On the reconstruction of planar lattice-convex sets from the covariogram

A finite subset $K$ of $\mathbb{Z}^d$ is said to be lattice-convex if $K$ is the intersection of $\mathbb{Z}^d$ with a convex set. The covariogram $g_K$ of $K\subseteq \mathbb{Z}^d$ is the function associating to each u \in \integer^d the cardinality of $K\cap (K+u)$. Daurat, G\'erard, and Nivat and independently Gardner, Gronchi, and Zong raised the problem on the reconstruction of lattice-convex sets $K$ from $g_K$. We provide a partial positive answer to this problem by showing that for $d=2$ and under mild extra assumptions, $g_K$ determines $K$ up to translations and reflections. As a complement to the theorem on reconstruction we also extend the known counterexamples (i.e., planar lattice-convex sets which are not reconstructible, up to translations and reflections) to an infinite family of counterexamples.Comment: accepted in Discrete and Computational Geometr

String amplitudes in the Hpp-wave limit of AdS3xS3

We compute string amplitudes on pp-waves supported by NS-NS 3-form fluxes and arising in the Penrose limit of AdS3xS3xM. We clarify the role of the non-chiral accidental SU(2) symmetry of the background. We comment on the extension of our results to the superstring and propose a holographic formula in the BMN limit of the AdS3/CFT2 correspondence valid for any correlator.Comment: Latex,no figures, 47 p

Massive higher spins and holography

We review recent progress towards the understanding of higher spin gauge symmetry breaking in AdS space from a holographic vantage point. According to the AdS/CFT correspondence, N=4 SYM theory at vanishing coupling constant should be dual to a theory in AdS which exhibits higher spin gauge symmetry enhancement. When the SYM coupling is non-zero, all but a handful of HS currents are violated by anomalies, and correspondingly local higher spin symmetry in the bulk gets spontaneously broken. In agreement with previous results and holographic expectations, we find that, barring one notable exception (spin 1 eating spin 0), the Goldstone modes responsible for HS symmetry breaking in AdS have non-vanishing mass even in the limit in which the gauge symmetry is restored. We show that spontaneous breaking a' la Stueckelberg implies that the mass of the relevant spin s'=s-1 Goldstone field is exactly the one predicted by the correspondence.Comment: 8 pages, talk presented by M.B. at the "Fourth Meeting on Constrained Dynamics and Quantum gravity" held in Cala Gonone (Sardinia, Italy), September 12-16, 200

X-ray reprocessing in Seyfert Galaxies: simultaneous XMM-Newton/BeppoSAX observations

We selected a sample of eight bright unobscured (at least at the iron line energy) Seyfert Galaxies observed simultaneously by XMM-Newton and BeppoSAX, taking advantage of the complementary characteristics of the two missions. The main results of our analysis can be summarized as follows: narrow neutral iron lines are confirmed to be an ubiquitous component in Seyfert spectra; none of the analyzed sources shows unambiguously a broad relativistic iron line; all the sources of our sample (with a single exception) show the presence of a Compton reflection component; emission lines from ionized iron are observed in some sources; peculiar weak features around 5-6 keV (possibly arising from rotating spots on the accretion disk) are detected in two sources. The scenario emerging from these results strongly requires some corrections for the classical model of reprocessing from the accretion disk. As for materials farther away from the Black Hole, our results represent a positive test for the Unification Model, suggesting the presence of the torus in (almost) all sources, even if unobscured.Comment: Accepted for publication in A&

3C 33: another case of photoionized soft X-ray emission in radio galaxies

All the observations available in the Chandra and XMM-Newton archives have been used to investigate the X-ray spectral properties of 3C 33. In this paper is presented a complete X-ray analysis of the nuclear emission of this narrow line radio galaxy. The broad band spectrum of 3C 33 is complex. The hard part resembles that of Seyfert 2 galaxies, with a heavily obscured nuclear continuum (N_H~10^23 cm^-2) and a prominent Fe Kalpha line. This represents the nuclear radiation directly observed in transmission through a cold circumnuclear gas. On the other hand an unabsorbed continuum plus emission lines seem to fit well the soft part of the spectrum (0.5-2 keV) suggesting that the jet does not significantly contribute to the X-ray emission. We discuss the possible collisional or photoionized origin of the gas that emits the soft X-ray lines. Our results, strengthened by optical spectroscopy favor the photoionization scenario.Comment: 7 pages, 5 figures, accepted for publication in A&

Non-response in the American Time Use Survey: Who Is Missing from the Data and How Much Does It Matter?

This paper examines non-response in a large government survey. The response rate for the American Time Use Survey (ATUS) has been below 60 percent for the first two years of its existence, raising questions about whether the results can be generalized to the target population. The paper begins with an analysis of the types of non-response encountered in the ATUS. We find that non-contact accounts for roughly 60 percent of ATUS non-response, with refusals accounting for roughly 40 percent. Next, we examine two hypotheses about the causes of this non-response. We find little support for the hypothesis that busy people are less likely to respond to the ATUS, but considerable support for the hypothesis that people who are weakly integrated into their communities are less likely to respond, mostly because they are less likely to be contacted. Finally, we compare aggregate estimates of time use calculated using the ATUS base weights without any adjustment for non-response to estimates calculated using the ATUS final weights with a non-response adjustment and to estimates calculated using weights that incorporate our own non-response adjustments based on a propensity model. While there are some modest differences, the three sets of estimates are broadly similar. The paper ends with a discussion of survey design features, their effect on the types and level of non-response, and the tradeoffs associated with different design choices.

Spectral Functions in Holographic Renormalization Group Flows

The spectrum of two-point functions in a holographic renormalization group flow from an ultraviolet (UV) to an infrared (IR) conformal fixed point is necessarily continuous. For a toy model, the spectral function does not only show the expected UV and IR behaviours, but other interesting features such as sharp peaks and oscillations in the UV. The spectral functions for the SU(3)xU(1) flow in AdS_4/CFT_3 and the SU(2)xU(1) flow in AdS_5/CFT_4 are calculated numerically. They exhibit a simple cross-over behaviour and reproduce the conformal dimensions of the dual operators in the UV and IR conformal phases.Comment: 20 pages, 6 figures v2: added referene

Simplifying one-loop amplitudes in superstring theory

We show that 4-point vector boson one-loop amplitudes, computed in ref.[1] in the RNS formalism, around vacuum configurations with open unoriented strings, preserving at least N=1 SUSY in D=4, satisfy the correct supersymmetry Ward identities, in that they vanish for non MHV configurations (++++) and (-+++). In the MHV case (--++) we drastically simplify their expressions. We then study factorisation and the limiting IR and UV behaviour and find some unexpected results. In particular no massless poles are exposed at generic values of the modular parameter. Relying on the supersymmetric properties of our bosonic amplitudes, we extend them to manifestly supersymmetric super-amplitudes and compare our results with those obtained in the D=4 hybrid formalism, pointing out difficulties in reconciling the two approaches for contributions from N=1,2 sectors.Comment: 38 pages plus appendice

Limitations of PLL simulation: hidden oscillations in MatLab and SPICE

Nonlinear analysis of the phase-locked loop (PLL) based circuits is a challenging task, thus in modern engineering literature simplified mathematical models and simulation are widely used for their study. In this work the limitations of numerical approach is discussed and it is shown that, e.g. hidden oscillations may not be found by simulation. Corresponding examples in SPICE and MatLab, which may lead to wrong conclusions concerning the operability of PLL-based circuits, are presented