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MIGUEL A. HERRERO (CURRICULUM VITAE)

 

CURRENT POSITION

 

Emeritus Professor of Applied Mathematics, Universidad Complutense (UCM), Madrid, Spain.

 

 

PERSONAL DATA

 

Name: Miguel Angel Herrero García.

 

Born: Madrid, August 5, 1951.

 

Address: Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, Plaza de las Ciencias s/n, 28040 Madrid, Spain.

 

E-mail: herrero@mat.ucm.es

 

 

EDUCATION

 

Ph.D (Mathematics), Universidad Complutense (1979).

 

M.Sc (Mathematics), Universidad Complutense (1973).

 

 

RESEARCH INTERESTS

 

Differential Equations, Mathematical Modeling, Simulation and Optimization in Natural and Social Sciences.

 

 

PROFESSIONAL EXPERIENCE

 

2008-2011. Director, Institute for Interdisciplinary Mathematics (Instituto de Matemática Interdisciplinar), Universidad Complutense.

 

1999, 2001. Visiting Professor, University of Florence (Italy).

 

1998 - . Professor of Applied Mathematics, Universidad Complutense (UCM ).

 

1993-1998. Associate Professor (UCM).


1988. Visiting Professor, Northwestern University (USA) 1986. Visiting Scholar, University of Minnesota (USA).

 

1983-1984. Postdoctoral Fellow, University of Oxford ( UK) 1982. Postdoctoral Fellow, University of Paris VI (France).

 

1979-1982. Assistant Professor (UCM).

 

 

SERVICES

 

2014. European Mathematical Society (EMS) Lecturer.

 

2005-2013. Director (together with Prof. Juan Soler) of the Granada International Summer School: BIOMAT: Mathematics in Life Sciences (http://www.ugr.es/~kinetic/biomat/). 

 

2008 - . Member, Board of the ESMTB (European Society for Mathematical and Theoretical Biology, http://esmtb.org/).

 

2004-2008. Head, Department of Applied Mathematics (UCM).

 

2001 - . Member, Board of the Series on Modelling and Simulation in Science, Engineering and Technology, BirkHäuse (Springer).

 

1999-2008. Member, Scientific Committee of RSME (Royal Spanish Society of Mathematics).

 

1997 - . Member, Board of the Journal: European Journal of Applied Mathematics

(http://journals.cambridge.org/action/displayJournal?jid=EJM), Cambridge University Press (UK).
 

1997-2002. Member, Board of the Journal: SIAM Journal of Mathematical Analysis (http://www.siam.org/journals/sima.php), SIAM (Society for Industrial and Applied Mathematics, USA).

 

 

Ph. D THESIS SUPERVISED

 

1.- Juan J. L. Velázquez (1990), currently Professor at University of Bonn, Germany.

 

2.- Luis A. Herraiz (1996).

 

3.- G. E. Oleaga (2000; jointly supervised with J. J. L. Velázquez), currently Professor Contratado Doctor at Universidad Complutense.

 

4.- A. Köhn-Luque (2012; jointly supervised with J. M. Pérez Pomares), currently Postdoctoral Researcher at University of Oslo, Norway. 

 

5.- J. C. L. Alfonso (2014; jointly supervised with B. García-Archilla and L. Núñez) currently Postodctoral Researcher at Dresden University, Germany.

 

6.- L. F. Echeverri (2015; jointly supervised with G. E. Oleaga) currently Associate Professor at University of Medellín, Colombia.

 

SELECTED PUBLICATIONS.

 

1.- J. I. Díaz and M. A. Herrero. Proprietés de support compact pour certaines equations elliptiques et paraboliques non llinéaires (1978). Compt. Rend. Acad. Sci. Paris 286 ; pp. 258-259.

 

2.- J. I. Díaz and M. A. Herrero. Estimates on the support of some nonlinear elliptic and parabolic problems (1981). Proc. Royal Society Edinburgh 89A; pp. 249-258.

 

3.- M. A. Herrero and J. L. Vázquez. Asymptotic behaviour of the solutions of a strongly nonlinear parabolic problem (1981). Ann. Fac. Sci. Toulouse 3; pp. 113-127.

