The successive projection algorithm (SPA) can quickly solve a nonnegative matrix factorization problem under a separability assumption. Even if noise is added to the problem, SPA is robust as long as the perturbations caused by the noise are small. In particular, robustness against noise should be high when handling the problems arising from real applications. The preconditioner proposed by Gil...

We introduce a method to study random Boolean networks with asynchronous stochastic update. Each node in the state space network starts with equal occupation probability, which then evolves to a steady state. Attractors and the sizes of their basins are determined by the nodes left occupied at late times. As for synchronous update, the basin entropy grows with system size only for critical netw...

The Hanna Neumann conjecture states that if F is a free group, then for all finitely generated subgroups H,K 6 F , rank(H ∩ K) − 1 6 [rank(H)− 1] [rank(K)− 1] In this paper, we show that if one of the subgroups, say H , has a generating set consisting of only positive words, then H is not part of any counterexample to the conjecture. We further show that if H ≤ F2 is part of a counterexample to...

Let F be a field. Given a simple graph G on n vertices, its minimal rank (with respect to F ) is the minimum rank of a symmetric n× n F -valued matrix whose off-diagonal zeroes are the same as in the adjacency matrix of G. If F is finite, then for every k, it is shown that the set of graphs of minimal rank at most k is characterized by finitely many forbidden induced subgraphs, each on at most ...

suppose $pi:mathcal{a}rightarrow mathcal{b}$ is a surjective unital $ast$-homomorphism between c*-algebras $mathcal{a}$ and $mathcal{b}$, and $0leq aleq1$ with $ain  mathcal{a}$. we give a sufficient condition that ensures there is a proection $pin mathcal{a}$ such that $pi left( pright) =pi left( aright) $. an easy consequence is a result of [l. g. brown and g. k. pedersen, c*-algebras of real...

Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices that are not themselves rank-deficient but have off-diagonal blocks that are—specifically, the classes of so-called hierarchically off-diagonal low rank (HODL...

A k-hitting set in a hypergraph is a set of at most k vertices that intersects all hyperedges. We study the union of all inclusion-minimal khitting sets in hypergraphs of rank r (where the rank is the maximum size of hyperedges). We show that this union is relevant for certain combinatorial inference problems and give worst-case bounds on its size, depending on r and k. For r = 2 our result is ...

Quasi-Newton methods are generally held to be the most efficient minimization methods for small to medium sized problems. From these the symmetric rank one update of Broyden [4] has been disregarded for a long time because of its potential failure. The work of Conn, Gould and Toint [6], Kelley and Sachs [13] and Khalfan, Byrd and Schnabel [14], [15] has renewed the interest in this method. Howe...

Probabilistic algorithms for constructing matrix decompositions have recently gained vast popularity due to their ability to handle very large problems. This paper pursues the idea of improving a standard Jacobi preconditioner with a low rank correction, to enhance its performance for the iterative solution of finite element discretizations. This is based on the well-known fact that, in the cas...