Energy and Momentum Distributions of Kantowski and Sachs Space-time

We use the Einstein, Bergmann-Thomson, Landau-Lifshitz and Papapetrou energy-momentum complexes to calculate the energy and momentum distributions of Kantowski and Sachs space-time. We show that the Einstein and Bergmann-Thomson definitions furnish a consistent result for the energy distribution, but the definition of Landau-Lifshitz do not agree with them. We show that a signature switch should affect about everything including energy distribution in the case of Einstein and Papapetrou prescriptions but not in Bergmann-Thomson and Landau-Lifshitz prescriptions.Comment: 12 page

The averaged tensors of the relative energy-momentum and angular momentum in general relativity and some their applications

There exist at least a few different kind of averaging of the differences of the energy-momentum and angular momentum in normal coordinates {\bf NC(P)} which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [1-8] giving the {\it canonical superenergy and angular supermomentum tensors}. In this paper we present another averaging of the differences of the energy-momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy-momentum and angular momentum densities. But these averaged relative energy-momentum and angular momentum tensors, closely related to the canonical superenergy and angular supermomentum tensors, {\it depend on some fundamental length $L>0$}. The averaged relative energy-momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to {\it coordinate independent} analysis (local and in special cases also global) of this field. We have applied the averaged relative energy-momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general) universes. The obtained results are very interesting, e.g., the averaged relative energy density is {\it positive definite} for the all Friedman universes.Comment: 30 pages, minor changes referring to Kasner universe

Fasting of Ramadan in peoples with diabetes in Benghazi, Libya: an exploratory study

Background: The epidemiology of diabetes and Ramadan fasting was reported from many Muslim countries, but not from Libya. Methodology: We interviewed 493 consecutive diabetic patients at Benghazi Diabetes and Endocrine Center for the potential complications of fasting during Ramadan. Results: We found 70% of diabetic patients completed the 30 days of Ramadan fasting. Hypo- and hyperglycemia was the most commonly reported complications especially during the first two weeks of Ramadan month. Conclusion: It seems majority of diabetic patients in Libya manage to fast during Ramadan month. Patient education and early planned adjustment of diabetic medication is needed to decrease the frequency of diabetic complication during Ramadan month

Energy-momentum Prescriptions in General Spherically Symmetric Space-times

Einstein, Landau-Lifshitz, Papapetrou, Weinberg, and M{\o}ller energy-momentum prescriptions in general spherically symmetric space-times are investigated. It is shown that for two special but not unusual classes of general spherically symmetric space-times several energy-momentum prescriptions in Schwarzschild Cartesian coordinates lead to some coincidences in energy distribution. It is also obtained that for a special class of spherically symmetric metrics M{\o}ller and Einstein energy-momentum prescriptions give the same result for energy distribution if and only if it has a specific dependence on radial coordinate.Comment: LaTeX, 7 pages: added reference

Energy and Momentum densities of cosmological models, with equation of state ρ=μ\rho=\mu, in general relativity and teleparallel gravity

We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex's value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.Comment: 15 pages, no figures, Minor typos corrected; version to appear in International Journal of Theoretical Physic

The effect of a high-polyphenol Mediterranean diet (Green-MED) combined with physical activity on age-related brain atrophy: The Dietary Intervention Randomized Controlled Trial Polyphenols Unprocessed Study (DIRECT PLUS)

Background: The effect of diet on age-related brain atrophy is largely unproven. Objectives: We aimed to explore the effect of a Mediterranean diet (MED) higher in polyphenols and lower in red/processed meat (Green-MED diet) on age-related brain atrophy. Methods: This 18-mo clinical trial longitudinally measured brain structure volumes by MRI using hippocampal occupancy score (HOC) and lateral ventricle volume (LVV) expansion score as neurodegeneration markers. Abdominally obese/dyslipidemic participants were randomly assigned to follow 1) healthy dietary guidelines (HDG), 2) MED, or 3) Green-MED diet. All subjects received free gym memberships and physical activity guidance. Both MED groups consumed 28 g walnuts/d (+440 mg/d polyphenols). The Green-MED group consumed green tea (3-4 cups/d) and Mankai (Wolffia-globosa strain, 100 g frozen cubes/d) green shake (+800 mg/d polyphenols). Results: Among 284 participants (88% men; mean age: 51 y; BMI: 31.2 kg/m2; APOE-ε4 genotype = 15.7%), 224 (79%) completed the trial with eligible whole-brain MRIs. The pallidum (-4.2%), third ventricle (+3.9%), and LVV (+2.2%) disclosed the largest volume changes. Compared with younger participants, atrophy was accelerated among those ≥50 y old (HOC change: -1.0% ± 1.4% compared with -0.06% ± 1.1%; 95% CI: 0.6%, 1.3%; P Conclusions: A Green-MED (high-polyphenol) diet, rich in Mankai, green tea, and walnuts and low in red/processed meat, is potentially neuroprotective for age-related brain atrophy.This trial was registered at clinicaltrials.gov as NCT03020186

Compactifying the state space for alternative theories of gravity

In this paper we address important issues surrounding the choice of variables when performing a dynamical systems analysis of alternative theories of gravity. We discuss the advantages and disadvantages of compactifying the state space, and illustrate this using two examples. We first show how to define a compact state space for the class of LRS Bianchi type I models in $R^n$-gravity and compare to a non--compact expansion--normalised approach. In the second example we consider the flat Friedmann matter subspace of the previous example, and compare the compact analysis to studies where non-compact non--expansion--normalised variables were used. In both examples we comment on the existence of bouncing or recollapsing orbits as well as the existence of static models.Comment: 18 pages, revised to match published versio

Graph-based topic models for trajectory clustering in crowd videos

Probabilistic topic modelings, such as latent Dirichlet allocation (LDA) and correlated topic models (CTM), have recently emerged as powerful statistical tools for processing video content. They share an important property, i.e., using a common set of topics to model all data. However such property can be too restrictive for modeling complex visual data such as crowd scenes where multiple fields of heterogeneous data jointly provide rich information about objects and events. This paper proposes graph-based extensions of LDA and CTM, referred to as GLDA and GCTM, to learn and analyze motion patterns by trajectory clustering in a highly cluttered and crowded environment. Unlike previous works that relied on a scene prior, we apply a spatio-temporal graph (STG) to uncover the spatial and temporal coherence between the trajectories of crowd motion during the learning process. The presented models advance the conventional approaches by integrating a manifold-based clustering as initialization and iterative statistical inference as optimization. The output of GLDA and GCTM are mid-level features that represent the motion patterns used later to generate trajectory clusters. Experiments on three different datasets show the effectiveness of the approaches in trajectory clustering and crowd motion modeling