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AUGMENTED COMPLEX MATRIX FACTORISATION
"... A novel framework for the factorisation of complexvalued data is derived using recent developments in complex statistics. Unlike existing factorisation tools the algorithms can cater for noncircularity of the input a necessary feature in applications for modelling realworld data. It is furthermo ..."
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. It is furthermore shown how the framework can be constrained to incorporate nonnegativity, helping generate results which allow a more realistic interpretation. Simulations illustrate the usefulness and enhanced accuracy for modelling synthetic data and a mixture of acoustic stimuli. Index Terms — complex matrix
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 502 (0 self)
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divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 547 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
Capacity of a Mobile MultipleAntenna Communication Link in Rayleigh Flat Fading
"... We analyze a mobile wireless link comprising M transmitter and N receiver antennas operating in a Rayleigh flatfading environment. The propagation coefficients between every pair of transmitter and receiver antennas are statistically independent and unknown; they remain constant for a coherence int ..."
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Cited by 495 (22 self)
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interval of T symbol periods, after which they change to new independent values which they maintain for another T symbol periods, and so on. Computing the link capacity, associated with channel coding over multiple fading intervals, requires an optimization over the joint density of T M complex transmitted
Factoring wavelet transforms into lifting steps
 J. FOURIER ANAL. APPL
, 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
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Cited by 584 (8 self)
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. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is wellknown to algebraists (and expressed by the formula); it is also used in linear systems theory in the electrical engineering community. We
Consensus and cooperation in networked multiagent systems
 Proceedings of the IEEE
, 2007
"... Summary. This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An ove ..."
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Cited by 807 (4 self)
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. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems
Stable isotope labeling by amino acids in cell culture, SILAC, as a simple and accurate approach to expression proteomics
 Mol. Cell. Proteomics
, 2002
"... The abbreviations used are: SILAC: Stable isotope labeling by amino acids in cell culture, 2DE: two dimensional (isoelectric focusing/SDSPAGE) gel electrophoresis: ICATTM: isotopecoded affinity tag; MS: mass spectrometry; MALDITOF: matrix assisted laser desorption ionizationtime of flight; PMF: ..."
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Cited by 595 (23 self)
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The abbreviations used are: SILAC: Stable isotope labeling by amino acids in cell culture, 2DE: two dimensional (isoelectric focusing/SDSPAGE) gel electrophoresis: ICATTM: isotopecoded affinity tag; MS: mass spectrometry; MALDITOF: matrix assisted laser desorption ionizationtime of flight; PMF
Implementation of Cyclomatic Complexity Matrix
"... Abstract – Cyclomatic complexity (or conditional complexity) is a software metric (measurement). It directly measures the number of linearly independent paths through a program's source code. The concept, although not the method, is somewhat similar to that of general text complexity measured b ..."
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Abstract – Cyclomatic complexity (or conditional complexity) is a software metric (measurement). It directly measures the number of linearly independent paths through a program's source code. The concept, although not the method, is somewhat similar to that of general text complexity measured
Complex matrix decomposition and quadratic programming
, 2006
"... This paper studies the possibilities of the Linear Matrix Inequality (LMI) characterization of the matrix cones formed by nonnegative complex Hermitian quadratic functions over specific domains in the complex space. In its real case analog, such studies were conducted in Sturm and Zhang [11]. In thi ..."
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Cited by 59 (16 self)
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This paper studies the possibilities of the Linear Matrix Inequality (LMI) characterization of the matrix cones formed by nonnegative complex Hermitian quadratic functions over specific domains in the complex space. In its real case analog, such studies were conducted in Sturm and Zhang [11
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