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International Conference on Apperceiving Computing and Intelligence Analysis, ICACIA

作者： Ke-Long Zheng Shou-Ming Zhong Mao Ye School of Applied Mathematics University of Electronic Science and Technology Chengdu Sichuan China School of Science Southwest University of Science and Technology Mianyang Sichuan China School of Computer Science and Engineering University of Electronic Science and Technology Chengdu Sichuan China

In this paper, more general discrete integral inequalities with more than one nonlinear term are established. These inequalities generalize some results in the literature and provide a convenient tool to study the con... 详细信息

关键词： Nonlinear control systems Control systems Asymptotic stability mathematics computer science

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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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On detection with partial information in the Gaussian setup

On detection with partial information in the Gaussian setup

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Annual Allerton Conference on Communication, Control, and Computing

作者： Onur Özyeşil M. Kivanç Mihçak Yğcel Altug PACM (the Program in Applied and Computational Mathematics) Princeton University Princeton NJ USA Electrical and Electronics Engineering Department Boğaziçi University Istanbul Turkey School of Electrical and Computer Engineering Cornell University Ithaca NY USA

We introduce the problem of communication with partial information, where there is an asymmetry between the transmitter and the receiver codebooks. Practical applications of the proposed setup include the robust signal hashing problem within the context of multimedia security and asymmetric communications with resource-lacking receivers. We study this setup in a binary detection theoretic context for the additive colored Gaussian noise channel. In our proposed setup, the partial information available at the detector consists of dimensionality-reduced versions of the transmitter codewords, where the dimensionality reduction is achieved via a linear transform. We first derive the corresponding MAP-optimal detection rule and the corresponding conditional probability of error (conditioned on the partial information the detector possesses). Then, we constructively quantify an optimal class of linear transforms, where the cost function is the expected Chernoff bound on the conditional probability of error of the MAP-optimal detector.

关键词： Transmitters Protection Context Detectors Noise robustness Information security engineering profession Signal processing Privacy Bidirectional control

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Measurement of the Z→ττ cross section with the ATLAS detector

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Physical Review D 2011年第11期84卷 112006-112006页

