A unique representation of polyhedral types

It is known that for each combinatorial type of convex 3-dimensional polyhedra, there is a representative with edges tangent to the unit sphere. This representative is unique up to projective transformations that fix the unit sphere. We show that there is a unique representative (up to congruence) with edges tangent to the unit sphere such that the origin is the barycenter of the points where the edges touch the sphere.Comment: 4 pages, 2 figures. v2: belated upload of final version (of March 2004

Occurrence of genes encoding spore germination in Clostridium species that cause meat spoilage

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The Random Discrete Action for 2-Dimensional Spacetime

A one-parameter family of random variables, called the Discrete Action, is defined for a 2-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this Discrete Action is calculated for various regions of 2D Minkowski spacetime. When a causally convex region of 2D Minkowski spacetime is divided into subregions using null lines the mean of the Discrete Action is equal to the alternating sum of the numbers of vertices, edges and faces of the null tiling, up to corrections that tend to zero as the discreteness scale is taken to zero. This result is used to predict that the mean of the Discrete Action of the flat Lorentzian cylinder is zero up to corrections, which is verified. The ``topological'' character of the Discrete Action breaks down for causally convex regions of the flat trousers spacetime that contain the singularity and for non-causally convex rectangles.Comment: 20 pages, 10 figures, Typos correcte

The Random Walk in Generalized Quantum Theory

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a certain condition of ``strong positivity'', the most general Markovian, translationally invariant ``decoherence functional'' with nearest neighbor transitions.Comment: 25 pages, no figure

Dense packing on uniform lattices

We study the Hard Core Model on the graphs ${\rm {\bf \scriptstyle G}}$ obtained from Archimedean tilings i.e. configurations in $\scriptstyle \{0,1\}^{{\rm {\bf G}}}$ with the nearest neighbor 1's forbidden. Our particular aim in choosing these graphs is to obtain insight to the geometry of the densest packings in a uniform discrete set-up. We establish density bounds, optimal configurations reaching them in all cases, and introduce a probabilistic cellular automaton that generates the legal configurations. Its rule involves a parameter which can be naturally characterized as packing pressure. It can have a critical value but from packing point of view just as interesting are the noncritical cases. These phenomena are related to the exponential size of the set of densest packings and more specifically whether these packings are maximally symmetric, simple laminated or essentially random packings.Comment: 18 page

Blood Flow Restriction Training After Patellar INStability (BRAINS Trial)

Background Patellar instability is a common and understudied condition that disproportionally affects athletes and military personnel. The rate of post-traumatic osteoarthritis that develops following a patellar dislocation can be up to 50% of individuals 5–15 years after injury. Conservative treatment is the standard of care for patellar instability however, there are no evidence-informed rehabilitation guidelines in the scientific literature. The purpose of this study is to assess the effectiveness of blood-flow restriction training (BFRT) for patellar instability. Our hypotheses are that this strategy will improve patient-reported outcomes and accelerate restoration of symmetric strength and knee biomechanics necessary to safely return to activity. Methods/Design This is a parallel-group, superiority, randomized, double-blinded, placebo-controlled clinical trial at the University of Kentucky, sports medicine clinic that aims to recruit 78 patients with acute patellar dislocations randomly allocated into two groups: (1) sham BFRT and (2) BFRT. Both groups will receive the current standard of care physical therapy 3 times per week for up to 9 weeks. Physical therapy sessions will consist of typical standard of care treatment followed by BFRT or sham BFRT. Primary outcomes include the Norwich Patellar Instability Scale, quadriceps strength, and imaging and biochemical biomarkers of cartilage degradation. Discussion The current standard of care for non-operative treatment of patellar instability is highly variable does not adequately address the mechanisms necessary to restore lower extremity function and protect the long-term health of articular cartilage following injury. This proposed novel intervention strategy uses an easily implementable therapy to evaluate if BFRT significantly improves patient-reported outcomes, function, and joint health over the first year of recovery. Trial Registration Blood Flow Restriction Training, Aspiration, and Intraarticular Normal Saline (BRAINS) NCT04554212. Registered on 18 September 2020

Pattern Avoidance in Poset Permutations

We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on $P$ that avoid the pattern $\pi$ is denoted $Av_P(\pi)$. We extend a proof of Simion and Schmidt to show that $Av_P(132) \leq Av_P(123)$ for any poset $P$, and we exactly classify the posets for which equality holds.Comment: 13 pages, 1 figure; v2: corrected typos; v3: corrected typos and improved formatting; v4: to appear in Order; v5: corrected typos; v6: updated author email addresse

Peer mentoring: evaluation of a novel programme in paediatrics

Background Mentoring is important for personal and professional development of doctors. Peer mentoring is a core skill in the UK paediatric postgraduate curriculum. However, there is a paucity of peer mentoring programmes aimed at postgraduate doctors in training (postgraduate trainees), and there are no such schemes within paediatrics described in the literature. We developed a regional peer mentoring programme for postgraduate trainees in paediatrics to assess demand and need for peer mentoring and to explore the benefits for both peer mentees and mentors. Programme design Junior postgraduate trainees, randomly selected from volunteers, received peer mentoring from more senior trainees for 1 year. Peer mentors were selected by competitive application and undertook tailored training followed by an experiential learning programme. The programme was evaluated using structured questionnaires. Results 90% (76/84) of first-year postgraduate trainees in paediatrics applied to participate, demonstrating high demand. 18 peer mentor–mentee pairs were matched. Peer mentors and mentees reported high satisfaction rates, acquisition of new and transferable skills and changed behaviours. All peer mentors intended to use the skills in their workplace and, later, as an educational supervisor. Conclusions Our programme represents a novel approach to meeting the demonstrated demand and the curriculum requirement for peer mentoring, and enabled peer mentors and mentees to develop a valuable and versatile skill set. To our knowledge, it is the first such programme in paediatrics and provides a feasibility model that may be adapted locally to allow education providers to offer this important experience to postgraduate trainees

Spatial Hypersurfaces in Causal Set Cosmology

Within the causal set approach to quantum gravity, a discrete analog of a spacelike region is a set of unrelated elements, or an antichain. In the continuum approximation of the theory, a moment-of-time hypersurface is well represented by an inextendible antichain. We construct a richer structure corresponding to a thickening of this antichain containing non-trivial geometric and topological information. We find that covariant observables can be associated with such thickened antichains and transitions between them, in classical stochastic growth models of causal sets. This construction highlights the difference between the covariant measure on causal set cosmology and the standard sum-over-histories approach: the measure is assigned to completed histories rather than to histories on a restricted spacetime region. The resulting re-phrasing of the sum-over-histories may be fruitful in other approaches to quantum gravity.Comment: Revtex, 12 pages, 2 figure