 

4.- M. A. Herrero. Sobre el comportamiento de las soluciones de ciertos problemas parabólicos no lineales (1981). Rev Real Acad. Ciencias Ex. Fis y Nat. 75/5; pp. 1165-1183.

 

5.- M. A. Herrero and J. L. Vázquez. On the propagation properties of a nonlinear degenerate parabolic equation (1982). Communications inPDE 7/12; pp. 1381-1402.

 

6.- M. A. Herrero. On the growth of the interfaces of a nonlinear degenerate parabolic equation (1990). Contributions to nonlinear PDE, C. Bardos et al. Ed Pitman Research Notes 86; pp. 218-224.

 

7.- M. A. Herrero and M. Pierre. The Cauchy problem for ut=Du m when 0 < m < 1 (1985). Trans. Amer. Mat. Soc. 291/1; pp. 145-158.

 

8.- C. M. Elliot, M. A. Herrero, J.R. King and J. R. Ockendon. The Mesa problem : diffusion patterns for ut=Ñ (umÑ u) as m ®¥ (1986). IMA J. Appl. Math. 37; pp. 147-154.

 

9.- M. A. Herrero and J. L. Vázquez. The one dimensional nonlinear heat equation with absorption: regularity of solutions and interfaces (1987). SIAM J. Math. Anal. 18/1; pp. 149-167.

 

10.- A Friedman and M. A. Herrero. Extinction properties of semilinear heat equations with strong absorption (1987). J. Math. Anal. and Appl. 124; pp. 530-546.

 

11.- M. A. Herrero. Temperature fronts in one-dimensional media, in Nonlinear parabolic equations: qualitative properties of solutions (1987). L. Boccardo et al. Ed. Pitman Research Notes; pp. 218-224.

 

12.- M. A. Herrero and J. L. Vázquez. Thermal waves in absorbing media (1988). J. Diff. Equations 74/2; pp. 218-233.

 

13.- B. H. Gilding and M. A. Herrero. Localization and blow-up of thermal waves in nonlinear heat conduction with peaking (1988). Mathematische Annalen 282; pp. 223-242.

 

14.- M. A. Herrero. A limit case in nonlinear diffusion (1989). J. Nonlinear Analysis 13/6; pp. 611-628.

 

15.- J. Esquinas and M. A. Herrero. Travelling wave solutions to a semilinear díffusion system (1990). SIAM J. Math. Anal. 21/1; pp. 123-136.

 

16.- M. A. Herrero and J. J. L. Velázquez. On the dynamics of a semilinear heat equation with strong absorption (1989). Communications in PDE 14/4; pp. 1653-1715.

 

17.- A. Friedman and M. A. Herrero. A nonlinear nonlocal wave equation arising in combustion theory (1990). J. Nonlinear Analysis 14/2; pp. 93-106.

 

18.- E. Di Benedetto and M. A. Herrero. On the Cauchy problem and initial traces for a degenerate parabolic problem (1989). Trans. Amer . Math. Soc. 3/14; pp. 187-224.

 

19.- M. A. Herrero and J. J. L. Velázquez. Stability analysis of a closed thermosyphon (1990). European J. Appl. Maths 1; pp. 1-24.

 

20.- E. Di Benedetto and M. A. Herrero. Nonnegative solutions of the evolution p-laplacian equation: Initial traces and Cauchy problem when 1 < p < 2 (1990). Archive for Rat. Mech. Analysis 11 1/3; pp. 225-290.

 

21.- M. Escobedo and M. A. Herrero. Boundedness and blow-up for a semilinear reaction diffusion system (1991). J. Diff. Equations 89/1; pp. 176-202.

 

22.- M. A. Herrero and J. J. L. Velázquez. Asymptotic properties of a semilinear heat equation with strong absorption and small diffusion (1990). Mathematische Annalen 288; pp. 675-695.

 

23.- V. A. Galaktionov, M. A. Herrero and J. J. L. Velázquez. The space structure near a blow-up point for semilinear heat equations: a formal approach (1991). USSR Journal of Computational Maths. and Math. Physics 31; pp. 399-411.

 

24.- M. Escobedo and M. A. Herrero. A uniqueness result for a semilinear reaction-diffusion system (1991). Proc. Amer. Math. Soc. 11 2/1; pp. 175-185.

