An explicit height bound for the classical modular polynomial

For a prime m, let Phi_m be the classical modular polynomial, and let h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values is provided for m <= 3607.Comment: Minor correction to the constants in Theorem 1 and Corollary 9. To appear in the Ramanujan Journal. 17 pages

Magnetic Moment of The Θ+\Theta^+ Pentaquark State

We have calculated the magnetic moment of the recently observed $\Theta^+$ pentaquark in the framework of the light cone QCD sum rules using the photon distribution amplitudes. We find that $\mu_{\Theta^+}=(0.12\pm 0.06) \mu_N$, which is quite small. We also compare our result with predictions of other groups.Comment: 1 eps figure, 13 page

An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions

This paper sketches a technique for improving the rate of convergence of a general oscillatory sequence, and then applies this series acceleration algorithm to the polylogarithm and the Hurwitz zeta function. As such, it may be taken as an extension of the techniques given by Borwein's "An efficient algorithm for computing the Riemann zeta function", to more general series. The algorithm provides a rapid means of evaluating Li_s(z) for general values of complex s and the region of complex z values given by |z^2/(z-1)|<4. Alternatively, the Hurwitz zeta can be very rapidly evaluated by means of an Euler-Maclaurin series. The polylogarithm and the Hurwitz zeta are related, in that two evaluations of the one can be used to obtain a value of the other; thus, either algorithm can be used to evaluate either function. The Euler-Maclaurin series is a clear performance winner for the Hurwitz zeta, while the Borwein algorithm is superior for evaluating the polylogarithm in the kidney-shaped region. Both algorithms are superior to the simple Taylor's series or direct summation. The primary, concrete result of this paper is an algorithm allows the exploration of the Hurwitz zeta in the critical strip, where fast algorithms are otherwise unavailable. A discussion of the monodromy group of the polylogarithm is included.Comment: 37 pages, 6 graphs, 14 full-color phase plots. v3: Added discussion of a fast Hurwitz algorithm; expanded development of the monodromy v4:Correction and clarifiction of monodrom

Addressing environmental justice under the National Environment Policy Act at Sandia National Laboratories/New Mexico

Under Executive Order 12898, Federal Actions to Address Environmental Justice in Minority Populations and Low-Income Populations, the Department of Energy (DOE) and Sandia National Laboratories New Mexico (SNL) are required to identify and address, as appropriate, disproportionately high, adverse human health or environmental effects of their activities on minority and low-income populations. The National Environmental Policy Act (NEPA) also requires that environmental justice issues be identified and addressed. This presents a challenge for SNL because it is located in a culturally diverse area. Successfully addressing potential impacts is contingent upon accurately identifying them through objective analysis of demographic information. However, an effective public participation process, which is necessarily subjective, is also needed to understand the subtle nuances of diverse populations that can contribute to a potential impact, yet are not always accounted for in a strict demographic profile. Typically, there is little or no coordination between these two disparate processes. This report proposes a five-step method for reconciling these processes and uses a hypothetical case study to illustrate the method. A demographic analysis and community profile of the population within 50 miles of SNL were developed to support the environmental justice analysis process and enhance SNL`s NEPA and public involvement programs. This report focuses on developing a methodology for identifying potentially impacted populations. Environmental justice issues related to worker exposures associated with SNL activities will be addressed in a separate report

A second row Parking Paradox

We consider two variations of the discrete car parking problem where at every vertex of the integers a car arrives with rate one, now allowing for parking in two lines. a) The car parks in the first line whenever the vertex and all of its nearest neighbors are not occupied yet. It can reach the first line if it is not obstructed by cars already parked in the second line (screening). b) The car parks according to the same rules, but parking in the first line can not be obstructed by parked cars in the second line (no screening). In both models, a car that can not park in the first line will attempt to park in the second line. If it is obstructed in the second line as well, the attempt is discarded. We show that both models are solvable in terms of finite-dimensional ODEs. We compare numerically the limits of first and second line densities, with time going to infinity. While it is not surprising that model a) exhibits an increase of the density in the second line from the first line, more remarkably this is also true for model b), albeit in a less pronounced way.Comment: 11 pages, 4 figure

Sums of products of Ramanujan sums

The Ramanujan sum $c_n(k)$ is defined as the sum of $k$-th powers of the primitive $n$-th roots of unity. We investigate arithmetic functions of $r$ variables defined as certain sums of the products $c_{m_1}(g_1(k))...c_{m_r}(g_r(k))$, where $g_1,..., g_r$ are polynomials with integer coefficients. A modified orthogonality relation of the Ramanujan sums is also derived.Comment: 13 pages, revise