作者： G. Aad B. Abbott J. Abdallah A. A. Abdelalim A. Abdesselam O. Abdinov B. Abi M. Abolins H. Abramowicz H. Abreu E. Acerbi B. S. Acharya D. L. Adams T. N. Addy J. Adelman M. Aderholz S. Adomeit P. Adragna T. Adye S. Aefsky J. A. Aguilar-Saavedra M. Aharrouche S. P. Ahlen F. Ahles A. Ahmad M. Ahsan G. Aielli T. Akdogan T. P. A. Åkesson G. Akimoto A. V. Akimov A. Akiyama M. S. Alam M. A. Alam J. Albert S. Albrand M. Aleksa I. N. Aleksandrov F. Alessandria C. Alexa G. Alexander G. Alexandre T. Alexopoulos M. Alhroob M. Aliev G. Alimonti J. Alison M. Aliyev P. P. Allport S. E. Allwood-Spiers J. Almond A. Aloisio R. Alon A. Alonso M. G. Alviggi K. Amako P. Amaral C. Amelung V. V. Ammosov A. Amorim G. Amorós N. Amram C. Anastopoulos N. Andari T. Andeen C. F. Anders K. J. Anderson A. Andreazza V. Andrei M-L. Andrieux X. S. Anduaga A. Angerami F. Anghinolfi N. Anjos A. Annovi A. Antonaki M. Antonelli A. Antonov J. Antos F. Anulli S. Aoun L. Aperio Bella R. Apolle G. Arabidze I. Aracena Y. Arai A. T. H. Arce J. P. Archambault S. Arfaoui J-F. Arguin E. Arik M. Arik A. J. Armbruster O. Arnaez C. Arnault A. Artamonov G. Artoni D. Arutinov S. Asai R. Asfandiyarov S. Ask B. Åsman L. Asquith K. Assamagan A. Astbury A. Astvatsatourov G. Atoian B. Aubert B. Auerbach E. Auge K. Augsten M. Aurousseau N. Austin G. Avolio R. Avramidou D. Axen C. Ay G. Azuelos Y. Azuma M. A. Baak G. Baccaglioni C. Bacci A. M. Bach H. Bachacou K. Bachas G. Bachy M. Backes M. Backhaus E. Badescu P. Bagnaia S. Bahinipati Y. Bai D. C. Bailey T. Bain J. T. Baines O. K. Baker M. D. Baker S. Baker F. Baltasar Dos Santos Pedrosa E. Banas P. Banerjee Sw. Banerjee D. Banfi A. Bangert V. Bansal H. S. Bansil L. Barak S. P. Baranov A. Barashkou A. Barbaro Galtieri T. Barber E. L. Barberio D. Barberis M. Barbero D. Y. Bardin T. Barillari M. Barisonzi T. Barklow N. Barlow B. M. Barnett R. M. Barnett A. Baroncelli G. Barone A. J. Barr F. Barreiro J. Barreiro Guimarães da Costa P. Barrillon R. Bartoldus A. E. Barton D. Bartsch V. Bartsch R. L. Bates L. Batkova J. R. Bat Fakultät für Mathematik und Physik Albert-Ludwigs-Universität Freiburg i.Br. Germany Homer L. Dodge Department of Physics and Astronomy University of Oklahoma Norman Oklahoma USA Institut de Física d’Altes Energies and Universitat Autònoma de Barcelona and ICREA Barcelona Spain Section de Physique Université de Genève Geneva Switzerland Department of Physics Oxford University Oxford United Kingdom Institute of Physics Azerbaijan Academy of Sciences Baku Azerbaijan Department of Physics Oklahoma State University Stillwater Oklahoma USA Department of Physics and Astronomy Michigan State University East Lansing Michigan USA Raymond and Beverly Sackler School of Physics and Astronomy Tel Aviv University Tel Aviv Israel LAL University Paris-Sud and CNRS/IN2P3 Orsay France INFN Sezione di Milano Italy Dipartimento di Fisica Università di Milano Milano Italy INFN Gruppo Collegato di Udine Italy ICTP Trieste Italy Physics Department Brookhaven National Laboratory Upton New York USA Department of Physics Hampton University Hampton Virginia USA Department of Physics Yale University New Haven Connecticut USA Max-Planck-Institut für Physik (Werner-Heisenberg-Institut) München Germany Fakultät für Physik Ludwig-Maximilians-Universität München München Germany Department of Physics Queen Mary University of London London United Kingdom Particle Physics Department Rutherford Appleton Laboratory Didcot United Kingdom Department of Physics Brandeis University Waltham Massachusetts USA Departamento de Fisica Teorica y del Cosmos and CAFPE Universidad de Granada Granada Spain Institut für Physik Universität Mainz Mainz Germany Department of Physics Boston University Boston Massachusetts USA Department of Physics and Astronomy Stony Brook University Stony Brook New York USA Physics Department University of Texas at Dallas Richardson Texas USA INFN Sezione di Roma Tor Vergata Italy Dipartimento di Fisica Università di Roma Tor Vergata Roma Italy Dep

The Z→ττ cross section is measured with the ATLAS experiment at the LHC in four different final states determined by the decay modes of the τ leptons: muon-hadron, electron-hadron, electron-muon, and muon-muon. The analysis is based on a data sample corresponding to an integrated luminosity of 36 pb−1, at a proton-proton center-of-mass energy of s=7 TeV. Cross sections are measured separately for each final state in fiducial regions of high detector acceptance, as well as in the full phase space, over the mass region 66–116 GeV. The individual cross sections are combined and the product of the total Z production cross section and Z→ττ branching fraction is measured to be 0.97±0.07(stat)±0.06(syst)±0.03(lumi) nb, in agreement with next-to-next-to-leading order calculations.

关键词： LARGE Hadron Collider (France & Switzerland) MUONS LEPTONS (Nuclear physics) SPECIAL relativity (Physics) PROTON-proton interactions

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Search for pair production of first or second generation leptoquarks in proton-proton collisions at s=7 TeV using the ATLAS detector at the LHC

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Physical Review D 2011年第11期83卷 112006-112006页

作者： G. Aad B. Abbott J. Abdallah A. A. Abdelalim A. Abdesselam O. Abdinov B. Abi M. Abolins H. Abramowicz H. Abreu E. Acerbi B. S. Acharya D. L. Adams T. N. Addy J. Adelman M. Aderholz S. Adomeit P. Adragna T. Adye S. Aefsky J. A. Aguilar-Saavedra M. Aharrouche S. P. Ahlen F. Ahles A. Ahmad M. Ahsan G. Aielli T. Akdogan T. P. A. Åkesson G. Akimoto A. V. Akimov A. Akiyama M. S. Alam M. A. Alam S. Albrand M. Aleksa I. N. Aleksandrov F. Alessandria C. Alexa G. Alexander G. Alexandre T. Alexopoulos M. Alhroob M. Aliev G. Alimonti J. Alison M. Aliyev P. P. Allport S. E. Allwood-Spiers J. Almond A. Aloisio R. Alon A. Alonso M. G. Alviggi K. Amako P. Amaral C. Amelung V. V. Ammosov A. Amorim G. Amorós N. Amram C. Anastopoulos T. Andeen C. F. Anders K. J. Anderson A. Andreazza V. Andrei M-L. Andrieux X. S. Anduaga A. Angerami F. Anghinolfi N. Anjos A. Annovi A. Antonaki M. Antonelli S. Antonelli A. Antonov J. Antos F. Anulli S. Aoun L. Aperio Bella R. Apolle G. Arabidze I. Aracena Y. Arai A. T. H. Arce J. P. Archambault S. Arfaoui J-F. Arguin E. Arik M. Arik A. J. Armbruster O. Arnaez C. Arnault A. Artamonov G. Artoni D. Arutinov S. Asai R. Asfandiyarov S. Ask B. Åsman L. Asquith K. Assamagan A. Astbury A. Astvatsatourov G. Atoian B. Aubert B. Auerbach E. Auge K. Augsten M. Aurousseau N. Austin R. Avramidou D. Axen C. Ay G. Azuelos Y. Azuma M. A. Baak G. Baccaglioni C. Bacci A. M. Bach H. Bachacou K. Bachas G. Bachy M. Backes M. Backhaus E. Badescu P. Bagnaia S. Bahinipati Y. Bai D. C. Bailey T. Bain J. T. Baines O. K. Baker M. D. Baker S. Baker F. Baltasar Dos Santos Pedrosa E. Banas P. Banerjee Sw. Banerjee D. Banfi A. Bangert V. Bansal H. S. Bansil L. Barak S. P. Baranov A. Barashkou A. Barbaro Galtieri T. Barber E. L. Barberio D. Barberis M. Barbero D. Y. Bardin T. Barillari M. Barisonzi T. Barklow N. Barlow B. M. Barnett R. M. Barnett A. Baroncelli A. J. Barr F. Barreiro J. Barreiro Guimarães da Costa P. Barrillon R. Bartoldus A. E. Barton D. Bartsch V. Bartsch R. L. Bates L. Batkova J. R. Batley A. Battaglia M. Battist Fakultät für Mathematik und Physik Albert-Ludwigs-Universität Freiburg i.Br. Germany Homer L. Dodge Department of Physics and Astronomy University of Oklahoma Norman Oklahoma USA Institut de Física d’Altes Energies and Universitat Autònoma de Barcelona and ICREA Barcelona Spain Section de Physique Université de Genève Geneva Switzerland Department of Physics Oxford University Oxford United Kingdom Institute of Physics Azerbaijan Academy of Sciences Baku Azerbaijan Department of Physics Oklahoma State University Stillwater Oklahoma USA Department of Physics and Astronomy Michigan State University East Lansing Michigan USA Raymond and Beverly Sackler School of Physics and Astronomy Tel Aviv University Tel Aviv Israel LAL Univ. Paris-Sud and CNRS/IN2P3 Orsay France INFN Sezione di Milano Italy Dipartimento di Fisica Università di Milano Milano Italy INFN Gruppo Collegato di Udine Italy ICTP Trieste Italy Physics Department Brookhaven National Laboratory Upton New York USA Department of Physics Hampton University Hampton Virginia USA Department of Physics Yale University New Haven Connecticut USA Max-Planck-Institut für Physik (Werner-Heisenberg-Institut) München Germany Fakultät für Physik Ludwig-Maximilians-Universität München München Germany Department of Physics Queen Mary University of London London United Kingdom Particle Physics Department Rutherford Appleton Laboratory Didcot United Kingdom Department of Physics Brandeis University Waltham Massachusetts USA Departamento de Fisica Teorica y del Cosmos and CAFPE Universidad de Granada Granada Portugal Institut für Physik Universität Mainz Mainz Germany Department of Physics Boston University Boston Massachusetts USA Department of Physics and Astronomy Stony Brook University Stony Brook New York USA Physics Department University of Texas at Dallas Richardson Texas USA INFN Sezione di Roma Tor Vergata Italy Dipartimento di Fisica Università di Roma Tor Vergata Roma Italy Depar

