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

Symmetrization in Geometry

The concept of an $i$-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of $i$-symmetrizations are introduced and the relations between them investigated. New expressions are provided for the Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual relationship between them. Characterizations of Steiner, Minkowski and central symmetrization, in terms of natural properties that they enjoy, are given and examples are provided to show that none of the assumptions made can be dropped or significantly weakened. Other familiar symmetrizations, such as Schwarz symmetrization, are discussed and several new ones introduced.Comment: A chacterization of central symmetrization has been added and several typos have been corrected. This version has been accepted for publication on Advances in Mathematic

Galaxy evolution in groups. USGC U268 and USGC U376 in the Leo cloud

With the aim of investigating galaxy evolution in nearby galaxy groups, we analysed the spectral energy distribution of 24 galaxies, members of two groups in the Leo cloud, USGC U268 and USGC U376. We estimated the ages and stellar masses of the galaxies by fitting their total apparent magnitudes from far-ultraviolet to near-infrared with population synthesis models. The comparison of the results for a subsample of galaxies with smooth particle hydrodynamic (SPH) simulations with chemo-photometric implementation, shows that in most cases the estimated stellar masses obtained with the two different approaches are in good agreement. The kinematical and dynamical analysis indicates that USGC U268 is in a pre-virial collapse phase while USGC U376 is likely in a more evolved phase towards virialization.Comment: 16 pages, 6 figures; accepted for publication in Advances in Space Research, Special Issue: Ultraviolet Astrophysic

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&

Identifying short motifs by means of extreme value analysis

The problem of detecting a binding site -- a substring of DNA where transcription factors attach -- on a long DNA sequence requires the recognition of a small pattern in a large background. For short binding sites, the matching probability can display large fluctuations from one putative binding site to another. Here we use a self-consistent statistical procedure that accounts correctly for the large deviations of the matching probability to predict the location of short binding sites. We apply it in two distinct situations: (a) the detection of the binding sites for three specific transcription factors on a set of 134 estrogen-regulated genes; (b) the identification, in a set of 138 possible transcription factors, of the ones binding a specific set of nine genes. In both instances, experimental findings are reproduced (when available) and the number of false positives is significantly reduced with respect to the other methods commonly employed.Comment: 6 pages, 5 figure

The broad-band X-ray spectrum of the Seyfert 1 galaxy, MCG+8-11-11

We present a long (100 ks) Suzaku observation of one of the X-ray brightest AGN, MCG+8-11-11. These data were complemented with the 54-month Swift BAT spectrum, allowing us to perform a broad-band fit in the 0.6-150 keV range. The fits performed in the 0.6-10 keV band give consistent results with respect to a previous XMM-Newton observation, i.e. the lack of a soft excess, warm absorption along the line of sight, a large Compton reflection component (R~1) and the absence of a relativistic component of the neutral iron K$\alpha$ emission line. However, when the PIN and Swift BAT data are included, the reflection amount drops significantly (R~0.2-0.3), and a relativistic iron line is required, the latter confirmed by a phenomenological analysis in a restricted energy band (3-10 keV). When a self-consistent model is applied to the whole broadband data, the observed reflection component appears to be all associated to the relativistic component of the iron K$\alpha$ line. The resulting scenario, though strongly model-dependent, requires that all the reprocessing spectral components from Compton-thick material must be associated to the accretion disc, and no evidence for the classical pc-scale torus is found. The narrow core of the neutral iron K$\alpha$ line is therefore produced in a Compton-thin material, like the BLR, similarly to what found in another Seyfert galaxy, NGC7213, but with the notable difference that MCG+8-11-11 presents spectral signatures from an accretion disc. The very low accretion rate of NGC7213 could explain the lack of relativistic signatures in its spectrum, but the absence of the torus in both sources is more difficult to explain, since their luminosities are comparable, and their accretion rates are completely different.Comment: 8 pages, 6 figure, accepted for publication in Astronomy and Astrophysic

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

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

Superconductivity without Fe or Ni in the phosphides BaIr2P2 and BaRh2P2

Heat capacity, resistivity, and magnetic susceptibility measurements confirm bulk superconductivity in single crystals of BaIr$_2$P$_2$ (T$_c$=2.1K) and BaRh$_2$P$_2$ (T$_c$ = 1.0 K). These compounds form in the ThCr$_2$Si$_2$ (122) structure so they are isostructural to both the Ni and Fe pnictides but not isoelectronic to either of them. This illustrates the importance of structure for the occurrence of superconductivity in the 122 pnictides. Additionally, a comparison between these and other ternary phosphide superconductors suggests that the lack of interlayer $P-P$ bonding favors superconductivity. These stoichiometric and ambient pressure superconductors offer an ideal playground to investigate the role of structure for the mechanism of superconductivity in the absence of magnetism.Comment: Published in Phys Rev B: Rapid Communication