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Low rank matrix recovery is about reconstructing a low rank matrix from incomplete measurements. It arises frequently in many research areas of science and engineering, for example, machine learning, ...
The constant rank theorem was initially developed by Caffarelli-Friedman in 1985 in two-dimensions for convex solutions of semilinear equations. Later, Korevaar-Lewis extended the result to higher dim...
The rank-tracking probability (RTP) is a useful statistical index for measuring the ``tracking ability'' of longitudinal disease risk factors in biomedical studies. A flexible nonparametric method for...
For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, ...
Goldman gratefully acknowledges partial support by NSF grants DMS-9504764, DMS-9803518, DMS-0103889 and a Semester Research Award from the General Research Board of the University of Maryland in Fa...
The present paper is a direct continuation of [2], where it is shown that any strongly minimal trivial theory is model complete after naming constants for a model. In this paper we show that this re...
We establish the lower bound p2t (e, e)  exp(−t1/3), for the large times asymptotic behaviours of the probabilities p2t (e, e) of return to the origin at even times 2t, for random walks assoc...
How many random entries of an n × nα, rank r matrix are necessary to reconstruct the matrix within an accuracy δ? We address this question in the case of a random matrix with bounded rank, whereby the...
Principal components analysis (PCA) is a well-known technique for approximating a data set represented by a matrix by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets c...
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that pro...
We consider the problem of recovering a lowrank matrix when some of its entries, whose locations are not known a priori, are corrupted by errors of arbitrarily large magnitude. It has recently been sh...
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one...
Durham, NC - A study of dominance in female baboons suggests that the route to a higher rank is to maintain close ties with mom, and to have lots of supportive sisters.
Let G be a non-compact connected semisimple Lie group of real rank one with finite center, K a maximal compact subgroup of G and X = G/K an associated symmetric space of real rank one. We will p...
Consider the moduli space of parabolic Higgs bundles (E,\Phi) of rank two on CP^1 such that the underlying holomorphic vector bundle for the parabolic vector bundle E is trivial. It is equipped with t...

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