Adaptive dynamics in two-dimensional phenotype space is investigated by computer simulation. The model assumes Lotka-Voltera-type competition and a stochastic mutation process. The carrying capacity has a single maximum in the origin of the strategy space and the competition coefficient decreases with strategy difference. Evolutionary branching, an asexual analog of adaptive speciation, is obse...

Let X = G/K be a symmetric space of noncompact type and let ∆ be the Laplacian associated with a G-invariant metric on X . We show that the resolvent kernel of ∆ admits a holomorphic extension to a Riemann surface depending on the rank of the symmetric space. This Riemann surface is a branched cover of the complex plane with a certain part of the real axis removed. It has a branching point at t...

In this paper we present a registration method for cerebral vascular structures in the 2D MRA images. The method is based on bifurcation structures. The usual registration methods, based on point matching, largely depend on the branching angels of each bifurcation point. This may cause multiple feature correspondence due to similar branching angels. Hence, bifurcation structures offer better re...

Various bacterial strains exhibit colonial branching patterns during growth on thin poor substrates. The growth can be either diiusion-limited or kinetic-limited, according to the imposed growth conditions. We present experimental observations of patterns exhibited by the bacterial strains Paenibacillus dendritiformis and Paenibacillus vortex. All manners of branching patterns are observed, the...

Shoot branching is a primary contributor to plant architecture, evolving independently in flowering plant sporophytes and moss gametophytes. Mechanistic understanding of branching is largely limited to flowering plants such as Arabidopsis, which have a recent evolutionary origin. We show that in gametophytic shoots of Physcomitrella, lateral branches arise by re-specification of epidermal cells...

We investigate the power of Algebraic Branching Programs (ABPs) augmented with help polynomials, and constant-depth Boolean circuits augmented with help functions. We relate the problem of proving explicit lower bounds in both these models to the Remote Point Problem (introduced in [3]). More precisely, proving lower bounds for ABPs with help polynomials is related to the Remote Point Problem w...

This study examined Leonardo da Vinci's rule (i.e., the sum of the cross-sectional area of all tree branches above a branching point at any height is equal to the cross-sectional area of the trunk or the branch immediately below the branching point) using simulations based on two biomechanical models: the uniform stress and elastic similarity models. Model calculations of the daughter/mother ra...

Imperfection sensitivity properties are derived for finite dimensional elastic conservative systems exhibiting hill-top branching at which arbitrary many bifurcation points coincide with a limit point. The critical load at a hill-top branching point is demonstrated to be insensitive to initial imperfections when all the bifurcation points are individually symmetric. Therefore, it is not dangero...

Recent experimental work has shown that activity in living neural networks can propagate as a critical branching process that revisits many metastable states. Neural network theory suggests that attracting states could store information, but little is known about how a branching process could form such states. Here we use a branching process to model actual data and to explore metastable states...

We consider a continuous-time branching random walk on multidimensional lattice with two types of particles and an infinite number initial particles. The main results are devoted to the study generating function limiting behavior moments subpopulations generated by single particle each type. assume that differ from other not only laws branching, as in multi-type processes, but also walking. For...