This paper describes searches for the pair production of first or second generation scalar leptoquarks using 35 pb−1 of proton-proton collision data recorded by the ATLAS detector at s=7 TeV. Leptoquarks are searched in events with two oppositely-charged muons or electrons and at least two jets, and in events with one muon or electron, missing transverse momentum and at least two jets. After event selection, the observed yields are consistent with the predicted backgrounds. Leptoquark production is excluded at the 95% CL for masses MLQ<376 (319) GeV and MLQ<422 (362) GeV for first and second generation scalar leptoquarks, respectively, when assuming the branching fraction of a leptoquark to a charged lepton is equal to 1.0 (0.5).

关键词： PAIR production QUARKS PROTON-proton interactions DETECTORS NUCLEAR reactions

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Properties of jets measured from tracks in proton-proton collisions at center-of-mass energy s=7 TeV with the ATLAS detector

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Physical Review D 2011年第5期84卷 054001-054001页

作者： G. Aad B. Abbott J. Abdallah A. A. Abdelalim A. Abdesselam O. Abdinov B. Abi M. Abolins H. Abramowicz H. Abreu E. Acerbi B. S. Acharya D. L. Adams T. N. Addy J. Adelman M. Aderholz S. Adomeit P. Adragna T. Adye S. Aefsky J. A. Aguilar-Saavedra M. Aharrouche S. P. Ahlen F. Ahles A. Ahmad M. Ahsan G. Aielli T. Akdogan T. P. A. Åkesson G. Akimoto A. V. Akimov A. Akiyama M. S. Alam M. A. Alam J. Albert S. Albrand M. Aleksa I. N. Aleksandrov F. Alessandria C. Alexa G. Alexander G. Alexandre T. Alexopoulos M. Alhroob M. Aliev G. Alimonti J. Alison M. Aliyev P. P. Allport S. E. Allwood-Spiers J. Almond A. Aloisio R. Alon A. Alonso M. G. Alviggi K. Amako P. Amaral C. Amelung V. V. Ammosov A. Amorim G. Amorós N. Amram C. Anastopoulos L. S. Ancu N. Andari T. Andeen C. F. Anders G. Anders K. J. Anderson A. Andreazza V. Andrei M-L. Andrieux X. S. Anduaga A. Angerami F. Anghinolfi N. Anjos A. Annovi A. Antonaki M. Antonelli A. Antonov J. Antos F. Anulli S. Aoun L. Aperio Bella R. Apolle G. Arabidze I. Aracena Y. Arai A. T. H. Arce J. P. Archambault S. Arfaoui J-F. Arguin E. Arik M. Arik A. J. Armbruster O. Arnaez C. Arnault A. Artamonov G. Artoni D. Arutinov S. Asai R. Asfandiyarov S. Ask B. Åsman L. Asquith K. Assamagan A. Astbury A. Astvatsatourov G. Atoian B. Aubert B. Auerbach E. Auge K. Augsten M. Aurousseau N. Austin G. Avolio R. Avramidou D. Axen C. Ay G. Azuelos Y. Azuma M. A. Baak G. Baccaglioni C. Bacci A. M. Bach H. Bachacou K. Bachas G. Bachy M. Backes M. Backhaus E. Badescu P. Bagnaia S. Bahinipati Y. Bai D. C. Bailey T. Bain J. T. Baines O. K. Baker M. D. Baker S. Baker E. Banas P. Banerjee Sw. Banerjee D. Banfi A. Bangert V. Bansal H. S. Bansil L. Barak S. P. Baranov A. Barashkou A. Barbaro Galtieri T. Barber E. L. Barberio D. Barberis M. Barbero D. Y. Bardin T. Barillari M. Barisonzi T. Barklow N. Barlow B. M. Barnett R. M. Barnett A. Baroncelli G. Barone A. J. Barr F. Barreiro J. Barreiro Guimarães da Costa P. Barrillon R. Bartoldus A. E. Barton D. Bartsch V. Bartsch R. L. Bates L. Batkova J. R. Batley A. Bat Fakultät für Mathematik und Physik Albert-Ludwigs-Universität Freiburg i.Br. Germany Homer L. Dodge Department of Physics and Astronomy University of Oklahoma Norman Oklahoma USA Institut de Física d’Altes Energies and Universitat Autònoma de Barcelona and ICREA Barcelona Spain Section de Physique Université de Genève Geneva Switzerland Department of Physics Oxford University Oxford United Kingdom Institute of Physics Azerbaijan Academy of Sciences Baku Azerbaijan Department of Physics Oklahoma State University Stillwater Oklahoma USA Department of Physics and Astronomy Michigan State University East Lansing Michigan USA Raymond and Beverly Sackler School of Physics and Astronomy Tel Aviv University Tel Aviv Israel LAL Université Paris-Sud and CNRS/IN2P3 Orsay France INFN Sezione di Milano Italy Dipartimento di Fisica Università di Milano Milano Italy INFN Gruppo Collegato di Udine Italy ICTP Trieste Italy Physics Department Brookhaven National Laboratory Upton New York USA Department of Physics Hampton University Hampton Virginia USA Department of Physics Yale University New Haven Connecticut USA Max-Planck-Institut für Physik (Werner-Heisenberg-Institut) München Germany Fakultät für Physik Ludwig-Maximilians-Universität München München Germany Department of Physics Queen Mary University of London London United Kingdom Particle Physics Department Rutherford Appleton Laboratory Didcot United Kingdom Department of Physics Brandeis University Waltham Massachusetts USA Departamento de Fisica Teorica y del Cosmos and CAFPE Universidad de Granada Granada Spain Institut für Physik Universität Mainz Mainz Germany Department of Physics Boston University Boston Massachusetts USA Department of Physics and Astronomy Stony Brook University Stony Brook New York USA Physics Department University of Texas at Dallas Richardson Texas USA INFN Sezione di Roma Tor Vergata Italy Dipartimento di Fisica Università di Roma Tor Vergata Roma Italy Dep

