Skip to main content
SpringerLink
Log in

Randomness and Geometric Structures in Biology

  • Conference paper
  • First Online:
Pattern Formation in Morphogenesis

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 15))

Abstract

Research in biomathematics has played an important role in identifying the biological principles that are responsible for patterns. What has been missing is the link between biological phenomena that occur at different scales.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

  1. Anderssen B, Capasso V (2008) SSQBM – pattern formation and functional morphology (PFFM). Personal notes of the debate on the turing methodology is the only way to model pattern formation in biology. RICAM, Linz, Jan 2008

    Google Scholar 

  2. Bailey NTJ (1975) The mathematical theory of infectious diseases. Griffin, London

    MATH  Google Scholar 

  3. Bellomo N, De Angelis E, Preziosi L (2004) Multiscale modelling and mathematical problems related to tumour evolution and medical therapy. J Theor Med 5:111–136

    Article  Google Scholar 

  4. Benes V, Rataj J (2004) Stochastic geometry. Kluwer, Dordrecht

    MATH  Google Scholar 

  5. Bookstein FL (1978) The measurement of biological shape and shape change, vol 24, Lecture notes in biomathematics. Springer, Heidelberg

    Book  MATH  Google Scholar 

  6. Bookstein FL (1991) Morphometric tools for landmark data. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  7. Burger M, Capasso V, Pizzocchero L (2006) Mesoscale averaging of nucleation and growth models. SIAM J Multiscale Model Simul 5:564–592

    Article  MathSciNet  MATH  Google Scholar 

  8. Byrne H, Chaplain M (1995) Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions. Bull Math Biol 57:461–486

    MATH  Google Scholar 

  9. Canic S, Mikelic A (2003) Effective equations modeling the flow of a viscous incompressible fluid through a long tube arising in the study of blood flow through small arteries. SIAM J Appl Dyn Syst 2:431–463

    Article  MathSciNet  MATH  Google Scholar 

  10. Capasso V, Dejana E, Micheletti A (2007) Methods of stochastic geometry, and related statistical problems in the analysis and therapy of tumour growth and tumour-driven angiogenesis. In: Bellomo N, Chaplain M, De Angelis E (eds) Mathematical methods in cancer diagnosis and therapy. Birkhauser, Boston

    Google Scholar 

  11. Capasso V, Engl HW, Kindermann S (2008) Parameter identification in a random environment exemplified by a multiscale model for crystal growth. SIAM J Multiscale Model Simul 7:814–841

    Google Scholar 

  12. Capasso V, Micheletti A, Morale D (2008) Stochastic geometric models, and related statistical issues in tumour-induced angiogenesis. Math Biosci 214:20–31

    Article  MathSciNet  MATH  Google Scholar 

  13. Capasso VM (2008) Rescaling stochastic processes: asymptotics. In: Capasso V, Lachowicz M (eds) Multiscale problems in the life sciences from microscopic to macroscopic, vol 1940, Lecture notes in mathematics/C.I.M.E.. Springer, Heidelberg

    Google Scholar 

  14. Capasso V, Morale D (2011) A multiscale approach leading to hybrid mathematical models for angiogenesis: the role of randomness. In: Friedman A et al (eds) Mathematical methods and models in biomedicine. Springer, New York, In Press

    Google Scholar 

  15. Carbone A, Gromov M, Prusinkiewicz P (2000) Preface. In: Carbone A, Gromov M, Prusinkiewicz P (eds) Pattern formation in biology, vision and dynamics. World Scientific, Singapore

    Google Scholar 

  16. Carmeliet P (2005) Angiogenesis in life, disease and medicine. Nature 438:932–936

    Article  Google Scholar 

  17. Carroll SB (2005) Endless forms most beautiful. The new science of evo-devo. Baror International Inc, Armonk, New York, USA

    Google Scholar 

  18. De Masi A, Luckhaus S, Presutti E (2007) Two scales hydrodynamic limit for a model of malignant tumor cells. Annales H Poincare, Probabilite et Statistiques 43:257–297

    Article  MATH  Google Scholar 

  19. Dryden IL, Mardia KV (1997) The statistical analysis of shape. Wiley, Chichester

    Google Scholar 

  20. Durrett R (1999) Stochastic spatial models. In: Capasso V, Diekmann O (eds) Mathematics inspired by biology, vol 1714, Lecture notes in mathematics/C.I.M.E. Springer, Heidelberg

    Chapter  Google Scholar 

  21. Durrett R, Levin SA (1994) The importance of being discrete (and spatial). Theor Pop Biol 46:363–394

    Article  MATH  Google Scholar 

  22. Fournier N, Meleard S (2004) A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann Appl Probab 14:1880–1919

    Google Scholar 

  23. Jaeger W (2001) Private discussion about MBIOS, a project of the Ruprecht-Karls-Universitaet. Heidelberg

    Google Scholar 

  24. Jagers P (2010) A plea for stochastic population dynamics. J Math Biol 60:761–764

    Google Scholar 

  25. Kendall DG, Barden D, Carne TK, Le H (1999) Shape and shape theory. Wiley, Chichester, N.Y

    Book  MATH  Google Scholar 

  26. Miles RE, Serra J (eds) (1978) Geometrical probability and biological structures: buffon’s 200th anniversary, vol 23, Lecture notes in biomathematics. Springer, Berlin-New York

