Elliptic curves, modular forms, and sums of Hurwitz class numbers

Let H(N) denote the Hurwitz class number. It is known that if $p$ is a prime, then {equation*} \sum_{|r|<2\sqrt p}H(4p-r^2) = 2p. {equation*} In this paper, we investigate the behavior of this sum with the additional condition $r\equiv c\pmod m$. Three different methods will be explored for determining the values of such sums. First, we will count isomorphism classes of elliptic curves over finite fields. Second, we will express the sums as coefficients of modular forms. Third, we will manipulate the Eichler-Selberg trace for ula for Hecke operators to obtain Hurwitz class number relations. The cases $m=2,3$ and 4 are treated in full. Partial results, as well as several conjectures, are given for $m=5$ and 7.Comment: Preprint of an old pape

Molecular brakes regulating mTORC1 activation in skeletal muscle following synergist ablation

The goal of the current work was to profile positive (mTORC1 activation, autocrine/paracrine growth factors) and negative [AMPK, unfolded protein response (UPR)] pathways that might regulate overload-induced mTORC1 (mTOR complex 1) activation with the hypothesis that a number of negative regulators of mTORC1 will be engaged during a supraphysiological model of hypertrophy. To achieve this, mTORC1- IRS-1/2 signaling, BiP/CHOP/IRE1, and AMPK activation were determined in rat plantaris muscle following synergist ablation (SA). SA resulted in significant increases in muscle mass of 4% per day throughout the 21 days of the experiment. The expression of the insulin-like growth factors (IGF) were high throughout the 21st day of overload. However, IGF signaling was limited, since IRS-1 and -2 were undetectable in the overloaded muscle from day 3 to day 9. The decreases in IRS-1/2 protein were paralleled by increases in GRB10 Ser501/503 and S6K1 Thr389 phosphorylation, two mTORC1 targets that can destabilize IRS proteins. PKB Ser473 phosphorylation was higher from 3&ndash; 6 days, and this was associated with increased TSC2 Thr939 phosphorylation. The phosphorylation of TSC2 Thr1345 (an AMPK site) was also elevated, whereas phosphorylation at the other PKB site, Thr1462, was unchanged at 6 days. In agreement with the phosphorylation of Thr1345, SA led to activation of AMPK1 during the initial growth phase, lasting the first 9 days before returning to baseline by day 12. The UPR markers CHOP and BiP were elevated over the first 12 days following ablation, whereas IRE1 levels decreased. These data suggest that during supraphysiological muscle loading at least three potential molecular brakes engage to downregulate mTORC1. m

High Sensitivity Array Observations of the z=1.87 Sub-Millimeter Galaxy GOODS 850-3

We present sensitive phase-referenced VLBI results on the radio continuum emission from the z=1.87 luminous submillimeter galaxy (SMG) GOODS 850-3. The observations were carried out at 1.4 GHz using the High Sensitivity Array (HSA). Our sensitive tapered VLBI image of GOODS 850-3 at 0.47 x 0.34 arcsec (3.9 x 2.9 kpc) resolution shows a marginally resolved continuum structure with a peak flux density of 148 \pm 38 uJy/beam, and a total flux density of 168 \pm 73 uJy, consistent with previous VLA and MERLIN measurements. The derived intrinsic brightness temperature is > 5 \pm 2 x 10^3 K. The radio continuum position of this galaxy coincides with a bright and extended near-infrared source that nearly disappears in the deep HST optical image, indicating a dusty source of nearly 9 kpc in diameter. No continuum emission is detected at the full VLBI resolution (13.2 x 7.2 mas, 111 x 61 pc), with a 4-sigma point source upper limit of 26 uJy/beam, or an upper limit to the intrinsic brightness temperature of 4.7 x 10^5 K. The extent of the observed continuum source at 1.4 GHz and the derived brightness temperature limits are consistent with the radio emission (and thus presumably the far-infrared emission) being powered by a major starburst in GOODS 850-3, with a star formation rate of ~2500 M_sun/yr. Moreover, the absence of any continuum emission at the full resolution of the VLBI observations indicates the lack of a compact radio AGN source in this z=1.87 SMG.Comment: 19 pages, 4 figures, accepted for publication in A

Moyo Vol. VII N 2

Durica, Paul. Editor\u27s Letter . 4. Spears, Amy L. As If Lipstick Was A Sign of My Declining Mind (How ChickRock Happened) . 5. Frey, Randall. Portrait of the Cartoonist as a Young Man . 6. Clements, Nina. Grease Me Up: One Woman\u27s Descent into the Depths of Pittsburgh Dinner Culture . 7. Levine, Robert. Under the Needle\u27s Point (The Healing Power of Acupuncture) . 8. Durica, Paul. The Glory that was/is Greek: Denison Three Years After the Decision . 12. Lamont, Jean. Smokin\u27 Joe Lights Up . 13. Durica, Paul. Ode on a Second Grecian Turn: An Interview with President Michele T. Myers . 14. Fisher, Dan. Lenane on the Social Scene . 19. Combe, Kirk. Intellectual Bio-Diversity: A Faculty Perspective on the Greek Residential Issue . 20. Williams, Adam. Elephants on the Floor Above and Brats in the Basement: Life on the North Quad . 22. Pfleeger, Jon. New Kid on the Block (Sigma Phi Epsilon\u27s President Speaks) . 23. Werne, Kirsten. Coffee Talk at the Bandersnatch (An Interview with Kevin Clay and Adam) . 29