Physician's attitudes towards diagnosing and treating glucocorticoid induced hyperglycaemia: Sliding scale regimen is still widely used despite guidelines

AbstractAimsTreatment with glucocorticoids for neoplasms and inflammatory disorders is frequently complicated by glucocorticoid induced hyperglycaemia (GCIH). GCIH is associated with adverse outcomes and its treatment has short term and long term benefits. Currently, treatment targets and modalities depend on local protocols and habits of individual clinicians. We explored current practice of screening and treatment of GCIH in patients receiving glucocorticoid pulse therapy.MethodsA factorial survey with written case vignettes. All vignette patients received glucocorticoid pulse therapy. Other characteristics (e.g., indication for glucocorticoid therapy, pre-existent diabetes) varied. The survey was held between November 2013 and May 2014 on 2 nationwide conferences and in hospitals across The Netherlands. Pulmonologists and internists expressed their level of agreement with statements on ordering capillary glucose testing and treatment initiation.ResultsRespondents ordered screening for GCIH in 85% of vignette patients and initiated treatment in 56%. When initiating treatment, respondents opt for sliding scale insulin in 62% of patients. Sliding scale insulin was more frequently prescribed in patients with pre-existent insulin dependent diabetes (OR 2.4, CI 1.3–4.2) and by residents (vs. specialists, OR 2.1, CI 1.2–3.5). Sixty-nine percent of clinicians experienced a lack of guidelines for GCIH.ConclusionsClinicians have a strong tendency to screen for GCIH but subsequent initiation of treatment was low. Sliding scale insulin is still widely used in episodic GCIH despite evidence against its effectiveness. This may be due to lacking evidence on feasible treatment options for GCIH

Arithmetical properties of Multiple Ramanujan sums

In the present paper, we introduce a multiple Ramanujan sum for arithmetic functions, which gives a multivariable extension of the generalized Ramanujan sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental arithmetic properties of the multiple Ramanujan sum and study several types of Dirichlet series involving the multiple Ramanujan sum. As an application, we evaluate higher-dimensional determinants of higher-dimensional matrices, the entries of which are given by values of the multiple Ramanujan sum.Comment: 19 page

Preceding rule induction with instance reduction methods

A new prepruning technique for rule induction is presented which applies instance reduction before rule induction. An empirical evaluation records the predictive accuracy and size of rule-sets generated from 24 datasets from the UCI Machine Learning Repository. Three instance reduction algorithms (Edited Nearest Neighbour, AllKnn and DROP5) are compared. Each one is used to reduce the size of the training set, prior to inducing a set of rules using Clark and Boswell's modification of CN2. A hybrid instance reduction algorithm (comprised of AllKnn and DROP5) is also tested. For most of the datasets, pruning the training set using ENN, AllKnn or the hybrid significantly reduces the number of rules generated by CN2, without adversely affecting the predictive performance. The hybrid achieves the highest average predictive accuracy

Tailoring WRF and Noah-MP to Improve Process Representation of Sierra Nevada Runoff: Diagnostic Evaluation and Applications

Watersheds at the western margin of the Sierra Nevada mountains in California are regulated by large dams providing crucial water supply, flood control, and electricity generation. Runoff in these basins is snowmelt dominated and therefore vulnerable to alteration due to climate change. Regional climate models coupled to land surface models can be used to study the hydrologic impacts of climate change, but there is little evidence that they accurately simulate watershed-scale runoff in complex terrain. This study evaluates capabilities of the Weather Research and Forecasting (WRF) regional climate model, coupled to the Noah-multiparameterization (MP) land surface model, to simulate runoff into nine Sierra Nevada reservoirs over the period 2007–2017. Default parameterizations lead to substantial inaccuracy in results, including median bias of 61%. Errors can be traced to process representations; specifically, we modify the representation of snowflake formation in the Thompson microphysics scheme and subsurface runoff generation in the Noah-MP land surface model, including a correction representing effects of groundwater storage. The resulting parameterization improves Nash-Sutcliffe efficiency to above 0.7 across all basins and reduces median bias to 21%. To assess capabilities of the modified WRF/Noah-MP system in supporting analysis of human-altered hydrology, we use its streamflow projections to force a reservoir operations model, results of which maintain high accuracy in predicting reservoir storage and releases (mean Nash-Sutcliffe efficiency > 0.41). This diagnostic analysis indicates that coupled climate and land surface models can be used to study climate change effects on reservoir systems in mountain regions via dynamical downscaling, when adequate physical parameterizations are used