How far can you see in a forest?

We address a visibility problem posed by Solomon & Weiss. More precisely, in any dimension $n := d + 1 \ge 2$, we construct a forest \F with finite density satisfying the following condition : if \e > 0 denotes the radius common to all the trees in \F, then the visibility \V therein satisfies the estimate \V(\e) = O(\e^{-2d-\eta}) for any $\eta > 0$, no matter where we stand and what direction we look in. The proof involves Fourier analysis and sharp estimates of exponential sums.Comment: This is an extended version of a paper to appear. Minor typos have been correcte

Rational approximation and arithmetic progressions

A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a metrical and a non-metrical point of view and, on the other hand, from an asymptotic and also a uniform point of view. The principal novelty is a Khintchine type theorem for uniform approximation in this context. Some applications of this theory are also discussed

Large scale analysis of protein stability in OMIM disease related human protein variants

Modern genomic techniques allow to associate several Mendelian human diseases to single residue variations in different proteins. Molecular mechanisms explaining the relationship among genotype and phenotype are still under debate. Change of protein stability upon variation appears to assume a particular relevance in annotating whether a single residue substitution can or cannot be associated to a given disease. Thermodynamic properties of human proteins and of their disease related variants are lacking. In the present work, we take advantage of the available three dimensional structure of human proteins for predicting the role of disease related variations on the perturbation of protein stability

Fast Separable Non-Local Means

We propose a simple and fast algorithm called PatchLift for computing distances between patches (contiguous block of samples) extracted from a given one-dimensional signal. PatchLift is based on the observation that the patch distances can be efficiently computed from a matrix that is derived from the one-dimensional signal using lifting; importantly, the number of operations required to compute the patch distances using this approach does not scale with the patch length. We next demonstrate how PatchLift can be used for patch-based denoising of images corrupted with Gaussian noise. In particular, we propose a separable formulation of the classical Non-Local Means (NLM) algorithm that can be implemented using PatchLift. We demonstrate that the PatchLift-based implementation of separable NLM is few orders faster than standard NLM, and is competitive with existing fast implementations of NLM. Moreover, its denoising performance is shown to be consistently superior to that of NLM and some of its variants, both in terms of PSNR/SSIM and visual quality

Zero NeRF: Registration with Zero Overlap

We present Zero-NeRF, a projective surface registration method that, to the best of our knowledge, offers the first general solution capable of alignment between scene representations with minimal or zero visual correspondence. To do this, we enforce consistency between visible surfaces of partial and complete reconstructions, which allows us to constrain occluded geometry. We use a NeRF as our surface representation and the NeRF rendering pipeline to perform this alignment. To demonstrate the efficacy of our method, we register real-world scenes from opposite sides with infinitesimal overlaps that cannot be accurately registered using prior methods, and we compare these results against widely used registration methods