The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Moritz Weber - One of the best experts on this subject based on the ideXlab platform.
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Intertwiner Spaces of Quantum Group Subrepresentations
Communications in Mathematical Physics, 2020Co-Authors: Daniel Gromada, Moritz WeberAbstract:We consider Compact Matrix quantum groups whose N -dimensional fundamental representation decomposes into an $$(N-1)$$ ( N - 1 ) -dimensional and a one-dimensional subrepresentation. Even if we know that the Compact Matrix quantum group associated to this $$(N-1)$$ ( N - 1 ) -dimensional subrepresentation is isomorphic to the given N -dimensional one, it is a priori not clear how the intertwiner spaces transform under this isomorphism. In the context of so-called easy and non-easy quantum groups, we are able to define a transformation of linear combinations of partitions and we explicitly describe the transformation of intertwiner spaces. As a side effect, this enables us to produce many new examples of non-easy quantum groups being isomorphic to easy quantum groups as Compact quantum groups but not as Compact Matrix quantum groups.
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New products and $\mathbb{Z}_2$-extensions of Compact Matrix quantum groups
arXiv: Quantum Algebra, 2019Co-Authors: Daniel Gromada, Moritz WeberAbstract:There are two very natural products of Compact Matrix quantum groups: the tensor product $G\times H$ and the free product $G*H$. We define a number of further products interpolating these two. We focus more in detail to the case where $G$ is an easy quantum group and $H=\hat{\mathbb{Z}}_2$, the dual of the cyclic group of order two. We study subgroups of $G*\hat{\mathbb{Z}}_2$ using categories of partitions with extra singletons. Closely related are many examples of non-easy bistochastic quantum groups.
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Generating linear categories of partitions
arXiv: Category Theory, 2019Co-Authors: Daniel Gromada, Moritz WeberAbstract:We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm and how we found new examples of Compact Matrix quantum groups (so called "non-easy" quantum groups) with it. This also led to further theoretical insights regarding the representation theory of such quantum groups. We interpret some of the new categories constructing anticommutative twists of quantum groups.
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Introduction to Compact (Matrix) quantum groups and Banica–Speicher (easy) quantum groups
Proceedings - Mathematical Sciences, 2017Co-Authors: Moritz WeberAbstract:This is a transcript of a series of eight lectures, 90 min each, held at IMSc Chennai, India from 5–24 January 2015. We give basic definitions, properties and examples of Compact quantum groups and Compact Matrix quantum groups such as the existence of a Haar state, the representation theory and Woronowicz’s quantum version of the Tannaka–Krein theorem. Building on this, we define Banica–Speicher quantum groups (also called easy quantum groups), a class of Compact Matrix quantum groups determined by the combinatorics of set partitions. We sketch the classification of Banica–Speicher quantum groups and we list some applications. We review the state-of-the-art regarding Banica–Speicher quantum groups and we list some open problems.
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introduction to Compact Matrix quantum groups and banica speicher easy quantum groups
Proceedings - Mathematical Sciences, 2017Co-Authors: Moritz WeberAbstract:This is a transcript of a series of eight lectures, 90 min each, held at IMSc Chennai, India from 5–24 January 2015. We give basic definitions, properties and examples of Compact quantum groups and Compact Matrix quantum groups such as the existence of a Haar state, the representation theory and Woronowicz’s quantum version of the Tannaka–Krein theorem. Building on this, we define Banica–Speicher quantum groups (also called easy quantum groups), a class of Compact Matrix quantum groups determined by the combinatorics of set partitions. We sketch the classification of Banica–Speicher quantum groups and we list some applications. We review the state-of-the-art regarding Banica–Speicher quantum groups and we list some open problems.
Piotr Podles - One of the best experts on this subject based on the ideXlab platform.
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Symmetries of quantum spaces. Subgroups and quotient spaces of quantumSU(2) andSO(3) groups
Communications in Mathematical Physics, 1995Co-Authors: Piotr PodlesAbstract:We prove that each action of a Compact Matrix quantum group on a Compact quantum space can be decomposed into irreducible representations of the group. We give the formula for the corresponding multiplicities in the case of the quotient quantum spaces. We describe the subgroups and the quotient spaces of quantum SU (2) and SO (3) groups.
