On the Weak Lefschetz Property for Artinian Gorenstein algebras of codimension three

We study the problem of whether an arbitrary codimension three graded artinian Gorenstein algebra has the Weak Lefschetz Property. We reduce this problem to checking whether it holds for all compressed Gorenstein algebras of odd socle degree. In the first open case, namely Hilbert function (1,3,6,6,3,1), we give a complete answer in every characteristic by translating the problem to one of studying geometric aspects of certain morphisms from $\mathbb P^2$ to $\mathbb P^3$, and Hesse configurations in $\mathbb P^2$.Comment: A few changes with respect to the previous version. 17 pages. To appear in the J. of Algebr

Carboxyl-modified single-wall carbon nanotubes improve bone tissue formation in vitro and repair in an in vivo rat model.

The clinical management of bone defects caused by trauma or nonunion fractures remains a challenge in orthopedic practice due to the poor integration and biocompatibility properties of the scaffold or implant material. In the current work, the osteogenic properties of carboxyl-modified single-walled carbon nanotubes (COOH-SWCNTs) were investigated in vivo and in vitro. When human preosteoblasts and murine embryonic stem cells were cultured on coverslips sprayed with COOH-SWCNTs, accelerated osteogenic differentiation was manifested by increased expression of classical bone marker genes and an increase in the secretion of osteocalcin, in addition to prior mineralization of the extracellular matrix. These results predicated COOH-SWCNTs' use to further promote osteogenic differentiation in vivo. In contrast, both cell lines had difficulties adhering to multi-walled carbon nanotube-based scaffolds, as shown by scanning electron microscopy. While a suspension of SWCNTs caused cytotoxicity in both cell lines at levels >20 μg/mL, these levels were never achieved by release from sprayed SWCNTs, warranting the approach taken. In vivo, human allografts formed by the combination of demineralized bone matrix or cartilage particles with SWCNTs were implanted into nude rats, and ectopic bone formation was analyzed. Histological analysis of both types of implants showed high permeability and pore connectivity of the carbon nanotube-soaked implants. Numerous vascularization channels appeared in the formed tissue, additional progenitor cells were recruited, and areas of de novo ossification were found 4 weeks post-implantation. Induction of the expression of bone-related genes and the presence of secreted osteopontin protein were also confirmed by quantitative polymerase chain reaction analysis and immunofluorescence, respectively. In summary, these results are in line with prior contributions that highlight the suitability of SWCNTs as scaffolds with high bone-inducing capabilities both in vitro and in vivo, confirming them as alternatives to current bone-repair therapies

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

Differences in Pre and Post Vascular Patterning of Retinas from ISS Crew Members and HDT Subjects by VESGEN Analysis

