Covariant Approach Research Articles

Equations of motion in scalar-tensor theories of gravity: A covariant multipolar approach

We discuss the dynamics of extended test bodies for a large class of scalar-tensor theories of gravitation. A covariant multipolar Mathisson---Papapetrou---Dixon type of approach is used to derive the equations of motion in a systematic way for both Jordan and Einstein formulations of these theories. The results obtained provide the framework to experimentally test scalar-tensor theories by means of extended test bodies.

An Isometric Dynamics for a Causal Set Approach to Discrete Quantum Gravity

We consider a covariant causal set approach to discrete quantum gravity. We first review the microscopic picture of this approach. In this picture a universe grows one element at a time and its geometry is determined by a sequence of integers called the shell sequence. We next present the macroscopic picture which is described by a sequential growth process. We introduce a model in which the dynamics is governed by a quantum transition amplitude. The amplitude satisfies a stochastic and unitary condition and the resulting dynamics becomes isometric. We show that the dynamics preserves stochastic states. By "doubling down" on the dynamics we obtain a unitary group representation and a natural energy operator. These unitary operators are employed to define canonical position and momentum operators.

Evaluation of a modified clinical prediction rule for use with spinal manipulative therapy in patients with chronic low back pain: a randomized clinical trial.

BackgroundSpinal Manipulative Therapy (SMT) and Active Exercise Therapy (AET) have both demonstrated efficacy in the treatment of Chronic Lower Back Pain (CLBP). A Clinical Prediction Rule (CPR) for responsiveness to SMT has been validated in a heterogeneous lower back pain population; however there is a need to evaluate this CPR specifically for patients with CLBP, which is a significant source of disability.MethodsWe conducted a randomized controlled trial (RCT) in Veteran Affairs and civilian outpatient clinics evaluating a modification of the original CPR (mCPR) in CLBP, eliminating acute low back pain and altering the specific types of SMT to improve generalizability. We enrolled and followed 181 patients with CLBP from 2007 to 2010. Patients were randomized by status on the mCPR to undergo either SMT or AET twice a week for four weeks. Providers and statisticians were blinded as to mCPR status. We collected outcome measures at 5, 12 and 24-weeks post baseline. We tested our study hypotheses by a general linear model repeated measures procedure following a univariate analysis of covariance approach. Outcome measures included, Visual Analogue Scale, Bodily pain subscale of SF-36 and the Oswestry Disability Index, Patient Satisfaction and Patient Expectation.ResultsOf the 89 AET patients, 69 (78%) completed the study and of the 92 SMT patients, 76 (83%) completed the study. As hypothesized, we found main effects of time where the SMT and AET groups showed significant improvements in pain and disability from baseline. There were no differences in treatment outcomes between groups in response to the treatment, given the lack of significant treatment x time interactions. The mCPR x treatment x time interactions were not significant. The differences in outcomes between treatment groups were the same for positive and negative on the mCPR groups, thus our second hypothesis was not supported.ConclusionsWe found no evidence that a modification of the original CPR can be used to discriminate CLBP patients that would benefit more from SMT. Further studies are needed to further clarify the patient characteristics that moderate treatment responsiveness to specific interventions for CLBP.Trial registrationISRCTN30511490

Quasilocal conserved charges and holography

We construct a quasi-local formalism for conserved charges in a theory of gravity in the presence of matter fields which may have slow falloff behaviors at the asymptotic infinity. This construction depends only on equations of motion and so it is irrespective of ambiguities in the total derivatives of the Lagrangian. By using identically conserved currents, we show that this formalism leads to the same expressions of conserved charges as those in the covariant phase space approach. At the boundary of the asymptotic AdS space, we also introduce an identically conserved boundary current which has the same structure as the bulk current and then show that this boundary current gives us the holographic conserved charges identical with those from the boundary stress tensor method. In our quasi-local formalism we present a general proof that conserved charges from the bulk potential are identical with those from the boundary current. Our results can be regarded as the extension of the existing results on the equivalence of conserved charges by the covariant phase space approach and by the boundary stress tensor method.