 

25.- M. A. Herrero and J. J. L. Velázquez. Radial solutions of a semilinear elliptic problem (1991). Proc. Royal Soc. Edinburgh 118; pp. 305-326.

 

26.- Ph. Benilan , L. Boccardo and M. A. Herrero. On the limit of solutions of u t=Dum as m ®¥ (1991). Rend. Sem. Mat. Univ. Pol. Torino. Fascicolo speciale on nonlinear PDE's; pp. 1-13.

 

27.- M. A. Herrero and J. J. L. Velázquez. Blow-up profiles in one dimensional, semilinear parabolic problems (1992). Comm. in PDE 17; pp. 215-236.

 

28.- V. A. Galaktionov , M. A. Herrero and J. J. L. Velázquez. The structure of solutions near an extinction point in a semilinear heat equation with strong absorption: a formal approach, in Nonlinear differential equations and their equilibrium states (1992). G . N. Lloyd et al. ed. Birkhauser Verlag. 11 2/1; pp. 215-236.

 

29.- A. Friedman and M. A. Herrero. Extinction and positivity for a system of parabolic variational inequalities (1992). J. Math. Anal. and App 167/1; pp. 167-175.

 

30.- M. A. Herrero and J. J. L. Velázquez. Blow-up behaviour of one-dimensional semilinear parabolic equations (1993). Ann. Inst. Henri Poincaré 10/2; pp. 131-189.

 

31.- M. A. Herrero and J. J. L. Velázquez. Approaching an extinction poínt in one-dimensional semilinear heat equations with strong absorption (1992). J. Math. Anal. and Appl. 170/2; pp. 353-381.

 

32.- M. A. Herrero and J. J. L. Velázquez. Plane structures in thermal runaway (1993). Israel J. Maths 81; pp. 321-341.

 

33.- M. A. Herrero and J. J. L. Velázquez. Flat blow-up in one-dimensional semilinear heat equations (1992). Diff. and Int. Equations 5; pp. 973-987.

 

34.- M. A. Herrero and J. J. L. Velázquez. Generic behaviour of one-dimensional blow-up patterns (1992). Annali Sc. Norm. Sup. Pisa 19; pp. 381-450.

 

35.- V. A. Galaktionov, M. A. Herrero, S. A. Posashkov and J. J. L. Velázquez. On a general approach to extinction and blow-up for quasilinear heat equations (1993). Journal of Comput. Maths. And Math. Phyiscs (en ruso) 33; pp. 246-258.

 

36.- M. A. Herrero and J. J. L. Velázquez. Some results on blow-up for semilinear parabolic problems, in Degenerate diffusions (1993). IMA volumes on Mathematics and its Applications, Springer Verlag 47; pp. 105-126.

 

37.- M. Escobedo and M. A. Herrero. A semilinear parabolic problem in a bounded domain (1993). Annali di Matematica Pura ed Applicata CLXV; pp. 315-336.

 

38.- M. A. Herrero, A. A. Lacey and J. J. L. Velázquez. Blow-up under oscillatory boundary conditions (1994). Asymptotic Analysis 9; pp. 1-22.

 

39.- M. A. Herrero and J. J. L. Velázquez. Explosion de solutions d' equations paraboliques semilineaires (1994). Compt. Rend. Acad. Sci. Paris 319,1; pp. 141-145.

 

40.- M. A. Herrero and J. J. L. Velázquez. Singularity formation in the one-dimensional, supercooled Stefan problem (1996). European J. Appl. Math. 7; pp. 119-150.

 

41.- M. A. Herrero and J.J.L.Velázquez. Singularity patterns in a chemotaxis model (1996). Mathematische Annalen 306,3; pp. 583-623.

 

42.- M. A. Herrero and J. J. L. Velázquez. Chemotactic collapse for the Keller-Segel model (1996). J. Math. Biology 35; pp. 177-194.

 

43.- M. A. Herrero and J. J. L. Velázquez . On the melting of ice balls (1997). SIAM J. Math. Anal. 28, 1; pp. 1-32.

 

44.- D. Andreucci, M. A. Herrero and J. J. L. Velázquez. Liouville theorems and blow-up behaviour in semiilinear reaction-diffusion systems (1997). Annales de l ' Institut Henri Poincaré 14, 1; pp. 1-53.

