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

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...

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.