ELA A NOTE ON THE CONVEXITY OF THE REALIZABLE SET OF EIGENVALUES FOR NONNEGATIVE SYMMETRIC MATRICES ∗

Abstract. Geometric properties of the set Rn of n–tuples of realizable spectra of nonnegative symmetric matrices, and the Soules set Sn introduced by McDonald and Neumann, are examined. It is established that S5 is properly contained in R5. Twointerestingexamplesarepresentedwhich show that neither Rn nor Sn need be convex. It is proved that Rn and Sn are star convex and centered at (1, 1,...,1). Key words. Symmetric matrices, inverse eigenvalue problem, realizable set, Soules set. AMS subject classifications. 15A18,15A29,15A57 1. Introduction, Definition

The lost sunspot cycle: New support from Be10 measurements

It has been suggested that the deficit in the number of spots on the surface of the Sun between 1790 and 1830, known as the Dalton minimum, contained an extra cycle that was not identified in the original sunspot record by Wolf. Though this cycle would be shorter and weaker than the average solar cycle, it would shift the magnetic parity of the solar magnetic field of the earlier cycles. This extra cycle is sometimes referred to as the 'lost solar cycle' or 'cycle 4b'. Here we reanalyse Be10 measurements with annual resolution from the NGRIP ice core in Greenland in order to investigate if the hypothesis regarding a lost sunspot cycle is supported by these measurements. Specifically, we make use of the fact that the Galactic cosmic rays, responsible for forming Be10 in the Earth's atmosphere, are affected differently by the open solar magnetic field during even and odd solar cycles. This fact enables us to evaluate if the numbering of cycles earlier than cycle 5 is correct. For the evaluation, we use Bayesian analysis, which reveals that the lost sunspot cycle hypothesis is likely to be correct. We also discuss if this cycle 4b is a real cycle, or a phase catastrophe, and what implications this has for our understanding of stellar activity cycles in general.Comment: accepted for publication in A&

Energy efficient engine: Low-pressure turbine subsonic cascade component development and integration program

A subsonic cascade test program was conducted to provide technical data for optimizing the blade and vane airfoil designs for the Energy Efficient Engine Low-Pressure Turbine component. The program consisted of three parts. The first involved an evaluation of the low-chamber inlet guide vane. The second, was an evaluation of two candidate aerodynamic loading philosophies for the fourth blade root section. The third part consisted of an evaluation of three candidate airfoil geometries for the fourth blade mean section. The performance of each candidate airfoil was evaluated in a linear cascade configuration. The overall results of this study indicate that the aft-loaded airfoil designs resulted in lower losses which substantiated Pratt & Whitney Aircraft's design philosophy for the Energy Efficient Engine low-pressure turbine component

Policy instruments in the Common Agricultural Policy

Policy changes in the Common Agricultural Policy (CAP) can be explained in terms of the exhaustion and long-term contradictions of policy instruments. Changes in policy instruments have reoriented the policy without any change in formal Treaty goals. The social and economic efficacy of instruments in terms of evidence-based policy analysis was a key factor in whether they were delegitimized. The original policy instruments were generally dysfunctional, but reframing the policy in terms of a multifunctionality paradigm permitted the development of more efficacious instruments. A dynamic interaction takes place between the instruments and policy informed by the predominant discourses

The Total Filmmaker: thinking of screenwriting, directing and editing as one role

As screenwriting continues to establish itself as a discrete discipline in academia, either in alignment with creative writing departments or film and media practice departments, there is a danger that such developments may entrench a distancing of the craft from the cinematic form itself and that such a distancing may ultimately reinforce the screenplay's propensity for dramaturgy and the dramatic, rather than the sensory and experiential of the cinematic. Closely related creative stages in telling cinematic stories include directing and editing and this article seeks to argue, with reference to personal screen practice, that screenwriting, directing and editing are, in fact, three variations of the same thing. The article proposes the notion of the Total Filmmaker who embraces all three aspects of the cinematic storyteller. If the ultimate aim is to create a narrative that fully utilises the unique properties of the cinematic form in telling a story, rather than being dominated by the theatricality of dramatically driven classical narratives. How might one explore the relationship between screenwriting, directing and editing? Can an integrated approach to creating the cinematic blueprint change the way we think of pedagogy and screenwriting

