In this paper we describe our effort on TREC Contextual Suggestion Track. Using resources such as description or websites of example suggestions to build user profile has been proven to be effective on last year’s TREC. This year we also leverage the power of using user profile. Real world opinions of the suggestions are used in our method to build both user profile and candidate suggestion pro...

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) has applications, among other areas, in efficient solving of sparse linear systems of equations and scheduling parallel assembly of products. Our main technical results improve upper and lower bounds for the ordered chromatic number of...

Carrier-phase ambiguity resolution is usually based on the assumption that the underlying model of observation equations is of full rank. In this contribution the model of observation equations is assumed to be of less than full rank. The well-known three-step procedure of integer least squares is generalized and it is shown how the solution can be affected by the rank deficiency. Although the ...

A new Z-basis for the space of quasisymmetric functions (QSym, for short) is presented. It is shown to have nonnegative structure constants, and several interesting properties relative to the quasisymmetric functions associated to matroids by the Hopf algebra morphism F of Billera, Jia, and Reiner [3]. In particular, for loopless matroids, this basis reflects the grading by matroid rank, as wel...

Nuclear norm minimization (NNM) has recently gained significant attention for its use in rank minimization problems. Similar to compressed sensing, using null space characterizations, recovery thresholds for NNM have been studied in [12, 4]. However simulations show that the thresholds are far from optimal, especially in the low rank region. In this paper we apply the recent analysis of Stojnic...

The low-rank representation (LRR) was presented recently and showed effective and robust for subspace segmentation. This paper presents a LRR-based discriminative projection method (LRR-DP) for robust feature extraction, by virtue of the underlying low-rank structure of data represesntation revealed by LRR. LRR-DP seeks a linear transformation such that in the transformed space, the betweenlarg...

The paper investigates the global ρ -exponential stabilizability of nonholonomic Caplygin systems. A novel decomposition of state is given first. When systems are linear in certain state variables, a simple and easily verified rank condition can be proposed to guarantee the global ρ -exponential stabilizability of Caplygin systems. In our design, all parameters can be explicitly determined from...

The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer to test whether a certain rate vector is achievable with vector linear network codes for a multisource network coding instance and whether there exists a mul...