Tuning the Mott transition in a Bose-Einstein condensate by multi-photon absorption

We study the time-dependent dynamics of a Bose-Einstein condensate trapped in an optical lattice. Modeling the system as a Bose-Hubbard model, we show how applying a periodic driving field can induce coherent destruction of tunneling. In the low-frequency regime, we obtain the novel result that the destruction of tunneling displays extremely sharp peaks when the driving frequency is resonant with the depth of the trapping potential (``multi-photon resonances''), which allows the quantum phase transition between the Mott insulator and the superfluid state to be controlled with high precision. We further show how the waveform of the field can be chosen to maximize this effect.Comment: Minor changes, this version to be published in Phys. Rev. Let

Convex Optimization Methods for Dimension Reduction and Coefficient Estimation in Multivariate Linear Regression

In this paper, we study convex optimization methods for computing the trace norm regularized least squares estimate in multivariate linear regression. The so-called factor estimation and selection (FES) method, recently proposed by Yuan et al. [22], conducts parameter estimation and factor selection simultaneously and have been shown to enjoy nice properties in both large and finite samples. To compute the estimates, however, can be very challenging in practice because of the high dimensionality and the trace norm constraint. In this paper, we explore a variant of Nesterov's smooth method [20] and interior point methods for computing the penalized least squares estimate. The performance of these methods is then compared using a set of randomly generated instances. We show that the variant of Nesterov's smooth method [20] generally outperforms the interior point method implemented in SDPT3 version 4.0 (beta) [19] substantially . Moreover, the former method is much more memory efficient.Comment: 27 page

The expectations hypothesis of the term structure: some empirical evidence for Portugal

The purpose of this paper is to test the (rational) expectations hypothesis of the term structure of interest rates using Portuguese data for the interbank money market. The results obtained support only a very weak, long-run or "asymptotic" version of the hypothesis, and broadly agree with previous evidence for other countries. The empirical evidence supports the cointegration of Portuguese rates and the "puzzle" well known in the literature: although its forecasts of future short-term rates are in the correct direction, the spread between longer and shorter rates fails to forecast future longer rates. In the single equation framework, the implications of the hypothesis in terms of the predictive ability of the spread are also clearly rejected