Symmetry as a sufficient condition for a finite flex

We show that if the joints of a bar and joint framework $(G,p)$ are positioned as `generically' as possible subject to given symmetry constraints and $(G,p)$ possesses a `fully-symmetric' infinitesimal flex (i.e., the velocity vectors of the infinitesimal flex remain unaltered under all symmetry operations of $(G,p)$), then $(G,p)$ also possesses a finite flex which preserves the symmetry of $(G,p)$ throughout the path. This and other related results are obtained by symmetrizing techniques described by L. Asimov and B. Roth in their paper `The Rigidity Of Graphs' from 1978 and by using the fact that the rigidity matrix of a symmetric framework can be transformed into a block-diagonalized form by means of group representation theory. The finite flexes that can be detected with these symmetry-based methods can in general not be found with the analogous non-symmetric methods.Comment: 26 pages, 10 figure

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 orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Management Activities of Private Forest Landowners in New York State

CaRDI Research & Policy Brief, Issue 15. Click on the PDF for the full report. Visit the HDRU website for a complete listing of HDRU publications at: http://hdru.dnr.cornell.edu/. A complete listing of CaRDI publications can be found on its site: https://cardi.cals.cornell.edu/

Interventions for improving clinical outcomes and health-related quality-of-life for people living with skeletal dysplasias: an evidence gap map

Purpose: Skeletal dysplasias are rare genetic disorders that are characterized by abnormal development of bone and cartilage. There are multiple medical and non-medical treatments for specific symptoms of skeletal dysplasias e.g. pain, as well as corrective surgical procedures to improve physical functioning. The aim of this paper was to develop an evidence-gap map of treatment options for skeletal dysplasias, and their impact on patient outcomes. Methods: We conducted an evidence-gap map to identify the available evidence on the impact of treatment options on people with skeletal dysplasias on clinical outcomes (such as increase in height), and dimensions of health-related quality of life. A structured search strategy was applied to five databases. Two reviewers independently assessed articles for inclusion in two stages: titles and abstracts (stage 1), and full text of studies retained at stage 2. Results: 58 studies fulfilled our inclusion criteria. The included studies covered 12 types of skeletal dysplasia that are non-lethal with severe limb deformities that could result in significant pain and numerous orthopaedic interventions. Most studies reported on the effect of surgical interventions (n = 40, 69%), followed by the effect of treatments on dimensions of health quality-of-life (n = 4, 6.8%) and psychosocial functioning (n = 8, 13.8%). Conclusion: Most studies reported on clinical outcomes from surgery for people living with Achondroplasia. Consequently, there are gaps in the literature on the full range of treatment options (including no active treatment), outcomes and the lived experience of people living with other skeletal dysplasias. More research is warranted to examine the impact of treatments on health-related quality-of-life of people living with skeletal dysplasias, including their relatives to enable them to make preference- and valued based decisions about treatment

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

Determination of Peptide and Protein Ion Charge States by Fourier Transformation of Isotope-Resolved Mass Spectra

We report an automated method for determining charge states from high-resolution mass spectra. Fourier transforms of isotope packets from high-resolution mass spectra are compared to Fourier transforms of modeled isotopic peak packets for a range of charge states. The charge state for the experimental ion packet is determined by the model isotope packet that yields the best match in the comparison of the Fourier transforms. This strategy is demonstrated for determining peptide ion charge states from “zoom scan” data from a linear quadrupole ion trap mass spectrometer, enabling the subsequent automated identification of singly- through quadruply-charged peptide ions, while reducing the numbers of conflicting identifications from ambiguous charge state assignments. We also apply this technique to determine the charges of intact protein ions from LC-FTICR data, demonstrating that it is more sensitive under these experimental conditions than two existing algorithms. The strategy outlined in this paper should be generally applicable to mass spectra obtained from any instrument capable of isotopic resolution

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

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