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SYMMETRIES OF QUANTUM SPACES. SUBGROUPS AND QUOTIENT SPACES OF QUANTUM SU(2) AND SO(3) GROUPS
Communications in Mathematical Physics, 1995Co-Authors: Piotr PodlesAbstract:We prove that each action of a Compact Matrix quantum group on a Compact quantum space can be decomposed into irreducible representations of the group. We give the formula for the corresponding multiplicities in the case of the quotient quantum spaces. We describe the subgroups and the quotient spaces of quantumSU(2) andSO(3) groups.
Osamu Moriwaki - One of the best experts on this subject based on the ideXlab platform.
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Compact Matrix-Switch-Based Hierarchical Optical Path Cross-Connect with Colorless Waveband Add/Drop Ratio Restriction
IEICE Transactions on Communications, 2011Co-Authors: Ryosuke Hirako, Kiyo Ishii, Hiroshi Hasegawa, Ken-ichi Sato, Osamu MoriwakiAbstract:We propose a Compact Matrix-switch-based hierarchical optical cross-connect (HOXC) architecture that effectively handles the colorless waveband add/drop ratio restriction so as to realize switch scale reduction. In order to implement the colorless waveband add/drop function, we develop a wavelength MUX/DMUX that can be commonly used by different wavebands. We prove that the switch scale of the proposed HOXC is much smaller than that of conventional single-layer optical cross-connects (OXCs) and a typical HOXC. Furthermore, we introduce a prototype system based on the proposed architecture that utilizes integrated novel wavelength MUXs/DMUXs. Transmission experiments prove its technical feasibility.
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Compact Matrix switch based hierarchical optical path cross connect with colorless waveband add drop ratio restriction
IEICE Transactions on Communications, 2011Co-Authors: Ryosuke Hirako, Kiyo Ishii, Hiroshi Hasegawa, Ken-ichi Sato, Osamu MoriwakiAbstract:We propose a Compact Matrix-switch-based hierarchical optical cross-connect (HOXC) architecture that effectively handles the colorless waveband add/drop ratio restriction so as to realize switch scale reduction. In order to implement the colorless waveband add/drop function, we develop a wavelength MUX/DMUX that can be commonly used by different wavebands. We prove that the switch scale of the proposed HOXC is much smaller than that of conventional single-layer optical cross-connects (OXCs) and a typical HOXC. Furthermore, we introduce a prototype system based on the proposed architecture that utilizes integrated novel wavelength MUXs/DMUXs. Transmission experiments prove its technical feasibility.
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PAPER Special Section on Photonic Network Technologies in Terabit Network Era Compact Matrix-Switch-Based Hierarchical Optical Path Cross-Connect with Colorless Waveband Add/Drop Ratio Restriction
2011Co-Authors: Ryosuke Hirako, Hiroshi Hasegawa, Ken-ichi Sato, Osamu MoriwakiAbstract:SUMMARY We propose a Compact Matrix-switch-based hierarchical optical cross-connect (HOXC) architecture that effectively handles the colorless waveband add/drop ratio restriction so as to realize switch scale reduction. In order to implement the colorless waveband add/drop function, we develop a wavelength MUX/DMUX that can be commonly used by different wavebands. We prove that the switch scale of the proposed HOXC is much smaller than that of conventional single-layer optical cross-connects (OXCs) and a typical HOXC. Furthermore, we introduce a prototype system based on the proposed architecture that utilizes integrated novel wavelength MUXs/DMUXs. Transmission experiments prove its technical feasibility.
Christos Faloutsos - One of the best experts on this subject based on the ideXlab platform.
