A topological classification of convex bodies

The shape of homogeneous, generic, smooth convex bodies as described by the Euclidean distance with nondegenerate critical points, measured from the center of mass represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale functions on S^2 by exhausting all combinatorial possibilities: every 2-colored quadrangulation of the sphere is isomorphic to a suitably represented Morse-Smale complex associated with a function in M_C (and vice versa). We prove our claim by an inductive algorithm, starting from the path graph P_2 and generating convex bodies corresponding to quadrangulations with increasing number of vertices by performing each combinatorially possible vertex splitting by a convexity-preserving local manipulation of the surface. Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist, this algorithm not only proves our claim but also generalizes the known classification scheme in [36]. Our expansion algorithm is essentially the dual procedure to the algorithm presented by Edelsbrunner et al. in [21], producing a hierarchy of increasingly coarse Morse-Smale complexes. We point out applications to pebble shapes.Comment: 25 pages, 10 figure

Interpopulation Variation in Contour Feather Structure Is Environmentally Determined in Great Tits

Background: The plumage of birds is important for flying, insulation and social communication. Contour feathers cover most of the avian body and among other functions they provide a critical insulation layer against heat loss. Feather structure and composition are known to vary among individuals, which in turn determines variation in the insulation properties of the feather. However, the extent and the proximate mechanisms underlying this variation remain unexplored. Methodology/Principal Findings: We analyzed contour feather structure from two different great tit populations adapted to different winter regimes, one northern population in Oulu (Finland) and one southern population in Lund (Sweden). Great tits from the two populations differed significantly in feather structure. Birds from the northern population had a denser plumage but consisting of shorter feathers with a smaller proportion containing plumulaceous barbs, compared with conspecifics from the southern population. However, differences disappeared when birds originating from the two populations were raised and moulted in identical conditions in a common-garden experiment located in Oulu, under ad libitum nutritional conditions. All birds raised in the aviaries, including adult foster parents moulting in the same captive conditions, developed a similar feather structure. These feathers were different from that of wild birds in Oulu but similar to wild birds in Lund, the latter moulting in more benign conditions than those of Oulu. Conclusions/Significance: Wild populations exposed to different conditions develop contour feather differences either due to plastic responses or constraints. Environmental conditions, such as nutrient availability during feather growth play a crucial role in determining such differences in plumage structure among populations

A study of 54 cases of left displacement of the abomasum: February to July 2005

Fifty-four cows with left displacement of the abomasum (LDA) submitted to the hospital facility at Riverview Veterinary Clinic from February to July 2005 were treated by right flank laparotomy and omentopexy. Five cows died (a survival rate 90.7%) and one cow (1.8%) was culled due to recurrence of the LDA post-operatively. Forty-one cows (76%) returned to good production post-operatively. Thirty-nine cows (72%) were pregnant six months after corrective surgery

Characterization of complex networks: A survey of measurements

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of measurements for inclusion are welcomed by the author

Unstated factors in orthopaedic decision-making: a qualitative study

<p>Abstract</p> <p>Background</p> <p>Total joint replacement (TJR) of the hip or knee for osteoarthritis is among the most common elective surgical procedures. There is some inequity in provision of TJR. How decisions are made about who will have surgery may contribute to disparities in provision. The model of shared decision-making between patients and clinicians is advocated as an ideal by national bodies and guidelines. However, we do not know what happens within orthopaedic practice and whether this reflects the shared model. Our study examined how decisions are made about TJR in orthopaedic consultations.</p> <p>Methods</p> <p>The study used a qualitative research design comprising semi-structured interviews and observations. Participants were recruited from three hospital sites and provided their time free of charge. Seven clinicians involved in decision-making about TJR were approached to take part in the study, and six agreed to do so. Seventy-seven patients due to see these clinicians about TJR were approached to take part and 26 agreed to do so. The patients' outpatient appointments ('consultations') were observed and audio-recorded. Subsequent interviews with patients and clinicians examined decisions that were made at the appointments. Data were analysed using thematic analysis.</p> <p>Results</p> <p>Clinical and lifestyle factors were central components of the decision-making process. In addition, the roles that patients assigned to clinicians were key, as were communication styles. Patients saw clinicians as occupying expert roles and they deferred to clinicians' expertise. There was evidence that patients modified their behaviour within consultations to complement that of clinicians. Clinicians acknowledged the complexity of decision-making and provided descriptions of their own decision-making and communication styles. Patients and clinicians were aware of the use of clinical and lifestyle factors in decision-making and agreed in their description of clinicians' styles. Decisions were usually reached during consultations, but patients and clinicians sometimes said that treatment decisions had been made beforehand. Some patients expressed surprise about the decisions made in their consultations, but this did not necessarily imply dissatisfaction.</p> <p>Conclusions</p> <p>The way in which roles and communication are played out in decision-making for TJR may affect the opportunity for shared decisions. This may contribute to variation in the provision of TJR. Making the importance of these factors explicit and highlighting the existence of patients' 'surprise' about consultation outcomes could empower patients within the decision-making process and enhance communication in orthopaedic consultations.</p

Polymorphisms of the prion protein gene and their effects on litter size and risk evaluation for scrapie in Chinese Hu sheep

It is well known that scrapie is a fatal, neurodegenerative disease in sheep and goat, which belongs to the group of transmissible spongiform encephalopathies (TSEs) or prion diseases. It has been confirmed that the polymorphisms of prion protein gene (PRNP) at codons 136, 154, and 171 have strong relationship with scrapie in sheep. In the present study, nine polymorphisms of PRNP at codons 136, 154, and 171 and other six loci (at codons 101, 112, 127, 137, 138, and 152) were detected in 180 Chinese Hu sheep. All the alleles at codons 136, 154, and 171 have been identified and resulted in three new genotypes. The frequencies of predominant alleles were 85% (A136), 99.40% (R154), and 37.78% (Q171), respectively. The predominant haplotype ARQ has a relatively high frequency of 57.77%. The frequencies of dominant genotypes of ARR/ARQ and ARQ/ARQ were 30 and 26.67%, respectively. Three new found genotypes named ARQ/TRK, ARQ/TRR, and TRR/TRQ had the same lower frequencies (0.56%). The relationship of PRNP genotype with scrapie risk and litter size showed that the predominant genotypes are corresponded to the risk score of R1 (1.67%), R2 (32.22%), and R3 (42.22%). Just at the first parity, the individuals with ARH/ARH genotype had significantly larger litter size than the mean value and those with ARQ/ARQ and ARR/ARQ genotypes. In short, this study provided preliminary information about alleles and genotypes of PRNP in Chinese Hu sheep. It could be concluded that Hu sheep has a low susceptibility to natural scrapie, and the predominant PRNP genotype at least has no significant effect on litter size

Liquid Biopsy in Breast Cancer

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