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.

Generic Global Rigidity in Complex and Pseudo-Euclidean Spaces

In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space R$^{2}$ with a metric of indefinite signature). We show that a graph is generically globally rigid in Euclidean space iff it is generically globally rigid in a complex or pseudo-Euclidean space. We also establish that global rigidity is always a generic property of a graph in complex space, and give a sufficient condition for it to be a generic property in a pseudo-Euclidean space. Extensions to hyperbolic space are also discussed.Engineering and Applied Science

Micro-Electromechanical Instrument and Systems Development at the Charles Stark Draper Laboratory

Several generations of micromechanical gyros and accelerometers have been developed at Draper. Current design effort centers on tuning-fork gyro design and pendulous accelerometer configurations. Over 200 gyros of different generations have been packaged and tested. These units have successfully performed across a temperature range of -40 to 85 degrees C, and have survived 30,000-g shock tests along all axes. Draper is currently under contract to develop an integrated micro-mechanical inertial sensor assembly (MMISA) and global positioning system (GPS) receiver configuration. The ultimate projections for size, weight, and power for an MMISA, after electronic design of the application specific integrated circuit (ASIC ) is completed, are 2 x 2 x 0.5 cm, 5 gm, and less than 1 W, respectively. This paper describes the fabrication process, the current gyro and accelerometer designs, and system configurations

Rigid ball-polyhedra in Euclidean 3-space

A ball-polyhedron is the intersection with non-empty interior of finitely many (closed) unit balls in Euclidean 3-space. One can represent the boundary of a ball-polyhedron as the union of vertices, edges, and faces defined in a rather natural way. A ball-polyhedron is called a simple ball-polyhedron if at every vertex exactly three edges meet. Moreover, a ball-polyhedron is called a standard ball-polyhedron if its vertex-edge-face structure is a lattice (with respect to containment). To each edge of a ball-polyhedron one can assign an inner dihedral angle and say that the given ball-polyhedron is locally rigid with respect to its inner dihedral angles if the vertex-edge-face structure of the ball-polyhedron and its inner dihedral angles determine the ball-polyhedron up to congruence locally. The main result of this paper is a Cauchy-type rigidity theorem for ball-polyhedra stating that any simple and standard ball-polyhedron is locally rigid with respect to its inner dihedral angles.Comment: 11 pages, 2 figure

"Othering" the health worker: self-stigmatization of HIV/AIDS care among health workers in Swaziland

<p>Abstract</p> <p>Background</p> <p>HIV is an important factor affecting healthcare workforce capacity in high-prevalence countries, such as Swaziland. It contributes to loss of valuable healthcare providers directly through death and absenteeism and indirectly by affecting family members, increasing work volume and decreasing performance. This study explored perceived barriers to accessing HIV/AIDS care and prevention services among health workers in Swaziland. We asked health workers about their views on how HIV affects Swaziland's health workforce and what barriers and strategies health workers have for addressing HIV and using healthcare treatment facilities.</p> <p>Methods</p> <p>Thirty-four semi-structured, in-depth interviews, including a limited set of quantitative questions, were conducted among health workers at health facilities representing the mixture of facility type, level and location found in the Swaziland health system. Data were collected by a team of Swazi nurses who had received training in research methods. Study sites were selected using a purposive sampling method while health workers were sampled conveniently with attention to representing a mixture of different cadres. Data were analyzed using Nvivo qualitative analysis software and Excel.</p> <p>Results</p> <p>Health workers reported that HIV had a range of negative impacts on their colleagues and identified HIV testing and care as one of the most important services to offer health workers. They overwhelmingly wanted to know their own HIV status. However, they also indicated that in general, health workers were reluctant to access testing or care as they feared stigmatization by patients <it>and </it>colleagues and breaches of confidentiality. They described a self-stigmatization related to a professional need to maintain a HIV-free status, contrasting with the HIV-vulnerable general population. Breaching of this boundary included feelings of professional embarrassment and fear of colleagues' and patients' judgements.</p> <p>Conclusions</p> <p>While care is available and relatively accessible, Swaziland health workers still face unique usage barriers that relate to a self-stigmatizing process of boundary maintenance - described here as a form of "othering" from the HIV-vulnerable general population - and a lack of trust in privacy and confidentiality. Interventions that target health workers should address these issues.</p

Systematic data-querying of large pediatric biorepository identifies novel Ehlers-Danlos Syndrome variant

BACKGROUND: Ehlers Danlos Syndrome is a rare form of inherited connective tissue disorder, which primarily affects skin, joints, muscle, and blood cells. The current study aimed at finding the mutation that causing EDS type VII C also known as "Dermatosparaxis" in this family. METHODS: Through systematic data querying of the electronic medical records (EMRs) of over 80,000 individuals, we recently identified an EDS family that indicate an autosomal dominant inheritance. The family was consented for genomic analysis of their de-identified data. After a negative screen for known mutations, we performed whole genome sequencing on the male proband, his affected father, and unaffected mother. We filtered the list of non-synonymous variants that are common between the affected individuals. RESULTS: The analysis of non-synonymous variants lead to identifying a novel mutation in the ADAMTSL2 (p. Gly421Ser) gene in the affected individuals. Sanger sequencing confirmed the mutation. CONCLUSION: Our work is significant not only because it sheds new light on the pathophysiology of EDS for the affected family and the field at large, but also because it demonstrates the utility of unbiased large-scale clinical recruitment in deciphering the genetic etiology of rare mendelian diseases. With unbiased large-scale clinical recruitment we strive to sequence as many rare mendelian diseases as possible, and this work in EDS serves as a successful proof of concept to that effect

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