Humans can rapidly detect regular patterns (i.e., within few cycles) without any special attention to the acoustic environment. This suggests that human sensory systems are equipped with a powerful mechanism for automatically predicting forthcoming stimuli to detect regularity. It has recently been hypothesized that the neural basis of sensory predictions exists for not only what happens (predi...

Let P be a polygon inscribed in a circle. The shadow of P is a polygon P ′ whose vertices are at the midpoints of the arcs of consecutive points of P . The shadow sequence P , P , P , . . . is a sequence of inscribed polygons such that each P t is the shadow of P t−1 for all t ≥ 0. We show in this abstract that the shadow sequence converges to the regular polygon, and in such way that variance ...

The discriminator of an integer sequence s = (s(i))i 0, introduced by Arnold, Benkoski, and McCabe in 1985, is the map Ds(n) that sends n 1 to the least positive integer m such that the n numbers s(0), s(1), . . . , s(n 1) are pairwise incongruent modulo m. In this note we consider the discriminators of a certain class of sequences, the k-regular sequences. We compute the discriminators of two ...

State elimination is an intuitive and easy-to-implement algorithm that computes a regular expression from a finite-state automaton (FA). The size of a regular expression from state elimination depends on the state removal sequence. Note that it is very hard to compute the shortest regular expression for a given FA in general and we cannot avoid the exponential blow-up from state elimination. Ne...

A = (ank) be a regular summability matrix. In the present paper we deal with subspaces of space A?statistically convergent sequences obtained by rate at which A?statistical limit tends to zero. We prove that sequence is A?strongly if and only it A?uniformly integrable o (an) where positive nonincreasing sequence. also make link between A?strong convergence A?distributional (an). Finally, as an ...

A set of n homogeneous polynomials in n variables is a regular sequence if the associated polynomial system has only the obvious solution (0, 0, . . . , 0). Denote by pk(n) the power sum symmetric polynomial in n variables x k 1 +x 2 + · · ·+xk n . The interpretation of the q-analogue of the binomial coefficient as Hilbert function leads us to discover that n consecutive power sums in n variabl...

R. Barua, The Hausdorff-Kuratowski hierarchy of o-regular languages and a hierarchy of Muller automata, Theoretical Computer Science 96 (1992) 345-360. Given a finite alphabet Z, we give a simple characterization of those Gd subsets of Z” which are deterministic w-regular (i.e. accepted by Biichi automata) over Z and then characterize the w-regular languages in terms of these (rational) G6 sets...

A not necessarily noetherian local ring O is called regular if every finitely generated ideal I O possesses finite projective dimension. In the article localizations O = Aq, q ∈ SpecA, of a finitely presented, flat algebra A over a Prüfer domain R are investigated with respect to regularity: this property of O is shown to be equivalent to the finiteness of the weak homological dimension wdimO. ...

Since regular expressions are often used to detect errors in sequences such as strings or date, it is natural to use them for data repair. Motivated by this, we propose a data repair method based on regular expression to make the input sequence data obey the given regular expression with minimal revision cost. The proposed method contains two steps, sequence repair and token value repair. For s...