Related papers: Growth Models for Tree Stems and Vines
Vine copulas, constructed using bivariate copulas as building blocks, provide a flexible framework for modeling multi-dimensional dependencies. However, this flexibility is accompanied by rapidly increasing complexity as dimensionality…
We define a minimization problem for paths on planar graphs that, on the honeycomb lattice, is equivalent to the exploration path of the critical site percolation and than has the same scaling limit of SLE_6. We numerically study this model…
We propose to use a simulation driven inverse inference approach to model the dynamics of tree branches under manipulation. Learning branch dynamics and gaining the ability to manipulate deformable vegetation can help with occlusion-prone…
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…
In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the…
Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens in a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under…
This paper considers the growth rates of positive solutions of scalar nonlinear functional and Volterra differential equations. The equations are assumed to be autonomous (or asymptotically so), and the nonlinear dependence grows less…
A new general equation to explain bending of arbitrary rods (from arbitrary materials, cross sections, densities, strengthnesses, bending angles, etc) was proposed. This equation can solve several problems found in classical equations,…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
The generation mechanism of growth strains is investigated theoretically by developing an elastic analysis of a wood cell viewed as a composite tube, with layers composed of a ligno-cellulosic material of varying composition and…
Classical rich-get-richer models have found much success in being able to broadly reproduce the statistics and dynamics of diverse real complex systems. These rich-get-richer models are based on classical urn models and unfold step-by-step…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
A nested family of growing or shrinking planar domains is called a Laplacian growth process if the normal velocity of each domain's boundary is proportional to the gradient of the domain's Green function with a fixed singularity on the…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
Actin growth is a fundamental biophysical process and it is, at the same time, a prototypical example of diffusion-mediated surface growth. We formulate a coupled chemo-mechanical, one-dimensional growth model encompassing both material…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
We have previously reported that a 'universal' growth law with fixed scaling exponent p, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. Here, we investigate…
Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a…
We review models of compositional growth, which were introduced to explain the growth statistics of various quantities ranging from firm sizes to GDP. In these models, entities are decomposed into units that grow independently. Thus, the…
A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential…