Hermitian symmetric polynomials and CR complexity

Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.Comment: 19 pages, latex, fixed typos, to appear in Journal of Geometric Analysi

Hydromagnetic and gravitomagnetic crust-core coupling in a precessing neutron star

We consider two types of mechanical coupling between the crust and the core of a precessing neutron star. First, we find that a hydromagnetic (MHD) coupling between the crust and the core strongly modifies the star's precessional modes when $t_a\le\sim (T_s\times T_p)^{1/2}$; here $t_a$ is the Alfven crossing timescale, and $T_s$ and $T_p$ are the star's spin and precession periods, respectively. We argue that in a precessing pulsar PSR B1828-11 the restoring MHD stress prevents a free wobble of the crust relative to the non-precessing core. Instead, the crust and the proton-electron plasma in the core must precess in unison, and their combined ellipticity determines the period of precession. Link has recently shown that the neutron superfluid vortices in the core of PSR B1828-11 cannot be pinned to the plasma; he has also argued that this lack of pinning is expected if the proton Fermi liquid in the core is type-I superconductor. In this case, the neutron superfluid is dynamically decoupled from the precessing motion. The pulsar's precession decays due to the mutual friction between the neutron superfluid and the plasma in the core. The decay is expected to occur over tens to hundreds of precession periods and may be measurable over a human lifetime. Such a measurement would provide information about the strong n-p interaction in the neutron-star core. Second, we consider the effect of gravitomagnetic coupling between the neutron superfluid in the core and the rest of the star and show that this coupling changes the rate of precession by about 10%. The general formalism developed in this paper may be useful for other applications.Comment: 6 page

Identifying entanglement using quantum "ghost" interference and imaging

We report a quantum interference and imaging experiment which quantitatively demonstrates that Einstein-Podolsky-Rosen (EPR) type entangled two-photon states exhibit both momentum-momentum and position-position correlations, stronger than any classical correlation. The measurements show indeed that the uncertainties in the sum of momenta and in the difference of positions of the entangled two-photon satisfy both EPR inequalities D(k1+k2)<min(D(k1),D(k2)) and D(x1-x2)<min(D(x1),D(x2)). These two inequalities, together, represent a non-classicality condition. Our measurements provide a direct way to distinguish between quantum entanglement and classical correlation in continuous variables for two-photons/two photons systems.Comment: We have changed Eq.(2) from one inequality to two inequalities. The two expressions are actually consistent with each other, but the new one represents a more stringent condition for entanglement and, in our opinion, better explains the original idea of EPR. We have clarified this point in the paper. 4 pages; submitted to PR

Evolution of Migrating Planets Undergoing Gas Accretion

We analyze the orbital and mass evolution of planets that undergo run-away gas accretion by means of 2D and 3D hydrodynamic simulations. The disk torque distribution per unit disk mass as a function of radius provides an important diagnostic for the nature of the disk-planet interactions. We first consider torque distributions for nonmigrating planets of fixed mass and show that there is general agreement with the expectations of resonance theory. We then present results of simulations for mass-gaining, migrating planets. For planets with an initial mass of 5 Earth masses, which are embedded in disks with standard parameters and which undergo run-away gas accretion to one Jupiter mass (Mjup), the torque distributions per unit disk mass are largely unaffected by migration and accretion for a given planet mass. The migration rates for these planets are in agreement with the predictions of the standard theory for planet migration (Type I and Type II migration). The planet mass growth occurs through gas capture within the planet's Bondi radius at lower planet masses, the Hill radius at intermediate planet masses, and through reduced accretion at higher planet masses due to gap formation. During run-away mass growth, a planet migrates inwards by only about 20% in radius before achieving a mass of ~1 Mjup. For the above models, we find no evidence of fast migration driven by coorbital torques, known as Type III migration. We do find evidence of Type III migration for a fixed mass planet of Saturn's mass that is immersed in a cold and massive disk. In this case the planet migration is assumed to begin before gap formation completes. The migration is understood through a model in which the torque is due to an asymmetry in density between trapped gas on the leading side of the planet and ambient gas on the trailing side of the planet.Comment: 26 pages, 29 figures. To appear in The Astrophysical Journal vol.684 (September 20, 2008 issue

Tomographic test of Bell's inequality for a time-delocalized single photon

Time-domain balanced homodyne detection is performed on two well-separated temporal modes sharing a single photon. The reconstructed density matrix of the two-mode system is used to prove and quantify its entangled nature, while the Wigner function is employed for an innovative tomographic test of Bell's inequality based on the theoretical proposal by Banaszek and Wodkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Provided some auxiliary assumptions are made, a clear violation of Banaszek-Bell's inequality is found.Comment: 7 pages, 3 figures: revised version with additional material; accepetd for publication in Phys. Rev.

