Volterra-Hamilton Models in the Ecology and Evolution of Colonial Organisms

Volterra-Hamilton Models in the Ecology and Evolution of Colonial Organisms

Author: Peter L. Antonelli

Publisher: World Scientific

Published: 1996

Total Pages: 227

ISBN-13: 9810224508

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This book begins with the modeling of evolutionary constraints on morphological diversity in ecology and then extends to development and evolution. The authors have used tractable, traditional models and mathematics, and carefully linked traditional ecological equations with production and consumption. This book contains new, more powerful models and has applied them, for example, in chemical ecology of coral reef. The production space serves as an appropriate background space from which the environmentally induced curvature in the allometric relations of superorganisms such as siphonophores, polymorphic bryozoans and ants can be measured. Projective differential geometry is used to formula dynamical models of evolution by heterochrony and by symbiosis and a theory of stable and weakly chaotic production, important in ecology and in modeling the evolution of individuality is developed.


Book Synopsis Volterra-Hamilton Models in the Ecology and Evolution of Colonial Organisms by : Peter L. Antonelli

Download or read book Volterra-Hamilton Models in the Ecology and Evolution of Colonial Organisms written by Peter L. Antonelli and published by World Scientific. This book was released on 1996 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book begins with the modeling of evolutionary constraints on morphological diversity in ecology and then extends to development and evolution. The authors have used tractable, traditional models and mathematics, and carefully linked traditional ecological equations with production and consumption. This book contains new, more powerful models and has applied them, for example, in chemical ecology of coral reef. The production space serves as an appropriate background space from which the environmentally induced curvature in the allometric relations of superorganisms such as siphonophores, polymorphic bryozoans and ants can be measured. Projective differential geometry is used to formula dynamical models of evolution by heterochrony and by symbiosis and a theory of stable and weakly chaotic production, important in ecology and in modeling the evolution of individuality is developed.

Volterra-Hamilton Models in the Ecology and Evolution of Colonial Organisms

Volterra-Hamilton Models in the Ecology and Evolution of Colonial Organisms

Author: P L Antonelli

Publisher: World Scientific

Published: 1996-08-22

Total Pages: 228

ISBN-13: 9814499706

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This book begins with the modeling of evolutionary constraints on morphological diversity in ecology and then extends to development and evolution. The authors have used tractable, traditional models and mathematics, and carefully linked traditional ecological equations with production and consumption. This book contains new, more powerful models and has applied them, for example, in chemical ecology of coral reef. The production space serves as an appropriate background space from which the environmentally induced curvature in the allometric relations of superorganisms such as siphonophores, polymorphic bryozoans and ants can be measured. Projective differential geometry is used to formula dynamical models of evolution by heterochrony and by symbiosis and a theory of stable and weakly chaotic production, important in ecology and in modeling the evolution of individuality is developed. Contents:Simple Growth of Populations and IndividualsCompetitive Interactions between Two SpeciesMedawar's Growth Energy and Optimal ProductionPredation and Herbivory on Optimally Producing Terrestrial and Marine EcosystemsThe Differential Geometry of Production StabilityA Dynamical Theory of Heterochrony: Time-Sequencing Changes in Ecology, Evolution and DevelopmentAppendices: On the Fundamental Lemma of Variational CalculusFuzzy Differential Inclusions as Substitutes for Stochastic Differential Equations in Population BiologyNormal Coordinates and Log-BiomassReferencesSome Frequently Used FormulasIndex Readership: Students and researchers in biomathematics, biostatistics, ecology and invertebrate evolution. keywords:Ecology;Evolution;Colonial;Differential Geometry;Secondary Production;Chemicals For Defence;Second Order Equations(ODE's)


Book Synopsis Volterra-Hamilton Models in the Ecology and Evolution of Colonial Organisms by : P L Antonelli

