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We apply ideas from renormalization theory to models of cluster formation in nucleation and growth processes. We study a simple case of the Becker-Doring system of equations and show how a novel coarse-graining procedure applied to the…
We develop a coagulation-fragmentation model to study a system composed of a small number of stochastic objects moving in a confined domain, that can aggregate upon binding to form local clusters of arbitrary sizes. A cluster can also…
Intracellular signaling often arises from ligand-induced oligomerization of cell surface receptors. This oligomerization or clustering process is fundamentally a cooperative behavior between near-neighbor receptor molecules; the properties…
Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the…
The fundamental biological processes of development of tissues and organs in multicellular organisms is governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in concentration…
Morphogen gradients play an essential role in the spatial regulation of cell patterning during early development. The classical mechanism of morphogen gradient formation involves the diffusion of morphogens away from a localized source…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Spatial gradients of diffusible signalling molecules play crucial roles in controlling diverse cellular behaviour such as cell differentiation, tissue patterning and chemotaxis. In this paper, we report the design and testing of a…
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
We introduce and analyse a variant of the Becker-D{\"o}ring equations that models the growth of clusters through the gain or loss of monomers. Motivated by enzymatic reactions in biology, this model incorporates irreversible fragmentation…
Spatial information from cell-surface receptors is crucial for processes that require signal processing and sensing of the environment. Here, we investigate the optimal placement of such receptors through a theoretical model that minimizes…
The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen…
High-order clustering aims to classify objects in multiway datasets that are prevalent in various fields such as bioinformatics, recommendation systems, and social network analysis. Such data are often sparse and high-dimensional, posing…
Improved understanding of charge-transport in single molecules is essential for harnessing the potential of molecules e.g. as circuit components at the ultimate size limit. However, interpretation and analysis of the large, stochastic…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
In many fields, researchers are interested in large and complex biological processes. Two important examples are gene expression and DNA methylation in genetics. One key problem is to identify aberrant patterns of these processes and…
In both biological and artificial systems, concentration gradients can serve as a convenient mechanism for manipulating particles and generating motility. Particles that interact with a solute will move along its gradient; if they…
We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models…
Position determination in biological systems is often achieved through protein concentration gradients. Measuring the local concentration of such a protein with a spatially-varying distribution allows the measurement of position within the…
One of the many ways cells transmit information within their volume is through steady spatial gradients of different proteins. However, the mechanism through which proteins without any sources or sinks form such single-cell gradients is not…