 

45.- L. L. Bonilla, P. J. Hernando, M. A. Herrero, M. Kindelán and J. J. L. Velázquez. Asymptotics of the trap-dominated Gunn effect in p- type Germanium (1997). Physica D. 108; pp. 168-190.

 

46.- M. A. Herrero, E. Medina and J. J. L. Velázquez. Finite-time aggregation into a single point in a reaction-diffusion system (1997). Nonlinearity 10; pp. 1739-1754.

 

47.- M. A. Herrero , A. A. Lacey and J. J. L. Velázquez. Global existence for a reaction-diffusion system modelling ignition (1998). Arch. Rat. Mech. Analysis 142; pp. 219-251.

 

48.- M. A. Herrero and J. J. L. Velázquez. A blow-up mechanism for a chemotaxis problem (1997). Ann. Scuola Normale Sup . Pisa Serie IV; pp. 633-683.

 

49.- M. A. Herrero, E. Medina and J. J. L. Velázquez. Self-similar blow-up in a reaction-diffusion system (1998). Journal of Computational and Applied Mathematics 97 1 & 2; pp. 99-119.

 

50.- M. Escobedo, M. A. Herrero and J. J. L. Velázquez. A nonlinear Fokker-Planck equation modelling the approach to thermal equilibrium in a homogeneous plasma (1998). Trans . Amer . Math. Soc 350, 10; pp. 3837-3901.

 

51.- M. Escobedo, M. A. Herrero and J. J. L Velázquez. Radiation dynamics in a homogeneous plasma (1999). Physica D 126; pp. 236-260.

 

52.- M. A. Herrero. Asymptotic properties of reaction-diffusion systems modeling chemotaxis. Invited Lecture in Proceedings of the Venice – 2 Symposium on Applied and Industrial Mathematic (2000). Kluwer Ac. Pub; pp. 89-108.

 

53.- M. A. Herrero, J. J. L. Velázquez and D. Wrzosek. Sol–gel transition in a coagulation–diffusion system (2000). Physica D 141; pp. 221-247.

 

54.- M. A. Herrero, E. Medina and J. J. L. Velázquez. The birth of a cusp in the two- dimensional, supercooled Stefan problem (2000). Quarterly of Applied Mathematics 3; pp. 473-494.

 

55.- S. Filippas, M.A. Herrero and J. J. L. Velázquez. Fast blow–up mechanisms for sign changing solutions of a semilinear parabolic equation with critical nonlinearity (2000). Proc. Royal Soc. London (A) 456; pp. 2957-2982.

 

56.- L. Herraiz, M.A. Herrero and J. J. L. Velázquez. A note on the dissolution of spherical crystals (2001). Proc. Royal Soc. Edinburgh A 131; pp. 371-389.

 

57.- D. Andreucci, M .A. Herrero and J. J. L. Velázquez. The classical one–phase Stefan problem: a catalogue of interface behaviours (2001). Surveys of Mathematics in Industry 9; pp. 247-337.

 

58.- M. A. Herrero. From nucleation to large aggregates: the growth of filamentary structures (2002). Invited Lecture at the European Conference on Industrial and Applied Mathematics, ECMI 2000, Springer; pp. 16-27.

 

59.- M. A. Herrero. Reaction–diffusion systems: a mathematical biology approach (2003). In Cancer Modelling and Simulation, L.Preziosi (ed). Chapman and Hall Mathematical Biology and Medicine Series; Chapter 13, pp. 367-420.

 

60.- M.A. Herrero, G. E. Oleaga and J. J. L. Velázquez. Planar cracks running along piecewise linear paths (2004). Proc. Royal Soc. London A 460; pp. 1-21.

 

61.- M. A. Herrero, M. Ughi and J. J. L. Velázquez. Approaching a vertex in a shrinking domain under a nonlinear flow (2004). Nonlinear Differential Equations and Applications 11; pp. 1-28.

 

62.- D. Andreucci, M. A. Herrero and J. J. L. Velázquez. On the growth of filamentary structures in planar media (2004). Math. Meth. In the Appl. Sci. 27; pp. 1935-1968.