Minor Illnesses, Temperament, and Toddler Social Functioning

Minor illnesses, such as upper respiratory infections, stomachaches, and fevers, have been associated with children’s decreased activity and increased irritability. Mothers of children who are frequently ill report more child behavior problems; however, previous research in this area has yet to simultaneously examine children’s temperament. This investigation examined whether experience with recurrent, minor illnesses and negative emotionality worked together to predict young children’s social functioning. This multi-method study utilized a sample of 110 daycare-attending children. Nurses went to the daycare centers weekly to perform health screens on the participating children. Minor illness experience was represented using a proportion created by dividing the number of illness diagnoses by the total number of health screenings completed from the time the child was enrolled in the study through his or her second birthday. Toddlers’ negative emotionality and social behavior were assessed using mothers’ and fathers’ reports. The two dimensions of negative emotionality and minor illness experience operated in different ways such that anger worked additively with minor illness experience and fearfulness interacted with minor illness experience to predict social behavior. Children who were described as more temperamentally angry displayed less social competence especially when they also experienced high proportions of minor illness. Temperamentally fearful children exhibited more externalizing problems when they experienced a higher frequency of illness whereas fearfulness was not associated to externalizing problems for children who experienced low proportions of illness

First pan-Arctic assessment of dissolved organic carbon in lakes of the permafrost region

Lakes in permafrost regions are dynamiclandscape components and play an important role for climatechange feedbacks. Lake processes such as mineralizationand flocculation of dissolved organic carbon (DOC), oneof the main carbon fractions in lakes, contribute to thegreenhouse effect and are part of the global carbon cycle.These processes are in the focus of climate research, butstudies so far are limited to specific study regions. Inour synthesis, we analyzed 2167 water samples from 1833lakes across the Arctic in permafrost regions of Alaska,Canada, Greenland, and Siberia to provide first pan-Arcticinsights for linkages between DOC concentrations andthe environment. Using published data and unpublisheddatasets from the author team, we report regional DOCdifferences linked to latitude, permafrost zones, ecoregions,geology, near-surface soil organic carbon contents, andground ice classification of each lake region. The lakeDOC concentrations in our dataset range from 0 to1130 mg L−1(10.8 mg L−1median DOC concentration).Regarding the permafrost regions of our synthesis, wefound median lake DOC concentrations of 12.4 mg L−1(Siberia), 12.3 mg L−1(Alaska), 10.3 mg L−1(Greenland),and 4.5 mg L−1(Canada). Our synthesis shows a significantrelationship between lake DOC concentration and lakeecoregion. We found higher lake DOC concentrationsat boreal permafrost sites compared to tundra sites. Wefound significantly higher DOC concentrations in lakesin regions with ice-rich syngenetic permafrost deposits(yedoma) compared to non-yedoma lakes and a weak butsignificant relationship between soil organic carbon contentand lake DOC concentration as well as between ground icecontent and lake DOC. Our pan-Arctic dataset shows that theDOC concentration of a lake depends on its environmentalproperties, especially on permafrost extent and ecoregion, aswell as vegetation, which is the most important driver of lakeDOC in this study. This new dataset will be fundamental toquantify a pan-Arctic lake DOC pool for estimations of theimpact of lake DOC on the global carbon cycle and climatechange

KSU Men\u27s Ensemble, KSU Community & Alumni Choir and KSU Chamber Singers, Illumination

KSU School of Music presents Illumination with KSU Men\u27s Ensemble, The Kennesaw State University Community and Alumni Choir and KSU Chamber Singers featuring John Rutter\u27s Gloria!https://digitalcommons.kennesaw.edu/musicprograms/1249/thumbnail.jp

Toward New Therapeutics for Skin and Soft Tissue Infections: Propargyl-Linked Antifolates Are Potent Inhibitors of MRSA and Streptococcus pyogenes

Hospital- and community-acquired, complicated skin and soft tissue infections, often attributed to Staphylococcus aureus and Streptococcus pyogenes, present a significant health burden that is associated with increased health care costs and mortality. As these two species are difficult to discern on diagnosis and are associated with differential profiles of drug resistance, the development of an efficacious antibacterial agent that targets both organisms is a high priority. Herein we describe a structure-based drug development effort that has produced highly potent inhibitors of dihydrofolate reductase from both species. Optimized propargyl-linked antifolates containing a key pyridyl substituent display antibacterial activity against both methicillin-resistant S. aureus and S. pyogenes at MIC values below 0.1 µg/mL and minimal cytotoxicity against mammalian cells. Further evaluation against a panel of clinical isolates shows good efficacy against a range of important phenotypes such as hospital- and community-acquired strains as well as strains resistant to vancomycin