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Distribution networks -- from vasculature to urban transportation systems -- are prevalent in both the natural and consumer worlds. These systems are intrinsically physical in composition and are embedded into real space, properties that…
Within animals, oxygen exchange occurs within networks containing potentially billions of microvessels that are distributed throughout the animal's body. Innovative imaging methods now allow for mapping of the architecture and blood flows…
Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the…
Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by…
Biological transport networks are highly optimized structures that ensure power-efficient distribution of fluids across various domains, including animal vasculature and plant venation. Theoretically, these networks can be described as…
As nutrients travel through microcirculation and are absorbed, their availability continuously decreases. However, a uniform nutrient distribution is critical, as it prevents tissue death in poorly supplied areas. How, then, do vascular…
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…
Vascular networks play a key role in the development, function, and survival of many organisms, facilitating transport of nutrients and other critical factors within and between systems. The development of these vessel networks has been…
Scientists have long sought to understand how vascular networks supply blood and oxygen to cells throughout the body. Recent work focuses on principles that constrain how vessel size changes through branching generations from the aorta to…
Branched actin networks at the leading edge of a crawling cell evolve via protein-regulated processes such as polymerization, depolymerization, capping, branching, and severing. A formulation of these processes is presented and analyzed to…
Many organs of higher organisms are heavily branched structures and arise by an at first sight similar process of branching morphogenesis. Yet the regulatory components and local interactions that have been identified differ greatly in…
While much of the work in the design of convolutional networks over the last five years has revolved around the empirical investigation of the importance of depth, filter sizes, and number of feature channels, recent studies have shown that…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
Biological cells, by definition, are the basic units which contain the fundamental molecules of life of which all living things are composed. Understanding how they function and differentiating cells from one another therefore is of…
Multicellular self-assembly into functional structures is a dynamic process that is critical in the development and diseases, including embryo development, organ formation, tumor invasion, and others. Being able to infer collective cell…
The brain is immensely complex, with diverse components and dynamic interactions building upon one another to orchestrate a wide range of functions and behaviors. Understanding patterns of these complex interactions and how they are…
Understanding design principles of complex cellular organization is one of the major challenges in biology. Recent analysis of the large-scale cellular organization has revealed the scale-free nature and robustness of metabolic and protein…
The analysis of biological networks encompasses a wide variety of fields from genomic research of protein-protein interaction networks, to the physiological study of biologically optimized tree-like vascular networks. It is certain that…
The actin and microtubule cytoskeletons are vital structures for cell growth and development across all species. While individual molecular mechanisms underpinning actin and microtubule dynamics have been intensively studied, principles…
Accurately determining and classifying the structure of complex networks is the focus of much current research. One class of network of particular interest are metabolic pathways, which have previously been studied from a graph theoretical…