Motivated by the works of Böinghoff and Huzenthaler [6] and Bansaye et al. [1], we introduce continuous state branching processes in a Brownian random environment. Roughly speaking, a process in this class behaves as a continuous state branching process but its dynamics are perturbed by an independent Brownian motion with drift. More precisely, we define a continuous state branching process in ...

The topology of a polymer molecule is normally characterized by the degree of polymerization (number of sites), degree of branching and Wiener index. The two latter parameters are of great importance when polymers studied have the same molecular weight. As mentioned in the previous Chapter, the degree of branching, defined as ( ) 2 2 B D D L = + where D and L are the numbers of fully and partia...

The observation of monophyly for a specified set of genealogical lineages is often used to place the lineages into a distinctive taxonomic entity. However, it is sometimes possible that monophyly of the lineages can occur by chance as an outcome of the random branching of lineages within a single taxon. Thus, especially for small samples, an observation of monophyly for a set of lineages--even ...

The notion of chaotic behavior is examined for particle production in branching processes. Two types of branching are considered: non-Abelian gauge interaction and an Abelian cascade model. Properties of the production processes are investigated by Monte Carlo stimulation. The \temporal" behavior is studied by following the uctuations in the multiplicities of each generation as the branching ev...

Internal iliac artery (IIA) shows frequent variations in its branching pattern. We saw variations in the branching pattern of right IIA in a male cadaver. The IIA divided into anterior and posterior divisions. The branches of the anterior division included umbilical artery, inferior vesical artery, obturator artery. The other branches arose from posterior trunk such as iliolumbar, lateral s...

We define complex projective n-space CP as C \ {0} under the equivalence relation (z0 : z1 : ... : zn) ∼ (cz0 : cz1 : ... : czn) where c ∈ C\{0}. A complex projective curve is then the set of points (a0 : a1 : ... : an) ∈ CP such that p(a0, a1, ..., an) = 0 for a fixed complex homogeneous polynomial p(z0, z1, ..., zn). Such a curve is a 2-dimensional, real, orientable Riemannian manifold, or Ri...

The notion of chaotic behavior is examined for particle production in branching processes. Two types of branching are considered: non-Abelian gauge interaction and an Abelian cascade model. Properties of the production processes are investigated by Monte Carlo stimulation. The “temporal” behavior is studied by following the fluctuations in the multiplicities of each generation as the branching ...

In [4] the trace space of parallel non-looped, non-branching processes is given as a prod-simplicial complex derived from an index category. For looped processes, the state space is a torus and the trace space is a disjoint union of tracespaces of deloopings. The index category for the trace space of the deloopings is developed from the once delooped case. When just one process is looped, the i...