Math Everywhere: Deterministic and Stochastic Modelling in Biomedicine, Economics and Industry

Cover Page......Page 1
Title Page......Page 3
ISBN 3540444459 Springer Berlin Heidelberg New York......Page 4
Preface......Page 7
Contents......Page 11
List of Contributors......Page 15
Introduction......Page 19
Part I Deterministic and Stochastic Systems......Page 23
1 Introduction......Page 25
2 Coupled Systems......Page 26
3 Quiescent Phases......Page 33
4 Proof of Theorem 1......Page 39
References......Page 40
1 Introduction......Page 43
3 Systems without Individual Dynamics: Non-existence of Invariant Distributions......Page 47
4 Systems with a Confining Potential: Existence of the Invariant Distribution......Page 51
Acknowledgments......Page 54
References......Page 55
1 Introduction......Page 57
2 Mean–Square Convergence......Page 59
3 Almost Sure Convergence......Page 64
4 Examples......Page 66
References......Page 67
1 Introduction......Page 69
2 Model, Notations and Preliminary Results......Page 71
3 Asymptotic Results......Page 74
References......Page 79
1 Introduction......Page 81
2 Stochastic Birth-and-growth Processes......Page 82
3 Mean Geometric Densities......Page 86
4 The Hazard Function......Page 90
References......Page 93
1 Introduction......Page 95
2 Generalized Densities......Page 97
3 Approximation of the Mean Densities......Page 100
4 Mean First Order Steiner Formulas......Page 102
5 Time Dependent Random Closed Sets......Page 103
Acknowledgements......Page 107
References......Page 108
2 Definition of the MpfBm......Page 111
3 Comparisons with Other Multiparameter Extensions of fBm......Page 113
4 Different Notions of Stationarity......Page 114
5 Characterization......Page 115
6 Projection on Flows and Regularity......Page 117
Acknowledgement......Page 118
References......Page 119
1 Introduction......Page 121
2 Framework and Definitions......Page 123
3 Precedence Tests on the Plane......Page 124
4 Survival Analysis on the Plane and the Nelson-Aalen Estimator......Page 128
References......Page 132
1 Introduction......Page 133
2 IFS with Maps (IFSM) on L2([ 0, 1])......Page 134
3 IFSM for Stochastic Processes on L2([ 0, 1])......Page 137
4 Simulation of Brownian Motion via IFSM......Page 139
5 Conclusions......Page 141
References......Page 142
1 Introduction......Page 143
2 Preliminary Results on Hausdorff Distance......Page 144
3 Some IFS Operators on Multifunctions......Page 146
4 Applications to Fractal Image Coding and the Inverse Problem......Page 150
References......Page 156
Part II Mathematical Problems in Biology, Medicine and Ecology......Page 157
Stochastic Modeling and Estimation in a Neutron Lifetime Experiment......Page 159
1 Introduction......Page 160
2 Stochastic Models for Two-stage Neutron Lifetime Experiment......Page 161
3 Likelihood Functions......Page 163
Acknowledgments......Page 166
References......Page 167
1 Introduction......Page 169
2 The Mathematical Model of Tumour Cords......Page 170
3 Transport of Antibodies in the Cord at Steady State......Page 175
4 Nondimensional Variables and Parameters......Page 177
5 Numerical Results......Page 178
References......Page 181
1 Introduction......Page 183
2 Summary of the Multi-scale Model......Page 184
3 Structural Adaptation in Normal Vasculature......Page 187
4 Deconstructing Normal Vasculature......Page 188
5 Conclusions and Discussion......Page 193
References......Page 196
1 A Model for Vasculogenesis......Page 197
2 Relaxation Approximation......Page 200
3 Numerical Results......Page 202
4 Conclusions......Page 206
References......Page 208
1 Introduction......Page 211
2 Uniform a Priori Estimates......Page 213
3 From Asymptotic Expansions to Reduced Equations......Page 214
4 An ε2- Approximation without the ad hoc Closure Assumption......Page 217
5 Conclusion: the Problem with Nonlinear Coupling in Dimensional Form......Page 221
Acknowledegments......Page 222
References......Page 223
1 Introduction......Page 225
2 Parallel Row Formation of Scale Cells......Page 226
3 Color Pattern Formation......Page 229
4 Conclusions and Discussion......Page 233
References......Page 234
1 Introduction......Page 237
2 A Stabilization Result......Page 239
3 The Derivative of λ1(ω) with Respect to Translations of ω......Page 241
4 Further Remarks......Page 245
References......Page 246
1 Introduction......Page 247
2 The Model......Page 248
3 Probabilistic Interpretation......Page 250
4 Properties of the Fixed Point Map......Page 251
5 Coupling Methods......Page 252
6 Equilibria and Asymptotic Behavior......Page 255
7 Different Household Sizes......Page 256
8 Discussion......Page 257
References......Page 258
1 Introduction......Page 259
2 The Glucose-Insulin Model......Page 260
3 Glucose Control: the Case of Hyperglycemic Patients......Page 262
4 Glucose Control: the Case of Hypoglycemic Patients......Page 264
5 Numerical Simulations......Page 266
References......Page 270
1 Introduction......Page 271
2 The Mathematical Inhibitory Model......Page 272
3 A Concentration Dependent Toxicant Production......Page 277
4 Discussion......Page 280
References......Page 281
1 Introduction......Page 283
2 The Multiphase and Multicomponent Transport Equations......Page 284
3 Bacteria Population and Biodegradation Kinetic......Page 287
4 Adsorbed Contaminant Equation......Page 290
5 Source Term Specifications......Page 291
6 The complete Model and Conclusions......Page 293
References......Page 294
Part III Mathematical Problems in Industry and Economics......Page 295
1 Introduction......Page 297
2 A Problem Formulation Using State-Task-Networks......Page 298
3 Models Using a Uniform Discretization of Time (UDM)......Page 300
4 A Continuous Time Model (CTM)......Page 302
5 Modifications of the Mixed-integer Linear Programs......Page 304
6 An Iterative Construction Algorithm......Page 305
7 Numerical Results......Page 306
References......Page 308
1 Introduction......Page 309
2 Transient Homogeneous Nucleation......Page 310
3 Formation of Helium Bubbles in Nuclear Materials......Page 315
References......Page 324
1 The Problem......Page 327
2 The Boolean Model......Page 328
3 Stochastic Model for the Crystallization Process......Page 329
4 Random Johnson-Mehl Tessellations......Page 330
5 Estimators......Page 336
6 Simulations and New Results......Page 338
References......Page 341
1 Introduction......Page 343
2 The Model......Page 344
3 The Dynamic Game......Page 347
References......Page 352
Appendix Color Plates......Page 353
Back Page......Page 362