Most general rasterization algorithms in computer graphics are based on point sampling of the image to be rendered. One peculiarity of computer graphics is that irregular sampling patterns are widely used, mainly to prevent moiré artifacts in rendered images. The best irregular sampling patterns have a blue noise characteristic in the spectral domain: such patterns attain a particularly good tr...

A review of the literature suggests that many hearing-impaired patients suffer from sensory deficits in addition to the reduced audibility of speech signals. Poor frequency resolution, or abnormal spread of masking, is a consistently identified deficit in sensorineural hearing loss. Frequency resolution was measured in individual subjects using the input filter pattern paradigm, and the minimum...

let ‎x be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎cartesian decomposition ‎‎x = a + i ‎b‎‎‎‎‎, ‎where ‎‎a ‎and ‎‎b ‎are ‎‎‎n ‎‎times n‎ ‎hermitian ‎matrices. ‎it ‎is ‎known ‎that ‎‎$vert x vert_p^2 ‎leq 2(vert a vert_p^2 + vert b vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎vert . vert_p$ ‎is ‎the ‎schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎in this paper‎, this inequality and some of its improvements ...

We consider the problem of enumerating permutations in the symmetric group on n elements which avoid a given set of consecutive pattern S, and in particular computing asymptotics as n tends to infinity. We develop a general method which solves this enumeration problem using the spectral theory of integral operators on L([0, 1]m), where the patterns in S has length m + 1. Krĕın and Rutman’s gene...