Jets are identified and their properties studied in center-of-mass energy s=7 TeV proton-proton collisions at the Large Hadron Collider using charged particles measured by the ATLAS inner detector. Events are selected using a minimum bias trigger, allowing jets at very low transverse momentum to be observed and their characteristics in the transition to high-momentum fully perturbative jets to be studied. Jets are reconstructed using the anti-kt algorithm applied to charged particles with two radius parameter choices, 0.4 and 0.6. An inclusive charged jet transverse momentum cross section measurement from 4 GeV to 100 GeV is shown for four ranges in rapidity extending to 1.9 and corrected to charged particle-level truth jets. The transverse momenta and longitudinal momentum fractions of charged particles within jets are measured, along with the charged particle multiplicity and the particle density as a function of radial distance from the jet axis. Comparison of the data with the theoretical models implemented in existing tunings of Monte Carlo event generators indicates reasonable overall agreement between data and Monte Carlo. These comparisons are sensitive to Monte Carlo parton showering, hadronization, and soft physics models.

关键词： JETS (Nuclear physics) NUCLEAR reactions SCATTERING (Physics) NEUTRINO mass ATOMIC mass PROTON-proton interactions

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Time Domain Analysis of Fields Reflected from Model of Human Body Surface Using Artificial Neural Network

Time Domain Analysis of Fields Reflected from Model of Human...

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European Conference on Antennas and Propagation

作者： Oleksandr M. Dumin Olga O. Dumina Dmytro V. Shyrokorad Department of Applied Electrodynamics School of Radio Physics V..N. Karazin Kharkiv National University Department of Higher Mathematics Ukrainian State Academy of Railway Transport School of Information Science and Computer Engineering Zaporizhzhja National Technical University

ISBN: (纸本)9781424447534

The impulse fields reflected from the model of human body surface are analyzed by artificial neural network in time domain directly. The normal incidence of plane wave with Gaussian time form on the layered medium with losses is considered. The reflected electromagnetic field is obtained by FDTD method. Initial data for neural network analysis are the values of amplitude of electrical component of reflected field. As an example, the network is trained to determine the thickness of one of the layers of the medium. The stability of the determination in presence of interferences and variations of the medium parameters is investigated.

