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.

'The UK is not innocent' : Black Lives Matter, policing and abolition in the UK

Purpose: The purpose of this article is to show that racism is not only a US problem. Rather, racism is endemic and pervasive in the UK context, manifesting at every level of policing. From stop and search, to deaths after police contact, the authors highlight long-standing and widespread racist disparities in UK policing. The authors therefore pierce through any delusions of UK “post-racialism” in order to show that, as protesters have reminded us, “the UK is not innocent”. Design/methodology/approach: In this piece, the authors reflect on the Black Lives Matter protests of 2020. Whilst the catalyst was the death of George Floyd in the United States, the authors explore what the protests mean in the UK context. To do so, the authors draw upon recent high-profile examples of police racism, before situating those events within a wider landscape of racist policing. Findings: Demonstrating that UK policing has to be understood as institutionally racist, the authors suggest that responses to police racism need to be radical and uncompromising – tweaks to the system are not enough. The authors therefore look towards defunding and abolition as ways in which one can begin to seek change. Originality/value: The piece takes up the challenges set by this Black Lives Matter moment and offers a critical take on policing that seeks to push beyond reformism whilst also highlighting the realities of UK racism

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

Preferences of children in grades two through eight in social studies subject areas

Thesis (Ed.M.)--Boston Universit

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)

Localizability of Wireless Sensor Networks: Beyond Wheel Extension

A network is called localizable if the positions of all the nodes of the network can be computed uniquely. If a network is localizable and embedded in plane with generic configuration, the positions of the nodes may be computed uniquely in finite time. Therefore, identifying localizable networks is an important function. If the complete information about the network is available at a single place, localizability can be tested in polynomial time. In a distributed environment, networks with trilateration orderings (popular in real applications) and wheel extensions (a specific class of localizable networks) embedded in plane can be identified by existing techniques. We propose a distributed technique which efficiently identifies a larger class of localizable networks. This class covers both trilateration and wheel extensions. In reality, exact distance is almost impossible or costly. The proposed algorithm based only on connectivity information. It requires no distance information

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

Post-traumatic stress disorder is associated with a higher rate of polypectomy independent of an increased frequency of colonoscopy in Australian veterans: a retrospective review

Background Post-traumatic stress disorder (PTSD) is associated with extensive physical comorbidities, including lower gastrointestinal symptoms. Diagnostic uncertainty and poor therapeutic responses may result in more frequent colonoscopies than clinically necessary. Polypectomy is standard practice when polyps are identified, and if PTSD is a risk factor for polyp formation, one would expect a higher rate of polyp detection and removal in veterans with PTSD than those without PTSD. Aim To determine the association between PTSD and the rate of colonoscopy and polypectomy in Australian veterans. Methods Diagnostic and therapeutic colonoscopy rates in Australian male Veterans aged >= 50 years were examined by reviewing case records of veterans who accessed Department of Veterans' Affairs funded health services between 1 January 2013 and 31 December 2018. Results A total of 138 471 veterans was included, of whom 28 018 had a diagnosis of PTSD; 56.4% were aged >= 65 years. Twenty-one percent of the entire cohort underwent at least one colonoscopy during the study period. Increased rates of diagnostic colonoscopy and polypectomy were associated with the presence of PTSD across all age brackets. The effect was empirically large as veterans with PTSD experience colonoscopy rates 76-81% greater than those without PTSD. Similarly, veterans with PTSD experienced polypectomy rates 76-81% greater than veterans without PTSD, and this increase persisted when controlling for the increased number of diagnostic colonoscopies they undergo. Conclusion The presence of PTSD has a marked impact on colonoscopy rates in Australian veterans. The increased polypectomy rate independent of increased colonoscopy rate suggests that PTSD is a risk factor for colonic polyp formation

Plasma Citrate Levels Are Associated with an Increased Risk of Cardiovascular Mortality in Patients with Type 2 Diabetes (Zodiac-64)

Circulating citrate may represent a proxy of mitochondrial dysfunction which plays a role in the development of vascular complications in type 2 diabetes (T2D). Here, we determined the associations between plasma citrate levels and cardiovascular (CV) mortality in T2D patients. In this prospective cohort study, 601 patients were included who participated in the Zwolle Outpatient Diabetes project Integrating Available Care (ZODIAC). Plasma citrate levels were measured by nuclear magnetic resonance spectroscopy. Cox proportional hazards regression models were used to evaluate the associations between plasma citrate and the risk of CV mortality. Over a median follow-up of 11.4 years, 119 (19.8%) of the 601 patients died from a CV cause. In multivariable Cox proportional hazards regression models, adjusting for conventional risk factors, plasma citrate was associated with an increased risk of CV mortality (the hazard ratio (HR) per 1-SD increment was 1.19 (95%CI: 1.00–1.40), p = 0.048). This association was prominent in males (n = 49 with CV mortality) (HR 1.52 (95%CI: 1.14–2.03), p = 0.005), but not in females (n = 70 with CV mortality) (HR 1.11 (95%CI: 0.90–1.37), p = 0.319) (age-adjusted Pinteraction = 0.044). In conclusion, higher plasma citrate levels are associated with an increased risk of CV mortality in patients with established T2D. Future studies are warranted to unravel the potential role of citrate-related pathways in the pathogenesis of T2D-related vascular complications