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.

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

X-Ray Groups of Galaxies in the Aegis Deep and Wide Fields

We present the results of a search for extended X-ray sources and their corresponding galaxy groups from 800-ks Chandra coverage of the All-wavelength Extended Groth Strip International Survey (AEGIS). This yields one of the largest X-ray selected galaxy group catalogs from a blind survey to date. The red-sequence technique and spectroscopic redshifts allow us to identify 100$$ of reliable sources, leading to a catalog of 52 galaxy groups. The groups span the redshift range $z\sim0.066-1.544$ and virial mass range $M_{200}\sim1.34\times 10^{13}-1.33\times 10^{14}M_\odot$. For the 49 extended sources which lie within DEEP2 and DEEP3 Galaxy Redshift Survey coverage, we identify spectroscopic counterparts and determine velocity dispersions. We select member galaxies by applying different cuts along the line of sight or in projected spatial coordinates. A constant cut along the line of sight can cause a large scatter in scaling relations in low-mass or high-mass systems depending on the size of cut. A velocity dispersion based virial radius can more overestimate velocity dispersion in comparison to X-ray based virial radius for low mass systems. There is no significant difference between these two radial cuts for more massive systems. Independent of radial cut, overestimation of velocity dispersion can be created in case of existence of significant substructure and also compactness in X-ray emission which mostly occur in low mass systems. We also present a comparison between X-ray galaxy groups and optical galaxy groups detected using the Voronoi-Delaunay method (VDM) for DEEP2 data in this field.Comment: Accepted for publication in AP

Violent and non-violent crimes against sex workers : the influence of the sex market on reporting practices in the United Kingdom

Previous research has shown that sex workers experience extremely high rates of victimization but are often reluctant to report their experiences to the police. This paper explores how the markets in which sex workers operate in the United Kingdom impact upon the violent and non-violent crimes they report to a national support organization and their willingness to report victimization to the police. We use a secondary quantitative data analysis of 2,056 crime reports submitted to the UK National Ugly Mugs (NUM) scheme between 2012 and 2016. The findings indicate that although violence is the most common crime type reported to NUM, sex workers operating in different markets report varying relative proportions of different types of victimization. We also argue that there is some variation in the level of willingness to share reports with the police across the different sex markets, even when the type crime, presence of violence, and other variables are taken into account. Our finding that street sex workers are most likely to report victimization directly to the police challenges previously held assumptions that criminalization is the key factor preventing sex workers from engaging with the police. Key words: sex work; violence; policing; reported victimizatio

Do Not Attempt Resuscitation (DNAR) status in people with suspected COVID-19 : secondary analysis of the PRIEST observational cohort study

Background: Cardiac arrest is common in people admitted with suspected COVID-19 and has a poor prognosis. Do Not Attempt Resuscitation (DNAR) orders can reduce the risk of futile resuscitation attempts but have raised ethical concerns. Objectives: We aimed to describe the characteristics and outcomes of adults admitted to hospital with suspected COVID-19 according to their DNAR status and identify factors associated with an early DNAR decision. Methods: We undertook a secondary analysis of 13977 adults admitted to hospital with suspected COVID-19 and included in the Pandemic Respiratory Infection Emergency System Triage (PRIEST) study. We recorded presenting characteristics and outcomes (death or organ support) up to 30 days. We categorised patients as early DNAR (occurring before or on the day of admission) or late/no DNAR (no DNAR or occurring after the day of admission). We undertook descriptive analysis comparing these groups and multivariable analysis to identify independent predictors of early DNAR. Results: We excluded 1249 with missing DNAR data, and identified 3929/12748 (31%) with an early DNAR decision. They had higher mortality (40.7% v 13.1%) and lower use of any organ support (11.6% v 15.7%), but received a range of organ support interventions, with some being used at rates comparable to those with late or no DNAR (e.g. non-invasive ventilation 4.4% v 3.5%). On multivariable analysis, older age (p<0.001), active malignancy (p<0.001), chronic lung disease (p<0.001), limited performance status (p<0.001), and abnormal physiological variables were associated with increased recording of early DNAR. Asian ethnicity was associated with reduced recording of early DNAR (p=0.001). Conclusions: Early DNAR decisions were associated with recognised predictors of adverse outcome, and were inversely associated with Asian ethnicity. Most people with an early DNAR decision survived to 30 days and many received potentially life-saving interventions. Registration: ISRCTN registry, ISRCTN28342533, http://www.isrctn.com/ISRCTN2834253

A Pluralistic Theory of Wordhood

What are words and how should we individuate them? There are two main answers on the philosophical market. For some, words are bundles of structural-functional features defining a unique performance profile. For others, words are non-eternal continuants individuated by their causal-historical ancestry. These conceptions offer competing views of the nature of words, and it seems natural to assume that at most one of them can capture the essence of wordhood. This paper makes a case for pluralism about wordhood: the view that there is a plurality of acceptable conceptions of the nature of words, none of which is uniquely entitled to inform us as to what wordhood consists in