The "Hot Spots" Conjecture on the Vicsek Set

We prove the Hot Spot conjecture on the Vicsek set. Specifically, we show that every eigenfunction of the second smallest eigenvalue of the Neumann Laplacian on the Vicsek set attains its maximum and minimum on the boundary.Comment: We made changes suggested by the anonymous referee and editors. The paper is accepted for publication in the Special Issue on Harmonic Analysis: Smooth and Non-Smooth, Demonstratio Mathematic

SPIFI: a Direct-Detection Imaging Spectrometer for Submillimeter Wavelengths

The South Pole Imaging Fabry-Perot Interferometer (SPIFI) is the first instrument of its kind -a direct-detection imaging spectrometer for astronomy in the submillimeter band. SPIFI ’s focal plane is a square array of 25 silicon bolometers cooled to 60 mK; the spectrometer consists of two cryogenic scanning Fabry-Perot interferometers in series with a 60-mK bandpass filter. The instrument operates in the short submillimeter windows (350 and 450 μm) available from the ground, with spectral resolving power selectable between 500 and 10,000. At present, SPIFI’s sensitivity is within a factor of 1.5-3 of the photon background limit, comparable with the best heterodyne spectrometers. The instrument ’s large bandwidth and mapping capability provide substantial advantages for specific astrophysical projects, including deep extragalactic observations. We present the motivation for and design of SPIFI and its operational characteristics on the telescope

Deuterium and the Local Interstellar Medium: Properties for the Procyon and Capella Lines of Sight

We present Goddard High-Resolution Spectrograph observations of the interstellar H I and D I Ly-alpha lines and the Mg II and Fe II resonance lines formed along the lines of sight toward the nearby stars Procyon (3.5 pc, l = 214 deg, b = 13 deg) and Capella (12.5 pc, l = 163 deg, b = 5 deg). New observations of Capella were obtained at orbital phase 0.80, when the radial velocities of the intrinsic Ly-alpha emission lines of each star were nearly reversed from those of the previous observations at phase 0.26. Since the intrinsic Ly-alpha line of the Capella system (the 'continuum' against which the interstellar absorption is measured) has different shapes at phases 0.26 and 0.80, we can derive both the intrinsic stellar profiles and the interstellar absorption lines more precisely by jointly analyzing the two data sets. For the analysis of the Procyon line of sight, we first assumed that the intrinsic Ly-alpha line profile is a broadened solar profile, but this assumption does not lead to a good fit to the observed D I line profile for any value of D/H. We then assumed that (D/H)(sub LISM) = 1.6 x 10(exp -5), the same value as for the Capella line of sight, and we modified the broadened solar profile to achieve agreement between the simulated and observed line profiles. The resulting asymmetric intrinsic stellar line profile is consistent with the shapes of the scaled Mg II line profiles. We believe therefore that the Procyon data are consistent with (D/H)(sub LISM) = 1.6 x 10(exp -5), but the uncertainty in the intrinsic Ly-alpha emission-line profile does not permit us to conclude that the D/H ratio is constant in the local interstellar medium (LISM). The temperature and turbulence in the Procyon line of sight are T = 6900 +/- 80 (+/- 300 systematic error) K and zeta = 1.21 +/- 0.27 km/s. These properties are similar to those of Capella, except that the gas toward Procyon is divided into two velocity components separated by 2.6 km/s and the Procyon line of sight has a mean neutral hydrogen density that is a factor of 2.4 larger than that of the Capella line of sight. This suggests that the first 5.3 pc along the Capella line of sight lies within the local cloud and the remaining 7.2 pc lies in the hot gas surrounding the local cloud. We propose that n(H I) = 0.1065 +/- 0.0028 cm(exp -2) be adopted for the neutral hydrogen density within the local cloud and that zeta = 1.21 +/- 0.27 km/s be adopted for the nonthermal motions. The existence of different second velocity components toward the nearby stars Procyon and Sirius provides the first glimpse of a turbulent cloudlet boundary layer between the local cloud and the surrounding hot interstellar gas

