Another positivity proof and gravitational energy localizations

Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other special orthonormal frames, are reviewed. A new quadratic 3-spinor-curvature identity is used to obtain another positive expression for the Hamiltonian and thereby a localization of gravitational energy and positive energy proof. These new results provide a link between the other two methods. Localization and prospects for quasi-localization are discussed.Comment: 14 pages REVTe

Automated design of robust discriminant analysis classifier for foot pressure lesions using kinematic data

In the recent years, the use of motion tracking systems for acquisition of functional biomechanical gait data, has received increasing interest due to the richness and accuracy of the measured kinematic information. However, costs frequently restrict the number of subjects employed, and this makes the dimensionality of the collected data far higher than the available samples. This paper applies discriminant analysis algorithms to the classification of patients with different types of foot lesions, in order to establish an association between foot motion and lesion formation. With primary attention to small sample size situations, we compare different types of Bayesian classifiers and evaluate their performance with various dimensionality reduction techniques for feature extraction, as well as search methods for selection of raw kinematic variables. Finally, we propose a novel integrated method which fine-tunes the classifier parameters and selects the most relevant kinematic variables simultaneously. Performance comparisons are using robust resampling techniques such as Bootstrap$632+$and k-fold cross-validation. Results from experimentations with lesion subjects suffering from pathological plantar hyperkeratosis, show that the proposed method can lead to$sim 96$correct classification rates with less than 10% of the original features

A Social-Ecological Framework of Theory, Assessment, and Prevention of Suicide

The juxtaposition of increasing suicide rates with continued calls for suicide prevention efforts begs for new approaches. Grounded in the Centers for Disease Control and Prevention (CDC) framework for tackling health issues, this personal views work integrates relevant suicide risk/protective factor, assessment, and intervention/prevention literatures. Based on these components of suicide risk, we articulate a Social-Ecological Suicide Prevention Model (SESPM) which provides an integration of general and population-specific risk and protective factors. We also use this multi-level perspective to provide a structured approach to understanding current theories and intervention/prevention efforts concerning suicide. Following similar multi-level prevention efforts in interpersonal violence and Human Immunodeficiency Virus (HIV) domains, we offer recommendations for social-ecologically informed suicide prevention theory, training, research, assessment, and intervention programming. Although the SESPM calls for further empirical testing, it provides a suitable backdrop for tailoring of current prevention and intervention programs to population-specific needs. Moreover, the multi-level model shows promise to move suicide risk assessment forward (e.g., development of multi-level suicide risk algorithms or structured professional judgments instruments) to overcome current limitations in the field. Finally, we articulate a set of characteristics of social-ecologically based suicide prevention programs. These include the need to address risk and protective factors with the strongest degree of empirical support at each multi-level layer, incorporate a comprehensive program evaluation strategy, and use a variety of prevention techniques across levels of prevention

Mass and Spin of Poincare Gauge Theory

We discuss two expressions for the conserved quantities (energy momentum and angular momentum) of the Poincar\'e Gauge Theory. We show, that the variations of the Hamiltonians, of which the expressions are the respective boundary terms, are well defined, if we choose an appropriate phase space for asymptotic flat gravitating systems. Furthermore, we compare the expressions with others, known from the literature.Comment: 16 pages, plain-tex; to be published in Gen. Rel. Gra

On the energy of homogeneous cosmologies

An energy for the homogeneous cosmological models is presented. More specifically, using an appropriate natural prescription, we find the energy within any region with any gravitational source for a large class of gravity theories--namely those with a tetrad description--for all 9 Bianchi types. Our energy is given by the value of the Hamiltonian with homogeneous boundary conditions; this value vanishes for all regions in all Bianchi class A models, and it does not vanish for any class B model. This is so not only for Einstein's general relativity but, moreover, for the whole 3-parameter class of tetrad-teleparallel theories. For the physically favored one parameter subclass, which includes the teleparallel equivalent of Einstein's theory as an important special case, the energy for all class B models is, contrary to expectation, negative.Comment: 11 pages, reformated with minor change

Quasi-local energy-momentum and energy flux at null infinity

The null infinity limit of the gravitational energy-momentum and energy flux determined by the covariant Hamiltonian quasi-local expressions is evaluated using the NP spin coefficients. The reference contribution is considered by three different embedding approaches. All of them give the expected Bondi energy and energy flux.Comment: 14 pages, accepted by Phys.Rev.

