Kooperativer Bibliotheksverbund

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Format: 1 Online-Ressource

ISBN: 9781461483014

Series Statement: Modeling and simulation in science, engineering and technology

Additional Edition: Erscheint auch als Druckausgabe ISBN 978-1-4614-8300-7

Language: English

DOI: 10.1007/978-1-4614-8301-4

URL: Volltext

URL: Volltext  (lizenzpflichtig)

URL: Cover

UID:

Format: Online-Ressource (XII, 316 S.)

ISBN: 9783110288537

Series Statement: De Gruyter Series in Mathematics and Life Sciences 1

Content: Biographical note: Alexandra V. Antoniouk, Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine; Roderick V. N. Melnik, Wilfrid Laurier University, Waterloo, Ontario, Canada.

Content: Main description: The book provides a unique collection of in-depth mathematical, statistical, and modeling methods and techniques for life sciences, as well as their applications in a number of areas within life sciences. It also includes arange of new ideas that represent emerging frontiers in life sciences where the application of such quantitative methods and techniques is becoming increasingly important. The bookis aimed at researchers in academia, practitioners and graduate students who want to foster interdisciplinary collaborations required to meet the challenges at the interface of modern life sciences and mathematics.

Additional Edition: ISBN 9783110288537

Additional Edition: ISBN 9783110288544

Language: English

URL: http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110288537&searchTitles=true

URL: Volltext

URL: Inhaltstext

URL: Inhaltstext

UID:

Format: 1 online resource (316 p.)

ISBN: 9783110288537 , 9783110238570

Series Statement: De Gruyter Series in Mathematics and Life Sciences , 1

Content: The book provides a unique collection of in-depth mathematical, statistical, and modeling methods and techniques for life sciences, as well as their applications in a number of areas within life sciences. The book provides also with a range of new ideas that represent emerging frontiers in life sciences where the application of such quantitative methods and techniques is becoming increasingly important. Many areas within life sciences are becoming increasingly quantitative and the progress in those areas will be more and more dependent on the successful development of advanced mathematical, statistical and modelling methodologies and techniques. The state-of-the-art developments in such methodologies and techniques are scattered throughout research journals and hardly accessible to the practitioners in those areas. This book identifies a number of frontier areas where such methodologies and techniques have recently been developed and are to be published here for the first time, bringing substantial potential benefit to a range of applications in life sciences. In addition, the book contains several state-of-the-art surveys at the interface of mathematics and life sciences that would benefit a larger interdisciplinary community. It is aimed at researchers in academia, practitioners and graduate students who want to foster interdisciplinary collaborations required to meet the challenges at the interface of modern life sciences and mathematics.

Note: Frontmatter -- , Preface -- , Contents -- , 1 Introduction -- , 1.1 Scientific Frontiers at the Interface of Mathematics and Life Sciences -- , 2 Mathematical and Statistical Modeling of Biological Systems -- , 2.1 Ensemble Modeling of Biological Systems -- , 3 Probabilistic Models for Nonlinear Processes and Biological Dynamics -- , 3.1 Nonlinear Lévy and Nonlinear Feller Processes: an Analytic Introduction -- , 4 New Results in Mathematical Epidemiology and Modeling Dynamics of Infectious Diseases -- , 4.1 Formal Solutions of Epidemic Equation -- , 5 Mathematical Analysis of PDE-based Models and Applications in Cell Biology -- , 5.1 Asymptotic Analysis of the Dirichlet Spectral Problems in Thin Perforated Domains with Rapidly Varying Thickness and Different Limit Dimensions -- , 6 Axiomatic Modeling in Life Sciences with Case Studies for Virus-immune System and Oncolytic Virus Dynamics -- , 6.1 AxiomaticModeling in Life Sciences -- , 7 Theory, Applications, and Control of Nonlinear PDEs in Life Sciences -- , 7.1 On One Semilinear Parabolic Equation of Normal Type -- , 7.2 On some Classes of Nonlinear Equations with L1-Data -- , 8 Mathematical Models of Pattern Formation and Their Applications in Developmental Biology -- , 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology -- , 9 Modeling the Dynamics of Genetic Mechanism, Pattern Formation, and the Genetics of "Geometry" -- , 9.1 Modeling the Positioning of Trichomes on the Leaves of Plants -- , 10 Statistical Modeling in Life Sciences and Direct Measurements -- , 10.1 Error Estimation for Direct Measurements in May-June 1986 of 131I Radioactivity in Thyroid Gland of Children and Adolescents and Their Registration in Risk Analysis -- , 11 Design and Development of Experiments for Life Science Applications -- , 11.1 Physiological Effects of Static Magnetic Field Exposure in an in vivo Acute Visceral Pain Model in Mice -- , 12 Mathematical Biomedicine and Modeling Avascular Tumor Growth -- , 12.1 Continuum Models of Avascular Tumor Growth -- , Index , Issued also in print. , Mode of access: Internet via World Wide Web. , In English.

