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

Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

Data Mining a Medieval Medical Text Reveals Patterns in Ingredient Choice That Reflect Biological Activity against Infectious Agents

We used established methodologies from network science to identify patterns in medicinal ingredient combinations in a key medieval text, the 15th-century Lylye of Medicynes, focusing on recipes for topical treatments for symptoms of microbial infection. We conducted experiments screening the antimicrobial activity of selected ingredients. These experiments revealed interesting examples of ingredients that potentiated or interfered with each other’s activity and that would be useful bases for future, more detailed experiments. Our results highlight (i) the potential to use methodologies from network science to analyze medieval data sets and detect patterns of ingredient combination, (ii) the potential of interdisciplinary collaboration to reveal different aspects of the ethnopharmacology of historical medical texts, and (iii) the potential development of novel therapeutics inspired by premodern remedies in a time of increased need for new antibiotics.The pharmacopeia used by physicians and laypeople in medieval Europe has largely been dismissed as placebo or superstition. While we now recognize that some of the materia medica used by medieval physicians could have had useful biological properties, research in this area is limited by the labor-intensive process of searching and interpreting historical medical texts. Here, we demonstrate the potential power of turning medieval medical texts into contextualized electronic databases amenable to exploration by the use of an algorithm. We used established methodologies from network science to reveal patterns in ingredient selection and usage in a key text, the 15th-century Lylye of Medicynes, focusing on remedies to treat symptoms of microbial infection. In providing a worked example of data-driven textual analysis, we demonstrate the potential of this approach to encourage interdisciplinary collaboration and to shine a new light on the ethnopharmacology of historical medical texts

Multimorbidity and co-morbidity in atrial fibrillation and effects on survival: findings from UK Biobank cohort

Aims: To examine the number and type of co-morbid long-term health conditions (LTCs) and their associations with all-cause mortality in an atrial fibrillation (AF) population. Methods and results: Community cohort participants (UK Biobank n = 502 637) aged 37–73 years were recruited between 2006 and 2010. Self-reported LTCs (n = 42) identified in people with AF at baseline. All-cause mortality was available for a median follow-up of 7 years (interquartile range 76–93 months). Hazard ratios (HRs) examined associations between number and type of co-morbid LTC and all-cause mortality, adjusting for age, sex, socio-economic status, smoking, and anticoagulation status. Three thousand six hundred fifty-one participants (0.7% of the study population) reported AF; mean age was 61.9 years. The all-cause mortality rate was 6.7% (248 participants) at 7 years. Atrial fibrillation participants with ≥4 co-morbidities had a six-fold higher risk of mortality compared to participants without any LTC. Co-morbid heart failure was associated with higher risk of mortality [HR 2.96, 95% confidence interval (CI) 1.83–4.80], whereas the presence of co-morbid stroke did not have a significant association. Among non-cardiometabolic conditions, presence of chronic obstructive pulmonary disease (HR 3.31, 95% CI 2.14–5.11) and osteoporosis (HR 3.13, 95% CI 1.63–6.01) was associated with a higher risk of mortality. Conclusion: Survival in middle-aged to older individuals with self-reported AF is strongly correlated with level of multimorbidity. This group should be targeted for interventions to optimize their management, which in turn may potentially reduce the impact of their co-morbidities on survival. Future AF clinical guidelines need to place greater emphasis on the issue of co-morbidity

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)

Inequalities in the dental health needs and access to dental services among looked after children in Scotland: a population data linkage study

