Rigidity and volume preserving deformation on degenerate simplices

Given a degenerate $(n+1)$-simplex in a $d$-dimensional space $M^d$ (Euclidean, spherical or hyperbolic space, and $d\geq n$), for each $k$, $1\leq k\leq n$, Radon's theorem induces a partition of the set of $k$-faces into two subsets. We prove that if the vertices of the simplex vary smoothly in $M^d$ for $d=n$, and the volumes of $k$-faces in one subset are constrained only to decrease while in the other subset only to increase, then any sufficiently small motion must preserve the volumes of all $k$-faces; and this property still holds in $M^d$ for $d\geq n+1$ if an invariant $c_{k-1}(\alpha^{k-1})$ of the degenerate simplex has the desired sign. This answers a question posed by the author, and the proof relies on an invariant $c_k(\omega)$ we discovered for any $k$-stress $\omega$ on a cell complex in $M^d$. We introduce a characteristic polynomial of the degenerate simplex by defining $f(x)=\sum_{i=0}^{n+1}(-1)^{i}c_i(\alpha^i)x^{n+1-i}$, and prove that the roots of $f(x)$ are real for the Euclidean case. Some evidence suggests the same conjecture for the hyperbolic case.Comment: 27 pages, 2 figures. To appear in Discrete & Computational Geometr

Characterizing the universal rigidity of generic frameworks

A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally rigid framework has a positive semi-definite stress matrix of maximal rank. Connelly showed that the existence of such a positive semi-definite stress matrix is sufficient for universal rigidity, so this provides a characterization of universal rigidity for generic frameworks. We also extend our argument to give a new result on the genericity of strict complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio

Linking routinely collected social work, education and health data to enable monitoring of the health and health care of school-aged children in state care (‘looked after children’) in Scotland: a national demonstration project

Background and objectives: Children in state care (‘looked after children’) have poorer health than children who are not looked after. Recent developments in Scotland and elsewhere have aimed to improve services and outcomes for looked after children. Routine monitoring of the health outcomes of looked after children compared to those of their non-looked after peers is currently lacking. Developing capacity for comparative monitoring of population based outcomes based on linkage of routinely collected administrative data has been identified as a priority. To our knowledge there are no existing population based data linkage studies providing data on the health of looked after and non-looked after children at national level. Smaller scale studies that are available generally provide very limited information on linkage methods and hence do not allow scrutiny of bias that may be introduced through the linkage process. Study design and methods: National demonstration project testing the feasibility of linking routinely collected looked after children, education, and health data. Participants: All children in publicly funded school in Scotland in 2011/12. Results: Linkage between looked after children data and the national pupil census classified 10,009 (1.5%) and 1,757 (0.3%) of 670,952 children as, respectively, currently and previously looked after. Recording of the unique pupil identifier (Scottish Candidate Number, SCN) on looked after children returns is incomplete, with 66% of looked after records for 2011/12 for children of possible school age containing a valid SCN. This will have resulted in some under-ascertainment of currently and, particularly, previously looked after children within the general pupil population. Further linkage of the pupil census to the NHS Scotland master patient index demonstrated that a safe link to the child’s unique health service (Community Health Index, CHI) number could be obtained for a very high proportion of children in each group (94%, 95%, and 95% of children classified as currently, previously, and non-looked after respectively). In general linkage rates were higher for older children and those living in more affluent areas. Within the looked after group, linkage rates were highest for children with the fewest placements and for those in permanent fostering. Conclusions: This novel data linkage demonstrates the feasibility of monitoring population based health outcomes of school aged looked after and non-looked after children using linked routine administrative data. Improved recording of the unique pupil identifier number on looked after data returns would be beneficial. Extending the range of personal identifiers on looked after children returns would enable linkage to health data for looked after children who are not in publicly funded schooling (i.e. those who are pre- or post-school, home schooled, or in independent schooling)

