Quantum superchemistry in an output coupler of coherent matter waves

We investigate the quantum superchemistry or Bose-enhanced atom-molecule conversions in a coherent output coupler of matter waves, as a simple generalization of the two-color photo-association. The stimulated effects of molecular output step and atomic revivals are exhibited by steering the rf output couplings. The quantum noise-induced molecular damping occurs near a total conversion in a levitation trap. This suggests a feasible two-trap scheme to make a stable coherent molecular beam.Comment: 3 figures, accepted by Phys.Rev.A (submitted to prl in July, transferred to pra in Sep. and accepted in Nov.

Random 3-noncrossing partitions

In this paper, we introduce polynomial time algorithms that generate random 3-noncrossing partitions and 2-regular, 3-noncrossing partitions with uniform probability. A 3-noncrossing partition does not contain any three mutually crossing arcs in its canonical representation and is 2-regular if the latter does not contain arcs of the form $(i,i+1)$. Using a bijection of Chen {\it et al.} \cite{Chen,Reidys:08tan}, we interpret 3-noncrossing partitions and 2-regular, 3-noncrossing partitions as restricted generalized vacillating tableaux. Furthermore, we interpret the tableaux as sampling paths of Markov-processes over shapes and derive their transition probabilities.Comment: 17 pages, 7 figure

The density profile of equilibrium and non-equilibrium dark matter halos

We study the diversity of the density profiles of dark matter halos based on a large set of high-resolution cosmological simulations of 256^3 particles. The cosmological models include four scale-free models and three representative cold dark matter models. The simulations have good force resolution, and there are about 400 massive halos with more than 10^4 particles within the virial radius in each cosmological model. Our unbiased selection of all massive halos enables to quantify how well the bulk of dark matter halos can be described by the Navarro, Frenk & White (NFW) profile which was established for equilibrium halos. We find that about seventy percent of the halos can be fitted by the NFW profile with a fitting residual dvi_{max} less than 30% in Omega_0=1 universes. This percentage is higher in lower density cosmological models. The rest of the halos exhibits larger deviations from the NFW profile for more significant internal substructures. There is a considerable amount of variation in the density profile even for the halos which can be fitted by the NFW profile (i.e. dvi_{max}<0.30). The distribution of the profile parameter, the concentration $c$, can be well described by a lognormal function with the mean value \bar c slightly smaller (15%) than the NFW result and the dispersion \sigma_c in \ln c about 0.25. The more virialized halos with dvi_{max}<0.15 have the mean value \bar c in good agreement with the NFW result and a slightly smaller dispersion \sigma_c (about 0.2). Our results can alleviate some of the conflicts found recently between the theoretical NFW profile and observational results. Implications for theoretical and observational studies of galaxy formation are discussed.Comment: The final version accepted for publication in ApJ; one figure and one paragraph added to demonstrate that all the conclusions of the first version are solid to the resoltuion effects; 19 pages with 6 figure

A Conjecture about Raising Operators for Macdonald Polynomials

A multivariable hypergeometric-type formula for raising operators of the Macdonald polynomials is conjectured. It is proved that this agrees with Jing and Jozefiak's expression for the two-row Macdonald polynomials, and also with Lassalle and Schlosser's formula for partitions with length three.Comment: 13 page

Enhanced Tau Lepton Signatures at LHC in Constrained Supersymmetric Seesaw

We discuss the possible enhancement of the tau lepton events at LHC when the left-handed stau doublet becomes light (which can be even lighter than the right-handed stau). This is illustrated in the constrained supersymmetric seesaw model where the slepton doublet mass is suppressed by the effects of a large neutrino Yukawa coupling. We study a few representative parameter sets in the sneutrino coannihilation regions where the tau sneutrino is NLSP and the stau coannihilation regions where the stau is NLSP both of which yield the thermal neutralino LSP abundance determined by WMAP.Comment: 15 pages, 3 figures, references adde

Functional linear regression that's interpretable

Regression models to relate a scalar $Y$ to a functional predictor $X(t)$ are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, $\beta(t)$, with $Y$ related to $X(t)$ through $\int\beta(t)X(t) dt$. Regions where $\beta(t)\ne0$ correspond to places where there is a relationship between $X(t)$ and $Y$. Alternatively, points where $\beta(t)=0$ indicate no relationship. Hence, for interpretation purposes, it is desirable for a regression procedure to be capable of producing estimates of $\beta(t)$ that are exactly zero over regions with no apparent relationship and have simple structures over the remaining regions. Unfortunately, most fitting procedures result in an estimate for $\beta(t)$ that is rarely exactly zero and has unnatural wiggles making the curve hard to interpret. In this article we introduce a new approach which uses variable selection ideas, applied to various derivatives of $\beta(t)$, to produce estimates that are both interpretable, flexible and accurate. We call our method "Functional Linear Regression That's Interpretable" (FLiRTI) and demonstrate it on simulated and real-world data sets. In addition, non-asymptotic theoretical bounds on the estimation error are presented. The bounds provide strong theoretical motivation for our approach.Comment: Published in at http://dx.doi.org/10.1214/08-AOS641 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org