Fitting Voronoi Diagrams to Planar Tesselations

Given a tesselation of the plane, defined by a planar straight-line graph $G$, we want to find a minimal set $S$ of points in the plane, such that the Voronoi diagram associated with $S$ "fits" \ $G$. This is the Generalized Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered recently in \cite{Baner12}. Here we give an algorithm that solves this problem with a number of points that is linear in the size of $G$, assuming that the smallest angle in $G$ is constant.Comment: 14 pages, 8 figures, 1 table. Presented at IWOCA 2013 (Int. Workshop on Combinatorial Algorithms), Rouen, France, July 201

Euclidean Distances, soft and spectral Clustering on Weighted Graphs

We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow data, properly conditioned, illustrate the procedure as well as visualization aspects.Comment: accepted for presentation (and further publication) at the ECML PKDD 2010 conferenc

Equilibrium poloidal field distributions in reversed-field-pinch toroidal discharges

A comparison between the analytic formulae of Shafranov for equilibrium in axisymmetric toroidal reversed field pinch (RFP) systems and fully toroidal numerical solutions of the Grad-Shafranov equation is presented as a function of poloidal beta, internal plasma inductance, and aspect ratio. The Shafranov formula for the equilibrium poloidal field distribution is accurate to within 5% for aspect ratios greater than 2, poloidal betas less than 50%, and for plasma current channels that exceed one-third of the minor toroidal radius. The analytic description for the center shift of the innermost flux surface that encloses the plasma current (the Shafranov shift) is accurate to within 15% for aspect ratios greater than 2 and poloidal betas below 50%, provided the shift does not exceed one-tenth of the minor conducting boundary radius. The behavior of the magnetic axis shift as a function of plasma parameters is included. The Shafranov formulae provide a convenient method for describing the equilibrium behavior of an RFP discharge. Examples illustrating the application of the analytic formulae to the Los Alamos ZT-40M RFP experiment are given

High-resolution Xist binding maps reveal 2-step spreading during X-inactivation

The Xist long noncoding RNA (lncRNA) is essential for X-chromosome inactivation (XCI), the process by which mammals compensate for unequal numbers of sex chromosomes1-3. During XCI, Xist coats the future inactive X (Xi)4 and recruits Polycomb Repressive Complex 2 (PRC2) to the X-inactivation center (Xic)5. How Xist spreads silencing on a 150 Mb scale is unclear. Here we generate high-resolution maps of Xist binding on the X chromosome across a developmental time course using CHART-seq. In female cells undergoing XCI de novo, Xist follows a two-step mechanism, initially targeting gene-rich islands before spreading to intervening gene-poor domains. Xist is depleted from genes that escape XCI but may concentrate near escapee boundaries. Xist binding is linearly proportional to PRC2 density and H3 lysine 27 trimethylation (H3K27me3), suggesting co-migration of Xist and PRC2. Interestingly, when the Xi is acutely stripped off Xist in post-XCI cells, Xist recovers quickly within both gene-rich and -poor domains on a time-scale of hours instead of days, suggesting a previously primed Xi chromatin state. We conclude that Xist spreading takes distinct stage-specific forms: During initial establishment, Xist follows a two-step mechanism, but during maintenance, Xist spreads rapidly to both gene-rich and -poor regions

Next-generation magnetic nozzle prototype

This is the final report of a one-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). This project sought to develop a next-generation magnetic nozzle. The project engaged the fundamental physics of plasma- magnetic field interactions to attain plasma accelerator control that is significantly more advanced than the present state-of-the-art. Central to next-generation magnetic nozzle design and development is the ability to precisely predict the interaction of flowing magnetized plasma with self-generated and applied magnetic fields. This predictive capability must order physical processes in a way that preserves accuracy while allowing for the rapid evaluation of many different nozzle configurations. Large, ``off-the-shelf``, numerical codes are not well suited to nozzle design applications in that they lack the necessary non-ideal physics and are not well disposed to rapid design evaluation. For example, we know that both non-ideal magnetohydrodynamic effects, such as Hall drifts and finite ion- gyro-radius kinetics, are important constituents of magnetic nozzle performance. We built a special purpose code to allow system design

Ginzburg-Landau-Gor'kov Theory of Magnetic oscillations in a type-II 2-dimensional Superconductor

We investigate de Haas-van Alphen (dHvA) oscillations in the mixed state of a type-II two-dimensional superconductor within a self-consistent Gor'kov perturbation scheme. Assuming that the order parameter forms a vortex lattice we can calculate the expansion coefficients exactly to any order. We have tested the results of the perturbation theory to fourth and eight order against an exact numerical solution of the corresponding Bogoliubov-de Gennes equations. The perturbation theory is found to describe the onset of superconductivity well close to the transition point $H_{c2}$. Contrary to earlier calculations by other authors we do not find that the perturbative scheme predicts any maximum of the dHvA-oscillations below $H_{c2}$. Instead we obtain a substantial damping of the magnetic oscillations in the mixed state as compared to the normal state. We have examined the effect of an oscillatory chemical potential due to particle conservation and the effect of a finite Zeeman splitting. Furthermore we have investigated the recently debated issue of a possibility of a sign change of the fundamental harmonic of the magnetic oscillations. Our theory is compared with experiment and we have found good agreement.Comment: 39 pages, 8 figures. This is a replacement of supr-con/9608004. Several sections changed or added, including a section on the effect of spin and the effect of a conserved number of particles. To be published in Phys. Rev.

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Integer Quantum Hall Effect in Double-Layer Systems

We consider the localization of independent electron orbitals in double-layer two-dimensional electron systems in the strong magnetic field limit. Our study is based on numerical Thouless number calculations for realistic microscopic models and on transfer matrix calculations for phenomenological network models. The microscopic calculations indicate a crossover regime for weak interlayer tunneling in which the correlation length exponent appears to increase. Comparison of network model calculations with microscopic calculations casts doubt on their generic applicability.Comment: 14 pages, 12 figures included, RevTeX 3.0 and epsf. Additional reference