The impact of posttraumatic stress disorder on upper gastrointestinal investigations in Australian Defence Force veterans: a retrospective review

Veterans with posttraumatic stress disorder (PTSD) commonly exhibit associated gastrointestinal (GI) symptoms. We compared upper GI endoscopy and abdominal ultrasound rates in veterans with and without PTSD. Veterans with PTSD were 77–81% more likely to undergo these procedures than those without PTSD. PTSD symptomatology influences GI investigation rate and more emphasis on clinician and patient education is recommended regarding stress-related gut symptoms

Inflammatory glycoproteins in cardiometabolic disorders, autoimmune diseases and cancer

AbstractThe physiological function initially attributed to the oligosaccharide moieties or glycans on inflammatory glycoproteins was to improve protein stability. However, it is now clear that glycans play a prominent role in glycoprotein structure and function and in some cases contribute to disease states. In fact, glycan processing contributes to pathogenicity not only in autoimmune disorders but also in atherosclerotic cardiovascular disease, diabetes and malignancy. While most clinical laboratory tests measure circulating levels of inflammatory proteins, newly developed diagnostic and prognostic tests are harvesting the information that can be gleaned by measuring the amount or structure of the attached glycans, which may be unique to individuals as well as various diseases. As such, these newer glycan-based tests may provide future means for more personalized approaches to patient stratification and improved patient care.Here we will discuss recent progress in high-throughput laboratory methods for glycomics (i.e. the study of glycan structures) and glycoprotein quantification by methods such as mass spectrometry and nuclear magnetic resonance spectroscopy. We will also review the clinical utility of glycoprotein and glycan measurements in the prediction of common low-grade inflammatory disorders including cardiovascular disease, diabetes and cancer, as well as for monitoring autoimmune disease activity

Higher Free Triiodothyronine Is Associated With Higher HDL Particle Concentration and Smaller HDL Particle Size

Context Thyroid function status has effects on the development of atherosclerotic cardiovascular disease by affecting lipid metabolism, but associations of high-density lipoprotein (HDL) particle concentrations and subfractions with thyroid hormone levels within the reference range remain elusive. Objective The aim of the present study was to determine the associations of free triiodothyronine (FT3), free thyroxine (FT4) and thyroid-stimulating hormone (TSH) levels with HDL particle characteristics in euthyroid individuals. Methods This cross-sectional study on the associations of thyroid hormones with HDL particle concentrations, HDL subfractions, and HDL particle size included 5844 euthyroid individuals (FT3, FT4, and TSH levels within the reference range and no medication use affecting thyroid function), participating in the Prevention of REnal and Vascular ENd-stage Disease (PREVEND) study. HDL particles and subfractions were measured by nuclear magnetic resonance using an optimized version of the NMR LipoProfile Test (LP4). Results In multivariable linear regression analyses, FT3 was positively associated with total HDL particle concentration (std.beta = 0.14; P < 0.001) and with small (std.beta = 0.13; P < 0.001) and medium-sized HDL particles (std.beta = 0.05; P = 0.001). Conversely, FT3 was inversely associated with large HDL particles (std.beta = -0.07; P < 0.001) and with HDL particle size (std.beta = -0.08; P < 0.001). Such associations with FT4 or reciprocally with TSH were less pronounced or nonsignificant. Conclusion In euthyroid individuals, higher FT3 is cross-sectionally associated with higher total HDL particle concentration and with lower HDL particle size. These associations may be relevant to better understand the role of HDL in thyroid function-associated atherosclerotic cardiovascular disease

Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections

In this note we analyze an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.Comment: Key words: Bootstrap percolation, anisotropy, finite-size effect

Short-range correlations in low-lying nuclear excited states

The electromagnetic transitions to various low-lying excited states of 16O, 48Ca and 208Pb are calculated within a model which considers the short-range correlations. In general the effects of the correlations are small and do not explain the required quenching to describe the data.Comment: 6 pages, 2 postscript figures, 1 tabl