A modular supercongruence for 6F5_6F_5: an Ap\'ery-like story

We prove a supercongruence modulo $p^3$ between the $p$th Fourier coefficient of a weight 6 modular form and a truncated ${}_6F_5$-hypergeometric series. Novel ingredients in the proof are the comparison of two rational approximations to $\zeta (3)$ to produce non-trivial harmonic sum identities and the reduction of the resulting congruences between harmonic sums via a congruence between the Apéry numbers and another Apéry-like sequence

Elevated organic carbon pulses persist in estuarine environment after major storm events

Estuaries regulate transport of dissolved organic carbon (DOC) from land to ocean. Export of terrestrial DOC from coastal watersheds is exacerbated by increasing major rainfall and storm events and human activities, leading to pulses of DOC that are shunted through rivers downstream to estuaries. Despite an upward trend of extreme events, the fate of the pulsed terrestrial DOC in estuaries remains unclear. We analyzed the effects of seven major tropical cyclones (TC) from 1999 to 2017 on the quantity and fate of DOC in the Neuse River Estuary (NC, USA). Significant TC-induced increases in DOC were observed throughout the estuary; the increase lasting from around 50 d at head-of-tide to over 6 months in lower estuary. Our results suggest that pulsed terrestrial DOC associated with TCs temporarily overwhelms the estuarine filter's abiotic and biotic degradation capacity under such high flow events, enhancing the shunt of terrestrial carbon to the coastal ocean.Non peer reviewe

Hazard mitigation and disaster preparedness planning at American Coastal University: Seeking the disaster-resistant university.

This study employed a qualitative case study method to evaluate the efforts of one university to conduct hazard mitigation and disaster preparedness planning activities and used the Federal Emergency Management Agency framework and selected writings of sociologist and disaster researcher E.L. Quarantelli as models for evaluating the institution's approach. The institution studied was assigned a fictitious name and the identities of the study participants withheld in order to protect the integrity of the institution's planning efforts and its personnel. The study utilized a 92-item questionnaire, field interviews, and review and analysis of documentary materials provided by the institution for data collection purposes. Pattern-matching techniques were applied to identify themes and trends that emerged through the course of data collection. The results indicate the institution has developed an organizational culture that is broadly responsive to and engaged in disaster preparedness planning at multiple levels in a manner generally consistent with principles identified in select writings of Quarantelli. Results further indicate the institution has engaged in identifying hazard mitigation priorities but not in a manner consistent with that advocated by the Federal Emergency Management Agency in its publication entitled Building a Disaster-Resistant University

Economics of agroforestry (1996)

Agroforestry provides a landowner the opportunity to develop a portfolio of short- and long-term investments that allow for some spreading of financial risk through diversification. In general, diversification of investment provides financial advantages, although it also introduces the need for additional management expertise to deal with the added complexity of the farm operation. For farms with land particularly unsuitable for crops, agroforestry provides a way to remove the unsuitable land from crop production over an extended period as the trees mature. Agroforestry also provides social benefits by functioning as a protective system that ensures resource conservation, although some of these benefits are not directly measurable.New 5/96/5M

Net heterotrophy and carbonate dissolution in two subtropical seagrass meadows

The net ecosystem productivity (NEP) of two seagrass meadows within one of the largest seagrass ecosystems in the world, Florida Bay, was assessed using direct measurements over consecutive diel cycles during a short study in the fall of 2018. We report significant differences between NEP determined by dissolved inorganic carbon (NEPDIC) and by dissolved oxygen (NEPDO), likely driven by differences in air–water gas exchange and contrasting responses to variations in light intensity. We also acknowledge the impact of advective exchange on metabolic calculations of NEP and net ecosystem calcification (NEC) using the “open-water” approach and attempt to quantify this effect. In this first direct determination of NEPDIC in seagrass, we found that both seagrass ecosystems were net heterotrophic, on average, despite large differences in seagrass net above-ground primary productivity. NEC was also negative, indicating that both sites were net dissolving carbonate minerals. We suggest that a combination of carbonate dissolution and respiration in sediments exceeded seagrass primary production and calcification, supporting our negative NEP and NEC measurements. However, given the limited spatial (two sites) and temporal (8 d) extent of this study, our results may not be representative of Florida Bay as a whole and may be season-specific. The results of this study highlight the need for better temporal resolution, accurate carbonate chemistry accounting, and an improved understanding of physical mixing processes in future seagrass metabolism studies

Multiple tracers demonstrate distinct sources of dissolved organic matter to lakes of the Mackenzie Delta, western Canadian Arctic