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less is more sparse graph mining with Compact Matrix decomposition
Statistical Analysis and Data Mining, 2008Co-Authors: Jimeng Sun, Yinglian Xie, Hui Zhang, Christos FaloutsosAbstract:Given a large sparse graph, how can we find patterns and anomalies? Several important applications can be modeled as large sparse graphs, e.g., network traffic monitoring, research citation network analysis, social network analysis, and financial transactions. Low-rank decompositions, such as singular value decomposition (SVD) and CUR, are powerful techniques for revealing latent-hidden variables and associated patterns from high dimensional data. However, those methods often ignore the sparsity property of the graph, and hence usually incur too high memory and computational cost to be practical. We propose a novel method, the Compact Matrix Decomposition (CMD), to compute sparse low-rank approximations. CMD dramatically reduces both the computation cost and the space requirements over existing decomposition methods singular value decomposition (SVD) and CUR. Using CMD as the key building block, we further propose procedures to efficiently construct and analyze dynamic graphs from real-time application data. We provide theoretical guarantee for our methods, and present results on two real, large datasets, one on network flow data (100 GB trace of 22K hosts over one month) and one on DBLP (200 MB over 25 years). We show that CMD is often an order of magnitude more efficient than the state of the art (SVD and CUR): it is over 10X faster, but requires less than 1-10 of the space, for the same reconstruction accuracy. Finally, we demonstrate how CMD is used for detecting anomalies and monitoring time-evolving graphs, in which it successfully detects worm-like hierarchical scanning patterns in real network data. Copyright © 2007 Wiley Periodicals, Inc., A Wiley Company Statistical Analy Data Mining 1: 000-000, 2007
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less is more Compact Matrix decomposition for large sparse graphs
SIAM International Conference on Data Mining, 2007Co-Authors: Jimeng Sun, Yinglian Xie, Hui Zhang, Christos FaloutsosAbstract:Given a large sparse graph, how can we find patterns and anomalies? Several important applications can be modeled as large sparse graphs, e.g., network traffic monitoring, research citation network analysis, social network analysis, and regulatory networks in genes. Low rank decompositions, such as SVD and CUR, are powerful techniques for revealing latent/hidden variables and associated patterns from high dimensional data. However, those methods often ignore the sparsity property of the graph, and hence usually incur too high memory and computational cost to be practical. We propose a novel method, the Compact Matrix Decomposition (CMD), to compute sparse low rank approximations. CMD dramatically reduces both the computation cost and the space requirements over existing decomposition methods (SVD, CUR). Using CMD as the key building block, we further propose procedures to efficiently construct and analyze dynamic graphs from real-time application data. We provide theoretical guarantee for our methods, and present results on two real, large datasets, one on network flow data (100GB trace of 22K hosts over one month) and one on DBLP (200MB over 25 years). We show that CMD is often an order of magnitude more efficient than the state of the art (SVD and CUR): it is over 10X faster, but requires less than 1/10 of the space, for the same reconstruction accuracy. Finally, we demonstrate how CMD is used for detecting anomalies and monitoring timeevolving graphs, in which it successfully detects worm-like hierarchical scanning patterns in real network data.
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SDM - Less is More: Compact Matrix Decomposition for Large Sparse Graphs.
2007Co-Authors: Jimeng Sun, Yinglian Xie, Hui Zhang, Christos FaloutsosAbstract:Given a large sparse graph, how can we find patterns and anomalies? Several important applications can be modeled as large sparse graphs, e.g., network traffic monitoring, research citation network analysis, social network analysis, and regulatory networks in genes. Low rank decompositions, such as SVD and CUR, are powerful techniques for revealing latent/hidden variables and associated patterns from high dimensional data. However, those methods often ignore the sparsity property of the graph, and hence usually incur too high memory and computational cost to be practical. We propose a novel method, the Compact Matrix Decomposition (CMD), to compute sparse low rank approximations. CMD dramatically reduces both the computation cost and the space requirements over existing decomposition methods (SVD, CUR). Using CMD as the key building block, we further propose procedures to efficiently construct and analyze dynamic graphs from real-time application data. We provide theoretical guarantee for our methods, and present results on two real, large datasets, one on network flow data (100GB trace of 22K hosts over one month) and one on DBLP (200MB over 25 years). We show that CMD is often an order of magnitude more efficient than the state of the art (SVD and CUR): it is over 10X faster, but requires less than 1/10 of the space, for the same reconstruction accuracy. Finally, we demonstrate how CMD is used for detecting anomalies and monitoring timeevolving graphs, in which it successfully detects worm-like hierarchical scanning patterns in real network data.
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the 2007 SIAM International Conference on Data Mining (SDM), Minneapolis, MN - Less is More: Compact Matrix Decomposition for Large Sparse Graphs (Best research paper award!)