K-essential covariant holography

The holographic principle is applied to a flat Friedmann–Robertson–Walker space-time dominated by dark energy when this is due to the presence of a k-essence scalar field, both for dark energy and phantom scenarios. In this framework, a geometrical covariant approach permits the construction of holographic hypersurfaces. The resulting covariant preferred screens, both for phantom and non-phantom regions, are then compared with those obtained by using the holographic dark energy model with the future event horizon as the infrared cut-off. In the phantom case, one of the two obtained holographic screens is placed on the big rip hypersurface, both for the covariant holographic formalism and the holographic phantom model. It is also analysed whether this covariant formalism allows a mathematically consistent formulation of fundamental theories based on the existence of a S-matrix at infinite distances.

Octet and decuplet masses: A covariant three-body Faddeev calculation

We determine the baryon octet and decuplet masses as well as their wave functions in a covariant three-body Faddeev approach. We work in an approximation where irreducible three-body forces are neglected. In the two-body interactions we take into account a well explored rainbow-ladder kernel as well as flavor dependent meson-exchange terms motivated from the underlying quark-gluon interaction. Without flavor dependent forces we find agreement with the experimental spectrum on the 5-10 percent level. Including the flavor dependent terms on an exploratory level delivers a Sigma/Lambda splitting with the correct sign although the magnitude is still too small.

Holographic reconstruction of general bulk surfaces

We propose a reconstruction of general bulk surfaces in any dimension in terms of the differential entropy in the boundary field theory. In particular, we extend the proof of Headrick et al. to calculate the area of a general class of surfaces, which have a 1-parameter foliation over a closed manifold. The area can be written in terms of extremal surfaces whose boundaries lie on ring-like regions in the field theory. We discuss when this construction has a description in terms of spatial entanglement entropy and suggest lessons for a more complete and covariant approach.

Synthesis of spacecraft covariance controls

For a linear multidimensional mathematical model of spacecraft motion, a method for designing a highly accurate feedback for the spacecraft control system is developed. The proposed method is based on the relationship between the modal, optimizing, and covariance approaches to the feedback synthesis aimed at satisfying the prescribed requirements for the spacecraft control quality; this relationship is established in the paper. An example of the application of the proposed approach to the orbital stabilization of a spacecraft is discussed and simulation results are presented.

Equations of motion in metric-affine gravity: A covariant unified framework

We derive the equations of motion of extended deformable bodies in metric-affine gravity. The conservation laws which follow from the invariance of the action under the general coordinate transformations are used as a starting point for the discussion of the dynamics of extended deformable test bodies. By means of a covariant approach, based on Synge's world function, we obtain the master equation of motion for an arbitrary system of coupled conserved currents. This unified framework is then applied to metric-affine gravity. We confirm and extend earlier findings; in particular, we once again demonstrate that it is only possible to detect the post-Riemannian spacetime geometry by ordinary (non-microstructured) test bodies if gravity is nonminimally coupled to matter.

Airborne flux measurements of biogenic isoprene over California

Abstract. Biogenic isoprene fluxes were measured onboard the CIRPAS Twin Otter aircraft as part of the California Airborne Biogenic volatile organic compound (BVOC) Emission Research in Natural Ecosystem Transects (CABERNET) campaign during June 2011. The airborne virtual disjunct eddy covariance (AvDEC) approach used measurements from a proton transfer reaction mass spectrometer (PTR–MS) and a wind radome probe to directly determine fluxes of isoprene over 7400 km of flight paths focusing on areas of California predicted to have the largest emissions. The fast Fourier transform (FFT) approach was used to calculate fluxes of isoprene over long transects of more than 15 km, most commonly between 50 and 150 km. The continuous wavelet transformation (CWT) approach was used over the same transects to also calculate instantaneous isoprene fluxes with localization of both frequency and time independent of non-stationarities. Fluxes were generally measured by flying consistently at 400 m ± 50 m (a.g.l.) altitude, and extrapolated to the surface according to the determined flux divergence determined in the racetrack-stacked profiles. The wavelet-derived surface fluxes of isoprene averaged to 2 km spatial resolution showed good correspondence to basal emission factor (BEF) land-cover data sets used to drive BVOC emission models. The surface flux of isoprene was close to zero over Central Valley crops and desert shrublands, but was very high (up to 15 mg m−2 h−1) above oak woodlands, with clear dependence of emissions on temperature and oak density. Isoprene concentrations of up to 8 ppb were observed at aircraft height on the hottest days and over the dominant source regions. Even though the isoprene emissions from agricultural crop regions, shrublands, and coniferous forests were extremely low, observations at the Walnut Grove tower south of Sacramento demonstrate that isoprene oxidation products from the high emitting regions in the surrounding oak woodlands accumulate at night in the residual layer above the valley and mix down into the valley in the morning. Thus, the isoprene emissions surrounding the valley have relevance for the regional photochemistry that is not immediately apparent solely from the direct emission flux distribution. This paper reports the first regional observations of fluxes from specific sources by eddy covariance from an aircraft which can finally constrain statewide isoprene emission inventories used for ozone simulations by state agencies. While previously there was no available means to constrain the biogenic models, our results provide a good understanding of what the major sources of isoprene are in California, their magnitude, and how they are distributed. This data set on isoprene fluxes will be particularly useful for evaluating potential model alternatives which will be dealt with in a separate paper to assess isoprene emission models and their driving variable data sets.

