On the difficult interplay between life, complexity, and mathematical sciences

Mathematical Models and Methods in Applied Sciences

Volumn 23, Issue 10, 2013, Pages 1861-1913

  Bellomo, N ^a   Knopoff, D ^a   Soler, J ^b  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

collective behavior; large deviations; learning; Living systems; nonlinear interactions; self organization

Indexed keywords

COLLECTIVE BEHAVIOR; LARGE DEVIATIONS; LEARNING; LIVING SYSTEMS; NONLINEAR INTERACTIONS; SELF ORGANIZATIONS;

KINETIC THEORY;

BIOLOGICAL SYSTEMS;

EID: 84880254372     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021820251350053X     Document Type: Article

References (151)

1. D. L. Abel and J. T. Trevors, Self-organization vs. self-ordering events in life-origin models, Phys. Life Rev. 3 (2006) 221-228.
2. D. Acemoglu and J. A. Robinson, Economic Origins of Dictatorship and Democracy (Cambridge Univ. Press, 2006).
3. S. Ahn, H.-O. Bae, S.-Y. Ha, Y. Kim and H. Lim, Application of flocking mechanism to the modeling of stochastic volatility, Math. Models Methods Appl. Sci. 23 (2013) 1603-1628.
4. G. Ajmone Marsan, N. Bellomo and M. Egidi, Towards a mathematical theory of complex socio-economical systems by functional subsystems representation, Kinet. Relat. Models 1 (2008) 249-278.
5. G. Ajmone Marsan, N. Bellomo and A. Tosin, Complex Social Systems-Modeling and Simulations (Springer, 2013).
6. H. Allen Orr, The genetic theory of adaption. A brief history, Nature Rev. Gen. 6 (2005) 119-127.
7. F. Andreu, V. Caselles, J. M. Mazon and S. Moll, Finite propagation speed for limited flux diffusion equations, Arch. Rational Mech. Anal. 182 (2006) 269-297.
8. F. Andreu, V. Caselles, J. M. Mazon, J. Soler and M. Verbeni, Radially symmetric solutions of a tempered diffusion equation. A porous media flux-limited case, SIAM J. Math. Anal. 44 (2012) 1019-1049.
9. C. Appert-Rolland, P. Degond and S. Motsch, Two-way multi-lane traffic model for pedestrians in corridors, Netw. Het. Media 6 (2011) 351-381.
10. M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proc. Nat. Acad. Sci. 105 (2008) 1232-1237.
11. A. L. Barabasi, R. Albert and H. Jeong, Mean-field theory for scale-free random networks, Physica A 272 (1999) 173-187.
12. U. Bastolla, M. A. Fortuna, A. Pascual-Garc?a, A. Ferrera, B. Luque and J. Bascompte, The architecture of mutualistic networks minimizes competition and increases biodiversity, Nature 458 (2009) 1018-1020.
13. R. N. Bearon and K. L. Grunbaum, From individual behavior to population models: A case study using swimming algae, J. Theor. Biol. 251 (2008) 33-42.
14. N. Bellomo, Modeling Complex Living Systems-A Kinetic Theory and Stochastic Game Approach (Birkhauser, 2008).
15. N. Bellomo and A. Bellouquid, On the modeling of crowd dynamics looking at the beautiful shapes of swarms, Netw. Heter. Media. 6 (2011) 383-399.
16. N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, Complexity and mathematical tools towards the modelling multicellular growing systems in Biology, Math. Comp. Model. 51 (2010) 441-451.
17. N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, Multiscale biological tissue models and flux-limited chemotaxis for multicellular growing systems, Math. Models Methods Sci. 20 (2010) 1179-1207.
18. N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, On the asymptotic theory from microscopic to macroscopic growing tissue models: An overview with perspectives, Math. Models Methods Sci. 22 (2012) 1130001.
19. N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, Modeling chemotaxis from L2-closure moments in kinetic theory of active particles, Discr. Cont. Dyn. Syst.-B 18 (2013) 847-863.