关键词： Manikins Time domain analysis Artificial neural networks Fields Electrical components one layer Network analysis TIME-DOMAIN Body Surface

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Linear network coordinated beamforming for cell-boundary users

Linear network coordinated beamforming for cell-boundary use...

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IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

作者： Chan-Byoung Chae Sang-hyun Kim Robert W. Heath School of Engineering and Applied Sciences Harvard University Cambridge MA USA Department of Mathematics University of Texas Austin Austin TX USA Wireless Networking and Communications Group (WNCG) Department of Electrical and Computer Engineering University of Texas Austin Austin TX USA

In this paper, low complexity linear network coordinated beamforming (N-CBF) algorithms under a zero inter-user interference constraint are proposed for the multi-cell downlink channel. We consider a downlink scenario with three base stations (BSs) equipped with one transmit antenna each and three mobile users, each of which has more than one receive antenna and is located on the cell-boundary. A single data stream is transmitted to all three cell-boundary users where each user receives his/her own independent data stream (called full broadcast channel), or where two users receive the same data stream while the third user receives a different data stream (called clustered broadcast channel). For the full and clustered broadcast channel scenarios, we propose low complexity linear N-CBF algorithms approaching the sum capacity realized by multi-cell dirty paper coding. Monte Carlo simulations are carried out to verify the proposed algorithms.

关键词： Array signal processing MIMO Receiving antennas Broadcasting Multicast algorithms Iterative algorithms Downlink Clustering algorithms Transmitting antennas Interference constraints

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A New Two-Directional Two-Dimensional Feature Extraction Based on Manifold Learning

A New Two-Directional Two-Dimensional Feature Extraction Bas...

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International Conference on Artificial Intelligence and Computational Intelligence (AICI)

作者： Yong-zhi Li Guo-dong Li Jing-yu Yang School of Computer Science & Technology Nanjing University of Science and Technology of PLA Nanjing China Department of Applied Mathematics Nanjing Forestry University Nanjing China Department of Electromechanical Engineering Zhonghua College of Vocational Technology Shanghai Shanghai China

A new feature extraction method based on manifold learning is proposed for face recognition in the paper; its criterion function is characterized by maximizing the difference between the nonlocal scatter and the local scatter. The novel method is called two-directional two-dimensional marginal discriminant projection ((2D) 2 MDP), which simultaneously works image matrix in the row direction and in the column direction for feature extraction. The experimental results on ORL face databases indicate that the proposed method has higher recognition rate and more stable.

关键词： Feature extraction Scattering Face recognition Principal component analysis Paper technology Image databases Spatial databases Manifolds Laplace equations Artificial intelligence

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Effective condition number of Trefftz methods for biharmonie equations with crack singularities

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Numerical Linear Algebra with Applications 2009年第2期16卷 145-171页

作者： Li, Zi-Cai Lu, Tzon-Tzer Wei, Yimin Department of Applied Mathematics National Sun Yat-sen University Kaohsiung Taiwan 80424 Taiwan Department of Computer Science and Engineering National Sun Yat-sen University Kaohsiung Taiwan 80424 Taiwan School of Mathematical Sciences Fudan University Shanghai 200433 China Key Laboratory of Mathematics for Nonlinear Sciences Ministry of Education Fudan University Shanghai China

The paper presents the new stability analysis for the collocation Trefftz method (CTM) for biharmonie equations, based on the new effective condition number Cond-eff. The Trefftz method is a special spectral method with the particular solutions as admissible functions, and it has been widely used in engineering. Three crack models in Li et al. (Eng. Anal. Boundary Elements 2004;28:79-96;Trefftz and. Collocation Methods. WIT Publishers: Southampton, Boston, 2008) are considered, and the bounds of Cond-eff and the traditional condition number Cond are derived, to give the polynomial and the exponential growth rates, respectively. The stability analysis explains well the numerical experiments. Hence, the new Cond-ciï is more advantageous than Cond. Besides since the bounds of Cond-eff and Cond involve the estimation of the minimal singular value 6_min of the discrete matrix F, and since the estimation of 6_min is challenging and difficult, the proof for lower bounds of 6_min in this paper is important and intriguing. © 2008 John Wiley & Sons, Ltd.

关键词： Biharmonie equation Boundary approximation method Collocation trefftz methods Effective condition number Singular problems Stability analysis

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