Multi-Pion States in Lattice QCD and the Charged-Pion Condensate

The ground-state energies of systems containing up to twelve $\pi^+$'s in a spatial volume V ~ (2.5 fm)^3 are computed in dynamical, mixed-action lattice QCD at a lattice spacing of ~ 0.125 fm for four different values of the light quark masses. Clean signals are seen for each ground state, allowing for a precise extraction of both the $\pi^+\pi^+$ scattering length and $\pi^+\pi^+\pi^+$-interaction from a correlated analysis of systems containing different numbers of $\pi^+$'s. This extraction of the $\pi^+\pi^+$ scattering length is consistent with than that from the $\pi^+\pi^+$-system alone. The large number of systems studied here significantly strengthens the arguments presented in our earlier work and unambiguously demonstrates the presence of a low energy $\pi^+\pi^+\pi^+$-interaction. The equation of state of a $\pi^+$ gas is investigated using our numerical results and the density dependence of the isospin chemical potential for these systems agrees well with the theoretical expectations of leading order chiral perturbation theory. The chemical potential is found to receive a substantial contribution from the $\pi^+\pi^+\pi^+$-interaction at the lighter pion masses. An important technical aspect of this work is the demonstration of the necessity of performing propagator contractions in greater than double precision to extract the correct results.Comment: 38 pages, 20 figure

An assessment of the population of cotton-top tamarins (Saguinus oedipus) and their habitat in Colombia

Numerous animals have declining populations due to habitat loss, illegal wildlife trade, and climate change. The cotton-top tamarin (Saguinus oedipus) is a Critically Endangered primate species, endemic to northwest Colombia, threatened by deforestation and illegal trade. In order to assess the current state of this species, we analyzed changes in the population of cotton-top tamarins and its habitat from 2005 to 2012. We used a tailor-made "lure strip transect" method to survey 43 accessible forest parcels that represent 30% of the species' range. Estimated population size in the surveyed region was approximately 2,050 in 2005 and 1,900 in 2012, with a coefficient of variation of approximately 10%. The estimated population change between surveys was -7% (a decline of approximately 1.3% per year) suggesting a relatively stable population. If densities of inaccessible forest parcels are similar to those of surveyed samples, the estimated population of cotton-top tamarins in the wild in 2012 was 6,946 individuals. We also recorded little change in the amount of suitable habitat for cotton-top tamarins between sample periods: in 2005, 18% of surveyed forest was preferred habitat for cotton-top tamarins, while in 2012, 17% percent was preferred. We attribute the relatively stable population of this Critically Endangered species to increased conservation efforts of Proyecto Tití, conservation NGOs, and the Colombian government. Due to continued threats to cotton-top tamarins and their habitat such as agriculture and urban expansion, ongoing conservation efforts are needed to ensure the long-term survival of cotton-top tamarins in Colombia.Publisher PDFPeer reviewe

Carbon amendment stimulates benthic nitrogen cycling during the bioremediation of particulate aquaculture waste

The treatment of organic wastes remains one of the key sustainability challenges facing the growing global aquaculture industry. Bioremediation systems based on coupled bioturbation-microbial processing offer a promising route for waste management. We present, for the first time, a combined biogeochemical-molecular analysis of the short-term performance of one such system that is designed to receive nitrogen-rich particulate aquaculture wastes. Using sea cucumbers (Holothuria scabra) as a model bioturbator we provide evidence that adjusting the waste CgN from 5g1 to 20g1 promoted a shift in nitrogen cycling pathways towards the dissimilatory nitrate reduction to ammonium (DNRA), resulting in net NH4+ efflux from the sediment. The carbon amended treatment exhibited an overall net N2 uptake, whereas the control receiving only aquaculture waste exhibited net N2 production, suggesting that carbon supplementation enhanced nitrogen fixation. The higher NH4+ efflux and N2 uptake was further supported by meta-genome predictions that indicate that organic-carbon addition stimulated DNRA over denitrification. These findings indicate that carbon addition may potentially result in greater retention of nitrogen within the system; however, longer-term trials are necessary to determine whether this nitrogen retention is translated into improved sea cucumber biomass yields. Whether this truly constitutes a remediation process is open for debate as there remains the risk that any increased nitrogen retention may be temporary, with any subsequent release potentially raising the eutrophication risk. Longer and larger-scale trials are required before this approach may be validated with the complexities of the in-system nitrogen cycle being fully understood

