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

In all books and papers on adaptive filtering, the input autocorrelation matrix Rxx is always considered positive definite and hence the theoretical Wiener–Hopf normal equations (Rxxh 1⁄4 rxd) have a unique solution h 1⁄4 hopt (‘‘there is only a single global optimum’’, [B. Widrow, S. Stearns, Adaptive Signal Processing, Prentice-Hall, 1985, p. 21]) due to the invertibility of Rxx (i.e., it is ...

As a continuation of the study of rank 3 permutation groups G begun in [4] we consider in this paper primitive rank 3 groups of even order in which the stabilizer Ga of a point a has an orbit of prime length. We show in particular that if G has no regular normal subgroup then the minimal normal subgroup M of G is a simple group of rank 3 and the constituent of 214, on the orbit of prime length ...

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.