Note that k must always equal i+ 1 in a binary tree. Prodinger [P] recently computed the probability that a random binary tree with n nodes has i nodes with 2 children (and hence i + 1 nodes without children and n − 2i − 1 nodes with 1 child). Since the total number of binary trees with n nodes is known—it is bn—, his formulas can be derived easily from the above theorem and vice versa. Proding...

Inhomogeneous random graphs are commonly used models for complex networks where nodes have varying degrees of connectivity. Computing the degree distribution such is a fundamental problem and has important applications in various fields. We define inhomogeneous graph as model edges drawn independently probability link between any two vertices can be different each node pair. In this paper, we p...

Amatrix analytic paradigm, termed Quasi-Birth-Death Markov chains on binomial-like trees, is introduced and a quadratically converging algorithm to assess its steady state is presented. In a bivariate Markov chain {(Xt, Nt), t ≥ 0}, the values of the variable Xt are nodes of a binomial-like tree of order d, where the i-th child has i children of its own. We demonstrate that it suffices to solve...

A binomial approximation to a diffusion is defined as “computationally simple” if the number of nodes grows at most linearly in the number of time intervals. It is shown how to construct computationally simple binomial processes that converge weakly to commonly employed diffusions in financial models. The convergence of the sequence of bond and European option prices from these processes to the...

this article focuses on the estimation of population proportion when the study variable is sensitive in nature. two implicit randomized response techniques are proposed where the unrelated trait can be chosen subjectively. in addition to unbiased estimation of population proportion and variance, an empirical study is conducted to inspect the relative efficiency facet of the proposed techniques....

This paper solves a long standing open problem of whether NP-complete problems could be solved in polynomial time on a deterministic Turing machine by showing that the indistinguishable binomial decision tree can be formed in a 3-SAT instance. This paper describes how to construct the decision tree and explains why 3-SAT has no polynomial-time algorithm when the decision tree is formed in the 3...

For a fixed number N of nodes, the number of links L in the line graph H(N,L) can only appear in consecutive intervals, called a band of L. We prove that some consecutive integers can never represent the number of links L in H(N,L), and they are called a bandgap of L. We give the exact expressions of bands and bandgaps of L. We propose a model which can randomly generate simple graphs which are...

This paper describes the frequency and number of Sphyrion laevigatum in the skin of Genypterus blacodes, an important economic resource in Chile. The analysis of a spatial distribution model indicated that the parasites tended to cluster. Variations in the number of parasites per host could be described by a negative binomial distribution. The maximum number of parasites observed per host was two.

Information gathering by crawlers on the web is of practical interest. We consider a simplified model for crawling complex networks such as the web graph, which is a variation of the robot vacuum edge-cleaning process of Messinger and Nowakowski. In our model, a crawler visits nodes via a deterministic walk determined by their weightings which change during the process deterministically. The mi...

In this paper, we propose a packet-level parallel data transfer and a Two-Phase Scheduling(TPS) algorithm for collective communication primitives in MPICH-G2. The algorithms are characterized by two unique features: 1) a concurrent data transfer of packets from a source node to multiple destination nodes and 2) a scheduling of enhancing the performance of collective communications by early iden...