Details

<p>Foreword ix</p> <p>Introduction xv</p> <p><b>Chapter 1. On the Status of Biology: On the Definition of Life</b> <b>1</b></p> <p>1.1. Causality in biology 4</p> <p>1.1.1. Vitalism 8</p> <p>1.1.2. Teleology 10</p> <p>1.2. Variability in biology 13</p> <p>1.2.1. Time-dependence of biological processes 15</p> <p>1.2.2. Environment-dependence of biological processes 17</p> <p><b>Chapter 2. On the Nature of the Contribution Made by Mathematics to Biology</b> <b>19</b></p> <p>2.1. On the affinity of mathematics with biology 20</p> <p>2.2. Mathematics, an instrument of work and thought on biology 25</p> <p><b>Chapter 3. Some Historical Reference Points: Biology Fashioned by Mathematics</b> <b>35</b></p> <p>3.1. The first remarkable steps in biomathematics 37</p> <p>3.1.1. On the continuous in biology 37</p> <p>3.1.2. On the discrete in biology 39</p> <p>3.1.3. The notion of laws in biology 43</p> <p>3.1.4. The beginning of classical science: Descartes and Pascal 44</p> <p>3.1.5. Buffon and hesitations relating to the utility of mathematics in biology 45</p> <p>3.2. Some pertinent contributions from mathematics in the modern era 48</p> <p>3.2.1. The laws of growth 48</p> <p>3.2.2. Formal genetics 49</p> <p>3.3. Introduction of the notion of a probabilistic model in biology 56</p> <p>3.4. The physiology of C. Bernard (1813–1878): the call to mathematics 58</p> <p>3.5. The principle of optimality in biology 60</p> <p>3.6. Introduction of the formalism of dynamic systems in biology 61</p> <p>3.7. Morphogenesis: the need for mathematics in the study of biological forms 63</p> <p>3.7.1. General principles from D’Arcy Thompson 64</p> <p>3.7.2. Turing’s reaction–diffusion systems (1952): morphogenesis, a “break of symmetry” 69</p> <p>3.8. The theory of automatons and cybernetics in biology 70</p> <p>3.8.1. The theory of automatons 70</p> <p>3.8.2. The contribution of cybernetics 73</p> <p>3.8.3. The case of L-systems 74</p> <p>3.8.4. Petri’s networks 74</p> <p>3.9. Molecular biology 78</p> <p>3.9.1. On genetic information 81</p> <p>3.9.2. The linguistic model in biology 83</p> <p>3.10. Information and communication, important notions in biology 84</p> <p>3.11. The property of self-organization in biology 86</p> <p>3.11.1. Structural self-organization 87</p> <p>3.11.2. Self-reproductive hypercycle 88</p> <p>3.12. Systemic biology 89</p> <p>3.12.1. On the notion of system 89</p> <p>3.12.2. Essay in relational biology 90</p> <p>3.12.3. Emergence and complexity 93</p> <p>3.12.4. Networks 98</p> <p>3.12.5. Order, innovation and complex networks 104</p> <p>3.13. Game theory in biology 105</p> <p>3.14. Artificial life 109</p> <p>3.14.1. Biomimetic automatons 110</p> <p>3.14.2. Psychophysiology and mathematics: controls on learning 111</p> <p>3.15. Bioinformatics 112</p> <p><b>Chapter 4. Laws and Models in Biology</b> <b>115</b></p> <p>4.1. Biological laws in literary language 118</p> <p>4.1.1. The law of Cuvier’s organic correlations (1825) 118</p> <p>4.1.2. The fundamental biogenetic law 118</p> <p>4.2. Biological laws in mathematical language 119</p> <p>4.2.1. Statistical laws 121</p> <p>4.3. Theoretical laws 131</p> <p>4.3.1. Formal genetics 131</p> <p>4.3.2. Growth laws 132</p> <p>4.3.3. Population dynamics 133</p> <p><b>Chapter 5. Mathematical Tools and Concepts in Biology</b> <b>135</b></p> <p>5.1. An old biomathematical subject: describing and/or explaining phyllotaxis 136</p> <p>5.2. The notion of invariant and its substrate: time and space 140</p> <p>5.2.1. Physical time/biological time 142</p> <p>5.2.2. Metric space/non-metric space 143</p> <p>5.2.3. Multi-scale processes 147</p> <p>5.3. Continuous formalism 147</p> <p>5.3.1. Dynamics of a univariate process 148</p> <p>5.3.2. Structured models 149</p> <p>5.3.3. Oscillatory dynamics 151</p> <p>5.3.4. On the stability of dynamic systems 154</p> <p>5.3.5. Multivariate structured models 160</p> <p>5.3.6. Dynamics of spatio-temporal process 163</p> <p>5.3.7. Multi-scale models 171</p> <p>5.4. Discreet formalism 174</p> <p>5.5. Spatialized models 175</p> <p>5.5.1. Multi-agent models: dynamics of a biological association of the individual-centered type 175</p> <p>5.5.2. Electrophysiological models: transmission of electrical signals 176</p> <p>5.6. Random processes in biology 178</p> <p>5.6.1. Poisson process 181</p> <p>5.6.2. Birth–death processes. 182</p> <p>5.7. Logic kinetics of regulation 184</p> <p>Conclusion 189</p> <p>Glossary 201</p> <p>References 217</p> <p>Index 221</p>

<p>Roger Buis, Emeritus Professor at the Université de Toulouse, France, has taught Statistical Biometry and Biomathematics at various universities and engineering schools (agronomy). His research – initially focused on plant growth and morphogenesis – has been developed in the context of differential dynamical systems. </p>

US