps - A probabilistic interpretation for spectral...

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作者： Nadler, Boaz Lafon, Stephane Coifman, Ronald Kevrekidis, Ioannis G. Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot 76100 Israel Google Inc. United States Department of Mathematics Yale University New Haven CT 06520-8283 United States Department of Chemical Engineering Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States

ISBN: (纸本)9783540737490

Spectral embedding and spectral clustering are common methods for non-linear dimensionality reduction and clustering of complex high dimensional datasets. In this paper we provide a diffusion based probabilistic analysis of algorithms that use the normalized graph Laplacian. Given the pairwise adjacency matrix of all points in a dataset, we define a random walk on the graph of points and a diffusion distance between any two points. We show that the diffusion distance is equal to the Euclidean distance in the embedded space with all eigenvectors of the normalized graph Laplacian. This identity shows that characteristic relaxation times and processes of the random walk on the graph are the key concept that governs the properties of these spectral clustering and spectral embedding algorithms. Specifically, for spectral clustering to succeed, a necessary condition is that the mean exit times from each cluster need to be significantly larger than the largest (slowest) of all relaxation times inside all of the individual clusters. For complex, multiscale data, this condition may not hold and multiscale methods need to be developed to handle such situations.

关键词： Relaxation time

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The SAT-tableau calculus

The SAT-tableau calculus

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21st International Workshop on Description Logics, DL 2008

作者： Keller, Uwe Heymans, Stijn University of Innsbruck Innsbruck Austria Knowledge-Based Systems Group Institute of Information Systems Technical University of Vienna Austria Department of Applied Mathematics and Computer Science Computational Web Intelligence Ghent University Belgium

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The attractor of the stochastic generalized Ginzburg-Landau equation

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science China mathematics 2008年第5期51卷 955-964页

作者： GUO BoLing~1 WANG GuoLian~(2+) Li DongLong~3 1 Institute of applied Physics and computational mathematics,P.O.Box 8009,Beijing 100088,China 2 The Graduate School of China Academy of Engineering Physics,P.O.Box 2101,Beijing 100088,China 3 Department of Information and computer science,Guangxi University of Technology,Liuzhou 545006,China Institute of Applied Physics Computational Mathematics P. O. Box 8009 Beijing 100088 China The Graduate School of China Academy of Engineering Physics P. O. Box 2101 Beijing 100088 China Department of Information Computer Science Guangxi University of Technology Liuzhou 545006 China

The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in ... 详细信息

关键词： generalized Ginzburg-Landau equation random dynamical systems random attractor 35K05

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