Download or read book Volterra-Hamilton Models in the Ecology and Evolution of Colonial Organisms written by P L Antonelli and published by World Scientific. This book was released on 1996-08-22 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book begins with the modeling of evolutionary constraints on morphological diversity in ecology and then extends to development and evolution. The authors have used tractable, traditional models and mathematics, and carefully linked traditional ecological equations with production and consumption. This book contains new, more powerful models and has applied them, for example, in chemical ecology of coral reef. The production space serves as an appropriate background space from which the environmentally induced curvature in the allometric relations of superorganisms such as siphonophores, polymorphic bryozoans and ants can be measured. Projective differential geometry is used to formula dynamical models of evolution by heterochrony and by symbiosis and a theory of stable and weakly chaotic production, important in ecology and in modeling the evolution of individuality is developed. Contents:Simple Growth of Populations and IndividualsCompetitive Interactions between Two SpeciesMedawar's Growth Energy and Optimal ProductionPredation and Herbivory on Optimally Producing Terrestrial and Marine EcosystemsThe Differential Geometry of Production StabilityA Dynamical Theory of Heterochrony: Time-Sequencing Changes in Ecology, Evolution and DevelopmentAppendices: On the Fundamental Lemma of Variational CalculusFuzzy Differential Inclusions as Substitutes for Stochastic Differential Equations in Population BiologyNormal Coordinates and Log-BiomassReferencesSome Frequently Used FormulasIndex Readership: Students and researchers in biomathematics, biostatistics, ecology and invertebrate evolution. keywords:Ecology;Evolution;Colonial;Differential Geometry;Secondary Production;Chemicals For Defence;Second Order Equations(ODE's)

The Theory of Finslerian Laplacians and Applications

The Theory of Finslerian Laplacians and Applications

Author: P.L. Antonelli

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 305

ISBN-13: 9401152829

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Finslerian Laplacians have arisen from the demands of modelling the modern world. However, the roots of the Laplacian concept can be traced back to the sixteenth century. Its phylogeny and history are presented in the Prologue of this volume. The text proper begins with a brief introduction to stochastically derived Finslerian Laplacians, facilitated by applications in ecology, epidemiology and evolutionary biology. The mathematical ideas are then fully presented in section II, with generalizations to Lagrange geometry following in section III. With section IV, the focus abruptly shifts to the local mean-value approach to Finslerian Laplacians and a Hodge-de Rham theory is developed for the representation on real cohomology classes by harmonic forms on the base manifold. Similar results are proved in sections II and IV, each from different perspectives. Modern topics treated include nonlinear Laplacians, Bochner and Lichnerowicz vanishing theorems, Weitzenböck formulas, and Finslerian spinors and Dirac operators. The tools developed in this book will find uses in several areas of physics and engineering, but especially in the mechanics of inhomogeneous media, e.g. Cofferat continua. Audience: This text will be of use to workers in stochastic processes, differential geometry, nonlinear analysis, epidemiology, ecology and evolution, as well as physics of the solid state and continua.


Book Synopsis The Theory of Finslerian Laplacians and Applications by : P.L. Antonelli

Download or read book The Theory of Finslerian Laplacians and Applications written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finslerian Laplacians have arisen from the demands of modelling the modern world. However, the roots of the Laplacian concept can be traced back to the sixteenth century. Its phylogeny and history are presented in the Prologue of this volume. The text proper begins with a brief introduction to stochastically derived Finslerian Laplacians, facilitated by applications in ecology, epidemiology and evolutionary biology. The mathematical ideas are then fully presented in section II, with generalizations to Lagrange geometry following in section III. With section IV, the focus abruptly shifts to the local mean-value approach to Finslerian Laplacians and a Hodge-de Rham theory is developed for the representation on real cohomology classes by harmonic forms on the base manifold. Similar results are proved in sections II and IV, each from different perspectives. Modern topics treated include nonlinear Laplacians, Bochner and Lichnerowicz vanishing theorems, Weitzenböck formulas, and Finslerian spinors and Dirac operators. The tools developed in this book will find uses in several areas of physics and engineering, but especially in the mechanics of inhomogeneous media, e.g. Cofferat continua. Audience: This text will be of use to workers in stochastic processes, differential geometry, nonlinear analysis, epidemiology, ecology and evolution, as well as physics of the solid state and continua.

