A sum-product theorem in function fields

Let $A$ be a finite subset of \ffield, the field of Laurent series in $1/t$ over a finite field $\mathbb{F}_q$. We show that for any $\epsilon>0$ there exists a constant $C$ dependent only on $\epsilon$ and $q$ such that $\max\{|A+A|,|AA|\}\geq C |A|^{6/5-\epsilon}$. In particular such a result is obtained for the rational function field $\mathbb{F}_q(t)$. Identical results are also obtained for finite subsets of the $p$-adic field $\mathbb{Q}_p$ for any prime $p$.Comment: Simplification of argument and note that methods also work for the p-adic

Improved bounds on the set A(A+1)

For a subset A of a field F, write A(A + 1) for the set {a(b + 1):a,b\in A}. We establish new estimates on the size of A(A+1) in the case where F is either a finite field of prime order, or the real line. In the finite field case we show that A(A+1) is of cardinality at least C|A|^{57/56-o(1)} for some absolute constant C, so long as |A| < p^{1/2}. In the real case we show that the cardinality is at least C|A|^{24/19-o(1)}. These improve on the previously best-known exponents of 106/105-o(1) and 5/4 respectively

Quantum Process Tomography of the Quantum Fourier Transform

The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently-developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive - although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors during the quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cummulative effect of small errors in the single qubit gates.Comment: 26 pages, 17 figures, four tables; in press, Journal of Chemical Physic

Systematic Reviews Published in Emergency Medicine Journals Do Not Routinely Search Clinical Trials Registries: A Cross-Sectional Analysis

Publication bias compromises the validity of systematic reviews. This problem can be addressed in part through searching clinical trials registries to identify unpublished studies. This study aims to determine how often systematic reviews published in emergency medicine journals include clinical trials registry searches

Three-Dimensional Spectral Classification of Low-Metallicity Stars Using Artificial Neural Networks

We explore the application of artificial neural networks (ANNs) for the estimation of atmospheric parameters (Teff, logg, and [Fe/H]) for Galactic F- and G-type stars. The ANNs are fed with medium-resolution (~ 1-2 A) non flux-calibrated spectroscopic observations. From a sample of 279 stars with previous high-resolution determinations of metallicity, and a set of (external) estimates of temperature and surface gravity, our ANNs are able to predict Teff with an accuracy of ~ 135-150 K over the range 4250 <= Teff <= 6500 K, logg with an accuracy of ~ 0.25-0.30 dex over the range 1.0 <= logg <= 5.0 dex, and [Fe/H] with an accuracy ~ 0.15-0.20 dex over the range -4.0 <= [Fe/H] <= +0.3. Such accuracies are competitive with the results obtained by fine analysis of high-resolution spectra. It is noteworthy that the ANNs are able to obtain these results without consideration of photometric information for these stars. We have also explored the impact of the signal-to-noise ratio (S/N) on the behavior of ANNs, and conclude that, when analyzed with ANNs trained on spectra of commensurate S/N, it is possible to extract physical parameter estimates of similar accuracy with stellar spectra having S/N as low as 13. Taken together, these results indicate that the ANN approach should be of primary importance for use in present and future large-scale spectroscopic surveys.Comment: 51 pages, 11 eps figures, uses aastex; to appear in Ap

Hadamard Products of Product Operators and the Design of Gradient-Diffusion Experiments for Simulating Decoherence by NMR Spectroscopy

An extension of the product operator formalism of NMR is introduced, which uses the Hadamard matrix product to describe many simple spin 1/2 relaxation processes. The utility of this formalism is illustrated by deriving NMR gradient-diffusion experiments to simulate several decoherence models of interest in quantum information processing, along with their Lindblad and Kraus representations. Gradient-diffusion experiments are also described for several more complex forms of decoherence, including the well-known collective isotropic model. Finally, it is shown that the Hadamard formalism gives a concise representation of decoherence with arbitrary correlations among the fluctuating fields at the different spins involved, and that this can be applied to both decoherence (T2) as well as nonadiabatic relaxation (T1) processes.Comment: RevTeX, 11 page single-spaced preprint, no figures. Version two has new title, abstract, introduction & conclusions, while the main body of the text remains substantially the sam