20. N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, On the multiscale modeling of vehicular traffic-From kinetic to hydrodynamics, preprint (2013).
21. N. Bellomo, A. Bellouquid and D. Knopoff, From the micro-scale to collective crowd dynamics, arXiv:1301.55/4v1.
22. N. Bellomo, H. Berestycki, F. Brezzi and J. P. Nadal, Mathematics and complexity in life and human sciences, Math. Models Methods Appl. Sci. 20 (2010) 1391-1395.
23. N. Bellomo and F. Brezzi, Mathematics and complexity of multi-particle systems Math. Models Methods Appl. Sci. 22 (2012) 1103001.
24. N. Bellomo and B. Carbonaro, Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives, Phys. Life Rev. 8 (2011) 1-18.
25. N. Bellomo and M. Delitala, From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells, Phys. Life Rev. 5 (2008) 183-206.
26. N. Bellomo and C. Dogbe, On the modelling of traffic and crowds-A survey of models, speculations and perspectives, SIAM Rev. 53 (2011) 409-463.
27. N. Bellomo and G. Forni, Complex multicellular systems and immune competition: New paradigms looking for a mathematical theory, Current Top. Developmental Biol. 81 (2008) 485-502.
28. N. Bellomo, M. Herrero and A. Tosin, On the dynamics of social conflicts: Looking for the black swan, Kinet. Relat. Models 6 (2013) 459-479.
29. N. Bellomo, N. K. Li and P. K. Maini, On the foundations of cancer modelling, Math. Models Methods Sci. 18 (2008) 593-646.
30. N. Bellomo, B. Piccoli and A. Tosin, Modeling crowd dynamics from a complex system view point, Math. Models Methods Appl. Sci. 22 (2012) 1230004.
31. N. Bellomo, L. Preziosi and G. Forni, A kinetic (cellular) theory for competition between tumors and the host immune system, J. Biol. Sys. 4 (1996) 479-502.
32. N. Bellomo and J. Soler, On the mathematical theory of the dynamics of swarms viewed as a complex system, Math. Models Methods Appl. Sci. 22 (2012) 1140006.
33. A. Bellouquid, E. De Angelis and L. Fermo, Towards the modeling of vehicular traffic as a complex system: A kinetic theory approach, Math. Models Methods Appl. Sci. 22 (2012) 1140003.
34. A. Bellouquid, E. De Angelis and D. Knopoff, From the modeling of the immune hallmarks of cancer to a black swan in biology, Math. Models Methods Appl. Sci. 23 (2013) 949-978.
35. A. Bellouquid and M. Delitala, Mathematical Modeling of Complex Biological Systems. A Kinetic Theory Approach (Birkhauser, 2006).
36. M. L. Bertotti and M. Delitala, On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders, Math. Models Methods Appl. Sci. 18 (2008) 913-934.
37. F. Bolley, J. A. Cagnizo and J. A. Carrillo, Stochastic mean-field limit: Non-Lipschitz forces and swarming, Math. Models Methods Appl. Sci. 21 (2011) 2179-2210.
38. E. Bonabeau, M. Dorigo and G. Theraulaz, Swarm Intelligence: From Natural to Artificial Systems (Oxford Univ. Press, 1999).
39. R. W. Brockett, On the control of a flock by a leader, Proc. of the Steklov Inst. Math. 268 (2010) 49-57.
40. S. Buchmuller and U. Weidman, Parameters of pedestrians, pedestrian traffic and walking facilities, ETH Report Nr. 132 (2006).
41. M. Burger, M. Di Francesco and Y. Dolak-Struss, The Keller-Segel model for chemotaxis with prevention of overcrowding: Linear vs. Nonlinear diffusion, SIAM J. Math. Anal. 38 (2006) 1288-1315.
42. C. F. Camerer, Behavioral Game Theory: Experiments in Strategic Interaction (Princeton Univ. Press, 2003).
43. J. Campos, P. Guerrero, O. Sanchez and J. Soler, On the analysis of traveling waves to a nonlinear flux limited reaction-diffusion equation, Ann. Inst. H. Poincare Anal. Non Lineaire 30 (2013) 141-155.
44. J. Calvo, J. Mazon, J. Soler and M. Verbeni, Qualitative properties of the solutions of a nonlinear flux-limited equation arising in the transport of morphogens, Math. Models Methods Appl. Sci. 21 (2011) 893-937.
