On Locality, Holography and Unfolding

We study the functional class and locality problems in the context of higher-spin theories and Vasiliev's equations. A locality criterion that is sufficient to make higher-spin theories well-defined as field theories on Anti-de-Sitter space is proposed. This criterion identifies admissible pseudo-local field redefinitions which preserve AdS/CFT correlation functions as we check in the 3d example. Implications of this analysis for known higher-spin theories are discussed. We also check that the cubic coupling coefficients previously fixed in 3d at the action level give the correct CFT correlation functions upon computing the corresponding Witten diagrams.Comment: 36 pages, LaTex. References added, typos corrected. Final version to appear in JHE

Beyond Diophantine Wannier diagrams: Gap labelling for Bloch-Landau Hamiltonians

It is well known that, given a $2d$ purely magnetic Landau Hamiltonian with a constant magnetic field $b$ which generates a magnetic flux $\varphi$ per unit area, then any spectral island $\sigma_b$ consisting of $M$ infinitely degenerate Landau levels carries an integrated density of states $\mathcal{I}_b=M \varphi$. Wannier later discovered a similar Diophantine relation expressing the integrated density of states of a gapped group of bands of the Hofstadter Hamiltonian as a linear function of the magnetic field flux with integer slope. We extend this result to a gap labelling theorem for any $2d$ Bloch-Landau operator $H_b$ which also has a bounded $\mathbb{Z}^2$-periodic electric potential. Assume that $H_b$ has a spectral island $\sigma_b$ which remains isolated from the rest of the spectrum as long as $\varphi$ lies in a compact interval $[\varphi_1,\varphi_2]$. Then $\mathcal{I}_b=c_0+c_1\varphi$ on such intervals, where the constant $c_0\in \mathbb{Q}$ while $c_1\in \mathbb{Z}$. The integer $c_1$ is the Chern marker of the spectral projection onto the spectral island $\sigma_b$. This result also implies that the Fermi projection on $\sigma_b$, albeit continuous in $b$ in the strong topology, is nowhere continuous in the norm topology if either $c_1\ne0$ or $c_1=0$ and $\varphi$ is rational. Our proofs, otherwise elementary, do not use non-commutative geometry but are based on gauge covariant magnetic perturbation theory which we briefly review for the sake of the reader. Moreover, our method allows us to extend the analysis to certain non-covariant systems having slowly varying magnetic fields.Comment: 20 pages, no figures. Appendix C added. Final version accepted for publication in Journal of the European Mathematical Societ

Role of cardiac resynchronization therapy in the development of new-onset atrial fibrillation: A single-center prospective study.

Albeit several studies examined the association between cardiac resynchronization therapy (CRT) and atrial fibrillation (AF) in heart failure (HF), results are still unclear and quite conflicting. We thereby designed a single-center prospective study to determine whether CRT has a favorable effect on the incidence of new-onset AF in a homogeneous population of patients with non-ischemic idiopathic dilated cardiomyopathy and severe heart failure HF. We enrolled 58 patients, AF naïve when received CRT. After 1 year of follow-up our population was subdivided into responders (72.4%) and non (27.6%), so to compare the incidence of AF after 1, 2 and 3 years of follow-up in these two groups. Already after 1 year, there is a significant (p<0.05) difference in new-onset AF in non-responder patients respect to responders (18.2% vs 3.3%). These data are confirmed at 2 year (33.3% vs 12.2%) and 3 year (50.0% vs 15.0%) follow-up. In particular, at 3 year follow-up, non-responders have an increased risk to develop new-onset AF (OR=5.67, 95% confidence interval = 1.36-23.59, p=0.019). The present work suggests a possible favorable role of this non-pharmacological therapy, on the prevention of AF

Nano-Hertz Gravitational Waves Searches with Interferometric Pulsar Timing Experiments

We estimate the sensitivity to nano-Hertz gravitational waves of pulsar timing experiments in which two highly-stable millisecond pulsars are tracked simultaneously with two neighboring radio telescopes that are referenced to the same time-keeping subsystem (i.e. "the clock"). By taking the difference of the two time-of-arrival residual data streams we can exactly cancel the clock noise in the combined data set, thereby enhancing the sensitivity to gravitational waves. We estimate that, in the band ($10^{-9} - 10^{-8}$) Hz, this "interferometric" pulsar timing technique can potentially improve the sensitivity to gravitational radiation by almost two orders of magnitude over that of single-telescopes. Interferometric pulsar timing experiments could be performed with neighboring pairs of antennas of the forthcoming large arraying projects.Comment: Paper submitted to Phys. Rev. Letters. It is 9 pages long, and includes 2 figure

Learning Features that Predict Cue Usage

Our goal is to identify the features that predict the occurrence and placement of discourse cues in tutorial explanations in order to aid in the automatic generation of explanations. Previous attempts to devise rules for text generation were based on intuition or small numbers of constructed examples. We apply a machine learning program, C4.5, to induce decision trees for cue occurrence and placement from a corpus of data coded for a variety of features previously thought to affect cue usage. Our experiments enable us to identify the features with most predictive power, and show that machine learning can be used to induce decision trees useful for text generation.Comment: 10 pages, 2 Postscript figures, uses aclap.sty, psfig.te