Quadratic deformation of Minkowski space

We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson bracket is quadratic. We show that the star product although defined on the polynomials can be extended differentiably. Finally we compute the Eucliden and Minkowskian real forms of the deformation.Comment: Presented at XVII European Workshop on String Theory 2011. Padova (Italy) September 05-09; Fortschr. Phys. 1-7 (2012

Revisiting the usurer: the portrayal of Shylock as an affectionate father in Howard Jacobson''s Shylock is my name

This article aims to re-interpret the figure of Shylock in William Shakespeare's The Merchant of Venice by exploring how its novel rewriting by Howard Jacobson provides a more positive portrayal of the Jewish usurer. I attempt to argue that Jacobson's Shylock Is My Name contributes to re-reading Shylock as a thoughtful father who truly loves his daughter Jessica. Indeed, this 21st-century retelling revolves around the connection between Shylock and Simon Strulovitch, a Jewish philanthropist who has also been neglected by his daughter. The novel presents Shylock as a trustworthy character that is determined to help his friend create an emotional bond with his daughter. Moreover, Jacobson succeeds in empowering Shakespeare's Shylock to such an extent that he evolves from being an underdog in Venice to being widely respected by English society. As regards methodology, I have used the rhizomatic model proposed by Douglas Lanier with the purpose of exploring the enriching dialogue between the source text and this rewriting

From historical map to online 3D recreation: the 1861 cadastral map of Horta (Barcelona)

The recent study and classification of over 200 cadastral maps created in the nineteenth century in Catalonia have provided a valuable source of information about the agricultural landscape country’s past, but by linking them with data recorded in tax books known as amillaramientos, it is possible to gain a better knowledge of the past. By applying this method to the 1861 cadastral map of Horta and its corresponding amillaramiento, a planimetric map showing the land use distribution in the town was created. The resulting land use map was subsequently overlaid on top of a digital elevation model to create 3D visualizations which show the altitudinal distribution of crops and other features. Finally, the article explores a way of distributing the results online, making them accessible to the public and increasing the research impact of future findings. Therefore, the method described in this article allows the systematic recreation and distribution of past landscapes by using Catalan cadastral maps of the nineteenth century, something which can help enrich the scientific knowledge of many disciplines

Stability of the replica symmetric solution for the information conveyed by by a neural network

The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts of noise. The region of instability depends on the contribution of the threshold and the sparseness: for distributed pattern distributions, the unstable region extends to higher noise variances than for very sparse distributions, for which it is almost nonexistant.Comment: 19 pages, LaTeX, 5 figures. Also available at http://www.mrc-bbc.ox.ac.uk/~schultz/papers.html . Submitted to Phys. Rev. E Minor change

Rigorous Bounds to Retarded Learning

We show that the lower bound to the critical fraction of data needed to infer (learn) the orientation of the anisotropy axis of a probability distribution, determined by Herschkowitz and Opper [Phys.Rev.Lett. 86, 2174 (2001)], is not always valid. If there is some structure in the data along the anisotropy axis, their analysis is incorrect, and learning is possible with much less data points.Comment: 1 page, 1 figure. Comment accepted for publication in Physical Review Letter

Precision radial velocities of double-lined spectroscopic binaries with an iodine absorption cell

A spectroscopic technique employing an iodine absorption cell (I_2) to superimpose a reference spectrum onto a stellar spectrum is currently the most widely adopted approach to obtain precision radial velocities of solar-type stars. It has been used to detect ~80 extrasolar planets out of ~130 know. Yet in its original version, it only allows us to measure precise radial velocities of single stars. In this paper, we present a novel method employing an I_2 absorption cell that enables us to accurately determine radial velocities of both components of double-lined binaries. Our preliminary results based on the data from the Keck I telescope and HIRES spectrograph demonstrate that 20-30 m/s radial velocity precision can be routinely obtained for "early" type binaries (F3-F8). For later type binaries, the precision reaches ~10 m/s. We discuss applications of the technique to stellar astronomy and searches for extrasolar planets in binary systems. In particular, we combine the interferometric data collected with the Palomar Testbed Interferometer with our preliminary precision velocities of the spectroscopic double-lined binary HD 4676 to demonstrate that with such a combination one can routinely obtain masses of the binary components accurate at least at the level of 1.0%.Comment: Accepted for publication in The Astrophysical Journa

Higher Order Analogues of Tracy-Widom Distributions via the Lax Method

We study the distribution of the largest eigenvalue in formal Hermitian one-matrix models at multicriticality, where the spectral density acquires an extra number of k-1 zeros at the edge. The distributions are directly expressed through the norms of orthogonal polynomials on a semi-infinite interval, as an alternative to using Fredholm determinants. They satisfy non-linear recurrence relations which we show form a Lax pair, making contact to the string literature in the early 1990's. The technique of pseudo-differential operators allows us to give compact expressions for the logarithm of the gap probability in terms of the Painleve XXXIV hierarchy. These are the higher order analogues of the Tracy-Widom distribution which has k=1. Using known Backlund transformations we show how to simplify earlier equivalent results that are derived from Fredholm determinant theory, valid for even k in terms of the Painleve II hierarchy.Comment: 24 pages. Improved discussion of Backlund transformations, in addition to other minor improvements in text. Typos corrected. Matches published versio