Nonleptonic Two-Body Decays of D Mesons in Broken SU(3)

Decays of the D mesons to two pseudoscalars, to two vectors, and to pseudoscalar plus vector are discussed in the context of broken flavor SU(3). A few assumptions are used to reduce the number of parameters. Amplitudes are fit to the available data, and predictions of branching ratios for unmeasured modes are made.Comment: LaTeX, 24 page

Unimodality Problems in Ehrhart Theory

Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart $h^*$-vectors and highlight open questions and problems.Comment: Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original versio

Review of methods for measuring β-cell function: Design considerations from the Restoring Insulin Secretion (RISE) Consortium

The Restoring Insulin Secretion (RISE) study was initiated to evaluate interventions to slow or reverse the progression of β-cell failure in type 2 diabetes (T2D). To design the RISE study, we undertook an evaluation of methods for measurement of β-cell function and changes in β-cell function in response to interventions. In the present paper, we review approaches for measurement of β-cell function, focusing on methodologic and feasibility considerations. Methodologic considerations included: (1) the utility of each technique for evaluating key aspects of β-cell function (first- and second-phase insulin secretion, maximum insulin secretion, glucose sensitivity, incretin effects) and (2) tactics for incorporating a measurement of insulin sensitivity in order to adjust insulin secretion measures for insulin sensitivity appropriately. Of particular concern were the capacity to measure β-cell function accurately in those with poor function, as is seen in established T2D, and the capacity of each method for demonstrating treatment-induced changes in β-cell function. Feasibility considerations included: staff burden, including time and required methodological expertise; participant burden, including time and number of study visits; and ease of standardizing methods across a multicentre consortium. After this evaluation, we selected a 2-day measurement procedure, combining a 3-hour 75-g oral glucose tolerance test and a 2-stage hyperglycaemic clamp procedure, augmented with arginine

Wide Field Photometry of the Galactic Globular Cluster M22

We present wide field photometry of the Galactic Globular Cluster M~22 in the B, V and I passbands for more than 186,000 stars. The study is complemented by the photometry in two narrowband filters centered on H$_{\alpha}$ and the adjacent continuum, and by infrared J, H and K magnitudes derived from the 2 MASS survey for $\sim$2000 stars. Profiting from this huge database, we completely characterized the evolved stellar sequences of the cluster by determining a variety of photometric parameters, including new photometric estimates of the mean metallicity, reddening and distance to the cluster. In particular, from our multi-wavelength analysis, we re-examined the long-standing metallicity spread problem in M~22. According to our dataset, we conclude that most of the observed width of the red giant branch must be due to differential reddening, which amounts to a maximum of $\Delta E(B-V)\simeq0.06$, although the presence of a small metallicity spread cannot be completely ruled out. More specifically, the maximum metallicity spread allowed by our data is of the order of $\Delta$[Fe/H]$\simeq 0.1\div 0.2$ dex, i.e., not much more than what allowed by the photometric errors. Finally, we identified most of the known variable stars and peculiar objects in our field of view. In particular, we find additional evidence supporting previous optical identifications of the central star of the Planetary Nebula IRAS 18333-2357, which is associated with M~22.Comment: 15 pages, 16 figures, accepted for publication in MNRA