In: DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570

In: DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471

In: DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205

In: E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012, De Gruyter, 9783110288995

In: E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012, De Gruyter, 9783110293722

In: E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012, De Gruyter, 9783110288926

Additional Edition: ISBN 9783110273724

Language: English

DOI: 10.1515/9783110288537

URL: https://doi.org/10.1515/9783110288537

URL: https://www.degruyter.com/isbn/9783110288537

URL: Cover

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Format: XVII, 514 S. , Ill., graph. Darst.

ISBN: 9789814566360

Note: Includes bibliographical references and index

Language: English

Subjects: Mathematics

Keywords: Onkologie ; Mathematische Methode

URL: Inhaltsverzeichnis

UID:

Format: 1 online resource (328p.)

ISBN: 9783110288537

Series Statement: De Gruyter Series in Mathematics and Life Sciences ; 1

Content: The book provides a unique collection of in-depth mathematical, statistical, and modeling methods and techniques for life sciences, as well as their applications in a number of areas within life sciences. It also includes a range of new ideas that represent emerging frontiers in life sciences where the application of such quantitative methods and techniques is becoming increasingly important. The book is aimed at researchers in academia, practitioners and graduate students who want to foster interdisciplinary collaborations required to meet the challenges at the interface of modern life sciences and mathematics.

Note: Frontmatter -- , Preface -- , Contents -- , 1 Introduction -- , 1.1 Scientific Frontiers at the Interface of Mathematics and Life Sciences -- , 2 Mathematical and Statistical Modeling of Biological Systems -- , 2.1 Ensemble Modeling of Biological Systems -- , 3 Probabilistic Models for Nonlinear Processes and Biological Dynamics -- , 3.1 Nonlinear Lévy and Nonlinear Feller Processes: an Analytic Introduction -- , 4 New Results in Mathematical Epidemiology and Modeling Dynamics of Infectious Diseases -- , 4.1 Formal Solutions of Epidemic Equation -- , 5 Mathematical Analysis of PDE-based Models and Applications in Cell Biology -- , 5.1 Asymptotic Analysis of the Dirichlet Spectral Problems in Thin Perforated Domains with Rapidly Varying Thickness and Different Limit Dimensions -- , 6 Axiomatic Modeling in Life Sciences with Case Studies for Virus-immune System and Oncolytic Virus Dynamics -- , 6.1 AxiomaticModeling in Life Sciences -- , 7 Theory, Applications, and Control of Nonlinear PDEs in Life Sciences -- , 7.1 On One Semilinear Parabolic Equation of Normal Type -- , 7.2 On some Classes of Nonlinear Equations with L1-Data -- , 8 Mathematical Models of Pattern Formation and Their Applications in Developmental Biology -- , 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology -- , 9 Modeling the Dynamics of Genetic Mechanism, Pattern Formation, and the Genetics of “Geometry” -- , 9.1 Modeling the Positioning of Trichomes on the Leaves of Plants -- , 10 Statistical Modeling in Life Sciences and Direct Measurements -- , 10.1 Error Estimation for Direct Measurements in May–June 1986 of 131I Radioactivity in Thyroid Gland of Children and Adolescents and Their Registration in Risk Analysis -- , 11 Design and Development of Experiments for Life Science Applications -- , 11.1 Physiological Effects of Static Magnetic Field Exposure in an in vivo Acute Visceral Pain Model in Mice -- , 12 Mathematical Biomedicine and Modeling Avascular Tumor Growth -- , 12.1 Continuum Models of Avascular Tumor Growth -- , Index , In English.

Additional Edition: ISBN 978-3-11-027372-4

Language: English

DOI: 10.1515/9783110288537

URL: https://doi.org/10.1515/9783110288537

UID:

Format: xiv, 250 p.

