Εκ του αλιευτικού βίου των Βυζαντινών

Dans cette etude fondee sur les temoignages des textes byzantins, Fauteur, en se servant aussi des habitudes de la peche de nos jours, s’occupe des ustensiles de peche a Fepoque byzantine, de la maniere dont on faisait la peche, de differentes especes et des differants noms de poissons et des endroits censes fort poissonneux. L’auteur y joint des renseignements sur les epoques favorables a la peche et sur les cas et coutumes religieux des pecheurs Byzantins, aussi bien que sur differentes questions ayant trait a la peche reglees par la loi

Wigner random matrices with non-symmetrically distributed entries

We show that the spectral radius of an $N\times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from above by 2 \*\sigma + o(N^{-6/11+\epsilon}), where $\sigma^2$ is the variance of the matrix entries and $\epsilon$ is an arbitrary small positive number. Our bound improves the earlier results by Z.F\"{u}redi and J.Koml\'{o}s (1981), and the recent bound obtained by Van Vu (2005).Comment: to appear in the Special Issue on Random Matrices of the Journal of Statistical Physic

On the lower bound of the spectral norm of symmetric random matrices with independent entries

We show that the spectral radius of an $N\times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by 2 \*\sigma - o(N^{-6/11+\epsilon}), where $\sigma^2$ is the variance of the matrix entries and $\epsilon$ is an arbitrary small positive number. Combining with our previous result from [7], this proves that for any $\epsilon >0,$ one has \|A_N\| =2 \*\sigma + o(N^{-6/11+\epsilon}) with probability going to 1 as $N \to \infty.

Engineering the optical properties of silicon using sub-wavelength structures

In most integrated optics platforms, including silicon-on-insulator, only minor modifications in refractive index are possible. The geometry of the waveguiding structure is thus the only degree of freedom for the design of devices. The use of sub-wavelength gratings (SWGs), i.e. structures that are small enough to suppress diffraction effects, enables local engineering of both refractive index and dispersion, thereby opening new possibilities for device design. Here we present some of the recent advances in refractive index and dispersion engineering using silicon SWGs, focussing on ultra-broadband and compact multimode interference couplers and directional couplersThis work was supported by the Spanish Ministerio de Ciencia (project TEC2009-10152), the European Mirthe project (FP7-2010-257980), and the Universidad de Málaga - Campus de Excelencia Internacional Andalucìa Tech

The Tracy--Widom limit for the largest eigenvalues of singular complex Wishart matrices

This paper extends the work of El Karoui [Ann. Probab. 35 (2007) 663--714] which finds the Tracy--Widom limit for the largest eigenvalue of a nonsingular $p$-dimensional complex Wishart matrix $W_{\mathbb{C}}(\Omega_p,n)$ to the case of several of the largest eigenvalues of the possibly singular $(n<p)$ matrix $W_{\mathbb{C}}(\Omega_p,n).$ As a byproduct, we extend all results of Baik, Ben Arous and Peche [Ann. Probab. 33 (2005) 1643--1697] to the singular Wishart matrix case. We apply our findings to obtain a 95% confidence set for the number of common risk factors in excess stock returns.Comment: Published in at http://dx.doi.org/10.1214/07-AAP454 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Boston University Coro da Camera and Collegium Musicum, April 27, 2007

This is the concert program of the Boston University Coro da Camera and Collegium Musicum performance on Friday, April 27, 2007 at 8:00 p.m., at the United Parish Church in Brookline, 210 Harvard Street, Brookline, Massachusetts. Works performed were In Windsor Forest by Ralph Vaughan Williams, Memento Domine David by Claudio Monteverdi, Credidi, propter quod locutus sum Confitebor tibi Domine by Adrian Willaert, and Dixit Dominus Domino meo by Claudio Monteverdi. Digitization for Boston University Concert Programs was supported by the Boston University Center for the Humanities Library Endowed Fund