Book•
Matrix computations (3rd ed.)
01 Nov 1996-
About: The article was published on 1996-11-01 and is currently open access. It has received 8608 citations till now. The article focuses on the topics: Matrix (mathematics).
Citations
More filters
TL;DR: Following the discussion of interference temperature as a new metric for the quantification and management of interference, the paper addresses three fundamental cognitive tasks: radio-scene analysis, channel-state estimation and predictive modeling, and the emergent behavior of cognitive radio.
Abstract: Cognitive radio is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spectrum. The cognitive radio, built on a software-defined radio, is defined as an intelligent wireless communication system that is aware of its environment and uses the methodology of understanding-by-building to learn from the environment and adapt to statistical variations in the input stimuli, with two primary objectives in mind: /spl middot/ highly reliable communication whenever and wherever needed; /spl middot/ efficient utilization of the radio spectrum. Following the discussion of interference temperature as a new metric for the quantification and management of interference, the paper addresses three fundamental cognitive tasks. 1) Radio-scene analysis. 2) Channel-state estimation and predictive modeling. 3) Transmit-power control and dynamic spectrum management. This work also discusses the emergent behavior of cognitive radio.
12,172 citations
01 Jan 2006
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.
6,340 citations
Cites methods from "Matrix computations (3rd ed.)"
...This may be performed using classical linear algebra techniques, such as singular value decomposition (SVD) [401, 961]....
[...]
...This can be solved using linear algebra techniques, such as singular value decomposition (SVD) [401, 961], to compute an orthonormal basis for the tangent space at q....
[...]
...If k < n, then n− k components of q̇ can be chosen independently, and then the remaining k are computed to satisfy the Pfaffian constraints (this can be accomplished using linear algebra techniques such as singular value decomposition [401, 961])....
[...]
TL;DR: Three algorithms for aligning multiple replicate analyses of the same data set using the computer program CLUMPP (CLUster Matching and Permutation Program) are described.
Abstract: Motivation: Clustering of individuals into populations on the basis of multilocus genotypes is informative in a variety of settings. In population-genetic clustering algorithms, such as BAPS, STRUCTURE and TESS, individual multilocus genotypes are partitioned over a set of clusters, often using unsupervised approaches that involve stochastic simulation. As a result, replicate cluster analyses of the same data may produce several distinct solutions for estimated cluster membership coefficients, even though the same initial conditions were used. Major differences among clustering solutions have two main sources: (1) ‘label switching’ of clusters across replicates, caused by the arbitrary way in which clusters in an unsupervised analysis are labeled, and (2) ‘genuine multimodality,’ truly distinct solutions across replicates. Results: To facilitate the interpretation of population-genetic clustering results, we describe three algorithms for aligning multiple replicate analyses of the same data set. We have implemented these algorithms in the computer program CLUMPP (CLUster Matching and Permutation Program). We illustrate the use of CLUMPP by aligning the cluster membership coefficients from 100 replicate cluster analyses of 600 chickens from 20 different breeds. Availability: CLUMPP is freely available at http://rosenberglab.
5,474 citations
TL;DR: It is concluded that the EzTaxon-e database provides a useful taxonomic backbone for the identification of cultured and uncultured prokaryotes and offers a valuable means of communication among microbiologists who routinely encounter taxonomically novel isolates.
Abstract: Despite recent advances in commercially optimized identification systems, bacterial identification remains a challenging task in many routine microbiological laboratories, especially in situations where taxonomically novel isolates are involved. The 16S rRNA gene has been used extensively for this task when coupled with a well-curated database, such as EzTaxon, containing sequences of type strains of prokaryotic species with validly published names. Although the EzTaxon database has been widely used for routine identification of prokaryotic isolates, sequences from uncultured prokaryotes have not been considered. Here, the next generation database, named EzTaxon-e, is formally introduced. This new database covers not only species within the formal nomenclatural system but also phylotypes that may represent species in nature. In addition to an identification function based on Basic Local Alignment Search Tool (blast) searches and pairwise global sequence alignments, a new objective method of assessing the degree of completeness in sequencing is proposed. All sequences that are held in the EzTaxon-e database have been subjected to phylogenetic analysis and this has resulted in a complete hierarchical classification system. It is concluded that the EzTaxon-e database provides a useful taxonomic backbone for the identification of cultured and uncultured prokaryotes and offers a valuable means of communication among microbiologists who routinely encounter taxonomically novel isolates. The database and its analytical functions can be found at http://eztaxon-e.ezbiocloud.net/.
4,974 citations
TL;DR: There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed.
Abstract: We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pair-wise symmetric tensors.
4,101 citations