Quotients of E^n by A_{n+1} and Calabi-Yau manifolds

We give a simple construction, starting with any elliptic curve E, of an n-dimensional Calabi-Yau variety of Kummer type (for any n>1), by considering the quotient Y of the n-fold self-product of E by a natural action of the alternating group A_{n+1} (in n+1 variables). The vanishing of H^m(Y, O_Y) for 0<m<n follows from the non-existence of (non-zero) fixed points in certain representations of A_{n+1}. For n<4 we provide an explicit crepant resolution X in characteristics different from 2,3. The key point is that Y can be realized as a double cover of P^n branched along a hypersurface of degree 2(n+1).Comment: 9 page

On the nonlinear statistics of range image patches

In [A. B. Lee, K. S. Pedersen, and D. Mumford, Int. J. Comput. Vis., 54 (2003), pp. 83–103], the authors study the distributions of 3 × 3 patches from optical images and from range images. In [G. Carlsson, T. Ishkanov, V. de Silva, and A. Zomorodian, Int. J. Comput. Vis., 76 (2008), pp. 1–12], the authors apply computational topological tools to the data set of optical patches studied by Lee, Pedersen, and Mumford and find geometric structures for high density subsets. One high density subset is called the primary circle and essentially consists of patches with a line separating a light and a dark region. In this paper, we apply the techniques of Carlsson et al. to range patches. By enlarging to 5×5 and 7×7 patches, we find core subsets that have the topology of the primary circle, suggesting a stronger connection between optical patches and range patches than was found by Lee, Pedersen, and Mumford

Efficient pairing computation with theta functions

The original publication is available at www.springerlink.comInternational audienceIn this paper, we present a new approach based on theta functions to compute Weil and Tate pairings. A benefit of our method, which does not rely on the classical Miller's algorithm, is its generality since it extends to all abelian varieties the classical Weil and Tate pairing formulas. In the case of dimension $1$ and $2$ abelian varieties our algorithms lead to implementations which are efficient and naturally deterministic. We also introduce symmetric Weil and Tate pairings on Kummer varieties and explain how to compute them efficiently. We exhibit a nice algorithmic compatibility between some algebraic groups quotiented by the action of the automorphism $-1$, where the $\Z$-action can be computed efficiently with a Montgomery ladder type algorithm

Solution of the generalized periodic discrete Toda equation II; Theta function solution

We construct the theta function solution to the initial value problem for the generalized periodic discrete Toda equation.Comment: 11 page

Aux Etats-Unis, l’enseignement des maths est totalement obsolète ! Favorisons des apprentissages concrets face aux cursus abscons et abstraits, Paris, 2011.

Recorte de um artigo do jornal francês Le Monde. O original pertence à professora Lydia Condé Lamparelli, fotografia autorizada pela mesma.Recorte de um artigo do jornal Le Monde, com criticas à realidade do ensino de matemática nos Estados Unidos. Os autores criticam o fato de boa parte dos conteúdos aprendidos não terão nenhuma utilidade para a vida da maioria dos alunos, a não ser aqueles que se dediquem a profissões como matemáticos, físicos, engenheiros. Advogam, portanto a restrição do ensino dos conteúdos de matemática àqueles conteúdos que podem, claramente, serem empregados no dia a dia, o trabalho com os quais possibilitará o conhecimento da parte mais abstrata desses conhecimentos, defende uma alfabetização numérica

General pure multipartite entangled states and the Segre variety

In this paper, we construct a measure of entanglement by generalizing the quadric polynomial of the Segre variety for general multipartite states. We give explicit expressions for general pure three-partite and four-partite states. Moreover, we will discuss and compare this measure of entanglement with the generalized concurrence.Comment: 5 page

Do it Right or Not at All: A Longitudinal Evaluation of a Conflict Managment System Implementation

We analyzed an eight-year multi-source longitudinal data set that followed a healthcare system in the Eastern United States as it implemented a major conflict management initiative to encourage line managers to consistently perform Personal Management Interviews (or PMIs) with their employees. PMIs are interviews held between two individuals, designed to prevent or quickly resolve interpersonal problems before they escalate to formal grievances. This initiative provided us a unique opportunity to empirically test key predictions of Integrated Conflict Management System (or ICMS) theory. Analyzing survey and personnel file data from 5,449 individuals from 2003 to 2010, we found that employees whose managers provided high-quality interviews perceived significantly higher participative work climates and had lower turnover rates. However, retention was worse when managers provided poor-quality interviews than when they conducted no interviews at all. Together these findings highlight the critical role that line mangers play in the success of conflict management systems

Statistical Analysis of Small Ellerman Bomb Events

The properties of Ellerman bombs (EBs), small-scale brightenings in the H-alpha line wings, have proved difficult to establish due to their size being close to the spatial resolution of even the most advanced telescopes. Here, we aim to infer the size and lifetime of EBs using high-resolution data of an emerging active region collected using the Interferometric BIdimensional Spectrometer (IBIS) and Rapid Oscillations of the Solar Atmosphere (ROSA) instruments as well as the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). We develop an algorithm to track EBs through their evolution, finding that EBs can often be much smaller (around 0.3") and shorter lived (less than 1 minute) than previous estimates. A correlation between G-band magnetic bright points and EBs is also found. Combining SDO/HMI and G-band data gives a good proxy of the polarity for the vertical magnetic field. It is found that EBs often occur both over regions of opposite polarity flux and strong unipolar fields, possibly hinting at magnetic reconnection as a driver of these events.The energetics of EB events is found to follow a power-law distribution in the range of "nano-flare" (10^{22-25} ergs).Comment: 19 pages. 7 Figure