Spectral arbitrariness for trees fails spectacularly

If $G$ is a graph and $\mathbf{m}$ is an ordered multiplicity list which is realizable by at least one symmetric matrix with graph $G$, what can we say about the eigenvalues of all such realizing matrices for $\mathbf{m}$? It has sometimes been tempting to expect, especially in the case that $G$ is a tree, that any spacing of the multiple eigenvalues should be realizable. In 2004, however, F. Barioli and S. Fallat produced the first counterexample: a tree on 16 vertices and an ordered multiplicity list for which every realizing set of eigenvalues obeys a nontrivial linear constraint. We extend this by giving an infinite family of trees and ordered multiplicity lists whose sets of realizing eigenvalues are very highly constrained, with at most 5 degrees of freedom, regardless of the size of the tree in this family. In particular, we give the first examples of multiplicity lists for a tree which impose nontrivial nonlinear eigenvalue constraints and produce an ordered multiplicity list which is achieved by a unique set of eigenvalues, up to shifting and scaling.Comment: 45 page

The Baryon Oscillation Spectroscopic Survey of SDSS-III

The Baryon Oscillation Spectroscopic Survey (BOSS) is designed to measure the scale of baryon acoustic oscillations (BAO) in the clustering of matter over a larger volume than the combined efforts of all previous spectroscopic surveys of large scale structure. BOSS uses 1.5 million luminous galaxies as faint as i=19.9 over 10,000 square degrees to measure BAO to redshifts z<0.7. Observations of neutral hydrogen in the Lyman alpha forest in more than 150,000 quasar spectra (g<22) will constrain BAO over the redshift range 2.15<z<3.5. Early results from BOSS include the first detection of the large-scale three-dimensional clustering of the Lyman alpha forest and a strong detection from the Data Release 9 data set of the BAO in the clustering of massive galaxies at an effective redshift z = 0.57. We project that BOSS will yield measurements of the angular diameter distance D_A to an accuracy of 1.0% at redshifts z=0.3 and z=0.57 and measurements of H(z) to 1.8% and 1.7% at the same redshifts. Forecasts for Lyman alpha forest constraints predict a measurement of an overall dilation factor that scales the highly degenerate D_A(z) and H^{-1}(z) parameters to an accuracy of 1.9% at z~2.5 when the survey is complete. Here, we provide an overview of the selection of spectroscopic targets, planning of observations, and analysis of data and data quality of BOSS.Comment: 49 pages, 16 figures, accepted by A

The Eighth Data Release of the Sloan Digital Sky Survey: First Data from SDSS-III

The Sloan Digital Sky Survey (SDSS) started a new phase in August 2008, with new instrumentation and new surveys focused on Galactic structure and chemical evolution, measurements of the baryon oscillation feature in the clustering of galaxies and the quasar Ly alpha forest, and a radial velocity search for planets around ~8000 stars. This paper describes the first data release of SDSS-III (and the eighth counting from the beginning of the SDSS). The release includes five-band imaging of roughly 5200 deg^2 in the Southern Galactic Cap, bringing the total footprint of the SDSS imaging to 14,555 deg^2, or over a third of the Celestial Sphere. All the imaging data have been reprocessed with an improved sky-subtraction algorithm and a final, self-consistent photometric recalibration and flat-field determination. This release also includes all data from the second phase of the Sloan Extension for Galactic Understanding and Evolution (SEGUE-2), consisting of spectroscopy of approximately 118,000 stars at both high and low Galactic latitudes. All the more than half a million stellar spectra obtained with the SDSS spectrograph have been reprocessed through an improved stellar parameters pipeline, which has better determination of metallicity for high metallicity stars.Comment: Astrophysical Journal Supplements, in press (minor updates from submitted version

Authoritarian Neoliberalism and Democratic Backsliding in Turkey: Beyond the Narratives of Progress

Unpacking the core themes that are discussed in this collection, this article both offers a research agenda to re-analyse Turkey’s ‘authoritarian turn’ and mounts a methodological challenge to the conceptual frameworks that reinforce a strict analytical separation between the ‘economic’ and the ‘political’ factors. The paper problematises the temporal break in scholarly analyses of the AKP period and rejects the argument that the party’s methods of governance have shifted from an earlier ‘democratic’ model – defined by ‘hegemony’ – to an emergent ‘authoritarian’ one. In contrast, by retracing the mechanisms of the state-led reproduction of neoliberalism since 2003, the paper demonstrates that the party’s earlier ‘hegemonic’ activities were also shaped by authoritarian tendencies which manifested at various levels of governance