Immunolocalization of Nesfatin-1 in the Gastrointestinal Tract of the Common Bottlenose Dolphin Tursiops truncatus

SIMPLE SUMMARY: Nesfatin-1 (Nesf-1) is a neuropeptide that plays important roles in regulating food intake, mainly related to its anorexigenic effect, and it is mainly distributed in the digestive systems of all vertebrates. With this study, we expand knowledge on the localization of Nesf-1 in the digestive tract of an aquatic mammalian species, the common bottlenose dolphin (Tursiops truncatus), allowing comparative study on terrestrial mammals. Dolphin tissue samples (three gastric chambers and intestine) were provided by the Mediterranean Marine Mammal Tissue Bank of the Department of Comparative Biomedicine and Food Science of the University of Padova (Italy). ABSTRACT: First identified as an anorexigenic peptide, in the last decades, several studies have suggested that Nesfatin-1 (Nesf-1) is a pleiotropic hormone implicated in numerous regulatory processes in peripheral organs and tissues. In vertebrates, Nesf-1 is indeed expressed in the central nervous system and peripheral organs. In this study, we characterized the pattern of Nesf-1 distribution within the digestive tract of the common bottlenose dolphin (Tursiops truncatus), composed of three gastric chambers and an intestine without a clear subdivision in the small and large intestine, also lacking a caecum. Our results indicated that Nesf-1 is widely distributed in cells of the mucosal epithelium of the gastric chambers. Most of the immunoreactivity was observed in the second chamber, compared to the first and third chambers. Immunopositivity was also found in nerve fibers and neurons, scattered or/and clustered in ganglion structures along all the examined gastrointestinal tracts. These observations add new data on the highly conserved role of Nesf-1 in the mammalian digestive system

Seismic assessment and rehabilitation of a historical theatre based on a macro-element strategy

The structural and seismic assessment of the 19th-century Petruzzelli theater in Bari (Italy) is presented. The macro-elements strategy was adopted to dismantle the whole structure in parts. The steel dome was verified through dynamic multi-modal analysis based on finite element model. Each masonry macro-element was firstly verified through a kinematic analysis aiming at excluding local collapse mechanisms. Afterwards, a nonlinear static analysis was carried out in order to evaluate its overall seismic capacity. The effectiveness of linear or nonlinear analyses and of the macro-element strategy compared with other modeling techniques is also discussed. After highlighting the structural deficiencies of the theater, upgrading solutions are proposed with consideration of the safety needs and the architectural preservation requirements based on the historical importance of the buildin

Evolution of Giant Planets in Eccentric Disks

We investigate the interaction between a giant planet and a viscous circumstellar disk by means of high-resolution, two-dimensional hydrodynamical simulations. We consider planet masses that range from 1 to 3 Jupiter masses (Mjup) and initial orbital eccentricities that range from 0 to 0.4. We find that a planet can cause eccentricity growth in a disk region adjacent to the planet's orbit, even if the planet's orbit is circular. Disk-planet interactions lead to growth in a planet's orbital eccentricity. The orbital eccentricities of a 2 Mjup and a 3 Mjup planet increase from 0 to 0.11 within about 3000 orbits. Over a similar time period, the orbital eccentricity of a 1 Mjup planet grows from 0 to 0.02. For a case of a 1 Mjup planet with an initial eccentricity of 0.01, the orbital eccentricity grows to 0.09 over 4000 orbits. Radial migration is directed inwards, but slows considerably as a planet's orbit becomes eccentric. If a planet's orbital eccentricity becomes sufficiently large, e > ~0.2, migration can reverse and so be directed outwards. The accretion rate towards a planet depends on both the disk and the planet orbital eccentricity and is pulsed over the orbital period. Planet mass growth rates increase with planet orbital eccentricity. For e~0.2 the mass growth rate of a planet increases by approximately 30% above the value for e=0. For e > ~0.1, most of the accretion within the planet's Roche lobe occurs when the planet is near the apocenter. Similar accretion modulation occurs for flow at the inner disk boundary which represents accretion toward the star.Comment: 20 pages 16 figures, 3 tables. To appear in The Astrophysical Journal vol.652 (December 1, 2006 issue

A decidable policy language for history-based transaction monitoring

Online trading invariably involves dealings between strangers, so it is important for one party to be able to judge objectively the trustworthiness of the other. In such a setting, the decision to trust a user may sensibly be based on that user's past behaviour. We introduce a specification language based on linear temporal logic for expressing a policy for categorising the behaviour patterns of a user depending on its transaction history. We also present an algorithm for checking whether the transaction history obeys the stated policy. To be useful in a real setting, such a language should allow one to express realistic policies which may involve parameter quantification and quantitative or statistical patterns. We introduce several extensions of linear temporal logic to cater for such needs: a restricted form of universal and existential quantification; arbitrary computable functions and relations in the term language; and a "counting" quantifier for counting how many times a formula holds in the past. We then show that model checking a transaction history against a policy, which we call the history-based transaction monitoring problem, is PSPACE-complete in the size of the policy formula and the length of the history. The problem becomes decidable in polynomial time when the policies are fixed. We also consider the problem of transaction monitoring in the case where not all the parameters of actions are observable. We formulate two such "partial observability" monitoring problems, and show their decidability under certain restrictions