Under suitable conditions on a measure, universality limits f ( ; ) that arise in the bulk, unitary case, are reproducing kernels of de Branges spaces of entire functions. In the classical case, f is the sinc kernel f (s; t) = sin (s t) (s t) ; but other kernels can arise. We study the linear operator L [h] (x) = Z 1 1 f (s; x)h (s) ds; establishing inequalities, and deducing some conditions fo...

We consider the block elimination problem Q A 1 A 2 = ?C 0 , where, given a matrix A 2 R mk , A 11 2 R kk , we try to nd a matrix C with C T C = A T A and an orthogonal matrix Q that eliminates A 2. Sun and Bischof recently showed that any orthogonal matrix can be represented in the so-called basis-kernel representation Q = Q(Y; S) = I ? Y ST T. Applying this framework to the block elimination ...

We consider the problem of recognizing star-polygons under staircase visibility (s-visibility). We show that the s-visibility polygon from a point inside a simple orthogonal polygon of n sides can be computed in O(n) time. When the polygon contains holes the algorithm runs in O(n log n) time, which we prove to be optimal by linear time reduction from sorting. We present an algorithm for computi...

Let D = (V , A) be a directed graph (digraph) without loops nor multiple arcs. A set of vertices S of a digraph D is a (k, l)-kernel of D if and only if for any two vertices u, v in S, d(u, v) ≥ k and for any vertex u in V \ S there exists v in S such that d(u, v) ≤ l. A digraph D is called quasi-transitive if and only if for any distinct vertices u, v, w of D such that u→ v → w, then u and w a...

The Nyström method is routinely used for out-of-sample extension of kernel matrices. We describe how this method can be applied to find the singular value decomposition (SVD) of general matrices and the eigenvalue decomposition (EVD) of square matrices. We take as an input a matrix M ∈ Rm×n, a user defined integer s ≤ min(m,n) and AM ∈ Rs×s, a matrix sampled from the columns and rows of M . The...

This study addresses two central problems in cloud microphysics. The first is the source of large droplets, which initiates the rapid production of warm rain. The second is the broadening of the cloud droplet spectrum at both tails of the spectrum. The study explores how in-cloud turbulence can help to close the gaps in our understanding. With box model simulations, the development of cloud dro...

In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dominating set of G and the subgraph induced by S is connected. This is a basic connectivity problem that is known to be NP-complete, and it has been extensively studied using several algorithmic approaches. In this paper...

Let S be a regular semigroup and let p be a congruence relation on S. The kernel of p, in notation kerp, is the union of the idempotent p-classes. The trace of p, in notation trp, is the restriction of p to the set of idempotents of S. The pair (kerp,trp) is said to be the congruence pair associated with p. Congruence pairs can be characterized abstractly, and it turns out that a congruence is ...