The main result is the prove of the linearity of the dp-rank. We also prove that the study of theories of finite dp-rank cannot be reduced to the study of its dp-minimal types and discuss the possible relations between dp-rank and VC-density.

We investigate a coloring problem, called ordered coloring, in grids and some other families of grid-like graphs. Ordered coloring (also known as vertex ranking) is related to conflict-free coloring and other traditional coloring problems. Such coloring problems can model (among others) efficient frequency assignments in cellular networks. Our main technical results improve upper and lower boun...

A way to compose a matrix P and a finite dimensional representation ρ of C via a map h into a new matrix P ∗h ρ is defined. Several results about the spectrum, eigenvectors, kernel and rank of P ∗h ρ are proved.

For many internet users, searching for health advice online is the first step in seeking treatment. We present a Learning to Rank system that uses a novel set of syntactic and semantic features to improve consumer health search. Our approach was evaluated on the 2016 CLEF eHealth dataset, outperforming the best method by 26.6% in NDCG@10.

In particular, this means that smaller entries of A lead to random variables with smaller variance. On the other hand, the bound on ∥∥∥A− Â∥∥∥ 2 depends on the maximum variance. Thus, to improve the results, one idea is to keep entries of Aij with probability pij ≤ p, so that all entries in  have roughly the same variance. This will help us to get sparser matrices, while keeping similar qualit...

We survey two basic techniques for showing that the monadic second-order theory of a structure is decidable. In the first approach, one deals with finite fragments of the theory (given for example by the restriction to formulas of a certain quantifier rank) and – depending on the fragment – reduces the model under consideration to a simpler one. In the second approach, one applies a global tran...

We consider the signature reversing transformation of the metric tensor g µν → −g µν induced by the chiral transformation of the curved space gamma matrices γ µ→ γγ µ in spacetimes with signature (S, T), which also induces a (−1) T spacetime orientation reversal. We conclude: (1) It is a symmetry only for chiral theories with S − T = 4k, with k integer. (2) Yang-Mills theories require dimension...

DEAHP as a weight derivation procedure for analytic hierarchy process (AHP) has been found suffering from some significant drawbacks. Recently, Mirhedayatian and Saen (2011) [5] proposed a new procedure entitled Revised DEAHP for AHP weight derivation [S.M. Mirhedayatian, R.F. Saen, A new approach for weight derivation using data envelopment analysis in the analytic hierarchy process, Journal o...