Fundamentals of Finslerian Diffusion with Applications

Fundamentals of Finslerian Diffusion with Applications

Author: P.L. Antonelli

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 208

ISBN-13: 9401148244

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The erratic motion of pollen grains and other tiny particles suspended in liquid is known as Brownian motion, after its discoverer, Robert Brown, a botanist who worked in 1828, in London. He turned over the problem of why this motion occurred to physicists who were investigating kinetic theory and thermodynamics; at a time when the existence of molecules had yet to be established. In 1900, Henri Poincare lectured on this topic to the 1900 International Congress of Physicists, in Paris [Wic95]. At this time, Louis Bachelier, a thesis student of Poincare, made a monumental breakthrough with his Theory of Stock Market Fluctuations, which is still studied today, [Co064]. Norbert Wiener (1923), who was first to formulate a rigorous concept of the Brownian path, is most often cited by mathematicians as the father of the subject, while physicists will cite A. Einstein (1905) and M. Smoluchowski. Both considered Markov diffusions and realized that Brownian behaviour nd could be formulated in terms of parabolic 2 order linear p. d. e. 'so Further more, from this perspective, the covariance of changes in position could be allowed to depend on the position itself, according to the invariant form of the diffusion introduced by Kolmogorov in 1937, [KoI37]. Thus, any time homogeneous Markov diffusion could be written in terms of the Laplacian, intrinsically given by the symbol (covariance) of the p. d. e. , plus a drift vec tor. The theory was further advanced in 1949, when K.


Book Synopsis Fundamentals of Finslerian Diffusion with Applications by : P.L. Antonelli

Download or read book Fundamentals of Finslerian Diffusion with Applications written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The erratic motion of pollen grains and other tiny particles suspended in liquid is known as Brownian motion, after its discoverer, Robert Brown, a botanist who worked in 1828, in London. He turned over the problem of why this motion occurred to physicists who were investigating kinetic theory and thermodynamics; at a time when the existence of molecules had yet to be established. In 1900, Henri Poincare lectured on this topic to the 1900 International Congress of Physicists, in Paris [Wic95]. At this time, Louis Bachelier, a thesis student of Poincare, made a monumental breakthrough with his Theory of Stock Market Fluctuations, which is still studied today, [Co064]. Norbert Wiener (1923), who was first to formulate a rigorous concept of the Brownian path, is most often cited by mathematicians as the father of the subject, while physicists will cite A. Einstein (1905) and M. Smoluchowski. Both considered Markov diffusions and realized that Brownian behaviour nd could be formulated in terms of parabolic 2 order linear p. d. e. 'so Further more, from this perspective, the covariance of changes in position could be allowed to depend on the position itself, according to the invariant form of the diffusion introduced by Kolmogorov in 1937, [KoI37]. Thus, any time homogeneous Markov diffusion could be written in terms of the Laplacian, intrinsically given by the symbol (covariance) of the p. d. e. , plus a drift vec tor. The theory was further advanced in 1949, when K.

Proc. of the Third Brazilian Symp. on Mathematical and Computational Biology - v2

Proc. of the Third Brazilian Symp. on Mathematical and Computational Biology - v2

Author:

Publisher: Editora E-papers

Published:

Total Pages: 392

ISBN-13: 8587922874

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Book Synopsis Proc. of the Third Brazilian Symp. on Mathematical and Computational Biology - v2 by :

Download or read book Proc. of the Third Brazilian Symp. on Mathematical and Computational Biology - v2 written by and published by Editora E-papers. This book was released on with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Models of Tumor Latency and Their Biostatistical Applications

Stochastic Models of Tumor Latency and Their Biostatistical Applications

Author: Andrej Yu Yakovlev

Publisher: World Scientific

Published: 1996

Total Pages: 287

ISBN-13: 9810218311

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This research monograph discusses newly developed mathematical models and methods that provide biologically meaningful inferences from data on cancer latency produced by follow-up and discrete surveillance studies. Methods for designing optimal strategies of cancer surveillance are systematically presented for the first time in this book. It offers new approaches to the stochastic description of tumor latency, employs biologically-based models for making statistical inference from data on tumor recurrence and also discusses methods of statistical analysis of data resulting from discrete surveillance strategies. It also offers insight into the role of prognostic factors based on the interpretation of their effects in terms of parameters endowed with biological meaning, as well as methods for designing optimal schedules of cancer screening and surveillance. Last but not least, it discusses survival models allowing for cure rates and the choice of optimal treatment based on covariate information, and presents numerous examples of real data analysis.


Book Synopsis Stochastic Models of Tumor Latency and Their Biostatistical Applications by : Andrej Yu Yakovlev

Download or read book Stochastic Models of Tumor Latency and Their Biostatistical Applications written by Andrej Yu Yakovlev and published by World Scientific. This book was released on 1996 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph discusses newly developed mathematical models and methods that provide biologically meaningful inferences from data on cancer latency produced by follow-up and discrete surveillance studies. Methods for designing optimal strategies of cancer surveillance are systematically presented for the first time in this book. It offers new approaches to the stochastic description of tumor latency, employs biologically-based models for making statistical inference from data on tumor recurrence and also discusses methods of statistical analysis of data resulting from discrete surveillance strategies. It also offers insight into the role of prognostic factors based on the interpretation of their effects in terms of parameters endowed with biological meaning, as well as methods for designing optimal schedules of cancer screening and surveillance. Last but not least, it discusses survival models allowing for cure rates and the choice of optimal treatment based on covariate information, and presents numerous examples of real data analysis.