Author Posting. © American Society of Limnology and Oceanography, 2011. This article is posted here by permission of American Society of Limnology and Oceanography for personal use, not for redistribution. The definitive version was published in Limnology and Oceanography 56 (2011): 1297-1309, doi:10.4319/lo.2011.56.4.1297.Lakes of the Mackenzie Delta occur across a gradient that contains three clear end members: those that remain connected to river-water channels throughout the summer; those that receive only brief inputs of river water during an annual spring flood but contain dense macrophyte stands; and those that experience significant permafrost thaw along their margins. We measured dissolved organic carbon (DOC) concentration, dissolved organic matter (DOM) absorption and fluorescence, and stable isotopes of DOM, DOM precursor materials, and bacteria to elucidate the importance of river water, macrophytes, and thermokarst as DOM sources to Mackenzie Delta lakes. Despite standing stocks of macrophyte C that are sevenfold to 12-fold greater than those of total DOC, stable isotopes indicated that autochthonous sources contributed less than 15% to overall DOM in macrophyte-rich lakes. Instead, fluorescence and absorption indicated that the moderate summertime increase in DOC concentration in macrophyte-rich lakes was the result of infrequent flushing, while bacterial δ13C indicated rapid bacterial removal of autochthonous DOC from the water column. In thermokarst lakes, summertime increases in DOC concentration were substantial, and stable isotopes indicated that much of this increase came from C released as a result of thermokarst-related processes. Our results indicate that these distinct sources of DOM to neighboring arctic Delta lakes may drive between-lake differences in C cycling and energy flow. Rapidly assimilated macrophyte DOM should be an important contributor to microbial food webs in our study lakes. In contrast, the accumulation of thermokarst-origin DOM allows for a significant role in physico-chemistry but indicates a lesser contribution of this DOM to higher trophic levels.This study was supported by a Discovery Grant and Northern Research Supplement from the Natural Sciences and Engineering Research Council of Canada (NSERC) to L.F.W.L.; funds from the Science Horizons Youth Internship Program, Northern Scientific Training Program, and NSERC Northern Research Internship. Personal financial support to S.E.T. was provided by a Simon Fraser University CD Nelson Memorial Graduate Scholarship, an NSERC Canada Graduate Scholarship-Doctoral, and a Garfield Weston Award for Northern Research

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.$

Perspectives on Proterozoic surface ocean redox from iodine contents in ancient and recent carbonate

© The Author(s), 2017. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Earth and Planetary Science Letters 463 (2017): 159-170, doi:10.1016/j.epsl.2017.01.032.The Proterozoic Eon hosted the emergence and initial recorded diversification of eukaryotes. Oxygen levels in the shallow marine settings critical to these events were lower than today’s, although how much lower is debated. Here, we use concentrations of iodate (the oxidized iodine species) in shallow-marine limestones and dolostones to generate the first comprehensive record of Proterozoic near-surface marine redox conditions. The iodine proxy is sensitive to both local oxygen availability and the relative proximity to anoxic waters. To assess the validity of our approach, Neogene-Quaternary carbonates are used to demonstrate that diagenesis most often decreases and is unlikely to increase carbonate-iodine contents. Despite the potential for diagenetic loss, maximum Proterozoic carbonate iodine levels are elevated relative to those of the Archean, particularly during the Lomagundi and Shuram carbon isotope excursions of the Paleo- and Neoproterozoic, respectively. For the Shuram anomaly, comparisons to Neogene-Quaternary carbonates suggest that diagenesis is not responsible for the observed iodine trends. The baseline low iodine levels in Proterozoic carbonates, relative to the Phanerozoic, are linked to a shallow oxic-anoxic interface. Oxygen concentrations in surface waters would have at least intermittently been above the threshold required to support eukaryotes. However, the diagnostically low iodine data from mid-Proterozoic shallow-water carbonates, relative to those of the bracketing time intervals, are consistent with a dynamic chemocline and anoxic waters that would have episodically mixed upward and laterally into the shallow oceans. This redox instability may have challenged early eukaryotic diversification and expansion, creating an evolutionary landscape unfavorable for the emergence of animals.TL, ZL, and DH thank NSF EAR-1349252. ZL further thanks OCE-1232620. DH, ZL, and TL acknowledge further funding from a NASA Early Career Collaboration Award. TL, AB, NP, DH, and AK thank the NASA Astrobiology Institute. TL and NP received support from the Earth-Life Transitions Program of the NSF. AB acknowledges support from NSF grant EAR-05-45484 and an NSERC Discovery and Accelerator Grants. CW acknowledges support from NSFC grant 40972021

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