Finite volume schemes for diffusion equations: introduction to and review of modern methods

We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construction principles of the methods, we review some literature results, focusing on two important properties of schemes (discrete versions of well-known properties of the continuous equation): coercivity and minimum-maximum principles. Coercivity ensures the stability of the method as well as its convergence under assumptions compatible with real-world applications, whereas minimum-maximum principles are crucial in case of strong anisotropy to obtain physically meaningful approximate solutions

Moduli-space structure of knots with intersections

It is well known that knots are countable in ordinary knot theory. Recently, knots {\it with intersections} have raised a certain interest, and have been found to have physical applications. We point out that such knots --equivalence classes of loops in $R^3$ under diffeomorphisms-- are not countable; rather, they exhibit a moduli-space structure. We characterize these spaces of moduli and study their dimension. We derive a lower bound (which we conjecture being actually attained) on the dimension of the (non-degenerate components) of the moduli spaces, as a function of the valence of the intersection.Comment: 15 pages, latex-revtex, no figure

A clever elimination strategy for efficient minimal solvers

We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image measurements enter the linear equations only. We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns. This can be generalized to fully non-linear systems by linearization via lifting. We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion. Our approach also generates new interesting constraints on the fundamental matrices of partially calibrated cameras, which were not known before.Comment: 13 pages, 7 figure

Determining γ\gamma using B±→DK±B^\pm \to D K^\pm with multibody D decays

We propose a method for determining $\gamma$ using $B^\pm\to D K^\pm$ decays followed by a multibody $D$ decay, such as $D \to K_S \pi^-\pi^+$, $D \to K_S K^-K^+$ and $D \to K_S \pi^-\pi^+\pi^0$. The main advantages of the method is that it uses only Cabibbo allowed $D$ decays, and that large strong phases are expected due to the presence of resonances. Since no knowledge about the resonance structure is needed, $\gamma$ can be extracted without any hadronic uncertainty.Comment: 17 pages, 1 figur

High dynamic range imaging with a single-mode pupil remapping system : a self-calibration algorithm for redundant interferometric arrays

The correction of the influence of phase corrugation in the pupil plane is a fundamental issue in achieving high dynamic range imaging. In this paper, we investigate an instrumental setup which consists in applying interferometric techniques on a single telescope, by filtering and dividing the pupil with an array of single-mode fibers. We developed a new algorithm, which makes use of the fact that we have a redundant interferometric array, to completely disentangle the astronomical object from the atmospheric perturbations (phase and scintillation). This self-calibrating algorithm can also be applied to any - diluted or not - redundant interferometric setup. On an 8 meter telescope observing at a wavelength of 630 nm, our simulations show that a single mode pupil remapping system could achieve, at a few resolution elements from the central star, a raw dynamic range up to 10^6; depending on the brightness of the source. The self calibration algorithm proved to be very efficient, allowing image reconstruction of faint sources (mag = 15) even though the signal-to-noise ratio of individual spatial frequencies are of the order of 0.1. We finally note that the instrument could be more sensitive by combining this setup with an adaptive optics system. The dynamic range would however be limited by the noise of the small, high frequency, displacements of the deformable mirror.Comment: 11 pages, 7 figures. Accepted for publication in MNRA

Novice Ideas: Handwriting Comparisons Conducted by an Untrained Individual

Forensic analysis of questioned documents includes chemical analyses of paper and ink as well as handwriting comparisons. Several elements affect handwriting analyses, including the presence of discriminatory factors that can individualize a handwriting sample and whether the handwriting has been disguised. Five handwriting samples were gathered from six individuals comprising of one reference, three natural unknowns, and one disguised sample per person. A novice conducted analyses on every collected sample and conducted comparisons of the reference sample to the unknown and disguised samples in an attempt to correctly source the unknown and disguised samples. The novice showed a high level of accuracy in correctly sourcing the natural sample but made erroneous conclusions when analyzing the disguised samples