 

63.- M. A. Herrero. The mathematics of chemotaxis, In the volume Simplicity, rigor and relevance in fluid mechanics, a volume in honour of Amable Liñán .F. J. Higuera, J. Jiménez and J. M. Vega Editors (2004); pp. 349-362.

 

64.- M. A. Herrero and M.R. Rodrigo. A note on Smoluchowski ́s equations with diffusion (2005). Appl. Math. Letters 18, 9; pp. 969-975.

 

65.- M. A. Herrero and J. M. López. Bone formation: biological aspects and modelling problems (2005). Journal of Theoretical Medicine 6,1; pp. 41-55.

 

66.- M. A. Herrero, G. E. Oleaga and J. J. L. Velázquez. On the Eshelby-Kostrov property for the wave equation in the plane (2006). Trans. Amer. Math. Soc. 358; pp. 3673-3695.

 

67.- M. A. Herrero and L. Sastre. Models of aggregation in Dyctiostelium discoideum: on the track of spiral waves (2006). Networks and Heterogeneous Media 1, 2; pp. 241-258.

 

68.- A. Bru and M. A. Herrero. From the physical laws of tumour growth to modelling cancer processes (2006). Mathematical Models and Methods in the Applied Sciences 16, 7; pp. 1199-1218.

 

69.- M. A. Herrero. The Mathematics of Chemotaxis (2007). Handbook of Differential Equations. Elsevier Pub. 3; pp. 137-193.

 

70.- M. A. Herrero and M. R. Rodrigo. Remarks on accessible steady states for some coagulation-fragmentation models (2007). Discrete and Continuous Dynamical Systems A 17, 3; pp. 541-552.

 

71.- N. Bellomo, A. Bellouquid and M. A. Herrero. From microscopic to macroscopic description of multicellular systems and biological growing tissues. Comp. and Maths. with Appl. (2007), 53; pp. 647-663.

 

72.- S. Veintemillas, S. Osuna and M. A. Herrero. The effect of stirring on sodium chlorate crystallization under symmetry breaking conditions (2007). Journal of Crystal Growth 303; pp. 562-567.

 

73.- M. A. Herrero. On the role of Mathematics in Biology (2007). Journal of Mathematical Biology 54; pp. 887-889.

 

74.- A. Bru, D. Casero, S. de Franciscis and M. A. Herrero. Fractal analysis and tumour growth (2007). Math. Comp. Modelling. doi:10.1016/j.mcm.2007.02.033.

 

75.- J. C. Nuño, M. A. Herrero and M. Primicerio. A triangle model of criminality (2008). Physica A 387, 54; pp. 2926-2936.

 

76.- A. Cappuccio, M. A. Herrero and L. Núñez. Biological Optimization of tumour radiosurgery (2009). Medical Physics 36, 1; pp. 98-104.

 

78.- G. Th. Guria, M. A. Herrero and K. Zlobina. A mathematical model of blood coagulation induced by tissue sources (2009). Discrete and Continuous Dynamical Systems, A 25, 1; pp. 175-194.

 

79.- A. Fasano, M. A. Herrero and M. R. Rodrigo. Slow and fast invasion waves in a model of acid–mediated tumour growth (2009). Mathematical Biosciences 220; pp. 45-56.

 

80.- M. A. Herrero, A. Köhn and J. M. Pèrez-Pomares. Modeling vascular morphogenesis: current views on blood vessel development (2009). Mathematical Models and Methods in the Applied Sciences 19, Suppl; pp. 1-55.

 

81.- A. Cappuccio, M. A. Herrero and L. Núñez. Tumour radiotherapy and its mathematical modelling (2009). In Mathematics, Developmental Biology and Tumour Growth, F. Giráldez and M. A. Herrero editors. 492; pp. 77-102.

 

82.- G. Th. Guria , M. A. Herrero and K. Zlobina. Ultrasound detection of externally induced microthrombi cloud formation: a theoretical study (2010). Journal of Engineering Mathematics 66, 1-3; pp. 293-310.

 

83.- A. Fasano, M. A.Herrero, J. M. López and E. Medina. On the dynamics of the growth plate in primary ossification (2010). Journal of Theoretical biology 265; pp. 543-553.

