Sums and differences of four k-th powers

We prove an upper bound for the number of representations of a positive integer $N$ as the sum of four $k$-th powers of integers of size at most $B$, using a new version of the Determinant method developed by Heath-Brown, along with recent results by Salberger on the density of integral points on affine surfaces. More generally we consider representations by any integral diagonal form. The upper bound has the form $O_{N}(B^{c/\sqrt{k}})$, whereas earlier versions of the Determinant method would produce an exponent for $B$ of order $k^{-1/3}$ in this case. Furthermore, we prove that the number of representations of a positive integer $N$ as a sum of four $k$-th powers of non-negative integers is at most $O_{\epsilon}(N^{1/k+2/k^{3/2}+\epsilon})$ for $k \geq 3$, improving upon bounds by Wisdom.Comment: 18 pages. Mistake corrected in the statement of Theorem 1.2. To appear in Monatsh. Mat

The Microscopic Structure of Adsorbed Water on Hydrophobic Surfaces under Ambient Conditions

The interaction of water vapor with hydrophobic surfaces is poorly understood. We utilize graphene templating to preserve and visualize the microscopic structures of adsorbed water on hydrophobic surfaces. Three well-defined surfaces [H–Si(111), graphite, and functionalized mica] were investigated, and water was found to adsorb as nanodroplets (~10–100 nm in size) on all three surfaces under ambient conditions. The adsorbed nanodroplets were closely associated with atomic-scale surface defects and step-edges and wetted all the hydrophobic substrates with contact angles < ~10°, resulting in total water adsorption that was similar to what is found for hydrophilic surfaces. These results point to the significant differences between surface processes at the atomic/nanometer scales and in the macroscopic world

When Mr. Cupid Comes To Town

https://digitalcommons.library.umaine.edu/mmb-vp/4506/thumbnail.jp

My pony boy

https://digitalcommons.library.umaine.edu/mmb-vp/2222/thumbnail.jp

Modelling the Northeast Atlantic circulation : implications for the spring invasion of shelf regions by Calanus finmarchicus

The appearance in spring of the copepod Calanus finmarchicus in continental shelf waters of the northeastern Atlantic has been hypothesized to be mainly attributable to invasion from across the continental slope rather than in situ overwintering. This paper describes the application of a hydrodynamic circulation model and a particle-tracking model to Northeast Atlantic waters in order to assess the influence of the flow field and ascent migration parameters on the spring invasion of C. finmarchicus. For hydrodynamic modelling, the Hamburg Shelf-Ocean Model (HAMSOM) was applied to the North Atlantic and Nordic Seas and forced with daily mean atmospheric data. Simulated flow fields from HAMSOM serve as forcing functions for a particle-tracking model of the same region. The robustness of the simulated shelf invasion in three target boxes of the Northeast Atlantic Shelf was assessed by means of a sensitivity analysis with respect to variations in four key migration parameters: overwintering depth, ascent rate, ascent timing, and depth during residence in upper layers. The invasion of the northern North Sea and Norwegian Shelf waters is more sensitive to ascent migration parameters than invasion of the Faroese Shelf. The main reason for enhanced sensitivity of the North Sea invasion is the time and space-dependent flow structure in the Faroe-Shetland Channel. Dense aggregations of overwintering C. finmarchicus are found in the Channel, but because of the complex flow field only a proportion of the overwintering stock has the capacity to reach the North Sea

International Laboratory Comparison of Influenza Microneutralization Assays for A(H1N1) pdm09, A(H3N2), and A(H5N1) Influenza Viruses by CONSISE

The microneutralization assay is commonly used to detect antibodies to influenza virus, and multiple protocols are used worldwide. These protocols differ in the incubation time of the assay as well as in the order of specific steps, and even within protocols there are often further adjustments in individual laboratories. The impact these protocol variations have on influenza serology data is unclear. Thus, a laboratory comparison of the 2-day enzyme-linked immunosorbent assay (ELISA) and 3-day hemagglutination (HA) microneutralization (MN) protocols, using A(H1N1)pdm09, A(H3N2), and A(H5N1) viruses, was performed by the CONSISE Laboratory Working Group. Individual laboratories performed both assay protocols, on multiple occasions, using different serum panels. Thirteen laboratories from around the world participated. Within each laboratory, serum sample titers for the different assay protocols were compared between assays to determine the sensitivity of each assay and were compared between replicates to assess the reproducibility of each protocol for each laboratory. There was good correlation of the results obtained using the two assay protocols in most laboratories, indicating that these assays may be interchangeable for detecting antibodies to the influenza A viruses included in this study. Importantly, participating laboratories have aligned their methodologies to the CONSISE consensus 2-day ELISA and 3-day HA MN assay protocols to enable better correlation of these assays in the future

The Mass Power Spectrum in Quintessence Cosmological Models

We present simple analytic approximations for the linear and fully evolved nonlinear mass power spectrum for spatially flat cold dark matter (CDM) cosmological models with quintessence (Q). Quintessence is a time evolving, spatially inhomogeneous energy component with negative pressure and an equation of state w_Q < 0. It clusters gravitationally on large length scales but remains smooth like the cosmological constant on small length scales. We show that the clustering scale is determined by the Compton wavelength of the Q-field and derive a shape parameter, \Gamma_Q, to characterize the linear mass power spectrum. The growth of linear perturbations as functions of redshift, w_Q, and matter density \Omega_m is also quantified. Calibrating to N-body simulations, we construct a simple extension of the formula by Ma (1998) that closely approximates the nonlinear power spectrum for a range of plausible QCDM models.Comment: 5 pages with 3 inserted postscript figures, AAS LaTeX v4.0 emulateapj.sty. Astrophysical Journal Letters, in pres

Probabilistic model checking of complex biological pathways

Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicability to a complex biological system: the FGF (Fibroblast Growth Factor) signalling pathway. We give a detailed description of how this case study can be modelled in the probabilistic model checker PRISM, discussing some of the issues that arise in doing so, and show how we can thus examine a rich selection of quantitative properties of this model. We present experimental results for the case study under several different scenarios and provide a detailed analysis, illustrating how this approach can be used to yield a better understanding of the dynamics of the pathway

Visualizing Local Doping Effects of Individual Water Clusters on Gold(111)-Supported Graphene

The local charge carrier density of graphene can exhibit significant and highly localized variations that arise from the interaction between graphene and the local environment, such as adsorbed water, or a supporting substrate. However, it has been difficult to correlate such spatial variations with individual impurity sites. By trapping (under graphene) nanometer-sized water clusters on the atomically well-defined Au(111) substrate, we utilize scanning tunneling microscopy and spectroscopy to characterize the local doping influence of individual water clusters on graphene. We find that water clusters, predominantly nucleated at the atomic steps of Au(111), induce strong and highly localized electron doping in graphene. A positive correlation is observed between the water cluster size and the local doping level, in support of the recently proposed electrostatic-field-mediated doping mechanism. Our findings quantitatively demonstrate the importance of substrate-adsorbed water on the electronic properties of graphene