In this paper, using the Hojman construction, we give examples of various Poisson brackets which differ from those which are usually analyzed in Hamiltonian mechanics. They possess a nonmaximal rank, and in the general case an invariant measure and Casimir functions can be globally absent for them.

In this paper we further develop the theory of matrices over the extended tropical semiring. Introducing a notion of tropical linear dependence allows for a natural definition of matrix rank in a sense that coincides with the notions of tropical regularity and invertibility.

Manually assigned keywords provide a valuable means for accessing large document collections. They can serve as a shallow document summary and enable more efficient retrieval and aggregation of information. In this paper we investigate keywords in the context of the Dutch Folktale Database, a large collection of stories including fairy tales, jokes and urban legends. We carry out a quantitative...

We revisit a formula that connects the minimal ranks of triangular parts of a matrix and its inverse and relate the result to structured rank matrices. We also address the generic minimal rank problem.

Learning to Rank: Online Learning, Statistical Theory and Applications by Sougata Chaudhuri

A common problem arising in many domains is how value the benefits of projects in a project portfolio. Recently, there has been some attention given to a decision analysis practice whereby analysts define a value function on some criterion by setting 0 as the value of the worst project. In particular, Clemen and Smith have argued this practice is not sound as it gives different results from the...

We study in this paper different strategies to rank keyword activities through a comparison of pointwise and pairwise learning to rank approaches, as well as the impact of keyword ambiguity, keyword activity and keyword set size on the prediction results. It is the first time, to our knowledge, that such dimensions are evaluated in this framework. Our experiments are conducted on a large datase...

In this paper we present a Smith-like updating technique to estimate a low rank approximation of the Gramians of a time-varying system. We obtain error estimates of our approximation and also explain how to use this for model reduction of time-varying systems.

We exhibit counterexamples to a Conjecture of Nesin, since we build a connected solvable group with finite center and of finite Morley rank in which no normal nilpotent subgroup has a nilpotent complement. The main result says that each centerless connected solvable group G of finite Morley has a normal nilpotent subgroup U and an abelian subgroup T such that G = U o T , if and only if, for any...