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Mathematics and Life Sciences

:	Alexandra V. Antoniouk, Roderick V. N. Melnik
:	Mathematics and Life Sciences
:	Walter de Gruyter GmbH& Co.KG
:	9783110288537
:	De Gruyter Series in Mathematics and Life SciencesISSN
:	1
:	CHF 159.70
:

:	Allgemeines, Lexika
:	English

:	328
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

< >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.

< >Alexandra V. Antoniouk, Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;Roderick V. N. Melnik, Wilfrid Laurier University, Waterloo, Ontario, Canada.

	1 Introduction	13
	1.1 Scientific Frontiers at the Interface of Mathematics and Life Sciences	15
	1.1.1 Developing the Language of Science and Its Interdisciplinary Character	15
	1.1.2 Challenges at the Interface: Mathematics and Life Sciences	17
	1.1.3 What This Book Is About	22
	1.1.4 Concluding Remarks	26
	2 Mathematical and Statistical Modeling of Biological Systems	29
	2.1 Ensemble Modeling of Biological Systems	31
	2.1.1 Introduction	31
	2.1.2 Background	33
	2.1.3 Ensemble Model	37
	2.1.4 Computational Techniques	39
	2.1.5 Application to Viral Infection Dynamics	42
	2.1.6 Ensemble Models in Biology	46
	2.1.7 Conclusions	48
	3 Probabilistic Models for Nonlinear Processes and Biological Dynamics	55
	3.1 Nonlinear Lévy and Nonlinear Feller Processes: an Analytic Introduction	57
	3.1.1 Introduction	57
	3.1.2 Dual Propagators	61
	3.1.3 Perturbation Theory for Weak Propagators	64
	3.1.4 T-Products	66
	3.1.5 Nonlinear Propagators	69
	3.1.6 Linearized Evolution Around a Path of a Nonlinear Semigroup	72
	3.1.7 Sensitivity Analysis for Nonlinear Propagators	76
	3.1.8 Back to Nonlinear Markov Semigroups	78
	3.1.9 Concluding Remarks	80
	4 New Results in Mathematical Epidemiology and Modeling Dynamics of Infectious Diseases	83
	4.1 Formal Solutions of Epidemic Equation	85
	4.1.1 Introduction	85
	4.1.2 Epidemic Models	87
	4.1.3 Formal Solutions	88
	4.1.4 Separation of Variables	91
	4.1.5 Solvability of General Equations	92
	4.1.6 Concluding Remarks	96
	5 Mathematical Analysis of PDE-based Models and Applications in Cell Biology	99
	5.1 Asymptotic Analysis of the Dirichlet Spectral Problems in Thin Perforated Domains with Rapidly Varying Thickness and Different Limit Dimensions	101
	5.1.1 Introduction	101
	5.1.2 Description of a Thin Perforated Domain with Quickly Oscillating Thickness and Statement of the Problem	102
	5.1.3 Equivalent Problem	104
	5.1.4 The Homogenized Theorem	106
	5.1.5 Asymptotic Expansions for the Eigenvalues and Eigenfunctions	112
	5.1.6 Conclusions	119
	6 Axiomatic Modeling in Life Sciences with Case Studies for Virus-immune System and Oncolytic Virus Dynamics	123
	6.1 Axiomatic Modeling in Life Sciences	125
	6.1.1 Introduction	125
	6.1.2 Boosting Immunity by Anti-viral Drug Therapy: Timing, Efficacy and Success	127
	6.1.3 Predictive Modeling of Oncolytic Virus Dynamics	135
	6.1.4 Conclusions	150
	7 Theory, Applications, and Control of Nonlinear PDEs in Life Sciences	157
	7.1 On One Semilinear Parabolic Equation of Normal Type	159
	7.1.1 Introduction	159
	7.1.2 Semilinear Parabolic Equation of Normal Type	160
	7.1.3 The Structure of NPE Dynamics	165
	7.1.4 Stabilization of Solution for NPE by Start Control	170
	7.1.5 Concluding Remarks	171
	7.2 On some Classes of Nonlinear Equations with L1 -Data	173
	7.2.1 Nonlinear Elliptic Second-order Equations with L1-data	174
	7.2.2 Nonlinear Fourth-order Equations with Strengthened Coercivity and L1-Data	190
	7.2.3 Concluding Remarks	197
	8 Mathematical Models of Pattern Formation and Their Applications in Developmental Biology	201
	8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology	203
	8.1.1 Introduction	203
	8.1.2 Mechanisms of Developmental Pattern Formation	205
	8.1.3 Motivating Application: Pattern Control in Hydra	206
	8.1.4 Diffusive Morphogens and Turing Patterns	209
	8.1.5 Receptor-based Models	212
	8.1.6 Multistability	218
	8.1.7 Discussion	219
	9 Modeling the Dynamics of Genetic Mechanism, Pattern Formation, and the Genetics of “Geometry”	225
	9.1 Modeling the Positioning of Trichomes on the Leaves of Plants	227
	9.1.1 Introduction	227
	9.1.2 Activator-inhibitor Reaction-diffusion Modeling of the Trichome Positioning	230
	9.1.3 Hexagonal Recursion	233
	9.1.4 Conclusions	237
	10 Statistical Modeling in Life Sciences and Direct Measurements	241
	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	243
	10.1.1 Introduction	243
	10.1.2 Materials and Methods	245
	10.1.3 Conclusion and Discussion	251
	10.1.4 Appendix. Approximation of Conditional Expectations	252
	11 Design and Development of Experiments for Life Science Applications	257
	11.1 Physiological Effects of Static Magnetic Field Exposure in an in vivo Acute Visceral Pain Model in Mice	259
	11.1.1 Introduction	259
	11.1.2 Methods	261
	11.1.3 Results	268
	11.1.4 Discussion	278
	11.1.5 Conclusions	281
	12 Mathematical Biomedicine and Modeling Avascular Tumor Growth	289
	12.1 Continuum Models of Avascular Tumor Growth	291
	12.1.1 Introduction	291
	12.1.2 Diffusion-limited Models of Avascular Tumor Growth	293
	12.1.3 Tumor Invasion	301
	12.1.4 Multiphase Models of Avascular Tumor Growth	307
	12.1.5 Conclusions	315
	Index	325