Estimating the material properties of heel pad sub-layers using inverse finite element analysis

Detailed information about the biomechanical behaviour of plantar heel pad tissue contributes to our understanding of load transfer when the foot impacts the ground. The objective of this work was to obtain the hyperelastic and viscoelastic material properties of heel pad sub-layers (skin, micro-chamber and macro-chamber layers) in-vivo. An anatomically detailed 3D Finite Element model of the human heel was used to derive the sub-layer material properties. A combined ultrasound imaging and motorised platform system was used to compress heel pad and to create input data for the Finite Element model. The force-strain responses of the heel pad and its sub-layers under slow compression (5mm/s) and rapid loading-hold-unloading cycles (225mm/s), were measured and hyperelastic and viscoelastic properties of the three heel pad sub-layers were estimated by the model. The loaded (under ~315N) thickness of the heel pad was measured from MR images and used for hyperelastic model validation. The capability of the model to predict peak plantar pressure was used for further validation. Experimental responses of the heel pad under different dynamic loading scenarios (loading-hold-unloading cycles at 141mm/s and sinusoidal loading with maximum velocity of 300mm/s) were used to validate the viscoelastic model. Good agreement was achieved between the predicted and experimental results for both hyperelastic (<6.4% unloaded thickness, 4.4% maximum peak plantar pressure) and viscoelastic (Root Mean Square errors for loading and unloading periods <14.7%, 5.8% maximum force) simulations. This paper provides the first definition of material properties for heel pad sub-layers by using in-vivo experimental force-strain data and an anatomically detailed 3D Finite Element model of the heel

Pseudotensors and quasilocal energy-momentum

Early energy-momentum investigations for gravitating systems gave reference frame dependent pseudotensors; later the quasilocal idea was developed. Quasilocal energy-momentum can be determined by the Hamiltonian boundary term, which also identifies the variables to be held fixed on the boundary. We show that a pseudotensor corresponds to a Hamiltonian boundary term. Hence they are quasilocal and acceptable; each is the energy-momentum density for a definite physical situation with certain boundary conditions. These conditions are identified for well-known pseudotensors.Comment: LaTeX (REVTex), 4 pages, no figures, revised Title, abstract, introduction and conclusio

Symmetric Teleparallel Gravity: Some exact solutions and spinor couplings

In this paper we elaborate on the symmetric teleparallel gravity (STPG) written in a non-Riemannian spacetime with nonzero nonmetricity, but zero torsion and zero curvature. Firstly we give a prescription for obtaining the nonmetricity from the metric in a peculiar gauge. Then we state that under a novel prescription of parallel transportation of a tangent vector in this non-Riemannian geometry the autoparallel curves coincides with those of the Riemannian spacetimes. Subsequently we represent the symmetric teleparallel theory of gravity by the most general quadratic and parity conserving lagrangian with lagrange multipliers for vanishing torsion and curvature. We show that our lagrangian is equivalent to the Einstein-Hilbert lagrangian for certain values of coupling coefficients. Thus we arrive at calculating the field equations via independent variations. Then we obtain in turn conformal, spherically symmetric static, cosmological and pp-wave solutions exactly. Finally we discuss a minimal coupling of a spin-1/2 field to STPG.Comment: Accepted for publication in the International Journal of Modern Physics

Subject-specific finite element modelling of the human foot complex during walking: sensitivity analysis of material properties, boundary and loading conditions

This is the final version of the article. Available from Springer Verlag via the DOI in this record.The objective of this study was to develop and validate a subject-specific framework for modelling the human foot. This was achieved by integrating medical image-based finite element modelling, individualised multi-body musculoskeletal modelling and 3D gait measurements. A 3D ankle–foot finite element model comprising all major foot structures was constructed based on MRI of one individual. A multi-body musculoskeletal model and 3D gait measurements for the same subject were used to define loading and boundary conditions. Sensitivity analyses were used to investigate the effects of key modelling parameters on model predictions. Prediction errors of average and peak plantar pressures were below 10% in all ten plantar regions at five key gait events with only one exception (lateral heel, in early stance, error of 14.44%). The sensitivity analyses results suggest that predictions of peak plantar pressures are moderately sensitive to material properties, ground reaction forces and muscle forces, and significantly sensitive to foot orientation. The maximum region-specific percentage change ratios (peak stress percentage change over parameter percentage change) were 1.935–2.258 for ground reaction forces, 1.528–2.727 for plantar flexor muscles and 4.84–11.37 for foot orientations. This strongly suggests that loading and boundary conditions need to be very carefully defined based on personalised measurement data.This work was supported by the Grant of Biotechnology and Biological Sciences Research Council of UK (No. BB/H002782/1) and the Project of National Natural Science Foundation of China (No.51475202 and No. 51675222)