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

Big Hole (41TV2161): Two Stratigraphically Isolated Middle Holocene Components in Travis County, Texas Volume I

During April and May 2006, an archeological team from the Cultural Resources Section of the Planning, Permitting and Licensing Practice of TRC Environmental Corporation’s (TRC) Austin office conducted geoarcheological documentation and data recovery excavations at prehistoric site 41TV2161 (CSJ: 0440-06-006). Investigations were restricted to a 70 centimeter (cm) thick target zone between ca. 220 and 290 cm below surface (bs) on the western side of site 41TV2161 – the Big Hole site in eastern Travis County, Texas. This cultural investigation was necessary under the requirements of Section 106 of the National Historic Preservation Act (NHPA), the implementing regulations of 36CRF Part 800 and the Antiquities Code of Texas (Texas Natural Resource Code, Title 9, Chapter 191 as amended) to recover a sample of the significant cultural materials prior to destruction by planned construction of State Highway 130 (SH 130). The latter by a private construction firm – Lone Star Infrastructure. This necessary data recovery was for Texas Department of Transportation (TxDOT), Environmental (ENV) Affairs Division under a Scientific Services Contract No. 577XXSA003 (Work Authorization No. 57701SA003). Over the years since the original award, multiple work authorizations between TxDOT and TRC were implemented and completed towards specific aspects of the analyses and reporting. The final analyses and report were conducted under contract 57-3XXSA004 (Work Authorization 57-311SA004). All work was under Texas Antiquities Committee Permit No. 4064 issued by the Texas Historical Commission (THC) to J. Michael Quigg. Initially, an archeological crew from Hicks & Company encountered site 41TV2161 during an intensive cultural resource inventory conducted south of Pearce Lane along the planned construction zone of SH 130 in the fall of 2005. Following the initial site discovery, archeologists expanded their investigations to the west across the SH 130 right-of-way, and completed excavation of 10 backhoe trenches, 13 shovel tests, and 11 test units at site 41TV2161. The investigations encountered at least seven buried cultural features and 1,034 artifacts, some in relatively good context. The survey and testing report to TxDOT presented their findings and recommendations (Campbell et al. 2006). The ENV Affairs Division of TxDOT and the THC reviewed the initial findings and recommendations, and determined site 41TV2161 was eligible for listing on the National Register of Historic Places and as State Antiquities Landmark as the proposed roadway development was to directly impact this important site and further excavations were required. Subsequently, TRC archeologists led by Paul Matchen (Project Archeologist) and J. Michael Quigg (Principal Investigator) initiated data recovery excavations through the mechanical-removal of between 220 and 250 cm of sediment from a 30-by-40 meter (m) block area (roughly 3,000 m3). This was conducted to allow hand-excavations to start just above the deeply buried, roughly 70 cm thick targeted zone of cultural material. Mechanical stripping by Lone Star Infrastructure staff created a large hole with an irregular bottom that varied between 220 and 260 cmbs. To locate specific areas to initiate hand-excavations within the mechanically stripped area, a geophysical survey that employed ground penetrating radar (GPR) was conducted by Tiffany Osburn then with Geo-Marine in Plano, Texas. Over a dozen electronic anomalies were detected through the GPR investigation. Following processing, data filtering, and assessment, Osburn identified and ranked the anomalies for investigation. The highest ranked anomalies (1 through 8) were thought to have the greatest potential to represent cultural features. Anomalies 1 through 6 were selected and targeted through hand-excavations of 1-by-1 m units that formed continuous excavation blocks of various sizes. Blocks were designated A, B, C, D, E, and F. The type, nature, quantity, and context of encountered cultural materials in each block led the direction and expansion of each excavation block as needed. In total, TRC archeologists hand-excavated 38.5 m3 (150 m2) from a vertically narrow target zone within this deep, multicomponent and stratified prehistoric site. Hand-excavation in the two largest Blocks, B and D (51 m2 and 62 m2 respectively), revealed two vertically separate cultural components between roughly 220 and 290 cmbs. The younger component was restricted to Block B and yielded a Bell/Andice point and point base, plus a complete Big Sandy point. These points were associated with at least eight small burned rock features, one cluster of ground stone tools, limited quantities of lithic debitage, few formal chipped and ground stone tools, and a rare vertebrate faunal assemblage. Roughly 20 to 25 cm below the Bell/Andice component in Block B and across Block D was a component identified by a single corner-notched Martindale dart point. This point was associated with a scattered burned rocks, three charcoal stained hearth features, scattered animal, bird, and fish bones, mussel shells, and less than a dozen formal chipped and ground stone tools. Both identified components contained cultural materials in good stratigraphic context with high spatial integrity. Significant, both were radiocarbon dated by multiple charcoal samples to a narrow 200-year period between 5250 and 5450 B.P. during the middle Holocene. With exception of the well-preserved faunal assemblages, perishable materials were poorly preserved in the moist silty clay loam. Charcoal lacked structure and was reduced to dark stains. Microfossils (e.g., phytoliths and starch gains) were present, although in very limited numbers and deteriorated conditions. The four much smaller Blocks (A, C, E, and F) yielded various quantities of cultural material and features, but these blocks also lacked sufficient charcoal dates and diagnostic artifacts Those artifacts and samples were left unassigned and analyzed separately from the Bell/Andice and Martindale components. The two well-defined components in Blocks B and D are the focus of this technical report. The components provide very significant data towards understanding rare and poorly understood hunter-gatherer populations during late stages of the Altithermal climate period. This final report builds upon the interim report submitted to TxDOT (Quigg et al. 2007) that briefly described the methods, excavations, preliminary findings, initial results from six feasibility studies, and proposed an initial research design for data analyses. Context and integrity of the cultural materials in the two identified components was excellent. This rare circumstance combined with detailed artifact analyses, solid documentation of their ages through multiple radiocarbon dates, and multidisciplinary approach to analyses, allowed significant insights and contributions concerning the two populations involved. Results provide a greater understanding of human behaviors during a rarely identified time in Texas Prehistory. The cultural materials and various collected samples were temporarily curated at TRC’s Austin laboratory. Following completion of analyses and acceptance of this final report, the artifacts, paper records, photographs, and electronic database were permanently curated at the Center for Archaeological Studies (CAS) at Texas State University in San Marcos

