Extending the support of 11- and 22-level densities for cusp form LL-functions under square-root cancellation hypotheses

The Katz-Sarnak philosophy predicts that the behavior of zeros near the central point in families of $L$-functions agrees with that of eigenvalues near 1 of random matrix ensembles. Under GRH, Iwaniec, Luo and Sarnak showed agreement in the one-level densities for cuspidal newforms with the support of the Fourier transform of the test function in $(-2, 2)$. They increased the support further under a square-root cancellation conjecture, showing that a ${\rm GL}(1)$ estimate led to additional agreement between number theory and random matrix theory. We formulate a two-dimensional analog and show it leads to improvements in the two-level density. Specifically, we show that a square-root cancellation of certain classical exponential sums over primes increases the support of the test functions such that the main terms in the $1$- and $2$-level densities of cuspidal newforms averaged over bounded weight $k$ (and fixed level $1$) converge to their random matrix theory predictions. We also conjecture a broad class of such exponential sums where we expect improvement in the case of arbitrary $n$-level densities, and note that the arguments in [ILS] yield larger support than claimed.Comment: 14 pages, to be submitted to Acta Arithmetic

Windowed and Wavelet Analysis of Marine Stratocumulus Cloud Inhomogeneity

To improve radiative transfer calculations for inhomogeneous clouds, a consistent means of modeling inhomogeneity is needed. One current method of modeling cloud inhomogeneity is through the use of fractal parameters. This method is based on the supposition that cloud inhomogeneity over a large range of scales is related. An analysis technique named wavelet analysis provides a means of studying the multiscale nature of cloud inhomogeneity. In this paper, the authors discuss the analysis and modeling of cloud inhomogeneity through the use of wavelet analysis. Wavelet analysis as well as other windowed analysis techniques are used to study liquid water path (LWP) measurements obtained during the marine stratocumulus phase of the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment. Statistics obtained using analysis windows, which are translated to span the LWP dataset, are used to study the local (small scale) properties of the cloud field as well as their time dependence. The LWP data are transformed onto an orthogonal wavelet basis that represents the data as a number of times series. Each of these time series lies within a frequency band and has a mean frequency that is half the frequency of the previous band. Wavelet analysis combined with translated analysis windows reveals that the local standard deviation of each frequency band is correlated with the local standard deviation of the other frequency bands. The ratio between the standard deviation of adjacent frequency bands is 0.9 and remains constant with respect to time. This ratio defined as the variance coupling parameter is applicable to all of the frequency bands studied and appears to be related to the slope of the data's power spectrum. Similar analyses are performed on two cloud inhomogeneity models, which use fractal-based concepts to introduce inhomogeneity into a uniform cloud field. The bounded cascade model does this by iteratively redistributing LWP at each scale using the value of the local mean. This model is reformulated into a wavelet multiresolution framework, thereby presenting a number of variants of the bounded cascade model. One variant introduced in this paper is the 'variance coupled model,' which redistributes LWP using the local standard deviation and the variance coupling parameter. While the bounded cascade model provides an elegant two- parameter model for generating cloud inhomogeneity, the multiresolution framework provides more flexibility at the expense of model complexity. Comparisons are made with the results from the LWP data analysis to demonstrate both the strengths and weaknesses of these models

Functional heterogeneity of forest landscapes and the distribution and abundance of the red-cockaded woodpecker

Red-cockaded woodpecker (RCW, Picoides borealis) populations are greatly affected by the fragmentation of forest habitat through its effect on the dispersal of individuals between active clusters and other areas of the suitable habitat. In order to assess the suitability of a given landscape structure for the maintenance and expansion of RCW populations, land managers need an index that correlates with the bird's awareness of that structure. Rather than assuming that common landscape metrics provide the necessary information, we applied an index of functional heterogeneity to a GIS coverage for the western portion of the Sam Houston National Forest (SHNF) in east Texas, using two observation scales. In contrast to measured heterogeneity, functional heterogeneity incorporates the RCW response to forest structure. The GIS coverage included information on habitat suitability and RCW cluster distribution and size. The analyses indicated that the presence of cavity trees is the most important factor for RCW population maintenance and that fragmentation of the foraging habitat has much less impact. The analyses also indicated that many areas that are currently of high functional importance for the RCW are effectively isolated from one another. This second result has signi®cant implications for the dispersal of individuals between areas of high functionality and thus also the maintenance of the RCW in this forest. The functional heterogeneity analyses can also be used to examine the trade offs involved in managing the multiple wildlife species simultaneously and for examining the effects of various harvesting regimes through time

Two-Person Cake-Cutting: The Optimal Number of Cuts

A cake is a metaphor for a heterogeneous, divisible good. When two players divide such a good, there is always a perfect division—one that is efficient (Pareto-optimal), envy-free, and equitable—which can be effected with a finite number of cuts under certain mild conditions; this is not always the case when there are more than two players (Brams, Jones, and Klamler, 2011b). We not only establish the existence of such a division but also provide an algorithm for determining where and how many cuts must be made, relating it to an algorithm, “Adjusted Winner” (Brams and Taylor, 1996, 1999), that yields a perfect division of multiple homogenous goods

Levels of growth factors from platelet-rich fibrin from chronic periodontitis versus periodontally healthy subjects: a pilot study

Objectives This study aimed to (1) compare the amounts of growth factors from platelet-rich fibrin (PRF) between chronic periodontitis and periodontally healthy subjects and (2) evaluate the relationships between the amounts of growth factors from PRF with complete blood counts (white blood cell (WBC) and platelet counts) and the serum concentrations of IL-1β, IL-6, and tumor necrosis factor-α (TNF-α). Materials and methods Venous blood was collected from chronic periodontitis (test) and periodontally healthy subjects (control). PRF and serum were collected from the centrifuged blood. Liquid exudates from the compression of PRF were collected. The compressed PRF membranes were incubated in saline, and eluted aliquots were collected at 1, 24, and 72 h, and the membranes were then digested with trypsin. Epidermal growth factor, insulin-like growth factor-1, platelet-derived growth factor-BB, transforming growth factor-β1, and vascular endothelial growth factor in the exudates and eluents were quantified by ELISA. Serum was used for IL-1β, IL-6, and TNF-α quantifications. Complete blood counts were measured. Results There were no significant differences in the amounts of growth factors from PRF exudates and membranes measured between groups (all p > 0.05). The test group had significantly higher WBC (p  0.05). Conclusions PRF can be utilized as an autologous source of growth factors not affected by periodontal condition and WBC level

Cone Photoreceptor Recovery after Experimental Detachment and Reattachment: An Immunocytochemical, Morphological, and Electrophysiological Study

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