The human auditory system can encode regularities in the acoustic environment without the requirement of attention. We investigated whether the auditory system of musicians is more sensitive than that of non-musicians in encoding complex regularities. We presented tone sequences containing either a temporal or a numerical regularity. The sequence with the temporal regularity could be divided in...

GP inherently is a technique for, and relies upon, exploration and exploitation of regularity. With ADFs, regularity translates into modularity. Regularity is explored both implicitly (evolution via crossover) and explicitly (as in ADFs). ACGP (Adaptable Constrained GP) offers a new way for GP to explore regularity of a different kind. It will have an impact on modularity as well. I will here b...

Property testing algorithms are “ultra”-efficient algorithms that decide whether a given object (e.g., a graph) has a certain property (e.g., bipartiteness), or is significantly different from any object that has the property. To this end property testing algorithms are given the ability to perform (local) queries to the input, though the decision they need to make usually concern properties wi...

In this paper, we deal with the semilinear wave equation with strong damping. By choosing a suitable state space, we characterize the interpolation and extrapolation spaces of the operator matrix Aθ, analysis the criticality of the ε-regular nonlinearity with critical growth. Finally, we investigate the global existence of the ε-regular solutions which have bounded X ×X norms on their existence...

For 0 < γ ≤ 1 and graphs G and H, write G→γ H if any γ-proportion of the edges of G span at least one copy of H in G. As customary, write Kr for the complete graph on r vertices. We show that for every fixed real η > 0 there exists a constant C = C(η) such that almost every random graph Gn,p with p = p(n) ≥ Cn−2/5 satisfies Gn,p →2/3+η K4. The proof makes use of a variant of Szemerédi’s regular...

Let 0 be any fixed 3-uniform hypergraph. For a 3-uniform hypergraph we define 0( ) to be the maximum size of a set of pairwise triple-disjoint copies of 0 in . We say a function from the set of copies of 0 in to [0, 1] is a fractional 0-packing of if ¥ e ( ) 1 for every triple e of . Then * 0( ) is defined to be the maximum value of ¥ 0 over all fractional 0-packings of . We show that * 0( ) 0(...

The asymptotics of 2-color Ramsey numbers of loose and tight cycles in 3-uniform hypergraphs have been recently determined ([16], [17]). We address here the same problem for Berge-cycles and for 3 colors. Our main result is that the 3-color Ramsey number of a 3-uniform Berge cycle of length n is asymptotic to 5n 4 . The result is proved with the Regularity Lemma via the existence of a monochrom...

We generalize the stable graph regularity lemma of Malliaris and Shelah to the case of finite structures in finite relational languages, e.g., finite hypergraphs. We show that under the model-theoretic assumption of stability, such a structure has an equitable regularity partition of size polynomial in the reciprocal of the desired accuracy, and such that for each k-ary relation and k-tuple of ...