45. J. A. Carrillo, M. Fornasier, J. Rosado and G. Toscani, Asymptotic flocking dynamics for the kinetic Cucker-Smale model, SIAM J. Math. Anal. 42 (2010) 218-236.
46. J. A. Carrillo, A. Klar, S. Martin and S. Tiwari, Self-propelled interacting particle systems with roosting force, Math. Models Methods Appl. Sci. 20 (2010) 1533-1552.
47. C. Cattani and A. Ciancio, Hybrid two scales mathematical tools for active particles modeling complex systems with learning hiding dynamics, Math. Models Methods Appl. Sci. 17 (2007) 171-188.
48. A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati, F. Stefanini and R. Tavarone, From empirical data to inter-individual interactions: Unveiling the rules of collective animal behavior, Math. Models Methods Appl. Sci. 20 (2010) 1491-1510.
49. A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati, F. Stefanini and M. Viale, Scale-free correlation in the bird flocks, Proc. Natl. Acad. Sci. USA 107 (2010) 11865-11870.
50. F. Cavallo, C. De Giovanni, P. Nanni, G. Forni and P.-L. Lollini, 2011: The immune hallmarks of cancer, Cancer Immunol. Immunother. 60 (2011) 319-326.
51. C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases (Springer, 1994).
52. F. Cerreti, B. Perthame, C. Schmeiser, M. Tang and V. Vauchelet, Waves for the hyperbolic Keller-Segel model, Math. Models Methods Appl. Sci. 21 (2011) 825-842.
53. M. A. J. Chaplain, Multiscale mathematical modelling in biology and medicine, IMA J. Appl. Math. 76 (2011) 371-388.
54. M. Chaplain, M. Lachowicz, Z. Szyman'ska and D.Wrzosek, Mathematical modelling of cancer invasion: The importance of cell-cell adhesion and cell-matrix adhesion, Math. Models Methods Appl. Sci. 21 (2011) 719-743.
55. Y. Chjang, M. D'Orsogna, D. Marthaler, A. Bertozzi and L. Chaves, State transition and the continuum limit for 2D interacting, self-propelled particles system, Physica D 232 (2007) 33-47.
56. R. Colombo, M. Garavello and M. Lucureux-Mercier, A class of nonlocal models for pedestrian traffic, Math. Models Methods Appl. Sci. 22 (2012) 1150023.
57. R. M. Colombo and M. D. Rosini, Existence of nonclassical solutions in a pedestrian flow model, Nonlinear Anal. RWA 10 (2010) 2710-2287.
58. P. Contucci and S. Ghirlanda, Modeling society with statistical mechanics: An application to cultural contact and immigration, Quality and Quantity 41 (2007) 569-578.
59. E. L. Cooper, Evolution of immune system from self/not self to danger to artificial immune system, Phys. Life Rev. 7 (2010) 55-78.
60. V. Coscia, L. Fermo and N. Bellomo, On the mathematical theory of living systems II: The interplay between mathematics and system biology, Comput. Math. Appl. 62 (2011) 3902-3911.
61. V. Coscia and C. Canavesio, First order macroscopic modelling of human crowds, Math. Models Methods Appl. Sci. 18 (2008) 1217-1247.
62. I. D. Couzin, Collective minds, Nature 445 (2007) 715.
63. I. D. Couzin, J. Krause, R. James, G. D. Ruxtion and N. R. Franks, Collective memory and spatial sorting in animal groups, J. Theor. Biol. 218 (2002) 1-11.
64. E. Cristiani, P. Frasca and B. Piccoli, Effects of anisotropic interactions in the structure of animal groups, J. Math. Biol. 62 (2011) 569-588.
65. B. D'Acunto and L. Frunzo, Qualitative analysis and simulations of a free boundary problem for multispecies biofilm models, Math. Comp. Model. 53 (2011) 1596-1606.
66. P. Degond and J. Hua, Self-organized hydrodynamics with congestion and path formation in crowds, J. Comp. Phys. 237 (2013) 299-319.
67. P. Degond and S. Motsch, Continuum limit of self-driven particles with orientation interaction, Math. Models Methods Appl. Sci. 18 (2008) 1193-1217.