Edition: Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.

Language: English

Keywords: Electronic books.

URL: Click to View

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Format: 1 online resource (533 p.)

ISBN: 981-4566-37-3

Content: The book aims to provide an introduction to mathematical models that describe the dynamics of tumor growth and the evolution of tumor cells. It can be used as a textbook for advanced undergraduate or graduate courses, and also serves as a reference book for researchers. The book has a strong evolutionary component and reflects the viewpoint that cancer can be understood rationally through a combination of mathematical and biological tools. It can be used both by mathematicians and biologists. Mathematically, the book starts with relatively simple ordinary differential equation models, and subs

Note: Description based upon print version of record. , Preface; Contents; 1. Teaching guide; 1.1 How to use this book; 1.2 A sample syllabus for a Mathematics course; 1.3 A sample syllabus for a Biology course; 2. Cancer and somatic evolution; 2.1 What is cancer?; 2.2 Basic cancer genetics; 2.3 Multi-stage carcinogenesis and colon cancer; 2.4 Genetic instability; 2.5 Barriers to cancer progression: importance of the micro-environment; 2.6 Cellular hierarchies in cancer; 2.7 Genetic and epigenetic changes; 2.8 Evolutionary theory and Darwinian selection; 3. Mathematical modeling of tumorigenesis; 3.1 Ordinary differential equations , 3.2 Extensions of ODE modeling3.2.1 Optimal control; 3.2.2 ODEs and cancer epidemiology; 3.3 Partial differential equations; 3.4 Stochastic modeling; 3.5 Cellular automaton models; 3.6 Hybrid and multiscale modeling; Basic growth dynamics and deterministic models; 4. Single species growth; 4.1 Exponential growth; 4.2 Surface growth; 4.3 Sigmoidal growth; 4.3.1 Logistic growth; 4.3.2 Other sigmoidal laws; 4.4 Atypical growth; 4.5 Multistep growth; 4.6 Conclusions; Problems; 5. Two-species competition dynamics; 5.1 Logistic growth of two species and the basic dynamics of competition , 5.2 Two-species dynamics: the axiomatic approach5.3 Summary; Problems; 6. Competition between genetically stable and unstable cells; 6.1 Competition dynamics; 6.2 Competition dynamics and cancer evolution; 6.2.1 A quasispecies model; 6.2.2 Strong apoptosis; 6.2.3 Weak apoptosis; 6.3 Overview of the insights obtained so far; 6.4 Can competition be reversed by chemotherapy?; 6.5 Summary; Problems; 7. Chromosomal instability and tumor growth; 7.1 The effect of chromosome loss on the generation of cancer; 7.2 Calculating the optimal rate of chromosome loss , 7.3 The optimal rate of LOH: a time-dependent problem7.3.1 Formulation of the time-dependent problem; 7.3.2 Mathematical apparatus; 7.3.2.1 Statement of the one-step problem; 7.3.2.2 The Maximum Principle; 7.3.3 The optimal strategy for cancer; 7.4 The bigger picture; 7.4.1 Does cancer solve an optimization problem?; 7.4.2 Summary; Problems; 8. Angiogenesis, inhibitors, promoters, and spatial growth; 8.1 Model 1: Angiogenesis inhibition induces cell death; 8.2 Model 2: Angiogenesis inhibition prevents tumor cell division; 8.2.1 Linear stability analysis of the ODEs , 8.2.2 Conclusions from the linear analysis8.3 Spread of tumors across space; 8.3.1 Turing stability analysis; 8.3.2 Stationary periodic solutions; 8.3.3 Biological implications and numerical simulations; 8.4 Somatic cancer evolution and progression; 8.5 Summary and clinical implications; Problems; Evolutionary dynamics and stochastic models; 9. Evolutionary dynamics of tumor initiation through oncogenes: the gain-of-function model; 9.1 Introduction; 9.2 Mutation-selection diagrams and the stochastic Moran process; 9.3 Analysis; 9.3.1 The method of differential equations , 9.3.2 The probability of absorption , English

Additional Edition: ISBN 981-4566-36-5

Language: English

UID:

Format: 1 online resource (328p.)

