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

Staphylococcus aureus protein A binding to von Willebrand factor A1 domain is mediated by conserved IgG binding regions.

Protein A (Spa) is a surface-associated protein of Staphylococcus aureus best known for its ability to bind to the Fc region of IgG. Spa also binds strongly to the Fab region of the immunoglobulins bearing V(H)3 heavy chains and to von Willebrand factor (vWF). Previous studies have suggested that the protein A-vWF interaction is important in S. aureus adherence to platelets under conditions of shear stress. We demonstrate that Spa expression is sufficient for adherence of bacteria to immobilized vWF under low fluid shear. The full length recombinant Ig-binding region of protein A, Spa-EDABC, fused to glutathione-S-transferase (GST), bound recombinant vWF in a dose-dependent and saturable fashion with half maximal binding of about 30 nm in immunosorbent assays. Full length-Spa did not bind recombinant vWF A3 domain but displayed binding to recombinant vWF domains A1 and D\u27-D3 (half maximal binding at 100 nm and 250 nm, respectively). Each recombinant protein A Ig-binding domain bound to the A1 domain in a similar manner to the full length-Spa molecule (half maximal binding 100 nm). Amino acid substitutions were introduced in the GST-SpaD protein at sites known to be involved in IgG Fc or in V(H)3 Fab binding. Mutants altered in residues that recognized IgG Fc but not those that recognized V(H)3 Fab had reduced binding to vWF A1 and D\u27-D3. This indicated that both vWF regions recognized a region on helices I and II that overlapped the IgG Fc binding site

Increased Panel Height Enhances Cooling for Photovoltaic Solar Farms

Solar photovoltaic (PV) systems suffer substantial efficiency loss due to environmental and internal heating. However, increasing the canopy height of these systems promotes surface heat transfer and boosts production. This work represents the first wind tunnel experiments to explore this concept in terms of array flow behavior and relative convective heat transfer, comparing model solar arrays of varied height arrangements - a nominal height, extended height, and a staggered height configuration. Analyses of surface thermocouple data show average Nusselt number () to increase with array elevation, where panel convection at double height improved up to 1.88 times that of the nominal case. This behavior is an effect of sub-array entrainment of high velocity flow and panel interactions as evidenced through flow statistics and mean kinetic energy budgets on particle image velocimetry (PIV) data. The staggered height arrangement encourages faster sub-panel flow than in the nominal array. Despite sub-array blockage due to the lower panel interaction, heat shedding at panel surfaces promotes improvements on over 1.3 times that of the nominal height case

Technoeconomic Analysis of Changing PV Array Convective Cooling Through Changing Array Spacing

Accuracy in photovoltaic (PV) module temperature modeling is crucial to achieving precision in energy performance yield calculations and subsequent economic evaluations of PV projects. While there have been numerous approaches to PV temperature modeling based on both the steady-state and transient thermal assumptions, there have been few attempts to account for changing convective cooling on PV module surfaces resulting from changes in the PV system layout. Changes in system row spacing, in particular, can have a meaningful impact on module electrical efficiency and subsequent economic performance, even when considering additional costs from the changes in row spacing. Using a heat transfer approach based on the spatial definition of a PV array, technoeconomic analyses of different plant configurations are presented here that show an improved system levelized cost of energy (LCOE) for fixed-tilt PV systems when increasing system row spacing. These LCOE improvements have been found to be as high as 2.15% in climates characterized by low ambient temperatures and higher average annual wind speeds in U.S. climates. While the LCOE improvements are primarily driven by incident irradiance changes for altered row spacing, the waterfall analysis of the different components of changing system LCOE show that modifications in the heat transfer dynamics have a 0.5% contribution to the LCOE reduction for the largest LCOE, compared with a 3.3% reduction from irradiance changes

Brief Report: Endothelial Progenitor Cell Phenotype and Function Are Impaired in Childhood‐Onset Systemic Lupus Erythematosus

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/112288/1/art39149.pd

Toward an understanding of tourists’ authentic heritage experiences: Evidence from Hong Kong

Authenticity in tourism has been a topic of discussion since the 1960s, but the concept is still to be fully developed. This study focuses on tourists’ perceptions of authenticity, and in particular how they evaluate authentic heritage experiences. The appearance and physical settings of attractions were found to be the initial and most important indicators of authentic or inauthentic experiences. Other criteria for assessing the authenticity of heritage experiences include the presence of local culture and customs, constructed elements, commodification, and atmosphere

Cyclin D2-knock-out mice with attenuated dentate gyrus neurogenesis have robust deficits in long-term memory formation.

