We study the parameterized complexity of learning k-juntas and some variations of juntas. We show the hardness of learning k-juntas and subclasses of k-juntas in the PAC model by reductions from a W[2]complete problem. On the other hand, as a consequence of a more general result we show that k-juntas are exactly learnable with improper equivalence queries and access to a W[P] oracle. Subject Cl...

OBJECTIVES To determine whether erosive osteoarthritis shares the same pattern of joint involvement and risk profile as increasing grades of non-erosive hand osteoarthritis. METHODS Participants were from two population-based cohorts, aged ≥50 years, reporting hand symptoms in the previous month. Interphalangeal joints were assessed for erosive osteoarthritis (Verbruggen-Veys erosive or remod...

We describe classes of existentially closed ordered difference fields and rings. We show an Ax-Kochen type result for a class of valued ordered difference fields. 1. Existentially closed real-closed difference fields. In the first part of this paper we will consider on one hand difference totally ordered fields, namely totally ordered fields with a distinguished automorphism σ and on the other ...

A graph G is (k, 0)-colorable if its vertices can be partitioned into subsets V1 and V2 such that in G[V1] every vertex has degree at most k, while G[V2] is edgeless. For every integer k ≥ 1, we prove that every graph with the maximum average degree smaller than 3k+4 k+2 is (k, 0)-colorable. In particular, it follows that every planar graph with girth at least 7 is (8, 0)-colorable. On the othe...

Color the edges of the n-vertex complete graph in red and blue, and suppose that red k-cliques are fewer than blue k-cliques. We show that the number of red k-cliques is always less than ckn , where ck ∈ (0, 1) is the unique root of the equation z = (1 − z) + kz(1 − z)k−1. On the other hand, we construct a coloring in which there are at least ckn k −O(nk−1) red k-cliques and at least the same n...

We study length-k-overlap-free binary infinite words, i.e., binary infinite words which can contain only overlaps xyxyx with |x| ≤ k− 1. We prove that no such word can be generated by a morphism, except if k = 1. On the other hand, for every k ≥ 2, there exist length-k-overlap-free binary infinite words which are not length-(k−1)-overlap-free. As an application, we prove that, for every non-neg...

In this paper matching upper and lower bounds for broadcast on general purpose parallel computation models that exploit network locality are proven. These models try to capture both the general purpose properties models like the PRAM or BSP on the one hand, and to exploit network locality of special purpose models like meshes, hypercubes, etc., on the other hand. They do so by charging a cost l...

Nearest neighbor search and k-nearest neighbor graph construction are two fundamental issues arise from many disciplines such as information retrieval, data-mining, machine learning and computer vision. Despite continuous efforts have been taken in the last several decades, these two issues remain challenging. They become more and more imminent given the big data emerges in various fields and h...

BACKGROUND Although age is the strongest predictor of osteoarthritis, the exact mechanism underlying this disorder remains elusive. OBJECTIVE To examine the association between leucocyte telomere length (LTL), a bio-indicator of ageing, and radiographic hand osteoarthritis. METHODS An unselected, predominantly female sample from the TwinsUK Adult Twin Registry (Twin Research and Genetic Epi...