Related papers: A space-averaged model of branched structures

Branched structures that evolve over time critically determine the function of various natural and engineered systems, including growing vasculature, neural arborization, pulmonary networks such as lungs, river basins, power distribution…

We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…

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…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Man-made slender structures are known to be sensitive to high levels of vibration, due to their flexibility, which often cause irreversible damage. In nature, trees repeatedly endure large amplitudes of motion, mostly caused by strong…

Vegetation in semi-arid environments self-organizes into striking spatial patterns -- bands, spots, labyrinths, and gaps -- with characteristic wavelengths on the order of tens to hundreds of meters. Existing reaction-diffusion models…

In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

Branching architecture characterizes numerous systems, ranging from synthetic (hyper)branched polymers and biomolecules such as lignin, amylopectin, and nucleic acids to tracheal and neuronal networks. Its ubiquity reflects the many…

Much of the information about the multi-valley structure of disordered spin systems can be convened in a simple tree structure -- a barrier tree -- the leaves and internal nodes of which represent, respectively, the local minima and the…

Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…

Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…

In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…

Coupled natural systems are generally modeled at multiple abstraction levels. Both structural scale and behavioral complexity of these models are determinants in the kinds of questions that can be posed and answered. As scale and complexity…

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…

When modeling complex robot systems such as branched robots, whose kinematic structures are a tree, current techniques often require modeling the whole structure from scratch, even when partial models for the branches are available. This…

A classic problem in computational biology is constructing a phylogenetic tree given a set of distances between n species. In most cases, a tree structure is too constraining. We consider a circular split network, a generalization of a tree…

Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…

A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class…

Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium in response to the flow, in turn causing flow pathways to evolve. We…