Accelerated research by NASA [1] has investigated the significant risks for visual and ocular impairments Spaceflight Associated Neuro-Ocular Syndrome /Visual Impairment/Intracranial Pressure (SANS/VIIP) incurred by microgravity spaceflight, especially long-duration missions. Our study investigates the role of blood vessels in the incidence and etiology of SANS/VIIP within the retinas of Astronaut crewmembers pre-and post-flight to the International Space Station (ISS) by NASA's VESsel GENeration Analysis (VESGEN). The response of retinal vessels in crewmembers to microgravity was compared to that of retinal vessels to Head-Down Tilt (HDT) in subjects undergoing 70-Day Bed Rest. The study tests the proposed hypothesis that cephalad fluid shifts missions, resulting in ocular and visual impairments, are necessarily mediated in part by retinal blood vessels, and are therefore accompanied by significant remodeling of retinal vasculature.Vascular patterns in the retinas of crew members and HDTBR subjects extracted from 30 infrared (IR) Heidelberg Spectralis images collected pre/postflight and pre/post HDTBR, respectively, were analyzed by VESGEN (patent pending). a mature, automated software developed as a research discovery tool for progressive vascular diseases in the retina and other tissues [2]. The weighted, multi-parametric VESGEN analysis generates maps of branching arterial and venous trees and quantification by parameters such as the fractal dimension (Df, a modern measure of vascular space-filling capacity), vessel diameters, and densities of vessel length and number classified into specific branching generations by vascular physiological branching rules [2,3]. The retrospective study approved by NASAs Institutional Review Board included six HDT subjects (NASA Flight Analogs Research Unit [FARU] Campaign 11; for example, [4]) and eight ISS crewmembers monitored by routine occupational surveillance who provided their study consents to NASAs Lifetime Surveillance of Astronaut Health (LSAH). For the initial blinded VESGEN phase, ophthalmic retinal images were masked as to subject identity and pre- and post-status. In the second unblinded phase, VESGEN results were analyzed according to the pre- and post-status of left and right retinas matched to each subject. To complete our study, vascular results will be subjected to NASA biostatistical analysis and correlated with other ophthalmic and medical findings. Preliminary results for changes in the pre- to post-status of vascular patterning in the retinas of crewmembers and HDT subjects are strikingly opposite. By Df and other vascular branching measures, the space-filling capacity of arterial and venous trees decreased in a substantial subset of crewmembers (11/16 retinas). In contrast, vascular densities increased in a substantial subset of HDT subjects by the same parameters (6/10 retinas, currently excluding one anomalous subject). To conclude the study, biostatistical and medical analyses will be of critical importance for investigating the validity of these vascular findings. Vascular densities appeared to decrease in the retinas of crewmembers following ISS Missions, and increase in subjects after HDT. The vascular increases and decreases most likely derive primarily from limits of resolution to the ophthalmic imaging that does not capture the smallest vessels, rather than from vessel growth or atrophy. Differences in arterial and venous response to cephalad fluid shifts induced by ISS and HDT may have resulted from a long-duration conditioning phenomenon (for example, 6-month ISS missions compared to 70-day HDT), or the presence of gravity in HDT compared to microgravity onboard the ISS. To conclude our study, the biostatistical and medical analyses will be of critical importance for investigating the validity and significance of the VESGEN findings

Anion-Dependent Construction of Two Hexanuclear 3D-4F Complexes with a Flexible Schiff Base Ligand

Two hexanuclear 3d-4f Ni-Eu and Cu-Eu complexes [Eu4Ni2L2(OAc)(12)(EtOH)(2)] (1) and [Eu4Cu2L2(OAc)(12)]center dot 2H(2)O (2) are reported which are formed from the salen type Schiff-base ligand H2L (H2L = N,N'-bis(3-methoxysalicylidene)butane-1,4-diamine). In both complexes, four Eu3+ cations are bridged by eight OAc- groups and the chain is terminated at each end by two ML (M = Ni and Cu) units. The structures of 1 and 2 were determined by single crystal X-ray crystallographic studies and the luminescence properties of the free ligand and metal complexes in solution were measured.HHMI Undergraduate Science Education Award 52005907National Science Foundation CHE-0629136, CHE-0741973, CHE-0847763Welch Foundation F-1631, F-816Hong Kong Baptist University FRG/06-07/II-16Hong Kong Research Grants Council HKBU 202407Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)Open Foundation of Jiangsu Province Key Laboratory of Fine Petrochemical Technology KF1005UT-CNM and UT-AustinChemistr

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

Direct Evidence for Hadronic Cosmic-Ray Acceleration in the Supernova Renmant IC 443

The Supernova Remnant (SNR) IC 443 is an intermediate-age remnant well known for its radio, optical, X-ray and gamma-ray energy emissions. In this Letter we study the gamma-ray emission above 100 MeV from IC 443 as obtained by the AGILE satellite. A distinct pattern of diffuse emission in the energy range 100 MeV-3 GeV is detected across the SNR with its prominent maximum (source "A") localized in the Northeastern shell with a flux F = (47 \pm 10) 10^{-8} photons cm^{-2} s^{-1} above 100 MeV. This location is the site of the strongest shock interaction between the SNR blast wave and the dense circumstellar medium. Source "A" is not coincident with the TeV source located 0.4 degree away and associated with a dense molecular cloud complex in the SNR central region. From our observations, and from the lack of detectable diffuse TeV emission from its Northeastern rim, we demonstrate that electrons cannot be the main emitters of gamma-rays in the range 0.1-10 GeV at the site of the strongest SNR shock. The intensity, spectral characteristics, and location of the most prominent gamma-ray emission together with the absence of co-spatial detectable TeV emission are consistent only with a hadronic model of cosmic-ray acceleration in the SNR. A high-density molecular cloud (cloud "E") provides a remarkable "target" for nucleonic interactions of accelerated hadrons: our results show enhanced gamma-ray production near the molecular cloud/shocked shell interaction site. IC 443 provides the first unambiguous evidence of cosmic-ray acceleration by SNRs.Comment: 5 pages, 2 figures; accepted by ApJLetters on Jan 21, 201

