Results 101 to 110 of about 41,020 (249)
Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences
Entropy, 2015 This work reviews and extends a family of log-determinant (log-det) divergences for symmetric positive definite (SPD) matrices and discusses their fundamental properties.
Andrzej Cichocki +2 more
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Positive semidefinite completions of partial Hermitian matrices
Linear Algebra and its Applications, 1992 AbstractWe classify the ranks of positive semidefinite completions of Hermitian band matrices and other partially specified Hermitian matrices with chordal graphs and specified main diagonals. Completing a partially specified matrix means filling in the unspecified entries.
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Breaking the Complexity of Cancer Using Computational Transcriptomic Network Biology
WIREs Computational Statistics, Volume 17, Issue 2, June 2025.ABSTRACT While the landscapes of cancer mutations have been mostly clarified, in this study, we focused on the connective aggregates between mutations and phenotypes, named here as “gene transcriptomic networks,” aiming to survey computational network biology processes that have achieved significant results in cancer biology.
Heewon Park, Satoru Miyano
wiley +1 more source
Positive Semidefinite Metric Learning with Boosting
, 2009 The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \BoostMetric, for learning a Mahalanobis distance metric.
Hengel, Anton van den +3 more
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Functions Operating on Positive Semidefinite Quaternionic Matrices
Monatshefte f�r Mathematik, 2001 We study functions \(\) on the quaternionic unit ball \(\) which operate on positive semidefinite matrices in the sense that \(\) is positive semidefinite whenever \(\) is a positive semidefinite square matrix with entries \(\).
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Gangster operators and invincibility of positive semidefinite matrices
Linear Algebra and its Applications, 2010 AbstractDecrease in absolute value of a symmetrically placed pair of off diagonal entries need not preserve positive definiteness of an n×n matrix, n⩾3. A gangster operator is one that replaces some such pairs by 0s. Circumstances in which gangster operators preserve positive definiteness are investigated.
Timothy Ferguson, Charles R. Johnson
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The small‐scale limit of magnitude and the one‐point property
Bulletin of the London Mathematical Society, Volume 57, Issue 6, Page 1841-1855, June 2025.Abstract The magnitude of a metric space is a real‐valued function whose parameter controls the scale of the metric. A metric space is said to have the one‐point property if its magnitude converges to 1 as the space is scaled down to a point. Not every finite metric space has the one‐point property: to date, exactly one example has been found of a ...
Emily Roff, Masahiko Yoshinaga
wiley +1 more source
Extremal positive semidefinite doubly stochastic matrices
Linear Algebra and its Applications, 1991 AbstractLet Kn denote the closed convex set of all n-by-n positive semidefinite doubly stochastic matrices. The extreme points of Kn have not been determined. In this paper, we find some extreme points. Our results are based primarily on rank and sparsity pattern. We have a complete classification in the case n=4.
Steve Pierce, Bob Grone
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On a higher dimensional worm domain and its geometric properties
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract We construct new three‐dimensional variants of the classical Diederich–Fornæss worm domain. We show that they are smoothly bounded, pseudoconvex, and have nontrivial Nebenhülle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices.
Steven G. Krantz +2 more
wiley +1 more source
From ƒ-Divergence to Quantum Quasi-Entropies and Their Use
Entropy, 2010 Csiszár’s ƒ-divergence of two probability distributions was extended to the quantum case by the author in 1985. In the quantum setting, positive semidefinite matrices are in the place of probability distributions and the quantum generalization is called ...
Dénes Petz
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