Background: There is limited evidence on the health needs and service access among children and young people who are looked after by the state. The aim of this study was to compare dental treatment needs and access to dental services (as an exemplar of wider health and well-being concerns) among children and young people who are looked after with the general child population. Methods: Population data linkage study utilising national datasets of social work referrals for ‘looked after’ placements, the Scottish census of children in local authority schools, and national health service’s dental health and service datasets. Results: 633 204 children in publicly funded schools in Scotland during the academic year 2011/2012, of whom 10 927 (1.7%) were known to be looked after during that or a previous year (from 2007–2008). The children in the looked after children (LAC) group were more likely to have urgent dental treatment need at 5 years of age: 23%vs10% (n=209/16533), adjusted (for age, sex and area socioeconomic deprivation) OR 2.65 (95% CI 2.30 to 3.05); were less likely to attend a dentist regularly: 51%vs63% (n=5519/388934), 0.55 (0.53 to 0.58) and more likely to have teeth extracted under general anaesthesia: 9%vs5% (n=967/30253), 1.91 (1.78 to 2.04). Conclusions: LAC are more likely to have dental treatment needs and less likely to access dental services even when accounting for sociodemographic factors. Greater efforts are required to integrate child social and healthcare for LAC and to develop preventive care pathways on entering and throughout their time in the care system

An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-space

We give an example of an infinitesimally nonrigid polyhedron in the Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron isn't stationary under the flex.Comment: 10 pages, 2 Postscript figure

Peripheral Vascular Responses to Acetylcholine as a Predictive Tool for Response to Cholinesterase Inhibitors in Alzheimer's Disease

Background: Cholinesterase inhibitors remain the first line therapy for people with mild to moderate Alzheimer's disease (AD). Response is modest and difficult to predict from pre-treatment characteristics. We hypothesise that skin vascular response to iontophoresis of acetylcholine, which is partly determined by the level of cholinesterase activity, may be a pre-treatment measure that could predict response to therapy.Methods: Twenty-four people with probable AD underwent iontophoresis of acetylcholine to the volar surface of the forearm skin prior to treatment with a cholinesterase inhibitor. The peak skin vascular response and the resolution to baseline levels were measured using laser Doppler perfusion imaging. Response to treatment was assessed after 6 months using criteria from the National Institute for Health and Care Excellence (NICE) and iontophoresis with acetylcholine was repeated. Blindness between clinical and laboratory assessments was maintained.Results: Fourteen out of twenty-four people responded to treatment using NICE criteria. By comparison to non-responders, responders to treatment had a faster resolution to baseline from acetylcholine-induced vasodilation prior to treatment, which slowed with treatment. In this pilot study there was a high level of accuracy in the classification of response using this variable. No baseline cognitive or functional measures discriminated end-point responders from non-responders.Conclusion: Cholinesterase inhibitors are well tolerated but the number of people with adverse effects would be reduced if it was possible to predict response. The role of vasodilator response to acetylcholine and recovery as a potential biomarker for efficacy of treatment should now be evaluated and may possibly be of relevance in stratifying samples for interventional studies in AD and other forms of dementia. We feel that a more definitive study is now justified

Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Simultaneous Triggered Collapse of the Presolar Dense Cloud Core and Injection of Short-Lived Radioisotopes by a Supernova Shock Wave

Cosmochemical evidence for the existence of short-lived radioisotopes (SLRI) such as $^{26}$Al and $^{60}$Fe at the time of the formation of primitive meteorites requires that these isotopes were synthesized in a massive star and then incorporated into chondrites within $\sim 10^6$ yr. A supernova shock wave has long been hypothesized to have transported the SLRI to the presolar dense cloud core, triggered cloud collapse, and injected the isotopes. Previous numerical calculations have shown that this scenario is plausible when the shock wave and dense cloud core are assumed to be isothermal at $\sim 10$ K, but not when compressional heating to $\sim 1000$ K is assumed. We show here for the first time that when calculated with the FLASH2.5 adaptive mesh refinement (AMR) hydrodynamics code, a 20 km/sec shock wave can indeed trigger the collapse of a 1 $M_\odot$ cloud while simultaneously injecting shock wave isotopes into the collapsing cloud, provided that cooling by molecular species such as H$_2$O, CO$_2$, and H$_2$ is included. These calculations imply that the supernova trigger hypothesis is the most likely mechanism for delivering the SLRI present during the formation of the solar system.Comment: 12 pages, 4 color figures. Astrophysical Journal Letters (in press