A decomposition of the Fourier-Jacobi coefficients of Klingen Eisenstein series

We investigate the relation between Klingen's decomposition of the space of Siegel modular forms and Dulinski's analogous decomposition of the space of Jacobi forms.Comment: Summary of a talk at the RIMS workshop "Automorphic Forms and Related Topics", February 2017, Kyot

Mapping Subsets of Scholarly Information

We illustrate the use of machine learning techniques to analyze, structure, maintain, and evolve a large online corpus of academic literature. An emerging field of research can be identified as part of an existing corpus, permitting the implementation of a more coherent community structure for its practitioners.Comment: 10 pages, 4 figures, presented at Arthur M. Sackler Colloquium on "Mapping Knowledge Domains", 9--11 May 2003, Beckman Center, Irvine, CA, proceedings to appear in PNA

Molecular production in two-component atomic Fermi gases

We provide a practical approach to the molecular production via linear downward sweeps of Feshbach resonances in degenerate Fermi gases containing incoherent mixtures of two atomic spin states. We show that the efficiency of the association of atoms is determined just by the Landau-Zener parameter in addition to the density of the gas. Our approach of pairwise summation of the microscopic binary transition probabilities leads to an intuitive explanation for the observed saturation of the molecular production and recovers all atomic loss curves of C.A. Regal et al. [Nature (London) 427, 47 (2003)] as well as K.E. Strecker et al. [Phys. Rev. Lett. 91, 080406 (2003)] without adjustable parameters.Comment: 4 pages, 3 eps figures; final versio

Making Cold Molecules by Time-dependent Feshbach Resonances

Pairs of trapped atoms can be associated to make a diatomic molecule using a time dependent magnetic field to ramp the energy of a scattering resonance state from above to below the scattering threshold. A relatively simple model, parameterized in terms of the background scattering length and resonance width and magnetic moment, can be used to predict conversion probabilities from atoms to molecules. The model and its Landau-Zener interpretation are described and illustrated by specific calculations for $^{23}$Na, $^{87}$Rb, and $^{133}$Cs resonances. The model can be readily adapted to Bose-Einstein condensates. Comparison with full many-body calculations for the condensate case show that the model is very useful for making simple estimates of molecule conversion efficiencies.Comment: 11 pages, 11 figures; talk for Quantum Challenges Symposium, Warsaw, Poland, September 4-7, 2003. Published in Journal of Modern Optics 51, 1787-1806 (2004). Typographical errors in Journal article correcte

Magnetogenesis from Rotating Cosmic String Loops

We present a mechanism to create vortices in a plasma via gravitational dragging behind rotating cosmic string loops. The vortical motions create magnetic fields by means of the Harrison-Rees mechanism; the fields are further enhanced through galactic collapse and dynamo amplification. Employing the Velocity dependent One Scale model (VOS) for the string network and incorporating loop dynamics, we compute the magnetic fields generated around the time of decoupling: these are just strong and coherent enough to account for presently observed magnetic fields in spiral galaxies if efficient dynamos with $\Gamma_{dy}^{-1}\approx 0.3$ Gyr are present.Comment: 4 pages, 1 figure. Contribution to the proceedings of PASCOS-07, 2-7 July 2007, Imperial College, Londo

Comparison between the regression depth method and the support vector machine to approximate the minimum number of misclassifications

The minimum number of misclassifications achievable with afine hyperplanes on a given set of labeled points is a key quantity in both statistics and computational learning theory. However, determining this quantity exactly is essentially NP-hard, c.f. Simon and van Horn (1995). Hence, there is a need to find reasonable approximation procedures. This paper compares three approaches to approximating the minimum number of misclassifications achievable with afine hyperplanes. The first approach is based on the regression depth method of Rousseeuw and Hubert (1999) in linear regression models. We compare the results of the regression depth method with the support vector machine approach proposed by Vapnik (1998), and a heuristic search algorithm