ISBN: 9783110288537

Series Statement: De Gruyter Series in Mathematics and Life Sciences ; 1

Content: The book provides a unique collection of in-depth mathematical, statistical, and modeling methods and techniques for life sciences, as well as their applications in a number of areas within life sciences. It also includes a range of new ideas that represent emerging frontiers in life sciences where the application of such quantitative methods and techniques is becoming increasingly important. The book is aimed at researchers in academia, practitioners and graduate students who want to foster interdisciplinary collaborations required to meet the challenges at the interface of modern life sciences and mathematics.

Note: Frontmatter -- , Preface -- , Contents -- , 1 Introduction -- , 1.1 Scientific Frontiers at the Interface of Mathematics and Life Sciences -- , 2 Mathematical and Statistical Modeling of Biological Systems -- , 2.1 Ensemble Modeling of Biological Systems -- , 3 Probabilistic Models for Nonlinear Processes and Biological Dynamics -- , 3.1 Nonlinear Lévy and Nonlinear Feller Processes: an Analytic Introduction -- , 4 New Results in Mathematical Epidemiology and Modeling Dynamics of Infectious Diseases -- , 4.1 Formal Solutions of Epidemic Equation -- , 5 Mathematical Analysis of PDE-based Models and Applications in Cell Biology -- , 5.1 Asymptotic Analysis of the Dirichlet Spectral Problems in Thin Perforated Domains with Rapidly Varying Thickness and Different Limit Dimensions -- , 6 Axiomatic Modeling in Life Sciences with Case Studies for Virus-immune System and Oncolytic Virus Dynamics -- , 6.1 AxiomaticModeling in Life Sciences -- , 7 Theory, Applications, and Control of Nonlinear PDEs in Life Sciences -- , 7.1 On One Semilinear Parabolic Equation of Normal Type -- , 7.2 On some Classes of Nonlinear Equations with L1-Data -- , 8 Mathematical Models of Pattern Formation and Their Applications in Developmental Biology -- , 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology -- , 9 Modeling the Dynamics of Genetic Mechanism, Pattern Formation, and the Genetics of “Geometry” -- , 9.1 Modeling the Positioning of Trichomes on the Leaves of Plants -- , 10 Statistical Modeling in Life Sciences and Direct Measurements -- , 10.1 Error Estimation for Direct Measurements in May–June 1986 of 131I Radioactivity in Thyroid Gland of Children and Adolescents and Their Registration in Risk Analysis -- , 11 Design and Development of Experiments for Life Science Applications -- , 11.1 Physiological Effects of Static Magnetic Field Exposure in an in vivo Acute Visceral Pain Model in Mice -- , 12 Mathematical Biomedicine and Modeling Avascular Tumor Growth -- , 12.1 Continuum Models of Avascular Tumor Growth -- , Index , In English.

Additional Edition: ISBN 978-3-11-027372-4

Language: English

DOI: 10.1515/9783110288537

URL: https://doi.org/10.1515/9783110288537

UID:

Format: 1 online resource (266 p.)

Edition: 1st ed.

ISBN: 1-281-89708-6 , 9786611897086 , 981-270-136-2

Content: The book shows how mathematical and computational models can be used to study cancer biology. It introduces the concept of mathematical modeling and then applies it to a variety of topics in cancer biology. These include aspects of cancer initiation and progression, such as the somatic evolution of cells, genetic instability, and angiogenesis. The book also discusses the use of mathematical models for the analysis of therapeutic approaches such as chemotherapy, immunotherapy, and the use of oncolytic viruses.

Note: Description based upon print version of record. , Preface; Contents; Chapter 1 Cancer and somatic evolution; Chapter 2 Mathematical modeling of tumorigenesis; Chapter 3 Cancer initiation: one-hit and two-hit stochastic models; Chapter 4 Microsatellite and chromosomal instability in sporadic and familial cancers; Chapter 5 Cellular origins of cancer; Chapter 6 Costs and benefits of chromosomal instability; Chapter 7 DNA damage and genetic instability; Chapter 8 Tissue aging and the development of cancer; Chapter 9 Basic models of tumor inhibition and promotion; Chapter 10 Mechanisms of tumor neovascularization , Chapter 11 Cancer and immune responsesChapter 12 Therapeutic approaches: viruses as anti-tumor weapons; Appendix A Exact formula for total probability of double mutations; Bibliography; Index , English

Additional Edition: ISBN 981-256-027-0

Language: English