 

84.- J. C. Nuño, M. A. Herrero and M. Primicerio. Fighting cheaters: how and how much to invest (2010). European journal of Applied Mathematics 21, 4-5; pp. 459-478.

 

85.- J. C. Nuño, M. A. Herrero and M. Primicerio. A mathematical model of a criminal-prone society (2011). Discrete and Continuous Dynamical Systems S 4, 1; pp. 193-207.

 

86.- M. A. Herrero (2011). Stability properties of biochemical cascades. In Evolution Equations and Materials with Memory, D. Andreucci, S. Carillo et al. ed . La Sapienza (Roma), ISBN: 978-88-95814-51-3; pp. 119-134.

 

87.- M. A. Herrero (2011). Through a glass, darkly: Biology seen from Mathematics. Physics of Life Reviews 8(1), doi: 10.1016/j. plrev 2010.12.001.

 

88.- A. Köhn-Luque, W. De Back, J. Starrruss, A. Mattiotti, A. Deutsch, J. M. Pérez-Pomares and M. A. Herrero (2011). Early embryonic vascular patterning by matrix- mediated paracrine signalling: a mathematical model study. PLoS ONE 6(9): e24175. doi:10.371/Journal.pne.0024175.

 

89.- R. Cuerno, C. Escudero, J. M. García-Ruiz and M. A. Herrero (2012). Pattern formation in stromatolites: insights from mathematical modelling. J. Roy. Soc. Interface doi: 10.1098/rsif.2011.0516.

 

90.- J. C. L. Alfonso, G. Buttazzo, B. García-Archilla, M. A. Herrero and L. Núñez (2012). A class of optimization problems in Radiotherapy dosimetry planning. Discr. Cont. Dyn. Systems B 17, 6; pp. 1651-1672.

 

91.- N. Bellomo, M. A. Herrero and A. Tosin (2013). On the dynamics of social conflicts: looking for the black swan. Kinetic and Related Models 6; pp. 459- 479.

 

92.- A. Köhn-Luque, W. De Back, Y. Yamaguchi, K. Yoshimura, M. A. Herrero and T. Miura (2013). Dynamics of VEGF matrix retention in vascular network patterning. Phys. Biol.: 10, 066007. doi:10.1088/1478-3975/10/6/066007.

 

93.- A. B. Holder, M. R. Rodrigo and M. A. Herrero (2104). A model for acid-mediated tumour growth with nonlinear acid production term. Applied Mathematics and Computation: 227; pp. 176- 198.​

 

94.- C. F. Arias, M. A. Herrero, F. J. Acosta and C. Fernández-Arias (2014). A mathematical model for a T cell fate decision algorithm during immune response. Journal of Theoretical Biology 349, 109-120.

 

95.- J. C. L. Alfonso, N. Jagiella, L. Núñez, M. A. Herrero and D. Drasdo (2014). Estimating dose painting effects in radiotherapy: a mathematical model. PLOS ONE 9 (2) e89380.

 

96.- J. C. L. Alfonso, G. Buttazzo, B. García-Archilla, M. A. Herrero and L. Núñez (2014). Selecting radiotherapy dose distributions by means of constrained optimization problems. Bulletin of Mathematical Biology doi:10.1007/s11538-014-9945-7.

 

97.- L. F. Echeverri, M. A. Herrero, J. M. Lopez and G. Oleaga. Early stages of bone fracture healing: formation of a fibrin-collagen scaffold in the fracture hematoma. Bull Math Biol. 2015 Jan;77(1):156-83. doi: 10.1007/s11538-014-0055-3.

 

98.- C. F. Arias, M. A. Herrero, J. A. Cuesta, F. J. Acosta and C. Fernández-Arias. The growth threshold conjecture: a theoretical framework for understanding T-cell tolerance. R. Soc. Open Sci. 2: 150016, 2015. doi: http://dx.doi.org/10.1098/rsos.150016.

 

99.- K. Böttger, H. Hatzikirou, A.Voss-Böhme, E.A. Cavalcanti-Adam,M.A. Herrero and A. Deutsch  (2015) An Emerging Allee Effect Is Critical for Tumor Initiation and Persistence. PLoS Comput Biol 11(9): e1004366. doi:10.1371/journal.pcbi.1004366.