Handbook of Finsler geometry. 1 (2003)

Handbook of Finsler geometry. 1 (2003)

Author: Peter L. Antonelli

Publisher: Springer Science & Business Media

Published: 2003

Total Pages: 760

ISBN-13: 9781402015557

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There are several mathematical approaches to Finsler Geometry, all of which are contained and expounded in this comprehensive Handbook. The principal bundles pathway to state-of-the-art Finsler Theory is here provided by M. Matsumoto. His is a cornerstone for this set of essays, as are the articles of R. Miron (Lagrange Geometry) and J. Szilasi (Spray and Finsler Geometry). After studying either one of these, the reader will be able to understand the included survey articles on complex manifolds, holonomy, sprays and KCC-theory, symplectic structures, Legendre duality, Hodge theory and Gauss-Bonnet formulas. Finslerian diffusion theory is presented by its founders, P. Antonelli and T. Zastawniak. To help with calculations and conceptualizations, a CD-ROM containing the software package FINSLER, based on MAPLE, is included with the book.


Book Synopsis Handbook of Finsler geometry. 1 (2003) by : Peter L. Antonelli

Download or read book Handbook of Finsler geometry. 1 (2003) written by Peter L. Antonelli and published by Springer Science & Business Media. This book was released on 2003 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are several mathematical approaches to Finsler Geometry, all of which are contained and expounded in this comprehensive Handbook. The principal bundles pathway to state-of-the-art Finsler Theory is here provided by M. Matsumoto. His is a cornerstone for this set of essays, as are the articles of R. Miron (Lagrange Geometry) and J. Szilasi (Spray and Finsler Geometry). After studying either one of these, the reader will be able to understand the included survey articles on complex manifolds, holonomy, sprays and KCC-theory, symplectic structures, Legendre duality, Hodge theory and Gauss-Bonnet formulas. Finslerian diffusion theory is presented by its founders, P. Antonelli and T. Zastawniak. To help with calculations and conceptualizations, a CD-ROM containing the software package FINSLER, based on MAPLE, is included with the book.

Towards a Mathematical Theory of Complex Biological Systems

Towards a Mathematical Theory of Complex Biological Systems

Author: C. Bianca

Publisher: World Scientific

Published: 2011

Total Pages: 227

ISBN-13: 9814340545

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This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy.The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, cellular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.


Book Synopsis Towards a Mathematical Theory of Complex Biological Systems by : C. Bianca

Download or read book Towards a Mathematical Theory of Complex Biological Systems written by C. Bianca and published by World Scientific. This book was released on 2011 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy.The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, cellular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.

Towards a Mathematical Theory of Complex Biological Systems

Towards a Mathematical Theory of Complex Biological Systems

Author: C Bianca

Publisher: World Scientific

Published: 2011-01-12

Total Pages: 228

ISBN-13: 9814460974

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This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy. The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, cellular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling. Contents:Looking for a Mathematical Theory of Biological SystemsOn the Complexity of Biological SystemsImmune System, Wound Healing Process, and System Biology:The Immune System: A Phenomenological OverviewWound Healing Process and Organ RepairFrom Levels of Biological Organization to System BiologyMathematical Tools:Mathematical Tools and StructuresMultiscale Modeling: Linking Molecular, Cellular, and Tissues ScalesApplications and Research Perspectives:A Model for the Malign Keloid Formation and Immune System CompetitionMacroscopic Models of Chemotaxis by KTAP Asymptotic MethodsLooking Ahead Readership: Researchers in mathematical modeling and biological systems. Keywords:Mathematical Theory;Biological Systems;SubsystemKey Features:Provides a new conceptual background to applied mathematicians involved in the challenging research field of living systems, and specifically biology systemsGives more accurate ODE, cellular-automata, and continuum models from the biological point of view


Book Synopsis Towards a Mathematical Theory of Complex Biological Systems by : C Bianca

