Kahng, A.B. and G. Robins, Optimal algorithms for extracting spatial regularity in images, Pattern Recognition Letters 12 (1991) 757-764. Finding spatial regularity in images is important in military applications (e.g., finding rows of landmines), texture analysis, and other areas. We give an optimal ®(n 2) algorithm for finding all maximal equally-spaced cnllinear subsets within a pointset in ...

We revisit regularity of SLE trace, for all κ 6= 8, and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia–Rodemich–Rumsey type, we obtain finite moments (and hence almost surely) optimal variation regularity with index min(1 + κ/8, 2), improving on previous works of Werness, and also (optimal) Hölder regularity à la Johansson Vik...

Green [Geometric and Functional Analysis 15 (2005), 340–376] established a version of the Szemerédi Regularity Lemma for abelian groups and derived the Removal Lemma for abelian groups as its corollary. We provide another proof of his Removal Lemma that allows us to extend its statement to all finite groups. We also discuss possible extensions of the Removal Lemma to systems of equations.

A popular wavelet reference [W] states that “in theoretical and practical studies, the notion of (wavelet) regularity has been increasing in importance.” Not surprisingly, the study of wavelet regularity is currently a major topic of investigation. Smoother wavelets provide sharper frequency resolution of functions. Also, the iterative algorithms to construct wavelets converge faster for smooth...

    M. and M.   Abstract: Existence and uniqueness of solution for singular 2-D systems depends on regularity condition. Simple regularity implies regularity and under this assumption, the generalized wave model (GWM) is introduced to cast singular 2-D system of equations as a family of non-singular 1-D models with variable structure.These index dependent models, along with a set of boundary co...

We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.

In this paper, we study a family of gradient descent algorithms to approximate the regression function from reproducing kernel Hilbert spaces. Here early stopping plays a role of regularization, where given a finite sample and some regularity condition on the regression function, a stopping rule is given and some probabilistic upper bounds are obtained for the distance between the function iter...

In this paper we show that metric regularity and strong metric regularity of a set-valued mapping imply convergence of inexact iterative methods for solving a generalized equation associated with this mapping. To accomplish this, we first focus on the question how these properties are preserved under changes of the mapping and the reference point. As an application, we consider discrete approxi...

Regularity is a shared memory consistency condition that has received considerable attention, notably in connection with quorumbased shared memory. Lamport’s original definition of regularity assumed a single-writer model, however, and is not well-defined when each shared variable may have multiple writers. In this paper, we address this need by formally extending the notion of regularity to a ...