Lower Bound for Convex Hull Area and Universal Cover Problems

In this paper, we provide a lower bound for an area of the convex hull of points and a rectangle in a plane. We then apply this estimate to establish a lower bound for a universal cover problem. We showed that a convex universal cover for a unit length curve has area at least 0.232239. In addition, we show that a convex universal cover for a unit closed curve has area at least 0.0879873.Comment: 12 pages, 9 figure

Heterocyst placement strategies to maximize growth of cyanobacterial filaments

Under conditions of limited fixed-nitrogen, some filamentous cyanobacteria develop a regular pattern of heterocyst cells that fix nitrogen for the remaining vegetative cells. We examine three different heterocyst placement strategies by quantitatively modelling filament growth while varying both external fixed-nitrogen and leakage from the filament. We find that there is an optimum heterocyst frequency which maximizes the growth rate of the filament; the optimum frequency decreases as the external fixed-nitrogen concentration increases but increases as the leakage increases. In the presence of leakage, filaments implementing a local heterocyst placement strategy grow significantly faster than filaments implementing random heterocyst placement strategies. With no extracellular fixed-nitrogen, consistent with recent experimental studies of Anabaena sp. PCC 7120, the modelled heterocyst spacing distribution using our local heterocyst placement strategy is qualitatively similar to experimentally observed patterns. As external fixed-nitrogen is increased, the spacing distribution for our local placement strategy retains the same shape while the average spacing between heterocysts continuously increases.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Physical Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version will be available onlin

Evaluation of the synoptic and mesoscale predictive capabilities of a mesoscale atmospheric simulation system

The overall performance characteristics of a limited area, hydrostatic, fine (52 km) mesh, primitive equation, numerical weather prediction model are determined in anticipation of satellite data assimilations with the model. The synoptic and mesoscale predictive capabilities of version 2.0 of this model, the Mesoscale Atmospheric Simulation System (MASS 2.0), were evaluated. The two part study is based on a sample of approximately thirty 12h and 24h forecasts of atmospheric flow patterns during spring and early summer. The synoptic scale evaluation results benchmark the performance of MASS 2.0 against that of an operational, synoptic scale weather prediction model, the Limited area Fine Mesh (LFM). The large sample allows for the calculation of statistically significant measures of forecast accuracy and the determination of systematic model errors. The synoptic scale benchmark is required before unsmoothed mesoscale forecast fields can be seriously considered

FORECASTING TECHNIQUE An Operational Ingredients-Based Methodology for Forecasting Midlatitude Winter Season Precipitation

ABSTRACT An ingredients-based methodology (IM) for the operational analysis and prediction of midlatitude winter season precipitation is developed. Diagnostics for five fundamental physical ingredients involved in the production of precipitation-forcing for ascent, moisture, instability, precipitation efficiency, and temperature-are incorporated into the IM. The forcing ingredient is combined with the instability ingredient to form a new parameter, PVQ, that serves as an indicator of heavy precipitation potential by identifying regions where these two ingredients coexist. The diagnostics and PVQ are incorporated into ingredients maps that facilitate a systematic approach to forecasting the duration, intensity, and type of winter precipitation

Measurement invariance of three narcissism questionnaires across the United States, the United Kingdom, and Germany

With a recent surge of research on narcissism, narcissism questionnaires are increasingly being translated and applied in various countries. The measurement invariance of an instrument across countries is a precondition for being able to compare scores across countries. We investigated the cross-cultural measurement invariance of three narcissism questionnaires (Brief Pathological Narcissism Inventory [B-PNI], Narcissistic Personality Inventory [NPI], and Narcissistic Admiration and Rivalry Questionnaire [NARQ]) and mean-level differences across samples from the United States (N = 2,464), the United Kingdom (N = 307), and Germany (N = 925). Overall, the B-PNI and NARQ functioned equivalently for the U.S. and U.K. participants. More violations of measurement invariance were found between Germany and the combined U.S. and U.K. samples, and for the NPI. In the B-PNI and NARQ, Americans scored higher than individuals from the United Kingdom regarding agentic aspects (self-sacrificing self-enhancement, admiration), while Germans scored lower than both Americans and U.K. individuals regarding antagonistic (entitlement rage, rivalry) and neurotic (hiding the self, contingent self-esteem) aspects. More inconsistent results were found for NPI facets. When noninvariance was present, observed means yielded biased results. Thus, the degree of measurement invariance across translated instrument versions should be considered in cross-cultural comparisons, even with culturally similar countries

A New Look at the Axial Anomaly in Lattice QED with Wilson Fermions

By carrying out a systematic expansion of Feynman integrals in the lattice spacing, we show that the axial anomaly in the U(1) lattice gauge theory with Wilson fermions, as determined in one-loop order from an irrelevant lattice operator in the Ward identity, must necessarily be identical to that computed from the dimensionally regulated continuum Feynman integrals for the triangle diagrams.Comment: 1 figure, LaTeX, 18 page

Nitrogen and phosphorus loads to temperate seepage lakes associated with allochthonous dissolved organic carbon loads

Terrestrial loads of dissolved organic matter (DOM) have increased in recent years in many north temperate lakes. While much of the focus on the “browning” phenomena has been on its consequences for carbon cycling, much less is known about how it influences nutrient loading to lakes. We characterize potential loads of nitrogen and phosphorus to seepage lakes in northern Wisconsin, USA, based on a laboratory soil leaching experiment and a model that includes landscape cover and watershed area. In these seepage lakes, nutrient concentrations are positively correlated with dissolved organic carbon concentrations (nitrogen: r = 0.68, phosphorus: r = 0.54). Using long‐term records of browning, we found that dissolved organic matter‐associated nutrient loadings may have resulted in substantial increases in nitrogen and phosphorus in seepage lakes and could account for currently observed nutrient concentrations in the lake. “Silent” nutrient loadings to brown‐water lakes may lead to future water‐quality concerns. PLAIN LANGUAGE SUMMARY: The color of many temperate lakes is changing; some lakes are becoming more darkly stained brown. The tea‐colored stain is due to dissolved organic matter from the surrounding landscape. Much of the research related to the causes and consequences of increased staining, or “brownification,” relate to its connection to the carbon cycle. However, by examining long‐term lake chemical records, analyzing the properties of the organic compounds, and modeling potential flows of the compounds, we find that carbon is not the only element that is influenced by browning. Nitrogen and phosphorus, two nutrients important to growth of organisms at the base of the food web, may also be increasing in lakes due to brownification."Funding for this research was supported by the Northern Research Station and the Chequamegon-Nicolet National Forest (CNNF) of the United States Department of Agriculture (USDA) Forest Service and a National Science Foundation (NSF) grant to the University of Wisconsin-Madison to support the North Temperate Lakes Long-Term Ecological Research (NTLLTER) Site (DEB-#1440297)."https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018GL07721