Flat coordinates and dilaton fields for three--dimensional conformal sigma models

Riemannian coordinates for flat metrics corresponding to three--dimensional conformal Poisson--Lie T--dualizable sigma models are found by solving partial differential equations that follow from the transformations of the connection components. They are then used for finding general forms of the dilaton fields satisfying the vanishing beta equations of the sigma models.Comment: 16 pages, no figure

On the Invariant Theory of Weingarten Surfaces in Euclidean Space

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal surfaces, surfaces of constant mean curvature and surfaces of constant Gauss curvature.Comment: 16 page

Affine Gravity, Palatini Formalism and Charges

Affine gravity and the Palatini formalism contribute both to produce a simple and unique formula for calculating charges at spatial and null infinity for Lovelock type Lagrangians whose variational derivatives do not depend on second-order derivatives of the field components. The method is based on the covariant generalization due to Julia and Silva of the Regge-Teitelboim procedure that was used to define properly the mass in the classical formulation of Einstein's theory of gravity. Numerous applications reproduce standard results obtained by other secure but mostly specialized methods. As a novel application we calculate the Bondi energy loss in five dimensional gravity, based on the asymptotic solution given by Tanabe, Tanahashi and Shiromizu, and obtain, as expected, the same result. We also give the superpotential for Einstein-Gauss-Bonnet gravity and find the superpotential for Lovelock theories of gravity when the number of dimensions tends to infinity with maximally symmetrical boundaries. The paper is written in standard component formalism.Comment: The work is dedicated to Joshua Goldberg from whom I learned and got interested in conservation laws in General Relativity (J.K

Biphasic investigation of contact mechanics in natural human hips during activities

The aim of this study was to determine the cartilage contact mechanics and the associated fluid pressurisation of the hip joint under eight daily activities, using a three-dimensional finite element hip model with biphasic cartilage layers and generic geometries. Loads with spatial and temporal variations were applied over time and the time-dependent performance of the hip cartilage during walking was also evaluated. It was found that the fluid support ratio was over 90% during the majority of the cycles for all the eight activities. A reduced fluid support ratio was observed for the time at which the contact region slid towards the interior edge of the acetabular cartilage, but these occurred when the absolute level of the peak contact stress was minimal. Over 10 cycles of gait, the peak contact stress and peak fluid pressure remained constant, but a faster process of fluid exudation was observed for the interior edge region of the acetabular cartilage. The results demonstrate the excellent function of the hip cartilage within which the solid matrix is prevented from high levels of stress during activities owing to the load shared by fluid pressurisation. The findings are important in gaining a better understanding of the hip function during daily activities, as well as the pathology of hip degeneration and potential for future interventions. They provide a basis for future subject-specific biphasic investigations of hip performance during activities

Accuracy of biplane x-ray imaging combined with model-based tracking for measuring in-vivo patellofemoral joint motion

<p>Abstract</p> <p>Background</p> <p>Accurately measuring <it>in-vivo</it> motion of the knee's patellofemoral (PF) joint is challenging. Conventional measurement techniques have largely been unable to accurately measure three-dimensional, <it>in-vivo</it> motion of the patella during dynamic activities. The purpose of this study was to assess the accuracy of a new model-based technique for measuring PF joint motion.</p> <p>Methods</p> <p>To assess the accuracy of this technique, we implanted tantalum beads into the femur and patella of three cadaveric knee specimens and then recorded dynamic biplane radiographic images while manually flexing and extending the specimen. The position of the femur and patella were measured from the biplane images using both the model-based tracking system and a validated dynamic radiostereometric analysis (RSA) technique. Model-based tracking was compared to dynamic RSA by computing measures of bias, precision, and overall dynamic accuracy of four clinically-relevant kinematic parameters (patellar shift, flexion, tilt, and rotation).</p> <p>Results</p> <p>The model-based tracking technique results were in excellent agreement with the RSA technique. Overall dynamic accuracy indicated errors of less than 0.395 mm for patellar shift, 0.875° for flexion, 0.863° for tilt, and 0.877° for rotation.</p> <p>Conclusion</p> <p>This model-based tracking technique is a non-invasive method for accurately measuring dynamic PF joint motion under <it>in-vivo</it> conditions. The technique is sufficiently accurate in measuring clinically relevant changes in PF joint motion following conservative or surgical treatment.</p

From Wald to Savage: homo economicus becomes a Bayesian statistician

Bayesian rationality is the paradigm of rational behavior in neoclassical economics. A rational agent in an economic model is one who maximizes her subjective expected utility and consistently revises her beliefs according to Bayes’s rule. The paper raises the question of how, when and why this characterization of rationality came to be endorsed by mainstream economists. Though no definitive answer is provided, it is argued that the question is far from trivial and of great historiographic importance. The story begins with Abraham Wald’s behaviorist approach to statistics and culminates with Leonard J. Savage’s elaboration of subjective expected utility theory in his 1954 classic The Foundations of Statistics. It is the latter’s acknowledged fiasco to achieve its planned goal, the reinterpretation of traditional inferential techniques along subjectivist and behaviorist lines, which raises the puzzle of how a failed project in statistics could turn into such a tremendous hit in economics. A couple of tentative answers are also offered, involving the role of the consistency requirement in neoclassical analysis and the impact of the postwar transformation of US business schools

Trabecular bone patterning in the hominoid distal femur

In addition to external bone shape and cortical bone thickness and distribution, the distribution and orientation of internal trabecular bone across individuals and species has yielded important functional information on how bone adapts in response to load. In particular, trabecular bone analysis has played a key role in studies of human and nonhuman primate locomotion and has shown that species with different locomotor repertoires display distinct trabecular architecture in various regions of the skeleton. In this study, we analyse trabecular structure throughout the distal femur of extant hominoids and test for differences due to locomotor loading regime