68. P. Degond and J.-G. Liu, Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Math. Models Methods Appl. Sci. 22 (2012) 1140001.
69. M. Delitala, P. Pucci and M. C. Salvatori, From methods of the mathematical kinetic theory for active particles to modelling virus mutations, Math. Models Methods Appl. Sci. 21 (2011) 843-870.
70. A. d'Onofrio and I. P. M. Tomlison, A nonlinear mathematical model of cell turnover, differentiation and tumorigenesis in the intestinal crypt, J. Theor. Biol. 244 (2007) 367-374.
71. K. Drucis, M. Kolev, W. Majda and B. Zubik-Kowal, Nonlinear modeling with mammographic evidence of carcinoma, Nonlin. Anal. RWA 10 (2010) 4326-4334.
72. H. Du, Z. Xu, J. D. Shrout and M. Alber, Multiscale modeling of pseudomona aeruginosa swarming, Math. Models Methods Appl. Sci. 21 (2011) 939-954.
73. B. During, P. Markowich, J. F. Pietschmann and M. T. Wolfram, Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders, Proc. R. Soc. London 465 (2009) 3687-3708.
74. R. Eftimie, J. L. Bramson and D. J. D. Earn, Interactions between the immune system and cancer: A brief review of non-spatial mathematical models, Bull. Math. Biol. 73 (2011) 2-32.
75. R. Eftimie, Hyperbolic and kinetic models for self-organized biological aggregations and movement: A brief review, J. Math. Biol. 65 (2012) 35-75.
76. G. Flierl, D. Grunbaum, S. Levin and D. Olson, From individuals to aggregations: The interplay between behavior and physics, J. Theor. Biol. 196 (1999) 397-454.
77. M. Fornasier, J. Haskovec and G. Toscani, Fluid dynamioc description of flocking via the Povzner-Boltzmann equation, Physica D 240 (2011) 21-31.
78. S. A. Frank, Dynamics of Cancer: Inheritance, and Evolution (Princeton Univ. Press, 2007).
79. A. Frouvelle, A continuum model for alignment of self-propelled particles with anisotropy and density-dependent parameters, Math. Models Methods Appl. Sci. 22 (2012) 1250011.
80. F. Ginelli and H. Chate, Relevance of metric-free interaction in flocking phenomena, Phys. Rev. Lett. 105 (2010) 168103-1-4.
81. H. Gintis, Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction (Princeton Univ. Press, 2009).
82. L. Gosse, Computing Qualitatively Correct Approximations of Balance Laws, SIMAI Springer Series, Vol. 2 (Springer, 2013).
83. D. Grunbaum, K. Chan, E. Tobin andM. T. Nishizaki, Non-linear advection diffusion equations approximate swarms but not schooling population, Math. Biosci. 214 (2008) 38-48.
84. S.-Y. Ha, M.-J. Kang, C. Lattanzio and B. Rubino, A class of interacting particle systems on the infinite cylinder with flocking phenomena, Math. Models Methods Appl. Sci. 22 (2012) 1250008.
85. D. Hanahan and R. A. Weinberg, The hallmarks of cancer, Cell 100 (2000) 57-70.
86. D. Hanahan and R. A. Weinberg, Hallmarks of cancer: The next generation, Cell 144 (2011) 646-674.
87. H. L. Hartwell, J. J. Hopfield, S. Leibner and A. W. Murray, From molecular to modular cell biology, Nature 402 (1999) c47-c52.
88. D. Helbing, Traffic and related self-driven many-particle systems, Rev. Mod. Phys. 73 (2001) 1067-1141.
89. D. Helbing, Quantitative Sociodynamics. Stochastic Methods and Models of Social Interaction Processes (Springer, 2010).
90. D. Helbing, A. Johansson and H. Z. Al-Abideen, Dynamics of crowd disasters: An empirical study, Phys. Rev. E 75 (2007) 046109.
91. C. K. Hemelrijk and H. Hildenbrandt, Self-organized shape and frontal density of fish schools, Ethol. 114 (2008) 245-254.
92. H. Hildenbrandt, C. Carere and C. K. Hemelrijk, Self-organized aerial displays of thousands of starlings: A model, Behav. Ecol. 21 (2010) 1349-1359.
93. H. Holden, K. Karlsen, K. Lie and N. Risebro, Splitting Methods for Partial Differential Equations with Rough Solutions, EMS Series of Lectures in Mathematics, Analysis and MATLAB programs (EMS, 2010).
