Let G be a Poisson–Lie group equipped with left invariant contravariant pseudo-Riemannian metric. There are many ways to lift the Poisson structure on tangent bundle TG of G. In this paper, we induce metric TG, and express in different cases Levi-Civita connection curvature terms We prove that space differential forms Ω*(G) is graded algebra if, only Ω*(TG) algebra. Moreover, show Sanchez de Al...

In association rule mining, interestingness refers to metrics that are applied to select association rules, beyond support and confidence. For example, Merceron & Yacef (2008) recommend that researchers use a combination of lift and cosine to select association rules, after first filtering out rules with low support and confidence. However, the empirical basis for considering these specific met...

This paper explores the feasibility of improving unmanned air vehicle (UAV) mission effectiveness by extracting energy from the atmosphere. Specifically, we consider an aerial surveillance mission in the vicinity of a geographic ridge. Cross winds flowing over the ridge produce regions of lift on the windward side that can be exploited to increase mission duration. Mission effectiveness is quan...

Optimal transport distances have been used for more than a decade in machine learning to compare histograms of features. They have one parameter: the ground metric, which can be any metric between the features themselves. As is the case for all parameterized distances, optimal transport distances can only prove useful in practice when this parameter is carefully chosen. To date, the only option...

The notion of upper distortion for graded submonoids embedded in groups and monoids is introduced. A finitely generated monoid M is graded if every element of M can be written in only finitely many ways in terms of some fixed system of generators. Examples of such monoids are free monoids, Artin monoids, and monoids satisfying certain small cancellation conditions. Whenever such a monoid is emb...

We prove the Ramsey property of classes of ordered structures with closures and given local properties. This generalises earlier results: the Nešetřil-Rödl Theorem, the Ramsey property of partial orders and metric spaces as well as the author’s Ramsey lift of bowtiefree graphs. We use this framework to give new examples of Ramsey classes. Among others, we show (and characterise) the Ramsey prop...

Hiring committees address the glut of highly qualified applicants for faculty positions by experimenting with new evaluation methods and adapting their expectations for today's increasingly competitive academic environment.

A gain graph is a graph whose oriented edges are labelled invertibly from a group G, the gain group. A gain graph determines a biased graph and therefore has three natural matroids (as shown in Parts I–II): the bias matroid G has connected circuits; the complete lift matroid L0 and its restriction to the edge set, the lift matroid L, have circuits not necessarily connected. We investigate repre...

One of the factors which affects the gas lift performance is specific gravity of a lift gas (or the Molecular weight), which can influence the gas solubility in oil and has a direct effect on the gas lift performance. There are some previous researches which have included the lift gas specific gravity in their modeling, but in none of them, a comprehensive research about the effect of lift gas ...