Related papers: The topological structure of 2D disordered cellula…
This review was written for the Encyclopedia of Complexity and System Science (Springer-Verlag, Berlin, 2008), and is intended as a guide to the growing literature which approaches the phenomena of cell biology from a more theoretical point…
The rheology of biological tissues is important for their function, and we would like to better understand how single cells control global tissue properties such as tissue fluidity. A confluent tissue can fluidize when cells diffuse by…
We study various notions of "tameness" for definably complete expansions of ordered fields. We mainly study structures with locally o-minimal open core, d-minimal structures, and dense pairs of d-minimal structures.
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
A cell's behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes,…
The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws.…
The two-gene Andrecut-Kauffman model describes gene expression within cells by a two-dimensional discrete dynamical system. Using periodic orbits of an one dimensional subsystem we, rigourously prove the existence of topological chaos in…
Whereas knowledge of a crystalline material's unit cell is fundamental to understanding the material's properties and behavior, there are not obvious analogues to unit cells for disordered materials despite the frequent existence of…
A class of Cantor-type spaces and related geometric structures are discussed.
In many tissues, cell type varies over single-cell length-scales, creating detailed spatial heterogeneities fundamental to physiological function. To gain understanding of this relationship between tissue function and detailed structure,…
The topological organization of several world cities are studied according to respective representations by complex networks. As a first step, the city maps are processed by a recently developed methodology that allows the most significant…
The size distributions of 2D and 3D Voronoi cells and of cells of $V_p(2,3)$,--2D cut of 3D Voronoi diagram--are explored, with the single-parameter (re-scaled) gamma distribution playing a central role in the analytical fitting.…
Topological defects (TDs) are crucial for understanding important physical properties of crystalline materials including mechanical failure, ion transport, and two-dimensional melting. This concept has not translated to disordered materials…
In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on 2D CA and aims at showing that the situation is different and more…
Exploring the structural topology of genome-based large-scale metabolic network is essential for investigating possible relations between structure and functionality. Visualization would be helpful for obtaining immediate information about…
Organoids are in vitro cellular collectives from which brain-like, or gut-like, or kidney-like structures emerge. To make quantitative predictions regarding the morphology and rheology of a cellular collective in its initial stages of…
Cell differentiation in multicellular organisms is a complex process whose mechanism can be understood by a reductionist approach, in which the individual processes that control the generation of different cell types are identified.…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…