Rising Population Cost for Treating People Living with HIV in the UK, 1997-2013

Background The number of people living with HIV (PLHIV) is increasing in the UK. This study estimated the annual population cost of providing HIV services in the UK, 1997–2006 and projected them 2007–2013. Methods Annual cost of HIV treatment for PLHIV by stage of HIV infection and type of ART was calculated (UK pounds, 2006 prices). Population costs were derived by multiplying the number of PLHIV by their annual cost for 1997–2006 and projected 2007–2013. Results Average annual treatment costs across all stages of HIV infection ranged from £17,034 in 1997 to £18,087 in 2006 for PLHIV on mono-therapy and from £27,649 in 1997 to £32,322 in 2006 for those on quadruple-or-more ART. The number of PLHIV using NHS services rose from 16,075 to 52,083 in 2006 and was projected to increase to 78,370 by 2013. Annual population cost rose from £104 million in 1997 to £483 million in 2006, with a projected annual cost between £721 and £758 million by 2013. When including community care costs, costs increased from £164 million in 1997, to £683 million in 2006 and between £1,019 and £1,065 million in 2013. Conclusions Increased number of PLHIV using NHS services resulted in rising UK population costs. Population costs are expected to continue to increase, partly due to PLHIV's longer survival on ART and the relative lack of success of HIV preventing programs. Where possible, the cost of HIV treatment and care needs to be reduced without reducing the quality of services, and prevention programs need to become more effective. While high income countries are struggling to meet these increasing costs, middle- and lower-income countries with larger epidemics are likely to find it even more difficult to meet these increasing demands, given that they have fewer resources

Antibody correlates of protection from SARS-CoV-2 reinfection prior to vaccination : a nested case-control within the SIREN study

Funding: This study was supported by the U.K. Health Security Agency, the U.K. Department of Health and Social Care (with contributions from the governments in Northern Ireland, Wales, and Scotland), the National Institute for Health Research, and grant from the UK Medical Research Council (grant number MR/W02067X/1). This work was supported by the Francis Crick Institute which receives its core funding from Cancer Research UK (CC2087, CC1283), the UK Medical Research Council (CC2087, CC1283), and the Wellcome Trust (CC2087, CC1283).Objectives To investigate serological differences between SARS-CoV-2 reinfection cases and contemporary controls, to identify antibody correlates of protection against reinfection. Methods We performed a case-control study, comparing reinfection cases with singly infected individuals pre-vaccination, matched by gender, age, region and timing of first infection. Serum samples were tested for anti-SARS-CoV-2 spike (anti-S), anti-SARS-CoV-2 nucleocapsid (anti-N), live virus microneutralisation (LV-N) and pseudovirus microneutralisation (PV-N). Results were analysed using fixed effect linear regression and fitted into conditional logistic regression models. Results We identified 23 cases and 92 controls. First infections occurred before November 2020; reinfections occurred before February 2021, pre-vaccination. Anti-S levels, LV-N and PV-N titres were significantly lower among cases; no difference was found for anti-N levels. Increasing anti-S levels were associated with reduced risk of reinfection (OR 0·63, CI 0·47-0·85), but no association for anti-N levels (OR 0·88, CI 0·73-1·05). Titres >40 were correlated with protection against reinfection for LV-N Wuhan (OR 0·02, CI 0·001–0·31) and LV-N Alpha (OR 0·07, CI 0·009–0·62). For PV-N, titres >100 were associated with protection against Wuhan (OR 0·14, CI 0·03–0·64) and Alpha (0·06, CI 0·008–0·40). Conclusions Before vaccination, protection against SARS-CoV-2 reinfection was directly correlated with anti-S levels, PV-N and LV-N titres, but not with anti-N levels. Detectable LV-N titres were sufficient for protection, whilst PV-N titres >100 were required for a protective effect. Trial registration number ISRCTN11041050Publisher PDFPeer reviewe

Invasion and Persistence of Infectious Agents in Fragmented Host Populations

One of the important questions in understanding infectious diseases and their prevention and control is how infectious agents can invade and become endemic in a host population. A ubiquitous feature of natural populations is that they are spatially fragmented, resulting in relatively homogeneous local populations inhabiting patches connected by the migration of hosts. Such fragmented population structures are studied extensively with metapopulation models. Being able to define and calculate an indicator for the success of invasion and persistence of an infectious agent is essential for obtaining general qualitative insights into infection dynamics, for the comparison of prevention and control scenarios, and for quantitative insights into specific systems. For homogeneous populations, the basic reproduction ratio plays this role. For metapopulations, defining such an ‘invasion indicator’ is not straightforward. Some indicators have been defined for specific situations, e.g., the household reproduction number . However, these existing indicators often fail to account for host demography and especially host migration. Here we show how to calculate a more broadly applicable indicator for the invasion and persistence of infectious agents in a host metapopulation of equally connected patches, for a wide range of possible epidemiological models. A strong feature of our method is that it explicitly accounts for host demography and host migration. Using a simple compartmental system as an example, we illustrate how can be calculated and expressed in terms of the key determinants of epidemiological dynamics

The Centrality of Mathematics in the History of Western Thought

This article explores the interplay of mathematics and philosophy in Western thought as well as applications to other fields