 

100.- M. A. Herrero and J. Soler (2015). Cooperation, Competition, Organization: The dynamics of interacting populations. Mathematical Models and Methods in the Applied Sciences. doi:10.1142/S0218202515020030.

 

101.- J. C. L. Alfonso, M. A. Herrero and L. Núñez (2015) A dose-volume histogram based decision-support system for dosimetric comparison of radiotherapy treatment plans. Radiation Oncology 10(1): 1-9. doi:10.1186/s13014-015-0569-3.

102.- T. Alarcón, J. Castillo, B. García-Ponce, M. A. Herrero and P. Padilla (2016). Growth rate and shape as possible control mechanisms for the selection of mode development in optimal biological branching processes. Eur. Phys, J. Special Topics 225, 2581-2589.

103.- C. F. Arias, M.A. Herrero, F. J. Acosta and C. Fernandez-Arias (2017). Population mechanics: a mathematical framework to study T cell homeostasis. Scientific Reports 7(1): 9511. doi:10.1038/s41598-017-09049-w.

​​104.- C. F. Arias, M.A. Herrero, C.D. Stern and F. Bertocchini(2017). A molecular mechanism of symmetry breaking in early chick embryo. Scientific Reports 7(1): 15776. doi:10.138/s41598-017-15881-8.

105.- C. Fr. Arias, C. F. Arias, M. Zhang, M. A.Herrero, F. J. Acosta and M. Tsuji (2018). Modeling the effect of boost timing in murine sporozoite prime-boost vaccines. PLOS ONE 13 (1): e0190940.​ doi.org/10.1371/journal.pone.0190940.

106.- C. F. Arias and M. A. Herrero. Emergent behaviour in T cell immune response (2018). Progress in Industrial Mathematics, P. Quintela et al (eds), 17-23. doi :10.1007/978-3-319-63082-3_2.

107.- C. F. Arias, M.A. Herrero, L. F. Echeverri, G. E. Oleaga and J. M. Lopez. Bone remodeling: a tissue-level process emerging from cell-level molecular algorithms (2018). PLoS ONE 13(9): e0204171. https://doi.org/10.1371/journal.pone.02041.

108. M. A. Herrero. Mobility and dominance in social dynamics (2018). Accademia Nazionale dei Lincei . Contributi del Centro Linceo Interdisciplinare Beniamino Segre 136. 59-70.

109.- C. F. Arias, F. Bertocchini, M. A. Herrero, J. M. Lopez and G. E. Oleaga. A proposed screening algorithm for bone remodelling (2020).  European J. Appl. Math; doi: 10.1017/S0956792520000418; 1-14.

 

110.- C. F. Arias, M. A. Herrero, ​F. Bertocchini, F. J. Acosta and C. Fr. Arias. Modeling the dependence of immunodominance in T cell dynamics in prime-boost vaccines (2021). Mathematics 9, 28 // dx.doi.org/10.3390/math 9010028 ; 1-13.​

 

111.- C. F. Arias, F. J. Acosta, F. Bertocchini, M. A. Herrero and C. Fernández-Arias. The coordination of anti-phage immunity mechanisms in bacterial cells (2022). Nature Communications 13 (1), 7412 https://doi.org/10.1038/s41467-022-35203-7

 

112.- B. Franchi, M. A. Herrero and V. Tora. Dynamics of a polymerization model on a graph (2022). Le Matematiche, Vol. LXXVII – Issue I, pp. 173–201 doi: 10.4418/2022.77.1.9

 

113.- B. Serrano-Antón, C. Mian, R. Fuente, F. Bertocchini, M. A. Herrero, J. M. López, G. E. Oleaga and C. F. Arias. A Computational Approach to Individual Cell-Based Decision Algorithms Involved in Bone Remodeling (2024). Mathematics 12 (3), 362 https://doi.org/10.3390/math12030362

 

114.- C. F. Arias, F. Bertocchini, F. J. Acosta, G. E. Oleaga, C. Fernández-Arias and M. A. Herrero. Predicting and Explaining with Models: A Few Remarks on Mathematical Immunology.Problems in Mathematical Biophysics (2024). SEMA SIMAI. Springer Series 38, A. d’Onofrio et al. (eds.) https://doi.org/10.1007/978-3-031-60773-8_2

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