Representations of integers by certain positive definite binary quadratic forms

We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte

Chemolithotrophy in the continental deep subsurface: Sanford Underground Research Facility (SURF), USA

The deep subsurface is an enormous repository of microbial life. However, the metabolic capabilities of these microorganisms and the degree to which they are dependent on surface processes are largely unknown. Due to the logistical difficulty of sampling and inherent heterogeneity, the microbial populations of the terrestrial subsurface are poorly characterized. In an effort to better understand the biogeochemistry of deep terrestrial habitats, we evaluate the energetic yield of chemolithotrophic metabolisms and microbial diversity in the Sanford Underground Research Facility (SURF) in the former Homestake Gold Mine, SD, USA. Geochemical data, energetic modeling, and DNA sequencing were combined with principle component analysis to describe this deep (down to 8100 ft below surface), terrestrial environment. SURF provides access into an iron-rich Paleoproterozoic metasedimentary deposit that contains deeply circulating groundwater. Geochemical analyses of subsurface fluids reveal enormous geochemical diversity ranging widely in salinity, oxidation state (ORP 330 to −328 mV), and concentrations of redox sensitive species (e.g., Fe(2+) from near 0 to 6.2 mg/L and Σ S(2-) from 7 to 2778μg/L). As a direct result of this compositional buffet, Gibbs energy calculations reveal an abundance of energy for microorganisms from the oxidation of sulfur, iron, nitrogen, methane, and manganese. Pyrotag DNA sequencing reveals diverse communities of chemolithoautotrophs, thermophiles, aerobic and anaerobic heterotrophs, and numerous uncultivated clades. Extrapolated across the mine footprint, these data suggest a complex spatial mosaic of subsurface primary productivity that is in good agreement with predicted energy yields. Notably, we report Gibbs energy normalized both per mole of reaction and per kg fluid (energy density) and find the later to be more consistent with observed physiologies and environmental conditions. Further application of this approach will significantly expand our understanding of the deep terrestrial biosphere

Mars Sulfate Formation Sourced in Sulfide-Enriched Subsurface Fluids: The Rio Tinto Model

The extensive evidence for sulfate deposits on Mars provided by analyses of MER and Mars Express data shows that the sulfur played an essential role in the geochemical cycles of the planet, including reservoirs in the atmosphere, hydro-sphere and geosphere. Overall the data are consistent with a fluvial/lacustrine-evaporative origin of at least some of the sulfate deposits, with mineral precipitation through oversaturation of salty acidic fluids enriched in sulfates. This scenario requires reservoirs of sulfur and associated cations, as well as an acidic and oxidizing hydrochemistry which could be provided by surface and subsurface catching of meteoric waters resulting in the presence of sulfur-bearing gases and steam photochemistry. In this work we suggest a new scenario for the extensive generation of sulfates in Mars based on the observation of seasonal changes in the redox and pH of subsurface waters enriched in sulfur that supply the acidic Mars process analog of Rio Tinto. This model considers the long-term subsurface storage of sulfur during most of Noachian and its release from the late Noachian to Hesperian time through weathering by meteoric fluids that would acidify and oxidize the sulfur bearing compounds stored in the subsurface

High treatment failure and default rates for patients with multidrug-resistant tuberculosis in KwaZulu-Natal, South Africa, 2000–2003.

SETTING: Multidrug-resistant tuberculosis (MDR-TB) has emerged as a significant public health threat in South Africa. OBJECTIVE: To describe treatment outcomes and determine risk factors associated with unfavorable outcomes among MDR-TB patients admitted to the provincial TB referral hospital in KwaZulu-Natal Province, South Africa. DESIGN: Retrospective observational study of MDR-TB patients admitted from 2000 to 2003. RESULTS: Of 1209 MDR-TB patients with documented treatment outcomes, 491 (41%) were cured, 35 (3%) completed treatment, 208 (17%) failed treatment, 223 (18%) died and 252 (21%) defaulted. Of the total number of patients with known human immunodeficiency virus (HIV) status, 52% were HIV-infected. Treatment failure, death and default each differed in their risk factors. Greater baseline resistance (aOR 2.3-3.0), prior TB (aOR 1.7), and diagnosis in 2001, 2002 or 2003 (aOR 1.9-2.3) were independent risk factors for treatment failure. HIV co-infection was a risk factor for death (aOR 5.6), and both HIV (aOR 2.0) and male sex (aOR 1.9) were risk factors for treatment default. CONCLUSION: MDR-TB treatment outcomes in KwaZulu-Natal were substantially worse than those published from other MDR-TB cohorts. Interventions such as concurrent antiretroviral therapy and decentralized MDR-TB treatment should be considered to improve MDR-TB outcomes in this high HIV prevalence setting