94. E. Jager and L. Segel, On the distribution of dominance in populations of social organisms, SIAM J. Appl. Math. 52 (1992) 1442-1468.
95. G. Jona Lasinio, La matematica come linguaggio delle scienze della natura, Public Speech, Centro "E. De Giorgi", Scuola Normale Superiore, Pisa (2004).
96. J. Kelkel and C. Surulescu, A multiscale approach to cell migration in tissue networks, Math. Models Methods Appl. Sci. 22 (2012) 1150017.
97. E. F. Keller and L. A. Segel, Traveling bands of chemotactic bacteria: A theoretical analysis, J. Theor. Biol. 30 (1971) 235-248.
98. D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction, J. Math. Biol. 37 (1998) 235-255.
99. I. Klapper and J. Dockeryt, Mathematical description of microbial biofilms, SIAM Rev. 52 (2010) 221-265.
100. D. Knopoff, On the modeling of migration phenomena on small networks, Math. Models Methods Appl. Sci. 23 (2013) 541-563.
101. D. L. Koch and G. Subramanian, Collective hydrodynamics of swimming microorganisms: Living fluids, Ann. Rev. Fluid Mech. 43 (2011) 637-659.
102. P. Koumoutsakos, B. Bayati, F. Milke and G. Tauriello, Particle simulations of morphogenesis, Math. Models Methods Appl. Sci. 21 (2011) 955-1006.
103. M. Lachowicz, Individually-based Markov processes modeling nonlinear systems in mathematical biology, Nonlinear Analy.: Real World Appl. 12 (2010) 2396-2407.
104. S. F. Matter, Synchrony, extinction and dynamics of spatially segregated, heterogeneous populations, Ecol. Model. 141 (2001) 217-226.
105. B. Maury, A. Roudneff-Chupin and F. Stantambrogio, A macroscopic crowd motion model of gradient flow type, Math. Models Methods Appl. Sci. 20 (2010) 1899-1940.
106. R. M. May, Uses and abuses of mathematics in biology, Science 303 (2004) 790-793.
107. E. Mayr, The philosophical foundation of Darwinism, Proc. Amer. Philos. Soc. 145 (2001) 488-495.
108. E. Mayr, What Evolution Is (Basic Books, 2001).
109. E. Mayr, 80 Years of watching the evolutionary scenary, Science 305 (2004) 46-47.
110. F. Michor, Y. Iwasa and M. A. Nowak, Dynamics of cancer progression, Nature Rev. Cancer 4 (2004) 197-205.
111. M. B. Miller and B. L. Bassler, Quorum sensing in bacteria, Ann. Rev. Microb. 55 (2001) 165-199.
112. A. Mogilner, L. Edelstein-Keshet, L. Bent and A. Spiros, Mutual interactions, potentials and individual distance in a social aggregation, J. Math. Biol. 47 (2003) 353-389.
113. S. Motsch and E. Tadmor, A new model for self-organized dynamics and its flocking behavior, J. Stat. Phys. 144 (2011) 923-947.
114. F. Mynard and G. J. Seal, Phenotype spaces, J. Math. Biol. 60 (2010) 247-266.
115. M. Musso and J. Wei, Stationary solutions to a Keller-Segel chemotaxis system, Asympt. Anal. 49 (2006) 217-247.
116. L. Navoret, A two-species hydrodynamics model of particles interacting through self-alignment, Math. Models Methods Appl. Sci. 22 (2012) 1140004.
117. T. Niizatoa and Y.-P. Gunj, Metric-topological interaction model of collective behavior, Ecol. Model. 222 (2011) 3041-3049.
118. M. A. Nowak, Evolutionary Dynamics. Exploring the Equations of Life (Harvard Univ. Press, 2006).
119. M. A. Nowak and K. Sigmund, Evolutionary dynamics of biological games, Science 303 (2004) 793-799.
120. J. T. Oden, A. Hawkins and S. Prudhomme, General diffuse-interface theories and an approach to predictive tumor growth modeling, Math. Models Methods Appl. Sci. 23 (2013) 477-517.
121. J. T. Oden and S. Prudhomme, Control of modeling error in calibration and validation processes for predictive stochastic models, Int. J. Numer. Meth. Engrg. 87 (2011) 262-272.
122. A. Okubo, Dynamical aspects of animal grouping: Swarms, schools, flocks and herds, Adv. Biophys. 22 (1986) 1-94.
