We investigate extremal statistical properties such as the maximal and the minimal heights of randomly generated binary trees. By analyzing the master evolution equations we show that the cumulative distribution of extremal heights approaches a traveling wave form. The wave front in the minimal case is governed by the small-extremal-height tail of the distribution, and conversely, the front in ...

Maximal left ventricular (LV) hydraulic power output (PWR(max)), corrected for preload as PWR(max)/(V(ed))(beta) (where V(ed) is the end-diastolic volume and beta is a constant coefficient), is an index of LV contractility. Whereas preload-adjusted maximal power (PAMP) is usually calculated with beta = 2, there is uncertainty about the optimal value of beta (beta = 1 for the normal LV and 2 for...

In a bipartite max-min LP, we are given a bipartite graph G = (V ∪ I ∪ K,E), where each agent v ∈ V is adjacent to exactly one constraint i ∈ I and exactly one objective k ∈ K. Each agent v controls a variable xv. For each i ∈ I we have a nonnegative linear constraint on the variables of adjacent agents. For each k ∈ K we have a nonnegative linear objective function of the variables of adjacent...

Three simple idealised models are studied in order to develop some intuition about the leading effect of non-sphericity on maximum turnaround size $R_{\rm TA,max}$ large scale bound cosmic structures. Two them describe intrinsically axisymmetric static mass distributions whereas other is Kerr-de Sitter metric where axisymmetry generated due rotation structure. In all cases fractional change $\d...

In a graph G = (V,E), a bisection (X,Y ) is a partition of V into sets X and Y such that |X| ≤ |Y | ≤ |X|+1. The size of (X,Y ) is the number of edges between X and Y . In the Max Bisection problem we are given a graph G = (V,E) and are required to find a bisection of maximum size. It is not hard to see that ⌈|E|/2⌉ is a tight lower bound on the maximum size of a bisection of G. We study parame...

Given a graph H = (U,E) and connectivity requirements r = {r(u, v) : u, v ∈ R ⊆ U}, we say that H satisfies r if it contains r(u, v) pairwise internally-disjoint uv-paths for all u, v ∈ R. We consider the Survivable Network with Minimum Number of Steiner Points (SN-MSP) problem: given a finite set V of points in a normed space (M, ‖·‖) and connectivity requirements, find a minimum size set S ⊂ ...

In the problem (Unweighted) Max-Cut we are given a graph $$G = (V,E)$$ and asked for set $$S \subseteq V$$ such that number of edges from S to $$V \setminus S$$ is maximal. this paper consider an even harder problem: (Weighted) Max-Bisection. Here undirected weight function $$w :E \rightarrow \mathbb {Q}_{>0}$$ task find (i) sum weights maximal; (ii) contains $$\lceil * \rceil {\frac{n}{2}}$$ v...

The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remainsMAX SNP{complete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNP{complete at the lowest possible degree bounds. Next we study better poly{time approximation of the problem for degree 3 graphs, and improve the previou...

The maximum stable matching problem (Max-SMP) and the minimum stable matching problem (Min-SMP) have been known to be NP-hard for subcubic bipartite graphs, while Max-SMP can be solved in polynomal time for a bipartite graph G with a bipartition (X,Y ) such that degG(v) ≤ 2 for any v ∈ X. This paper shows that both Max-SMP and Min-SMP can be solved in linear time for trees. This is the first po...