We present new links between some remarkable martingales found in the study of the Binary Search Tree or of the bisection problem, looking at them on the probability space of a continuous time binary branching process.

Abstract For a quadratic Markov branching process (QMBP), we show that the decay parameter is equal to first eigenvalue of Sturm–Liouville operator associated with partial differential equation generating function transition probability satisfies. The proof based on spectral properties operator. Both upper and lower bounds are given explicitly by means version Hardy’s inequality. Two examples p...

Turing mechanisms can yield a large variety of patterns from noisy, homogenous initial conditions and have been proposed as patterning mechanism for many developmental processes. However, the molecular components that give rise to Turing patterns have remained elusive, and the small size of the parameter space that permits Turing patterns to emerge makes it difficult to explain how Turing patte...

Applying the results about harmonic moments of classical Galton-Watson process, we obtain deviations for random sums indexed by generations a branching process. Our show that decay rates large and moderate depend heavily on degree heavy tail asymptotic distributions normalizing constants. If underlying process belongs to Schr?der case, both deviation probabilities three rates, where critical ca...

With the growing importance of XML in data exchange, much research has been done in proving flexible query mechanisms to extract data from structured XML documents. The semi-structured nature of XML data and the requirements on query flexibility pose unique challenges to database indexing methods. Recently, ViST that uses suffix tree and BTree was proposed to reduce the search time of the docum...

In this paper we explore the variation of sentences as a function of the sentence number. We demonstrate that while the entropy of the sentence increases with the sentence number, it decreases at the paragraph boundaries in accordance with the Entropy Rate Constancy principle (introduced in related work). We also demonstrate that the principle holds for different genres and languages and explor...