Pattern Formation in Morphogenesis is a rich source of interesting and challenging mathematical problems. The volume aims at showing how a combination of new discoveries in developmental biology and associated modelling and computational techniques has stimulated or may stimulate relevant advances in the field. Finally it aims at facilitating the process of unfolding a mutual recognition between Biologists and Mathematicians of their complementary skills, to the point where the resulting synergy generates new and novel discoveries. It offers an interdisciplinary interaction space between biologists from embryology, genetics and molecular biology who present their own work in the perspective of the advancement of their specific fields, and mathematicians who propose solutions based on the knowledge grasped from biologists.

Preface.-
Why Would a Mathematician Care About Embryology?

M.Gromov.- 

PART I.BIOLOGICAL BACKGROUND.-

Preface to the Biological Part.- Pattern Formation in Regenerating Tissues. A.Hoffmann and P.A. Tsonis.- Gradients and Regulatory Networks of Wnt Signalling in
Hydra
Pattern Formation. T.W. Holstein.- Modeling of Planar Cell Polarity Signaling.

J.D. Axelrod
.- Integrated Molecular Circuits for Stem Cell Activity in Arabidopsis Roots.
B. Scheres.- The Mechanics of Tissue Morphogenesis.

T. Lecuit.- Small Regulatory RNAs and Skeletal Muscle Cell Differentiation. A. Harel-Bellan, A.Polesskaya, I.Naguibneva, M.Ameyar-Zazoua, C.Degerny, J.Kropp, N.Nonne, M.Souidi, G.Kratassiouk, G.Pinna, L.L.Pritchard.
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Pattern Formation in Sea Urchin Endomesoderm as Instructed by Gene Regulatory Network Topologies.

I.S. Peter and E.H. Davidson.-

PART II. MATHEMATICAL MODELS.-

Modelling Oscillator Synchronisation During Vertebrate Axis Segmentation.

P.J. Murray, P.K. Maini, and R.E. Baker
.-
Pattern Formation in Hybrid Models of Cell Populations. N. Bessonov, P. Kurbatova, V. Volpert.
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An Integrative Approach to the Analysis of Pattern Formation in Butterfly Wings
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Experiments and Models. T. Sekimura.
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Modeling Morphogenesis in Multicellular Structures with Cell Complexes and L-systems. P. Prusinkiewicz and B. Lane.- Multistability and Hysteresis-based Mechanism of Pattern Formation in Biology. A. Marciniak-Czochra and A. Köthe.- How to knock out feedback Circuits in Gene Networks? H. Gruber, A. Richard, C. Soulé.- Formation of Evolutionary Patterns in Cancer Dynamics. M. Delitala and T. Lorenzi.- How Cell Decides Between Life and Death: Mathematical Modeling of Epigenetic Landscapes of Cellular Fates. A. Zinovyev, L. Calzone, S.Fourquet and E. Barillot.-

PART  III.  IDEAS, HYPOTHESIS, SUGGESTIONS.-


From Hydra to Vertebrates: Models for the Transition from Radial- to Bilateral-symmetric Body Plans, H. Meinhardt.- Cell Division and Hyperbolic Geometry. M. Gromov.- Formalistic Representation of the Cellular Architecture in the Course of Plant Tissue Development. I.V. Rudskiy.- The Geometry of Morphogenesis and the Morphogenetic Field Concept. N.Morozova and M.Shubin.- Randomness and Geometric Structures in Biology. V. Capasso.