On the shape of a pure O-sequence

An order ideal is a finite poset X of (monic) monomials such that, whenever M is in X and N divides M, then N is in X. If all, say t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h=(1,h_1,...,h_e), counting the monomials of X in each degree. Equivalently, in the language of commutative algebra, pure O-sequences are the h-vectors of monomial Artinian level algebras. Pure O-sequences had their origin in one of Richard Stanley's early works in this area, and have since played a significant role in at least three disciplines: the study of simplicial complexes and their f-vectors, level algebras, and matroids. This monograph is intended to be the first systematic study of the theory of pure O-sequences. Our work, making an extensive use of algebraic and combinatorial techniques, includes: (i) A characterization of the first half of a pure O-sequence, which gives the exact converse to an algebraic g-theorem of Hausel; (ii) A study of (the failing of) the unimodality property; (iii) The problem of enumerating pure O-sequences, including a proof that almost all O-sequences are pure, and the asymptotic enumeration of socle degree 3 pure O-sequences of type t; (iv) The Interval Conjecture for Pure O-sequences (ICP), which represents perhaps the strongest possible structural result short of an (impossible?) characterization; (v) A pithy connection of the ICP with Stanley's matroid h-vector conjecture; (vi) A specific study of pure O-sequences of type 2, including a proof of the Weak Lefschetz Property in codimension 3 in characteristic zero. As a corollary, pure O-sequences of codimension 3 and type 2 are unimodal (over any field); (vii) An analysis of the extent to which the Weak and Strong Lefschetz Properties can fail for monomial algebras; (viii) Some observations about pure f-vectors, an important special case of pure O-sequences.Comment: iii + 77 pages monograph, to appear as an AMS Memoir. Several, mostly minor revisions with respect to last year's versio

Pure O-sequences and matroid h-vectors

We study Stanley's long-standing conjecture that the h-vectors of matroid simplicial complexes are pure O-sequences. Our method consists of a new and more abstract approach, which shifts the focus from working on constructing suitable artinian level monomial ideals, as often done in the past, to the study of properties of pure O-sequences. We propose a conjecture on pure O-sequences and settle it in small socle degrees. This allows us to prove Stanley's conjecture for all matroids of rank 3. At the end of the paper, using our method, we discuss a first possible approach to Stanley's conjecture in full generality. Our technical work on pure O-sequences also uses very recent results of the third author and collaborators.Comment: Contains several changes/updates with respect to the previous version. In particular, a discussion of a possible approach to the general case is included at the end. 13 pages. To appear in the Annals of Combinatoric

The ATLAS Barrel Level-1 Muon Trigger Calibration

The ATLAS experiment uses a system of three concentric Resistive Plate Chambers detectors layers for the level-1 muon trigger in the air-core barrel toroid region. The trigger classifies muons within different programmable transverse momentum ranges, and tags the identified tracks with the corresponding bunch crossing number. The algorithm looks for hit coincidences within different detector layers inside the programmed geometrical road which defines the transverse momentum cut. The on-detector electronics providing the trigger and detector readout functionalities collects input signals coming from the RPC front-end. Because of the different time-of-flights and cables and optical fibres lengths, signals have to be adjusted in time in order to be correctly aligned before being processed. Programmable delay logics are provided in the trigger and readout system to allow for time adjustment, for hit signals as well as for LHC Timing, Trigger and Control signals. The trigger calibration provides the set of numbers used during electronics initialization for correctly aligning signals inside the trigger and readout system. The functionality scheme and the algorithm of the calibration are presented

Large Eddy Simulations of sediment entrainment induced by a lock-exchange gravity current

Large Eddy simulations of lock-exchange gravity currents propagating over a mobile reach are presented. The numerical setting allows to investigate the sediment pick up induced by the currents and to study the underlying mechanisms leading to sediment entrainment for different Grashof numbers and grain sizes. First, the velocity field and the bed shear-stress distribution are investigated, along with turbulent structures formed in the flow, before the current reaches the mobile bed. Then, during the propagation of the current above the erodible section of the bed the contour plots of the entrained material are pre- sented as well as the time evolution of the areas covered by the current and by the sediment at this section. The numerical outcomes are compared with experimental data showing a very good agreement. Overall, the study confirms that sediment pick up is prevalent at the head of the current where the strongest turbulence occurs. Further, above the mobile reach of the bed, settling process seems to be of minor importance, with the entrained material being advected downstream by the current. Additionally, the study shows that, although shear stress is the main mechanism that sets particles in motion, turbu- lent bursts as well as vertical velocity fluctuations are also necessary to counteract the falling velocity of the particles and maintain them into suspension. Finally, the analysis of the stability conditions of the current shows that, from one side, sediment concentration gives a negligible contribution to the stability of the front of the current and from the other side, the stability conditions provided by the current do not allow sediments to move into the ambient fluid

