Keywords:
Biomathematics.
;
Life sciences -- Mathematics.
;
Electronic books.
Description / Table of Contents:
The De Gruyter Series in Mathematics and Life Sciences is devoted to the publication of monographs in the field. They cover topics and methods in fields of current interest that use mathematical approaches to understand and explain, model and influence phenomena in all areas of life sciences. This includes, among others, theory and application of biological mathematical modeling, complex systems biology, bioinformatics, computational biomodeling stochastic modeling, biostatistics, computational evolutionary biology, comparative genomics, or structural bioinformatics. Also, new types of mathematical problems that arise from biological knowledge shall be covered.
Type of Medium:
Online Resource
Pages:
1 online resource (328 pages)
Edition:
1st ed.
ISBN:
9783110288537
Series Statement:
De Gruyter Series in Mathematics and Life Sciences Series ; v.1
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=893694
Language:
English
Note:
Intro -- 1 Introduction -- 1.1 Scientific Frontiers at the Interface of Mathematics and Life Sciences -- 1.1.1 Developing the Language of Science and Its Interdisciplinary Character -- 1.1.2 Challenges at the Interface: Mathematics and Life Sciences -- 1.1.3 What This Book Is About -- 1.1.4 Concluding Remarks -- 2 Mathematical and Statistical Modeling of Biological Systems -- 2.1 Ensemble Modeling of Biological Systems -- 2.1.1 Introduction -- 2.1.2 Background -- 2.1.3 Ensemble Model -- 2.1.4 Computational Techniques -- 2.1.5 Application to Viral Infection Dynamics -- 2.1.6 Ensemble Models in Biology -- 2.1.7 Conclusions -- 3 Probabilistic Models for Nonlinear Processes and Biological Dynamics -- 3.1 Nonlinear Lévy and Nonlinear Feller Processes: an Analytic Introduction -- 3.1.1 Introduction -- 3.1.2 Dual Propagators -- 3.1.3 Perturbation Theory for Weak Propagators -- 3.1.4 T-Products -- 3.1.5 Nonlinear Propagators -- 3.1.6 Linearized Evolution Around a Path of a Nonlinear Semigroup -- 3.1.7 Sensitivity Analysis for Nonlinear Propagators -- 3.1.8 Back to Nonlinear Markov Semigroups -- 3.1.9 Concluding Remarks -- 4 New Results in Mathematical Epidemiology and Modeling Dynamics of Infectious Diseases -- 4.1 Formal Solutions of Epidemic Equation -- 4.1.1 Introduction -- 4.1.2 Epidemic Models -- 4.1.3 Formal Solutions -- 4.1.4 Separation of Variables -- 4.1.5 Solvability of General Equations -- 4.1.6 Concluding Remarks -- 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 -- 5.1.1 Introduction -- 5.1.2 Description of a Thin Perforated Domain with Quickly Oscillating Thickness and Statement of the Problem -- 5.1.3 Equivalent Problem -- 5.1.4 The Homogenized Theorem.
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5.1.5 Asymptotic Expansions for the Eigenvalues and Eigenfunctions -- 5.1.6 Conclusions -- 6 Axiomatic Modeling in Life Sciences with Case Studies for Virus-immune System and Oncolytic Virus Dynamics -- 6.1 Axiomatic Modeling in Life Sciences -- 6.1.1 Introduction -- 6.1.2 Boosting Immunity by Anti-viral Drug Therapy: Timing, Efficacy and Success -- 6.1.3 Predictive Modeling of Oncolytic Virus Dynamics -- 6.1.4 Conclusions -- 7 Theory, Applications, and Control of Nonlinear PDEs in Life Sciences -- 7.1 On One Semilinear Parabolic Equation of Normal Type -- 7.1.1 Introduction -- 7.1.2 Semilinear Parabolic Equation of Normal Type -- 7.1.3 The Structure of NPE Dynamics -- 7.1.4 Stabilization of Solution for NPE by Start Control -- 7.1.5 Concluding Remarks -- 7.2 On some Classes of Nonlinear Equations with L1 -Data -- 7.2.1 Nonlinear Elliptic Second-order Equations with L1-data -- 7.2.2 Nonlinear Fourth-order Equations with Strengthened Coercivity and L1-Data -- 7.2.3 Concluding Remarks -- 8 Mathematical Models of Pattern Formation and Their Applications in Developmental Biology -- 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology -- 8.1.1 Introduction -- 8.1.2 Mechanisms of Developmental Pattern Formation -- 8.1.3 Motivating Application: Pattern Control in Hydra -- 8.1.4 Diffusive Morphogens and Turing Patterns -- 8.1.5 Receptor-based Models -- 8.1.6 Multistability -- 8.1.7 Discussion -- 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 -- 9.1.1 Introduction -- 9.1.2 Activator-inhibitor Reaction-diffusion Modeling of the Trichome Positioning -- 9.1.3 Hexagonal Recursion -- 9.1.4 Conclusions -- 10 Statistical Modeling in Life Sciences and Direct Measurements.
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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 -- 10.1.1 Introduction -- 10.1.2 Materials and Methods -- 10.1.3 Conclusion and Discussion -- 10.1.4 Appendix. Approximation of Conditional Expectations -- 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 -- 11.1.1 Introduction -- 11.1.2 Methods -- 11.1.3 Results -- 11.1.4 Discussion -- 11.1.5 Conclusions -- 12 Mathematical Biomedicine and Modeling Avascular Tumor Growth -- 12.1 Continuum Models of Avascular Tumor Growth -- 12.1.1 Introduction -- 12.1.2 Diffusion-limited Models of Avascular Tumor Growth -- 12.1.3 Tumor Invasion -- 12.1.4 Multiphase Models of Avascular Tumor Growth -- 12.1.5 Conclusions -- Index.
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