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

Simulated Response of St. Joseph Bay, Florida, Seagrass Meadows and Their Belowground Carbon to Anthropogenic and Climate Impacts

Seagrass meadows are degraded globally and continue to decline in areal extent due to human pressures and climate change. This study used the bio-optical model GrassLight to explore the impact of climate change and anthropogenic stressors on seagrass extent, leaf area index (LAI) and belowground organic carbon (BGC) in St. Joseph Bay, Florida, using water quality data and remotely-sensed sea surface temperature (SST) from 2002 to 2020. Model predictions were compared with satellite-derived measurements of seagrass extent and shoot density from the Landsat images for the same period. The GrassLight-derived area of potential seagrass habitat ranged from 36.2 km2 to 39.2 km2, averaging 38.0 ± 0.8 km2 compared to an observed seagrass extent of 23.0 ± 3.0 km2 derived from Landsat (range = 17.9–27.4 km2). GrassLight predicted a mean seagrass LAI of 2.7 m2 leaf m−2 seabed, compared to a mean LAI of 1.9 m2 m−2 estimated from Landsat, indicating that seagrass density in St. Joseph Bay may have been below its light-limited ecological potential. Climate and anthropogenic change simulations using GrassLight predicted the impact of changes in temperature, pH, chlorophyll a, chromophoric dissolved organic matter and turbidity on seagrass meadows. Simulations predicted a 2–8% decline in seagrass extent with rising temperatures that was offset by a 3–11% expansion in seagrass extent in response to ocean acidification when compared to present conditions. Simulations of water quality impacts showed that a doubling of turbidity would reduce seagrass extent by 18% and total leaf area by 21%. Combining climate and water quality scenarios showed that ocean acidification may increase seagrass productivity to offset the negative effects of both thermal stress and declining water quality on the seagrasses growing in St. Joseph Bay. This research highlights the importance of considering multiple limiting factors in understanding the effects of environmental change on seagrass ecosystems

Effects of end-stage osteoarthritis on markers of skeletal muscle Long INterspersed Element-1 activity

