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.

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...

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...

In this research, we extract paraphrases from Japanese Web news articles that are long and aimed at displaying on personal computer screens and mobile news articles that are short and compact and aimed at mobile terminals’ small screens. We have collected them for more than two years, and aligned them at article level and then at sentence level. As the result, we got more than 88,000 pairs of a...

Blood vessels and other anatomic objects in the human body can be described as trees of branching tubes. The focus of this paper is the extraction of the branching geometry in 3D, as well as the extraction of the tubes themselves via skeletons computed as cores. Cores are height ridges of a graded measure of medial strength called medialness, which measures how much a given location resembles t...

We present a method for solving service allocation problems in which a set of services must be allocated to a set of agents so as to maximize a global utility. The method is completely distributed so it can scale to any number of services without degradation. We first formalize the service allocation problem and then present a simple hill-climbing, a global hillclimbing, and a bidding-protocol ...

The thermal oxidation of propane in the temperature range 350-425oC was studied in order to elucidate the role of higher aldehydes as degenerate branching intermediates in the oxidation of hydrocarbons. In the slow combustion of propane, the high yield of propylene and methanol as the primary products, the formation of hydrogen peroxide, carbon monoxide, carbon dioxide, formaldehyde and steam a...