Neurobehavioral studies have produced contradictory findings concerning the function of neurogenesis in the adult dentate gyrus. Previous studies have proved inconsistent across several behavioral endpoints thought to be dependent on dentate neurogenesis, including memory acquisition, short-term and long-term retention of memory, pattern separation, and reversal learning. We hypothesized that the main function of dentate neurogenesis is long-term memory formation because we assumed that a newly formed and integrated neuron would have a long-term impact on the local neural network. We used a cyclin D2-knock-out (cyclin D2-/-) mouse model of endogenously deficient dentate neurogenesis to test this hypothesis. We found that cyclin D2-/- mice had robust and sustained loss of long-term memory in two separate behavioral tasks, Morris water maze (MWM) and touchscreen intermediate pattern separation. Moreover, after adjusting for differences in brain volumes determined by magnetic resonance (MR) imaging, reduced dentate neurogenesis moderately correlated with deficits in memory retention after 24 hours. Importantly, cyclin D2-/- mice did not show deficits in learning acquisition in a touchscreen paradigm of intermediate pattern separation or MWM platform location, indicating intact short-term memory. Further evaluation of cyclin D2-/- mice is necessary to confirm that deficits are specifically linked to dentate gyrus neurogenesis since cyclin D2-/- mice also have a reduced size of the olfactory bulb, hippocampus, cerebellum and cortex besides reduced dentate gyrus neurogenesis

Active Galactic Nuclei in Groups and Clusters of Galaxies: Detection and Host Morphology

The incidence and properties of Active Galactic Nuclei (AGN) in the field, groups, and clusters can provide new information about how these objects are triggered and fueled, similar to how these environments have been employed to study galaxy evolution. We have obtained new XMM-Newton observations of seven X-ray selected groups and poor clusters with 0.02 < z < 0.06 for comparison with previous samples that mostly included rich clusters and optically-selected groups. Our final sample has ten groups and six clusters in this low-redshift range (split at a velocity dispersion of $\sigma = 500$ km/s). We find that the X-ray selected AGN fraction increases from $f_A(L_X>10^{41}; M_R<M_R^*+1) = 0.047^{+0.023}_{-0.016}$ in clusters to $0.091^{+0.049}_{-0.034}$ for the groups (85% significance), or a factor of two, for AGN above an 0.3-8keV X-ray luminosity of $10^{41}$ erg/s hosted by galaxies more luminous than $M_R^*+1$. The trend is similar, although less significant, for a lower-luminosity host threshold of $M_R = -20$ mag. For many of the groups in the sample we have also identified AGN via standard emission-line diagnostics and find that these AGN are nearly disjoint from the X-ray selected AGN. Because there are substantial differences in the morphological mix of galaxies between groups and clusters, we have also measured the AGN fraction for early-type galaxies alone to determine if the differences are directly due to environment, or indirectly due to the change in the morphological mix. We find that the AGN fraction in early-type galaxies is also lower in clusters $f_{A,n>2.5}(L_X>10^{41}; M_R<M_R^*+1) = 0.048^{+0.028}_{-0.019}$ compared to $0.119^{+0.064}_{-0.044}$ for the groups (92% significance), a result consistent with the hypothesis that the change in AGN fraction is directly connected to environment.Comment: 18 pages, 9 figures; accepted by The Astrophysical Journal; for higher-resolution versions of some figures, see http://u.arizona.edu/~tjarnold/Arnold09

Securing Our Economic Future

The American economy is in the midst of a wrenching crisis, one caused by the COVID-19 pandemic and aggravated further by a series of climate-driven natural disasters. While the economy has made some steps towards recovery, the pandemic has laid bare the reality that too many Americans are unable to meet many of their urgent and basic needs. At the same time, it has become painfully clear that American society is not equipped to deal with the risks emerging from our changing climate. This book is a contribution towards policy options for addressing these challenges. Although it was largely written before the pandemic crises beset our country, the analyses, diagnoses, and prescriptions contained within all shed new light on the underlying fragilities that have since been exposed. The volume is composed of nine commissioned chapters and is divided into three sections, covering the 'Economics of the American Middle Class'; the 'Geographic Disparities in Economic Opportunity'; and the 'Geopolitics of the Climate and Energy Challenge and the US Policy Response.' Part I focuses on the economic wellbeing of the American middle class and the chapters in this section evaluate the prevailing narrative of its decline. The chapters in part II investigate the large variation in income and economic opportunities across places, and include a specific policy proposal for emergency rental assistance. Part III is devoted to the global climate crisis. The chapters in this final section emphasize the mounting social and economic costs of inaction and discuss potential policy approaches for tackling the climate challenge