This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient ...algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part.
Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied ...mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations.
Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.
This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real ...numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices.
This study aimed to determine possible association of eight polymorphisms of seven MMP genes with essential hypertension (EH) in a Caucasian population of Central Russia. Eight SNPs of the MMP1, ...MMP2, MMP3, MMP7, MMP8, MMP9, and MMP12 genes and their gene-gene (epistatic) interactions were analyzed for association with EH in a cohort of 939 patients and 466 controls using logistic regression and assuming additive, recessive, and dominant genetic models. The functional significance of the polymorphisms associated with EH and 114 variants linked to them (r
≥ 0.8) was analyzed in silico. Allele G of rs11568818 MMP7 was associated with EH according to all three genetic models (OR = 0.58-0.70, p
= 0.01-0.03). The above eight SNPs were associated with the disorder within 12 most significant epistatic models (OR = 1.49-1.93, p
< 0.02). Loci rs1320632 MMP8 and rs11568818 MMP7 contributed to the largest number of the models (12 and 10, respectively). The EH-associated loci and 114 SNPs linked to them had non-synonymous, regulatory, and eQTL significance for 15 genes, which contributed to the pathways related to metalloendopeptidase activity, collagen degradation, and extracellular matrix disassembly. In summary, eight studied SNPs of MMPs genes were associated with EH in the Caucasian population of Central Russia.
Extracellular matrix (ECM) remodeling is necessary for a health adipose tissue (AT) expansion and also has a role during weight loss. We investigate the ECM alteration during weight cycling (WC) in ...mice and the role of matrix metalloproteinases (MMPs) was assessed using GM6001, an MMP inhibitor, during weight loss (WL). Obesity was induced in mice by a high-fat diet. Obese mice were subject to caloric restriction for WL followed by reintroduction to high-fat diet for weight regain (WR), resulting in a WC protocol. In addition, mice were treated with GM6001 during WL period and the effects were observed after WR. Activity and expression of MMPs was intense during WL. MMP inhibition during WL results in inflammation and collagen content reduction. MMP inhibition during WL period interferes with the period of subsequent expansion of AT resulting in improvements in local inflammation and systemic metabolic alterations induced by obesity. Our results suggest that MMPs inhibition could be an interesting target to improve adipose tissue inflammation during WL and to support weight cyclers.
•Weight loss induces an intense MMP activity on adipose tissue.•The intense tissue remodeling is associated with adipose tissue inflammation.•GM6001 inhibit MMPs and inflammation during weight loss.•MMPs inhibition during weight loss modifies adipose tissue during weight regain.•Metabolic and inflammatory improvements were observed after weight regain.
This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, ...including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems.
The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.
The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.
This book has been adopted as a textbook at the following universities:
University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA
This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry and numerical analysis. It consists of seven chapters that are loosely connected ...and interdependent. The choice of the topics is very personal and reflects the subjects that the was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume is also devoted to various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of non-negative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operations research, physics and statistics.Contents:Domains, Modules and MatricesCanonical Forms for SimilarityFunctions of Matrices and Analytic SimilarityInner Product SpacesElements of Multilinear AlgebraNon-Negative MatricesVarious TopicsReadership: Graduate students, researchers in mathematics, applied mathematics, statistics, computer science, bioinformatics, engineering, and physics.Keywords:Analytic Similarity of Matrices;Application to Cellular Communication;Companion Matrix;Cones;Convexity;CUR-Approximation;Determinants;Equivalence of Matrices;Functions of Matrices;Graphs;Inequalities;Inner Product Spaces;Inverse Eigenvalue Problems;Low Rank Approximation;Matrix Exponents;Max-Min Characterization of Eigenvalues;Majorization;Markov Chains;Max-Min Characterization of Eigenvalues;Moore-Penrose Inverse;Normal Forms of Matrices;Norms;Pencils of Matrices;Perturbations;Positive Definite Operators and Matrices;Property L;Perron-Frobenius Theorem;Rellich's Theorem;Singular Value Decomposition;Sparse Bases;Spectral Functions;Strict Similarity of Pencils;Symmetric and Hermitian Forms;Tensor ProductsKey Features:Includes a number of selected related topics in matrix theory that the was actively working on for 40 yearsIncludes many results that are not available in the books that are currently on the market
An innovative noniterative approach based on the matrix enhancement and matrix pencil (MEMP) is proposed for the synthesis of arbitrary sparse planar arrays. In this study, the estimation of array ...parameters is recast as a 2-D pole extraction problem, and the number of array elements is minimized by the reduced rank processing. Subsequently, the Hankel matrix decomposition algorithm is exploited to accelerate the singular value decomposition (SVD) of the Hankel matrix constructed by the desired pattern samples, which conquers the restriction on the matrix dimension of the sampled Hankel matrix with the increasing of the number of array elements. The MEMP approach is further extended to the synthesis of shaped-beam patterns by using the forward-backward matrix enhancement and matrix pencil method (FBMEMP). A set of representative numerical experiments is provided to validate the effectiveness and advantages of the proposed method.
The extracellular matrix (ECM) is a macromolecules network, in which the most abundant molecule is collagen. This protein in triple helical conformation is highly resistant to proteinases ...degradation, the only enzymes capable of degrading the collagen are matrix metalloproteinases (MMPs). This resistance and maintenance of collagen, and consequently of ECM, is involved in several biological processes and it must be strictly regulated by endogenous inhibitors (TIMPs). The deregulation of MMPs activity leads to development of numerous diseases. This review shows MMPs complexity.
The matrix metalloproteinases (MMP) are a family of proteolytic enzymes that degrade multiple components of the extracellular matrix. A large body of experimental and clinical evidence has implicated ...MMPs in tumor invasion, neoangiogenesis, and metastasis, and therefore they represent ideal pharmacologic targets for cancer therapy. From the 1990s to early 2000s, synthetic inhibitors of MMPs (MMPI) were studied in various cancer types. Unexpectedly, despite strongly promising preclinical data, all trials were unsuccessful in reducing tumor burden or improving overall survival; in addition, MMPIs had unforeseen, severe side effects. Two main reasons can explain the failure of MMPIs in clinical trials. It has now become apparent that some MMPs have antitumor effects; therefore, the broad-spectrum MMPIs used in the initial trials might block these MMPs and result in tumor progression. In addition, although MMPs are involved in the early stages of tumor progression, MMPIs were tested in patients with advanced disease, beyond the stage when these compounds could be effective. As more specific MMPIs are now available, MMP targeting could be reconsidered for cancer therapy; however, new trials should be designed to test their antimetastatic properties in early-stage tumors, and endpoints should focus on parameters other than decreasing metastatic tumor burden.
.
PDF