    MATH  Google Scholar 

  27. Murray JD (1989) Mathematical biology. Springer, Heidelberg

    MATH  Google Scholar 

  28. Murray JD et al (2003) Foreword. In: Sekimura T et al (eds) Morphogenesis and pattern formation in biological systems. Springer, Tokyo

    Google Scholar 

  29. Oelschlaeger K (1989) On the derivation of reaction–diffusion equations as lilit dynamics of systems of moderately interacting stochastic processes. Prob Th Rel Fields 82:565–586

    Article  MATH  Google Scholar 

  30. Plank MJ, Sleeman BD (2003) A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies. IMA J Math Med Biol 20:135–181

    Article  MATH  Google Scholar 

  31. Schiaparelli GV (1898) Studio comparativo tra le forme organiche naturali e le forme geometriche pure. Hoepli, Milano

    Google Scholar 

  32. Segel LA (1984) Modelling dynamic phenomena in molecular and cellular biology. Cambridge University Press, Cambridge, New York

    Google Scholar 

  33. Serra J (1984) Image analysis and mathematical morphology. Academic Press Inc, London

    Google Scholar 

  34. Sun S, Wheeler MF, Obeyesekere M, Patrick CW Jr (2005) A deterministic model of growth factor-induced angiogenesis. Bull Math Biol 67:313–337

    Article  MathSciNet  Google Scholar 

  35. Thompson DW (1917) On growth and form. Cambridge University Press, Cambridge

    Google Scholar 

  36. Turing AM (1952) The chemical basis of morphogenesis. Philos Trans Roy Soc London B 237:37–72

    Google Scholar 

  37. Watson JD, Crick FHC (1953) Molecular structure of nucleic acids: a structure for deoxyribose nucleic acid. Nature 171(4356):737–738

    Article  Google Scholar 

  38. Levin SA (ed) (1992) Mathematics and biology: the interface, challenges and opportunities. Lawrence Berkeley Laboratory, University of California, Berkeley (CA)

    Google Scholar 

  39. Capasso V et al (eds) (1985) Mathematics in biology and medicine, vol 57, Lecture notes in biomathematics. Springer, Heidelberg

    MATH  Google Scholar 

  40. Jaeger W, Murray JD (eds) (1984) Modelling of patterns in space and in time, vol 55, Lecture notes in biomathematics. Springer, Heidelberg

    Google Scholar 

  41. Capasso V, Periaux J (eds) (2005) Multidisciplinary methods for analysis, optimization and control of complex systems, vol 6, Mathematics in industry. Springer, Heidelberg

    Google Scholar 

  42. Capasso V, Lachowicz M (eds) (2008) Multiscale problems in the life sciences from microscopic to macroscopic, vol 1940, Lecture notes in mathematics/C.I.M.E. Springer, Heidelberg

    MATH  Google Scholar 

  43. Chaplain et al (eds) (1999) On growth and form. Spatio-temporal pattern formation in biology. Wiley, New York

    MATH  Google Scholar 

  44. PITAC (2005) Report, computational sciences ensuring America’s competitiveness. Executive Office of the President of the United States of America

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Milano, Milan, Italy

    Vincenzo Capasso

Authors
  1. Vincenzo Capasso
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vincenzo Capasso .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, MIRIAM, Università Milano-Bicocca, Via Saldini 50, Milano, 20133, Italy

    Vincenzo Capasso

  2. Études Scientifiques, Institut des Hautes, route des Chartres 35, Bures-sur-Yvette, 91440, France

    Misha Gromov

  3. Cancer Institut Andre Lwoff, CNRS FRE 3239, Laboratoire Epigenetique et, rue Guy Moquet 7, Villejuif, 94800, France

    Annick Harel-Bellan

  4. Cancer Institut Andre Lwoff, CNRS FRE 3239, Laboratoire Epigenetique et, rue Guy Moquet 7, Villejuif, 94800, France

    Nadya Morozova

  5. Cancer Institut Andre Lwoff, CNRS FRE 3239, Laboratoire Epigenetique et, rue Guy Môquet, Villejuif, 94801, France

    Linda Louise Pritchard

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Capasso, V. (2013). Randomness and Geometric Structures in Biology. In: Capasso, V., Gromov, M., Harel-Bellan, A., Morozova, N., Pritchard, L. (eds) Pattern Formation in Morphogenesis. Springer Proceedings in Mathematics, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20164-6_21

Download citation

Publish with us

Policies and ethics

Search

Navigation