Pruning Algorithms for Pretropisms of Newton Polytopes

Pretropisms are candidates for the leading exponents of Puiseux series that represent solutions of polynomial systems. To find pretropisms, we propose an exact gift wrapping algorithm to prune the tree of edges of a tuple of Newton polytopes. We prefer exact arithmetic not only because of the exact input and the degrees of the output, but because of the often unpredictable growth of the coordinates in the face normals, even for polytopes in generic position. We provide experimental results with our preliminary implementation in Sage that compare favorably with the pruning method that relies only on cone intersections.Comment: exact, gift wrapping, Newton polytope, pretropism, tree pruning, accepted for presentation at Computer Algebra in Scientific Computing, CASC 201

Strong Balmer lines in old stellar populations: No need for young ages in ellipticals?

Comparing models of Simple Stellar Populations (SSP) with observed line strengths generally provides a tool to break the age-metallicity degeneracy in elliptical galaxies. Due to the wide range of Balmer line strengths observed, ellipticals have been interpreted to exhibit an appreciable scatter in age. In this paper, we analyze Composite Stellar Population models with a simple mix of an old metal-rich and an old metal-poor component. We show that these models simultaneously produce strong Balmer lines and strong metallic lines without invoking a young population. The key to this result is that our models are based on SSPs that better match the steep increase of Hbeta in metal-poor globular clusters than models in the literature. Hence, the scatter of Hbeta observed in cluster and luminous field elliptical galaxies can be explained by a spread in the metallicity of old stellar populations. We check our model with respect to the so-called G-dwarf problem in ellipticals. For a galaxy subsample covering a large range in UV-V colors we demonstrate that the addition of an old metal-poor subcomponent does not invalidate other observational constraints like colors and the flux in the mid-UV.Comment: Accepted for publication in ApJ Main Journal, 9 pages, 5 figure

Star formation activity of intermediate redshift cluster galaxies out to the infall regions

We present a spectroscopic analysis of two galaxy clusters out to ~4Mpc at z~0.2. The two clusters VMF73 and VMF74 identified by Vikhlinin et al. (1998) were observed with MOSCA at the Calar Alto 3.5m telescope. Both clusters lie in the ROSAT PSPC field R285 and were selected from the X-ray Dark Cluster Survey (Gilbank et al. 2004) that provides optical V- and I-band data. VMF73 and VMF74 are located at respective redshifts of z=0.25 and z=0.18 with velocity dispersions of 671 km/s and 442 km/s, respectively. The spectroscopic observations reach out to ~2.5 virial radii. Line strength measurements of the emission lines H_alpha and [OII]3727 are used to assess the star formation activity of cluster galaxies which show radial and density dependences. The mean and median of both line strength distributions as well as the fraction of star forming galaxies increase with increasing clustercentric distance and decreasing local galaxy density. Except for two galaxies with strong H_alpha and [OII] emission, all of the cluster galaxies are normal star forming or passive galaxies. Our results are consistent with other studies that show the truncation in star formation occurs far from the cluster centre.Comment: 15 pages, 12 figures. A&A in pres

A first-in-human, randomized, controlled, subject- and reviewer-blinded multicenter study of Actamax™ Adhesion Barrier

Purpose: Post-surgical adhesions remain a significant concern following abdominopelvic surgery. This study was to assess safety, manageability and explore preliminary efficacy of applying a degradable hydrogel adhesion barrier to areas of surgical trauma following gynecologic laparoscopic abdominopelvic surgery. Methods: This first-in-human, prospective, randomized, multicenter, subject- and reviewer-blinded clinical study was conducted in 78 premenopausal women (18–46 years) wishing to maintain fertility and undergoing gynecologic laparoscopic abdominopelvic surgery with planned clinically indicated second-look laparoscopy (SLL) at 4–12 weeks. The first two patients of each surgeon received hydrogel, up to 30 mL sprayed over all sites of surgical trauma, and were assessed for safety and application only (n = 12). Subsequent subjects (n = 66) were randomized 1:1 to receive either hydrogel (Treatment, n = 35) or not (Control, n = 31); 63 completed the SLL. Results: No adverse event was assessed as serious, or possibly device related. None was severe or fatal. Adverse events were reported for 17 treated subjects (17/47, 36.2%) and 13 Controls (13/31, 41.9%). For 95.7% of treated subjects, surgeons found the device “easy” or “very easy” to use; in 54.5%, some residual material was evident at SLL. For 63 randomized subjects who completed the SLL, adjusted between-group difference in the change from baseline adhesion score demonstrated a 41.4% reduction for Treatment compared with Controls (p = 0.017), with a 49.5% reduction (p = 0.008) among myomectomy subjects (n = 34). Conclusion: Spray application of a degradable hydrogel adhesion barrier during gynecologic laparoscopic abdominopelvic surgery was performed easily and safely, without evidence of clinically significant adverse outcomes. Data suggest the hydrogel was effective in reducing postoperative adhesion development, particularly following myomectomy

Orbital M1 versus E2 strength in deformed nuclei: A new energy weighted sum rule

Within the unified model of Bohr and Mottelson we derive the following linear energy weighted sum rule for low energy orbital 1$^+$ excitations in even-even deformed nuclei S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) \epsilon (B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2^2) \mu^2_N with B(E2) the E2 strength for the transition from the ground state to the first excited state in the ground state rotational band, $$ the charge r.m.s. radius squared and $\epsilon$ the binding energy per nucleon in the nuclear ground state. It is shown that this energy weighted sum rule is in good agreement with available experimental data. The sum rule is derived using a simple ansatz for the intrinsic ground state wave function that predicts also high energy 1$^+$ strength at 2$\hbar \omega$ carrying 50\% of the total $m_1$ moment of the orbital M1 operator.Comment: REVTEX (3.0), 9 pages, RU924