123. A. Okubo and S. A. Levin, Diffusion and Ecological Problems: Modern Perspectives (Springer, 2001).
124. H. Othmer, S. R. Dunbar and W. Alt, Models of dispersal in biological systems, J. Math. Biol. 26 (1988) 263-298.
125. H. Othmer and T. Hillen, The diffusion limit of transport equations II: Chemotaxis equations, SIAM J. Appl. Math. 62 (2002) 1222-1250.
126. K. J. Painter and T. Hillen, Spatio-temporal chaos in a chemotaxis model, Physica D 240 (2011) 363-375.
127. J. Paulsonn, Models of stochastic gene expression, Phy. Life Rev. 2 (2005) 157-175.
128. A. Perelson and G. Weisbuch, Immunology for physicists, Rev. Mod. Phys. 69 (1997) 1219-1267.
129. B. Perthame, Transport Equations in Biology (Birtkauser, 2007).
130. B. Piccoli and A. Tosin, Time-evolving measures and macroscopic modeling of pedestrian flow, Arch. Rational Mech. An. 199 (2011) 707-738.
131. I. Prigogine and R. Herman, Kinetic Theory of Vehicular Traffic (Elsevier, 1971).
132. F. C. Santos, J. M. Pacheco and T. Lenaerts, Evolutionary dynamics of social dilemmas in structured heterogeneous populations, Proc. Natl. Acad. Sci. USA 103 (2006) 3490-3494.
133. R. Reed, Why is mathematical biology so hard? Not. Amer. Math Soc. 51 (2004) 338-342.
134. C.W. Reynolds, Flocks, herds, and schools: A distributed behavioral model, Comput. Graph. 21 (1987) 25-34.
135. F. C. Santos, V. Vasconcelos, M. D. Santos, P. Neves and J. M. Pacheco, Evolutionary dynamics of climate change under collective-risk dilemmas, Math. Models Methods Appl. Sci. 22 (2012) 1140004.
136. A. Schadschneider and A. Seyfried, Empirical results for pedestrian dynamics and their implications for modeling, Netw. Heterog. Media 6 (2011) 545-560.
137. E. Schrodinger, What is Life? The Physical Aspect of the Living Cell (Cambridge Univ. Press, 1944).
138. M. B. Short, P. J. Brantingham, A. L. Bertozzi and G. E. Titad, Dissipation and displacement of hotspots in reaction-diffusion models of crime, PNAS 107 (2010) 3961-3965.
139. B. Stadler, P. Stadler, G. Wagner and W. Fontana, The topology of the possible: Formal spaces underlying patterns of evolutionary change, J. Theor. Biol. 213 (2001) 241-274.
140. P. Stadler and B. Stadler, Genotype phenotype maps, Biol. Th. 3 (2006) 268-279.
141. N. N. Taleb, The Black Swan: The Impact of the Highly Improbable (Random House, 2007).
142. C. M. Topaz and A. Bertozzi, Swarming patterns in a two dimensional kinematic model for biological groups, SIAM J. Appl. Math. 65 (2004) 152-174.
143. G. Toscani, Kinetic models of opinion formation, Commun. Math. Sci. 4 (2006) 481-496.
144. C. van Honk and P. Hogeweg, The ontogeny of the social structure in a captive Bombus terrestris colony, Behav. Ecol. Biol. 113 (1985) 311-330.
145. N. Verstraeten, K. Braeken, B. Debkumari, M. Fauvart, J. Fransaer, J. Vermant, and J. Michiels, Living on a surface: Swarming and biofilm formation, Trends in Microbiol. 16 (2008) 496-506.
146. B. Vogelstein and K.W. Kinzler, Cancer genes and the pathways they control, Nature Med. 10 (2004) 789-799.
147. J. von Brecht, T. Kolokolnikov, A. L. Bertozzi and H. Sun, Swarming on random graphs, J. Statist. Phys. 151 (2013) 150-173.
148. R. A. Weinberg, The Biology of Cancer (Taylor and Francis, 2007).
149. E. P. Wigner, The unreasonable effectiveness of mathematics in the natural sciences, Comm. Pure Appl. Math. 13 (1960) 1-14.
150. C. Xu and Z. Li, Effect of diffusion and spatially varying predation risk on the dynamics and equilibrium density of a predator prey system, J. Theor. Biol. 219 (2002) 73-82.
151. M. Zheng, Y. Kashimori, O. Hoshino, K. Fujita and T. Kambara, Behavior pattern (innate action) of individuals in fish schools generating collective evasion from predation, J. Theor. Biol. 235 (2005) 153-157.