Constructive Relationships Between Algebraic Thickness and Normality

We study the relationship between two measures of Boolean functions; \emph{algebraic thickness} and \emph{normality}. For a function $f$, the algebraic thickness is a variant of the \emph{sparsity}, the number of nonzero coefficients in the unique GF(2) polynomial representing $f$, and the normality is the largest dimension of an affine subspace on which $f$ is constant. We show that for $0 < \epsilon<2$, any function with algebraic thickness $n^{3-\epsilon}$ is constant on some affine subspace of dimension $\Omega\left(n^{\frac{\epsilon}{2}}\right)$. Furthermore, we give an algorithm for finding such a subspace. We show that this is at most a factor of $\Theta(\sqrt{n})$ from the best guaranteed, and when restricted to the technique used, is at most a factor of $\Theta(\sqrt{\log n})$ from the best guaranteed. We also show that a concrete function, majority, has algebraic thickness $\Omega\left(2^{n^{1/6}}\right)$.Comment: Final version published in FCT'201

A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D

A direct reconstruction algorithm for complex conductivities in $W^{2,\infty}(\Omega)$, where $\Omega$ is a bounded, simply connected Lipschitz domain in $\mathbb{R}^2$, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.Comment: This is an author-created, un-copyedited version of an article accepted for publication in [insert name of journal]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0266-5611/28/9/09500

Multi-decadal marine- and land-terminating glacier recession in the Ammassalik region, southeast Greenland

Landsat imagery was applied to elucidate glacier fluctuations of land- and marine-terminating outlet glaciers from the Greenland Ice Sheet (GrIS) and local land-terminating glaciers and ice caps (GIC) peripheral to the GrIS in the Ammassalik region, Southeast Greenland, during the period 1972–2011. Data from 21 marine-terminating glaciers (including the glaciers Helheim, Midgaard, and Fenris), the GrIS land-terminating margin, and 35 GIC were examined and compared to observed atmospheric air temperatures, precipitation, and reconstructed ocean water temperatures (at 400 m depth in the Irminger Sea). Here, we document that net glacier recession has occurred since 1972 in the Ammassalik region for all glacier types and sizes, except for three GIC. The land-terminating GrIS and GIC reflect lower marginal and areal changes than the marine-terminating outlet glaciers. The mean annual land-terminating GrIS and GIC margin recessions were about three to five times lower than the GrIS marine-terminating recession. The marine-terminating outlet glaciers had an average net frontal retreat for 1999–2011 of 0.098 km yr&lt;sup&gt;−1&lt;/sup&gt;, which was significantly higher than in previous sub-periods 1972–1986 and 1986–1999. For the marine-terminating GrIS, the annual areal recession rate has been decreasing since 1972, while increasing for the land-terminating GrIS since 1986. On average for all the observed GIC, a mean net frontal retreat for 1986–2011 of 0.010 ± 0.006 km yr&lt;sup&gt;−1&lt;/sup&gt; and a mean areal recession of around 1% per year occurred; overall for all observed GIC, a mean recession rate of 27 ± 24% occurred based on the 1986 GIC area. Since 1986, five GIC melted away in the Ammassalik area

Response and Resistance to Paradox-Breaking BRAF Inhibitor in Melanomas

FDA-approved BRAF inhibitors produce high response rates and improve overall survival in patients with BRAF V600E/K-mutant melanoma, but are linked to pathologies associated with paradoxical ERK1/2 activation in wild-type BRAF cells. To overcome this limitation, a next-generation paradox-breaking RAF inhibitor (PLX8394) has been designed. Here, we show that by using a quantitative reporter assay, PLX8394 rapidly suppressed ERK1/2 reporter activity and growth of mutant BRAF melanoma xenografts. Ex vivo treatment of xenografts and use of a patient-derived explant system (PDeX) revealed that PLX8394 suppressed ERK1/2 signaling and elicited apoptosis more effectively than the FDA-approved BRAF inhibitor, vemurafenib. Furthermore, PLX8394 was efficacious against vemurafenibresistant BRAF splice variant-expressing tumors and reduced splice variant homodimerization. Importantly, PLX8394 did not induce paradoxical activation of ERK1/2 in wild-type BRAF cell lines or PDeX. Continued in vivo dosing of xenografts with PLX8394 led to the development of acquired resistance via ERK1/2 reactivation through heterogeneous mechanisms; however, resistant cells were found to have differential sensitivity to ERK1/2 inhibitor. These findings highlight the efficacy of a paradox-breaking selective BRAF inhibitor and the use of PDeX system to test the efficacy of therapeutic agents. © 2017 American Association for Cancer Research