Objective: Long INterspersed Element-1 (L1) is an autonomous transposable element in the genome. L1 transcripts that are not reverse transcribed back into the genome can accumulate in the cytoplasm and activate an inflammatory response via the cyclic GMP-AMP (cGAS)-STING pathway. We examined skeletal muscle L1 markers as well as STING protein levels in 10 older individuals (63 ± 11 y, BMI= 30.2 ± 6.8 kg/m2) with end-stage osteoarthritis (OA) undergoing total hip (THA, n= 4) or knee (TKA, n= 6) arthroplasty versus 10 young, healthy comparators (Y, 22 ± 2 y, BMI= 23.2 ± 2.5 kg/m2). For OA, muscle was collected from surgical (SX) and contralateral (CTL) sides whereas single vastus lateralis samples were collected from Y. Results: L1 mRNA was higher in CTL and SX compared to Y (p \u3c 0.001 and p= 0.001, respectively). Protein expression was higher in SX versus Y for ORF1p (p= 0.002) and STING (p= 0.022). While these data are preliminary due to limited n-sizes and the lack of a BMI-matched younger control group, higher L1 mRNA expression, ORF1p and STING protein are evident in older versus younger adults. More research is needed to determine whether cGAS-STING signaling contributes to heightened muscle inflammation during aging and/or OA

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.$

An intron variant of the GLI family zinc finger 3 (GLI3) gene differentiates resistance training-induced muscle fiber hypertrophy in younger men

We examined the association between genotype and resistance training-induced changes (12 wk) in dual x-ray energy absorptiometry (DXA)-derived lean soft tissue mass (LSTM) as well as muscle fiber cross-sectional area (fCSA; vastus lateralis; n = 109; age = 22 ± 2 y, BMI = 24.7 ± 3.1 kg/m2). Over 315 000 genetic polymorphisms were interrogated from muscle using DNA microarrays. First, a targeted investigation was performed where single nucleotide polymorphisms (SNP) identified from a systematic literature review were related to changes in LSTM and fCSA. Next, genome-wide association (GWA) studies were performed to reveal associations between novel SNP targets with pre- to post-training change scores in mean fCSA and LSTM. Our targeted investigation revealed no genotype-by-time interactions for 12 common polymorphisms regarding the change in mean fCSA or change in LSTM. Our first GWA study indicated no SNP were associated with the change in LSTM. However, the second GWA study indicated two SNP exceeded the significance level with the change in mean fCSA (P = 6.9 × 10–7 for rs4675569, 1.7 × 10–6 for rs10263647). While the former target is not annotated (chr2:205936846 (GRCh38.p12)), the latter target (chr7:41971865 (GRCh38.p12)) is an intron variant of the GLI Family Zinc Finger 3 (GLI3) gene. Follow-up analyses indicated fCSA increases were greater in the T/C and C/C GLI3 genotypes than the T/T GLI3 genotype (P \u3c.05). Data from the Auburn cohort also revealed participants with the T/C and C/C genotypes exhibited increases in satellite cell number with training (P \u3c.05), whereas T/T participants did not. Additionally, those with the T/C and C/C genotypes achieved myonuclear addition in response to training (P \u3c.05), whereas the T/T participants did not. In summary, this is the first GWA study to examine how polymorphisms associate with the change in hypertrophy measures following resistance training. Future studies are needed to determine if the GLI3 variant differentiates hypertrophic responses to resistance training given the potential link between this gene and satellite cell physiology

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

Intramolecular hydrogen transfer reactions of thiyl radicals from glutathione: formation of carbon-centered radical at Glu, Cys and Gly

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Chemical Research in Toxicology, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/tx3000494Glutathione thiyl radicals (GS•) were generated in H2O and D2O by either exposure of GSH to AAPH#, photoirradiation of GSH in the presence of acetone, or photoirradiation of GSSG. Detailed interpretation of the fragmentation pathways of deuterated GSH and GSH-derivatives during mass spectrometry analysis allowed us to demonstrate that reversible intramolecular H-atom transfer reactions between GS• and C-H bonds at Cys[αC], Cys[βC], and Gly[αC] are possible

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