2007Co-Authors: Jimeng Sun, Yinglian Xie, Hui Zhang, Christos FaloutsosAbstract:Given a large sparse graph, how can we find patterns and anomalies? Several important applications can be modeled as large sparse graphs, e.g., network traffic monitoring, research citation network analysis, social network analysis, and regulatory networks in genes. Low rank decompositions, such as SVD and CUR, are powerful techniques for revealing latent/hidden variables and associated patterns from high dimensional data. However, those methods often ignore the sparsity property of the graph, and hence usually incur too high memory and computational cost to be practical. We propose a novel method, the Compact Matrix Decomposition (CMD), to compute sparse low rank approximations. CMD dramatically reduces both the computation cost and the space requirements over existing decomposition methods (SVD, CUR). Using CMD as the key building block, we further propose procedures to efficiently construct and analyze dynamic graphs from real-time application data. We provide theoretical guarantee for our methods, and present results on two real, large datasets, one on network flow data (100GB trace of 22K hosts over one month) and one on DBLP (200MB over 25 years). We show that CMD is often an order of magnitude more efficient than the state of the art (SVD and CUR): it is over 10X faster, but requires less than 1/10 of the space, for the same reconstruction accuracy. Finally, we demonstrate how CMD is used for detecting anomalies and monitoring timeevolving graphs, in which it successfully detects worm-like hierarchical scanning patterns in real network data.
Ryosuke Hirako - One of the best experts on this subject based on the ideXlab platform.
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Compact Matrix-Switch-Based Hierarchical Optical Path Cross-Connect with Colorless Waveband Add/Drop Ratio Restriction
IEICE Transactions on Communications, 2011Co-Authors: Ryosuke Hirako, Kiyo Ishii, Hiroshi Hasegawa, Ken-ichi Sato, Osamu MoriwakiAbstract:We propose a Compact Matrix-switch-based hierarchical optical cross-connect (HOXC) architecture that effectively handles the colorless waveband add/drop ratio restriction so as to realize switch scale reduction. In order to implement the colorless waveband add/drop function, we develop a wavelength MUX/DMUX that can be commonly used by different wavebands. We prove that the switch scale of the proposed HOXC is much smaller than that of conventional single-layer optical cross-connects (OXCs) and a typical HOXC. Furthermore, we introduce a prototype system based on the proposed architecture that utilizes integrated novel wavelength MUXs/DMUXs. Transmission experiments prove its technical feasibility.
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Compact Matrix switch based hierarchical optical path cross connect with colorless waveband add drop ratio restriction
IEICE Transactions on Communications, 2011Co-Authors: Ryosuke Hirako, Kiyo Ishii, Hiroshi Hasegawa, Ken-ichi Sato, Osamu MoriwakiAbstract:We propose a Compact Matrix-switch-based hierarchical optical cross-connect (HOXC) architecture that effectively handles the colorless waveband add/drop ratio restriction so as to realize switch scale reduction. In order to implement the colorless waveband add/drop function, we develop a wavelength MUX/DMUX that can be commonly used by different wavebands. We prove that the switch scale of the proposed HOXC is much smaller than that of conventional single-layer optical cross-connects (OXCs) and a typical HOXC. Furthermore, we introduce a prototype system based on the proposed architecture that utilizes integrated novel wavelength MUXs/DMUXs. Transmission experiments prove its technical feasibility.
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PAPER Special Section on Photonic Network Technologies in Terabit Network Era Compact Matrix-Switch-Based Hierarchical Optical Path Cross-Connect with Colorless Waveband Add/Drop Ratio Restriction
2011Co-Authors: Ryosuke Hirako, Hiroshi Hasegawa, Ken-ichi Sato, Osamu MoriwakiAbstract:SUMMARY We propose a Compact Matrix-switch-based hierarchical optical cross-connect (HOXC) architecture that effectively handles the colorless waveband add/drop ratio restriction so as to realize switch scale reduction. In order to implement the colorless waveband add/drop function, we develop a wavelength MUX/DMUX that can be commonly used by different wavebands. We prove that the switch scale of the proposed HOXC is much smaller than that of conventional single-layer optical cross-connects (OXCs) and a typical HOXC. Furthermore, we introduce a prototype system based on the proposed architecture that utilizes integrated novel wavelength MUXs/DMUXs. Transmission experiments prove its technical feasibility.
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Development of Compact hierarchical optical path cross-connect prototype utilizing integrated colorless multi/demultiplexers
36th European Conference and Exhibition on Optical Communication, 2010Co-Authors: Ryosuke Hirako, Kiyo Ishii, Hiroshi Hasegawa, Ken-ichi SatoAbstract:We introduce a Compact Matrix-switch-based hierarchical optical path cross-connect prototype system that exploits integrated colorless waveband multi/demultiplexers. Its performance ensures cost-effective networks can be created.