Adaptive dynamics formalism demonstrates that, in a constant environment, a continuous trait may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called "evolutionary branching." Most previous analyses of evolutionary branching have been conducted in an infinitely large population. Here, we study the effect of ...

Evolutionary branching is the process by which ecological interactions induce evolutionary diversification. In asexual populations with sufficiently rare mutations, evolutionary branching occurs through trait-substitution sequences caused by the sequential invasion of successful mutants. A necessary and sufficient condition for evolutionary branching of univariate traits is the existence of a c...

In 3] we exhibited a simple boolean functions fn in n variables such that: 1) fn can be computed by polynomial size randomized ordered read-once branching program with one sided small error; 2) any nondeterministic ordered read-once branching program that computes fn has exponential size. In this paper we present a simple boolean function gn in n variables such that: 1) gn can be computed by po...

State-of-the-art branch and bound algorithms for mixed integer programming make use of special methods for making branching decisions. Strategies that have gained prominence include modern variants of so-called strong branching (Applegate, et al.,1995) and reliability branching (Achterberg, Koch and Martin, 2005; Hendel, 2015), which select variables for branching by solving associated linear p...

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.