The genotype-phenotype relationship in multicellular pattern-generating models - the neglected role of pattern descriptors

Background: A deep understanding of what causes the phenotypic variation arising from biological patterning processes, cannot be claimed before we are able to recreate this variation by mathematical models capable of generating genotype-phenotype maps in a causally cohesive way. However, the concept of pattern in a multicellular context implies that what matters is not the state of every single cell, but certain emergent qualities of the total cell aggregate. Thus, in order to set up a genotype-phenotype map in such a spatiotemporal pattern setting one is actually forced to establish new pattern descriptors and derive their relations to parameters of the original model. A pattern descriptor is a variable that describes and quantifies a certain qualitative feature of the pattern, for example the degree to which certain macroscopic structures are present. There is today no general procedure for how to relate a set of patterns and their characteristic features to the functional relationships, parameter values and initial values of an original pattern-generating model. Here we present a new, generic approach for explorative analysis of complex patterning models which focuses on the essential pattern features and their relations to the model parameters. The approach is illustrated on an existing model for Delta-Notch lateral inhibition over a two-dimensional lattice. Results: By combining computer simulations according to a succession of statistical experimental designs, computer graphics, automatic image analysis, human sensory descriptive analysis and multivariate data modelling, we derive a pattern descriptor model of those macroscopic, emergent aspects of the patterns that we consider of interest. The pattern descriptor model relates the values of the new, dedicated pattern descriptors to the parameter values of the original model, for example by predicting the parameter values leading to particular patterns, and provides insights that would have been hard to obtain by traditional methods. Conclusion: The results suggest that our approach may qualify as a general procedure for how to discover and relate relevant features and characteristics of emergent patterns to the functional relationships, parameter values and initial values of an underlying pattern-generating mathematical model

Cosmological stabilization of moduli with steep potentials

A scenario which overcomes the well-known cosmological overshoot problem associated with stabilizing moduli with steep potentials in string theory is proposed. Our proposal relies on the fact that moduli potentials are very steep and that generically their kinetic energy quickly becomes dominant. However, moduli kinetic energy red-shifts faster than other sources when the universe expands. So, if any additional sources are present, even in very small amounts, they will inevitably become dominant. We show that in this case cosmic friction allows the dissipation of the large amount of moduli kinetic energy that is required for the field to be able to find an extremely shallow minimum. We present the idea using analytic methods and verify with some numerical examples.Comment: 15 pages, 5 figure

Solvable Model of Spiral Wave Chimeras

Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to zero. But if the coupling is nonlocal, a new kind of spiral can occur, with a circular core consisting of desynchronized oscillators running at full amplitude. Here we provide the first analytical description of such a spiral wave chimera, and use perturbation theory to calculate its rotation speed and the size of its incoherent core.Comment: 4 pages, 4 figures; added reference, figure, further numerical test

Tensile Properties of Five Low-Alloy and Stainless Steels Under High-Heating-Rate and Constant-Temperature Conditions

Tensile properties of five low-alloy and stainless steels under high heating rate and constant temperatur

Stably non-synchronizable maps of the plane

Pecora and Carroll presented a notion of synchronization where an (n-1)-dimensional nonautonomous system is constructed from a given $n$-dimensional dynamical system by imposing the evolution of one coordinate. They noticed that the resulting dynamics may be contracting even if the original dynamics are not. It is easy to construct flows or maps such that no coordinate has synchronizing properties, but this cannot be done in an open set of linear maps or flows in $\R^n$, $n\geq 2$. In this paper we give examples of real analytic homeomorphisms of $\R^2$ such that the non-synchronizability is stable in the sense that in a full $C^0$ neighborhood of the given map, no homeomorphism is synchronizable