Risk factors for high anti-HHV-8 antibody titers (≥1:51,200) in black, HIV-1 negative South African cancer patients: a case control study

Background: Infection with human herpesvirus 8 (HHV-8) is the necessary causal agent in the development of Kaposi's sarcoma (KS). Infection with HIV-1, male gender and older age all increase risk for KS. However, the geographic distribution of HHV-8 and KS both prior to the HIV/AIDS epidemic and with HIV/AIDS suggest the presence of an additional co-factor in the development of KS. Methods: Between January 1994 and October 1997, we interviewed 2576 black in-patients with cancer in Johannesburg and Soweto, South Africa. Blood was tested for antibodies against HIV-1 and HHV-8 and the study was restricted to 2191 HIV-1 negative patients. Antibodies against the latent nuclear antigen of HHV-8 encoded by orf73 were detected with an indirect immunofluorescence assay. We examined the relationship between high anti-HHV-8 antibody titers (≥1:51,200) and sociodemographic and behavioral factors using unconditional logistic regression models. Variables that were significant at p = 0.10 were included in multivariate analysis. Results: Of the 2191 HIV-1 negative patients who did not have Kaposi's sarcoma, 854 (39.0%) were positive for antibodies against HHV-8 according to the immunofluorescent assay. Among those seropositive for HHV-8, 530 (62.1%) had low titers (1:200), 227 (26.6%) had medium titers (1:51,200) and 97 (11.4%) had highest titers (1:204,800). Among the 2191 HIV-1 negative patients, the prevalence of high anti-HHV-8 antibody titers (≥1:51,200) was independently associated with increasing age (ptrend = 0.04), having a marital status of separated or divorced (p = 0.003), using wood, coal or charcoal as fuel for cooking 20 years ago instead of electricity (p = 0.02) and consuming traditional maize beer more than one time a week (p = 0.02; p-trend for increasing consumption = 0.05) although this may be due to chance given the large number of predictors considered in this analysis. Conclusions: Among HIV-negative subjects, patients with high anti-HHV-8 antibody titers are characterized by older age. Other associations that may be factors in the development of high anti- HHV-8 titers include exposure to poverty or a low socioeconomic status environment and consumption of traditional maize beer. The relationship between these variables and high anti- HHV-8 titers requires further, prospective study

The influence of Ga+^+-irradiation on the transport properties of mesoscopic conducting thin films

We studied the influence of 30keV Ga$^+$-ions -- commonly used in focused ion beam (FIB) devices -- on the transport properties of thin crystalline graphite flake, La$_{0.7}$Ca$_{0.3}$MnO$_3$ and Co thin films. The changes of the electrical resistance were measured in-situ during irradiation and also the temperature and magnetic field dependence before and after irradiation. Our results show that the transport properties of these materials strongly change at Ga$^+$ fluences much below those used for patterning and ion beam induced deposition (IBID), limiting seriously the use of FIB when the intrinsic properties of the materials of interest are of importance. We present a method that can be used to protect the sample as well as to produce selectively irradiation-induced changes.Comment: 14 pages, 11 figures, will be published in Nanotechnology 201

The epochs of early-type galaxy formation as a function of environment

The aim of this paper is to set constraints of the epochs of early-type galaxy formation through the 'archaeology' of the stellar populations in local galaxies. Using our models of absorption line indices that account for variable abundance ratios, we derive the stellar population parameters of 124 early-type galaxies in high and low density environments. We find that all three parameters age, metallicity, and alpha/Fe ratio are correlated with velocity dispersion. We further find evidence for an influence of the environment on the stellar population properties. Massive early-type galaxies in low-density environments appear on average ~2 Gyrs younger and slightly more metal-rich than their counterparts in high density environments. No offsets in the alpha/Fe ratios, instead, are detected. We translate the derived ages and alpha/Fe ratios into star formation histories. We show that most star formation activity in early-type galaxies is expected to have happened between redshifts 3 and 5 in high density and between redshifts 1 and 2 in low density environments. We conclude that at least 50 per cent of the total stellar mass density must have already formed at z 1, in good agreement with observational estimates of the total stellar mass density as a function of redshift. Our results suggest that significant mass growth in the early-type galaxy population below z 1 must be restricted to less massive objects, and a significant increase of the stellar mass density between redshifts 1 and 2 should be present caused mainly by the field galaxy population. The results of this paper further imply vigorous star formation episodes in massive objects at z 2-5 and the presence of evolved ellipticals around z 1, both observationally identified as SCUBA galaxies and EROs.Comment: 20 pages, 10 figures, plus appendix, accepted by Ap

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

A Generating Function for all Semi-Magic Squares and the Volume of the Birkhoff Polytope

We present a multivariate generating function for all n x n nonnegative integral matrices with all row and column sums equal to a positive integer t, the so called semi-magic squares. As a consequence we obtain formulas for all coefficients of the Ehrhart polynomial of the polytope B_n of n x n doubly-stochastic matrices, also known as the Birkhoff polytope. In particular we derive formulas for the volumes of B_n and any of its faces.Comment: 24 pages, 1 figure. To appear in Journal of Algebraic Combinatoric