Noise permeates biology on all levels, from the most basic molecular, sub-cellular
processes to the dynamics of tissues, organs, organisms and populations. The functional …

Self-organization is pervasive in development, from symmetry breaking in the early embryo
to tissue patterning and morphogenesis. For a few model systems, the underlying molecular …

Abstract The Notch–Delta signalling pathway allows communication between neighbouring
cells during development. It has a critical role in the formation of 'fine-grained'patterns …

In this chapter we have presented mathematical modeling approaches to biological pattern
formation. While reaction-diffusion models are appropriate to describe the spatio-temporal …

Dynamical processes on networks have generated widespread interest in recent years. The
theory of pattern formation in reaction–diffusion systems defined on symmetric networks has …

Computational and biological systems are often distributed so that processors (cells) jointly
solve a task, without any of them receiving all inputs or observing all outputs. Maximal …

Developmental patterning requires juxtacrine signaling in order to tightly coordinate the
fates of neighboring cells. Recent work has shown that Notch and Delta, the canonical …

INTRODUCTION Spatial patterning in developing multicellular organisms relies on
positional cues and cell-cell interactions. Stereotyped sensory organ arrangements in …

Multi-patch models–also known as metapopulation models–provide a simple framework
within which the role of spatial processes in disease transmission can be examined. An n …

Although there is general agreement that the network plays an essential role in the
biological system, how the connection probability of network affects the natural model …