Related papers: A space-averaged model of branched structures
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field…
The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a…
To aid in prediction of turbulent boundary layer flows over rough surfaces, a new model is proposed to estimate hydrodynamic roughness based solely on geometric surface information. The model is based on a fluid-mechanics motivated…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
Uniform fluid flow distribution in a symmetric volume can be realized through a symmetric branched tree. It is shown here, however, that the flow partitioning can be highly sensitive to deviations from exact symmetry if inertial effects are…
Segmenting tree structures is common in several image processing applications. In medical image analysis, reliable segmentations of airways, vessels, neurons and other tree structures can enable important clinical applications. We present a…
In a rooted tree, we call a vertex {\em balanced} if it is at equal distance from all its descendant leaves. We count balanced vertices in three different tree varieties. For decreasing binary trees, we can prove that the probability that a…
Random point configurations are said to be in hyperuniform states, if density fluctuations are anomalously suppressed in large-scale. Typical examples are found in Coulomb gas systems in two dimensions especially called log-gases in random…
We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation,…
Simulation-based problems involving mixed-variable inputs frequently feature domains that are hierarchical, conditional, heterogeneous, or tree-structured. These characteristics pose challenges for data representation, modeling, and…
We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the…
We introduce weaves, which are random sets of non-crossing c\`{a}dl\`{a}g paths that cover space-time $\overline{\mathbb{R}}\times\overline{\mathbb{R}}$. The Brownian web is one example of a weave, but a key feature of our work is that we…
Tree covering is a technique for decomposing a tree into smaller-sized trees with desirable properties, and has been employed in various succinct data structures. However, significant hurdles stand in the way of a practical implementation…
Sampling with the Generalised Atmospheric Rosenbluth Method (GARM) is a technique for estimating the distributions of lattice polymer models that has had some success in the study of linear polymers and lattice polygons. In this paper we…
We tackle the challenging problem of creating full and accurate three dimensional reconstructions of botanical trees with the topological and geometric accuracy required for subsequent physical simulation, e.g. in response to wind forces.…
When modeling of tumor-driven angiogenesis, a major source of analytical and computational complexity is the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the…