A map f : [n]` → [n]n has locality d if each output symbol in [n] = {1, 2, . . . , n} depends only on d of the ` input symbols in [n]. We show that the output distribution of a d-local map has statistical distance at least 1−2 · exp(−n/ logcd n) from a uniform permutation of [n]. This seems to be the first lower bound for the well-studied problem of generating permutations. Because poly(n)-size...

◦ Geodesic flows on compact manifolds with negative sectional curvature. Later, we relax uniform hyperbolicity to an asymptotic one, called non-uniform hyperbolicity. Two examples of such systems are: ◦ Slow down of fA : T → T, see [9]. ◦ Geodesic flows on surfaces with nonpositive curvature. Introductory example: Smale’s horseshoe [21]. Let g : K → K be Smale’s horseshoe map, and σ : Σ→ Σ the ...

in this article, by using chebyshev’s polynomials and chebyshev’s expansion, we obtain the best uniform polynomial approximation out of p2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

UNLABELLED Two-photon fluorescence microscopy and conscious, restrained optical biosensor mice were used to study smooth muscle Ca(2+) signaling in ear arterioles. Conscious mice were used in order to preserve normal mean arterial blood pressure (MAP) and sympathetic nerve activity (SNA). ExMLCK mice, which express a genetically-encoded smooth muscle-specific FRET-based Ca(2+) indicator, were e...

Attenuation correction is very important for quantitative SPECT imaging. We designed an uncollimated non-uniform line array source (non-uniform LAS) for attenuation correction based on transmission computed tomography (TCT) using Tc-99m and compared its performance with an uncollimated uniform line array source (uniform LAS) in a thorax phantom study. This non-uniform LAS was attached to one ca...

Sensory maps are often distorted representations of the environment, where ethologically-important ranges are magnified. The implication of a biased representation extends beyond increased acuity for having more neurons dedicated to a certain range. Because neurons are functionally interconnected, non-uniform representations influence the processing of high-order features that rely on compariso...

1: Seeds of sunflowers are often modelled by the map n 7−→ φθ(n) = √ ne2iπnθ leading to a roughly uniform repartition with two consecutive seeds separated by the divergence angle 2πθ for θ the golden ratio. We associate to an arbitrary real divergence angle 2πθ a geodesic path γθ : R>0 −→ PSL2(Z)\H of the modular curve and use it for local descriptions of the image φθ(N) of the phyllotactic map...

In this paper, we present a system to redistribute computational power in plane sweeping. Plane sweeping allows the generation of novel viewpoints of a scene by testing different depth hypotheses across input cameras. Typical plane sweeping approaches incorporate a uniform depth plane distribution to investigate different depth hypotheses to generate a depth map. When the scene consists of a sp...