AGILE detection of delayed gamma-ray emission from GRB 080514B

GRB 080514B is the first gamma ray burst (GRB), since the time of EGRET, for which individual photons of energy above several tens of MeV have been detected with a pair-conversion tracker telescope. This burst was discovered with the Italian AGILE gamma-ray satellite. The GRB was localized with a cooperation by AGILE and the interplanetary network (IPN). The gamma-ray imager (GRID) estimate of the position, obtained before the SuperAGILE-IPN localization, is found to be consistent with the burst position. The hard X-ray emission observed by SuperAGILE lasted about 7 s, while there is evidence that the emission above 30 MeV extends for a longer duration (at least ~13 s). Similar behavior was seen in the past from a few other GRBs observed with EGRET. However, the latter measurements were affected, during the brightest phases, by instrumental dead time effects, resulting in only lower limits to the burst intensity. Thanks to the small dead time of the AGILE/GRID we could assess that in the case of GRB 080514B the gamma-ray to X-ray flux ratio changes significantly between the prompt and extended emission phase.Comment: A&A letters, in pres

AGILE detection of GeV gamma-ray emission from the SNR W28

Supernova remnants (SNRs) are believed to be the main sources of Galactic cosmic rays. Molecular clouds associated with SNRs can produce gamma-ray emission through the interaction of accelerated particles with the concentrated gas. The middle aged SNR W28, for its associated system of dense molecular clouds, provides an excellent opportunity to test this hypothesis. We present the AGILE/GRID observations of SNR W28, and compare them with observations at other wavelengths (TeV and 12CO J=1-->0 molecular line emission). The gamma-ray flux detected by AGILE from the dominant source associated with W28 is (14 +- 5) 10^-8 ph cm^-2 s^-1 for E > 400 MeV. This source is positionally well correlated with the TeV emission observed by the HESS telescope. The local variations of the GeV to TeV flux ratio suggest a difference between the CR spectra of the north-west and south molecular cloud complexes. A model based on a hadronic-induced interaction and diffusion with two molecular clouds at different distances from the W28 shell can explain both the morphological and spectral features observed by AGILE in the MeV-GeV energy range and by the HESS telescope in the TeV energy range. The combined set of AGILE and H.E.S.S. data strongly support a hadronic model for the gamma-ray production in W28.Comment: Accepted for publication in Astronomy & Astrophysics Letter

Effects of Mild Hypercapnia During Head-Down Bed Rest on Ocular Structures, Cerebral Blood Flow, aud Visual Acuity in Healthy Human Subjects

The cephalad fluid shift induced by microgravity has been hypothesized to cause an elevation in intracranial pressure (ICP) and contribute to the development of the Visual Impairment/Intracranial Pressure (VIIP) syndrome, as experienced by some astronauts during long-duration space flight. Elevated ambient partial pressure of carbon dioxide (PCO2) on ISS may also raise ICP and contribute to VIIP development. We seek to determine if the combination of mild CO2 exposure, similar to that occurring on the International Space Station, with the cephalad fluid shift induced by head-down tilt, will induce ophthalmic and cerebral blood flow changes similar to those described in the VIIP syndrome. We hypothesize that mild hypercapnia in the head-down tilt position will increase choroidal blood volume and cerebral blood flow, raise intraocular pressure (IOP), and transiently reduce visual acuity as compared to the seated or the head-down tilt position without elevated CO2, respectively