Download or read book Towards a Mathematical Theory of Complex Biological Systems written by C Bianca and published by World Scientific. This book was released on 2011-01-12 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy. The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, cellular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling. Contents:Looking for a Mathematical Theory of Biological SystemsOn the Complexity of Biological SystemsImmune System, Wound Healing Process, and System Biology:The Immune System: A Phenomenological OverviewWound Healing Process and Organ RepairFrom Levels of Biological Organization to System BiologyMathematical Tools:Mathematical Tools and StructuresMultiscale Modeling: Linking Molecular, Cellular, and Tissues ScalesApplications and Research Perspectives:A Model for the Malign Keloid Formation and Immune System CompetitionMacroscopic Models of Chemotaxis by KTAP Asymptotic MethodsLooking Ahead Readership: Researchers in mathematical modeling and biological systems. Keywords:Mathematical Theory;Biological Systems;SubsystemKey Features:Provides a new conceptual background to applied mathematicians involved in the challenging research field of living systems, and specifically biology systemsGives more accurate ODE, cellular-automata, and continuum models from the biological point of view

Advances in Bioinformatics and Its Applications

Advances in Bioinformatics and Its Applications

Author: Matthew He

Publisher: World Scientific

Published: 2005-05-03

Total Pages: 632

ISBN-13: 9814481017

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This unique volume presents major developments and trends in bioinformatics and its applications. Comprising high-quality scientific research papers and state-of-the-art survey articles, the book has been divided into five main sections: Microarray Analysis and Regulatory Networks; Machine Learning and Statistical Analysis; Biomolecular Sequence and Structure Analysis; Symmetry in Sequences; and Signal Processing, Image Processing and Visualization. The results of these investigations help the practicing biologist in many ways: in identifying unknown connections, in narrowing down possibilities for a search, in suggesting new hypotheses, designing new experiments, validating existing models or proposing new ones. It is an essential source of reference for researchers and graduate students in bioinformatics, computer science, mathematics, statistics, and biological sciences based on select papers from the “The International Conference on Bioinformatics and Its Application” (ICBA), held December 16–19, 2004 in Fort Lauderdale, Florida, USA. Contents:Microarray Analysis and Regulatory NetworksMachine Learning and Statistical AnalysesBiomolecular Sequence and Structure AnalysisSymmetry in SequencesSignal Processing, Image Processing and Visualization Readership: Researchers and graduate students in bioinformatics, computer science, mathematics and biological sciences. Keywords:Bioinformatics;Mathematical Biology;Genetic Codes;Medical Informatics;Biological Networks;System BiologyKey Features:High quality collection of recent significant advances in bioinformaticsUnique collection of articles on symmetry of genetic code and pattern discoveryWide coverage of bioinformatics applications including computational epidemiologySignificant computational algorithms and statistical analysis of genomic/proteomic data


Book Synopsis Advances in Bioinformatics and Its Applications by : Matthew He

Download or read book Advances in Bioinformatics and Its Applications written by Matthew He and published by World Scientific. This book was released on 2005-05-03 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume presents major developments and trends in bioinformatics and its applications. Comprising high-quality scientific research papers and state-of-the-art survey articles, the book has been divided into five main sections: Microarray Analysis and Regulatory Networks; Machine Learning and Statistical Analysis; Biomolecular Sequence and Structure Analysis; Symmetry in Sequences; and Signal Processing, Image Processing and Visualization. The results of these investigations help the practicing biologist in many ways: in identifying unknown connections, in narrowing down possibilities for a search, in suggesting new hypotheses, designing new experiments, validating existing models or proposing new ones. It is an essential source of reference for researchers and graduate students in bioinformatics, computer science, mathematics, statistics, and biological sciences based on select papers from the “The International Conference on Bioinformatics and Its Application” (ICBA), held December 16–19, 2004 in Fort Lauderdale, Florida, USA. Contents:Microarray Analysis and Regulatory NetworksMachine Learning and Statistical AnalysesBiomolecular Sequence and Structure AnalysisSymmetry in SequencesSignal Processing, Image Processing and Visualization Readership: Researchers and graduate students in bioinformatics, computer science, mathematics and biological sciences. Keywords:Bioinformatics;Mathematical Biology;Genetic Codes;Medical Informatics;Biological Networks;System BiologyKey Features:High quality collection of recent significant advances in bioinformaticsUnique collection of articles on symmetry of genetic code and pattern discoveryWide coverage of bioinformatics applications including computational epidemiologySignificant computational algorithms and statistical analysis of genomic/proteomic data