Interpolated sequences and critical LL-values of modular forms

Recently, Zagier expressed an interpolated version of the Ap\'ery numbers for $\zeta(3)$ in terms of a critical $L$-value of a modular form of weight 4. We extend this evaluation in two directions. We first prove that interpolations of Zagier's six sporadic sequences are essentially critical $L$-values of modular forms of weight 3. We then establish an infinite family of evaluations between interpolations of leading coefficients of Brown's cellular integrals and critical $L$-values of modular forms of odd weight.Comment: 23 pages, to appear in Proceedings for the KMPB conference: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theor

Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

Controls on the composition and lability of dissolved organic matter in Siberia's Kolyma River basin

High-latitude northern rivers export globally significant quantities of dissolved organic carbon (DOC) to the Arctic Ocean. Climate change, and its associated impacts on hydrology and potential mobilization of ancient organic matter from permafrost, is likely to modify the flux, composition, and thus biogeochemical cycling and fate of exported DOC in the Arctic. This study examined DOC concentration and the composition of dissolved organic matter (DOM) across the hydrograph in Siberia's Kolyma River, with a particular focus on the spring freshet period when the majority of the annual DOC load is exported. The composition of DOM within the Kolyma basin was characterized using absorbance-derived measurements (absorbance coefficienta330, specific UV absorbance (SUVA254), and spectral slope ratio SR) and fluorescence spectroscopy (fluorescence index and excitation-emission matrices (EEMs)), including parallel factor analyses of EEMs. Increased surface runoff during the spring freshet led to DOM optical properties indicative of terrestrial soil inputs with high humic-like fluorescence, SUVA254, and low SRand fluorescence index (FI). Under-ice waters, in contrast, displayed opposing trends in optical properties representing less aromatic, lower molecular weight DOM. We demonstrate that substantial losses of DOC can occur via biological (∼30% over 28 days) and photochemical pathways (>29% over 14 days), particularly in samples collected during the spring freshet. The emerging view is therefore that of a more dynamic and labile carbon pool than previously thought, where DOM composition plays a fundamental role in controlling the fate and removal of DOC at a pan-Arctic scale

Simplifying Multiple Sums in Difference Fields

In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and how the derived results in the given difference field can be reinterpreted as solutions of the input problem. The algorithms are illustrated with the Mathematica package \SigmaP\ by discovering and proving new harmonic number identities extending those from (Paule and Schneider, 2003). In addition, the newly developed package \texttt{EvaluateMultiSums} is introduced that combines the presented tools. In this way, large scale summation problems for the evaluation of Feynman diagrams in QCD (Quantum ChromoDynamics) can be solved completely automatically.Comment: Uses svmult.cls, to appear as contribution in the book "Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions" (www.Springer.com

Character and environmental lability of cyanobacteria-derived dissolved organic matter

Autotrophic dissolved organic matter (DOM) is central to the carbon biogeochemistry of aquatic systems, and the full complexity of autotrophic DOM has not been extensively studied, particularly by high-resolution mass spectrometry (HRMS). Terrestrial DOM tends to dominate HRMS studies in freshwaters due to the propensity of such compounds to ionize by negative mode electrospray, and possibly also because ionizable DOM produced by autotrophy is decreased to low steady-state concentrations by heterotrophic bacteria. In this study, we investigated the character of DOM produced by the widespread cyanobacteriaMicrocystis aeruginosausing high-pressure liquid chromatography-electrospray ionization-high-resolution mass spectrometry.M. aeruginosaproduced thousands of detectable compounds in axenic culture. These compounds were chromatographically resolved and the majority were assigned to aliphatic formulas with a broad polarity range. We found that the DOM produced byM. aeruginosawas highly susceptible to removal by heterotrophic freshwater bacteria, supporting the hypothesis that this autotroph-derived organic material is highly labile and accordingly only seen at low concentrations in natural settings