Surface and subsurface contributions to the build-up of forces on bed particles

In nature and in many industrial applications, the boundary of a channel flow is made of solid particles which form a porous wall, so that there is a mutual influence between the free flow and the subsurface flow developing inside the pores. While the influence of the porous wall on the free flow has been well studied, less well characterized is the subsurface flow, due to the practical difficulties in gathering information in the small spaces given by the pores. It is also not clear whether the subsurface flow can host turbulent events able to contribute significantly to the build-up of forces on the particles, potentially leading to their dislodgement. Through large eddy simulations, we investigate the interface between a free flow and a bed composed of spherical particles in a cubic arrangement. The communication between surface and subsurface flow is in this case enhanced, with relatively strong turbulent events happening also inside the pores. After comparing the simulation results with a previous experimental work from a similar setting, the forces experienced by the boundary particles are analysed. While it remains true that the lift forces are largely dependent on the structure of the free flow, turbulence inside the pores can also give a significant contribution. Pressure inside the pores is weakly correlated to the pressure in the free flow, and strong peaks above and below a particle can happen independently. Ignoring the porous layer below the particle from the computations leads then in this case to an underestimation of the lift forces

The role of integrative and complementary medicine in the management of breast cancer patients on behalf of the Integrative Medicine Research Group (IMRG)

The aim of this conference was to explain the role of integrative and complementary medicine in breast cancer patients. The topics covered are numerous and their peculiarities are the multidisciplinary characteristics of the researchers involved. The Integrative Medicine Research Group (IMRG) believes in the complementary and integrative approach in cancer patients to improve the quality of life in this particular setting

AGILE detection of a strong gamma-ray flare from the blazar 3C 454.3

We report the first blazar detection by the AGILE satellite. AGILE detected 3C 454.3 during a period of strongly enhanced optical emission in July 2007. AGILE observed the source with a dedicated repointing during the period 2007 July 24-30 with its two co-aligned imagers, the Gamma-Ray Imaging Detector and the hard X-ray imager Super-AGILE sensitive in the 30 MeV-50 GeV and 18-60 keV, respectively. Over the entire period, AGILE detected gamma-ray emission from 3C 454.3 at a significance level of 13.8-$\sigma$ with an average flux (E$>$100 MeV) of $(280 \pm 40) \times 10^{-8}$ photons cm$^{-2}$ s$^{-1}$. The gamma-ray flux appears to be variable towards the end of the observation. No emission was detected by Super-AGILE in the energy range 20-60 keV, with a 3-$\sigma$ upper limit of $2.3 \times 10^{-3}$ photons cm$^{-2}$ s$^{-1}$. The gamma-ray flux level of 3C 454.3 detected by AGILE is the highest ever detected for this quasar and among the most intense gamma-ray fluxes ever detected from Flat Spectrum Radio Quasars.Comment: Accepted by Astrophysical Journal Letters; 14 pages, 3 EPS Figures, 1 Tabl

The first level muon trigger in the central toroid of the ATLAS experiment

We present the design of the first level muon trigger in the central toroid of the ATLAS experiment at the Large Hadron Collider (LHC). A trigger is foreseen based on fast, finely segmented gaseous detectors, Resistive Plate Chambers (RPC), to unambiguously identify the interaction bunch crossing. We describe the detectors and the logic scheme of the trigger. © 1995

Detection of Gamma-ray Emission from the Eta-Carinae Region

We present the results of extensive observations by the gamma-ray AGILE satellite of the Galactic region hosting the Carina nebula and the remarkable colliding wind binary Eta Carinae (Eta Car) during the period 2007 July to 2009 January. We detect a gamma-ray source (1AGL J1043-5931) consistent with the position of Eta Car. If 1AGL J1043-5931 is associated with the Eta Car system our data provide the long sought first detection above 100 MeV of a colliding wind binary. The average gamma-ray flux above 100 MeV and integrated over the pre-periastron period 2007 July to 2008 October is F = (37 +/- 5) x 10-8 ph cm-2 s-1 corresponding to an average gamma-ray luminosity of L = 3.4 x 10^34 erg s-1 for a distance of 2.3 kpc. We also report a 2-day gamma-ray flaring episode of 1AGL J1043-5931 on 2008 Oct. 11-13 possibly related to a transient acceleration and radiation episode of the strongly variable shock in the system.Comment: 5 pages, 4 figure, accepted for publication in ApJ Letter

Episodic Transient Gamma-Ray Emission from the Microquasar Cygnus X-1

Cygnus X-1 is the archetypal black hole (BH) binary system in our Galaxy. We report the main results of an extensive search for transient gamma-ray emission from Cygnus X-1 carried out in the energy range 100 MeV - 3 GeV by the AGILE satellite, during the period 2007 July - 2009 October. The total exposure time is about 300 days, during which the source was in the "hard" X-ray spectral state. We divided the observing intervals in 2 or 4 week periods, and searched for transient and persistent emission. We report an episode of significant transient gamma-ray emission detected on 2009, October 16 in a position compatible with Cygnus X-1 optical position. This episode, occurred during a hard spectral state of Cygnus X-1, shows that a 1-2 day time variable emission above 100 MeV can be produced during hard spectral states, having important theoretical implications for current Comptonization models for Cygnus X-1 and other microquasars. Except for this one short timescale episode, no significant gamma-ray emission was detected by AGILE. By integrating all available data we obtain a 2$\sigma$ upper limit for the total integrated flux of $F_{\gamma,U.L.} = 3 \times 10^{-8} \rm ph cm^{-2} s^{-1}$ in the energy range 100 MeV - 3 GeV. We then clearly establish the existence of a spectral cutoff in the energy range 1-100 MeV that applies to the typical hard state outside the flaring period and that confirms the historically known spectral cutoff above 1 MeV.Comment: Accepted for publication by ApJ on the 9th of Feb 2010, 5 pages, 3 figure