Age-related increases in long-range connectivity in fetal functional neural connectivity networks in utero

Formation of operational neural networks is one of the most significant accomplishments of human fetal brain growth. Recent advances in functional magnetic resonance imaging (fMRI) have made it possible to obtain information about brain function during fetal development. Specifically, resting-state fMRI and novel signal covariation approaches have opened up a new avenue for non-invasive assessment of neural functional connectivity (FC) before birth. Early studies in this area have unearthed new insights about principles of prenatal brain function. However, very little is known about the emergence and maturation of neural networks during fetal life. Here, we obtained cross-sectional rs-fMRI data from 39 fetuses between 24 and 38 weeks postconceptual age to examine patterns of connectivity across ten neural FC networks. We identified primitive forms of motor, visual, default mode, thalamic, and temporal networks in the human fetal brain. We discovered the first evidence of increased long-range, cerebral-cerebellar, cortical-subcortical, and intra-hemispheric FC with advancing fetal age. Continued aggregation of data about fundamental neural connectivity systems in utero is essential to establishing principles of connectomics at the beginning of human life. Normative data provides a vital context against which to compare instances of abnormal neurobiological development.

Concentrations and fluxes of isoprene and oxygenated VOCs at a French Mediterranean oak forest

Abstract. The CANOPEE project aims to better understand the biosphere–atmosphere exchanges of biogenic volatile organic compounds (BVOCs) in the case of Mediterranean ecosystems and the impact of in-canopy processes on the atmospheric chemical composition above the canopy. Based on an intensive field campaign, the objective of our work was to determine the chemical composition of the air inside a canopy as well as the net fluxes of reactive species between the canopy and the boundary layer. Measurements were carried out during spring 2012 at the field site of the Oak Observatory of the Observatoire de Haute Provence (O3HP) located in the southeast of France. The site is a forest ecosystem dominated by downy oak, Quercus pubescens Willd., a typical Mediterranean species which features large isoprene emission rates. Mixing ratios of isoprene, its degradation products methylvinylketone (MVK) and methacrolein (MACR) and several other oxygenated VOC (OxVOC) were measured above the canopy using an online proton transfer reaction mass spectrometer (PTR-MS), and fluxes were calculated by the disjunct eddy covariance approach. The O3HP site was found to be a very significant source of isoprene emissions, with daily maximum ambient concentrations ranging between 2–16 ppbv inside and 2–5 ppbv just above the top of the forest canopy. Significant isoprene fluxes were observed only during daytime, following diurnal cycles with midday net emission fluxes from the canopy ranging between 2.0 and 9.7 mg m−2 h1. Net isoprene normalized flux (at 30 °C, 1000 μmol quanta m−2 s−1) was estimated at 7.4 mg m−2 h−1. Evidence of direct emission of methanol was also found exhibiting maximum daytime fluxes ranging between 0.2 and 0.6 mg m−2 h−1, whereas flux values for monoterpenes and others OxVOC such as acetone and acetaldehyde were below the detection limit. The MVK+MACR-to-isoprene ratio provided useful information on the oxidation of isoprene, and is in agreement with recent findings proposing weak production yields of MVK and MACR, in remote forest regions where the NOx concentrations are low. In-canopy chemical oxidation of isoprene was found to be weak and did not seem to have a significant impact on isoprene concentrations and fluxes above the canopy.

A recommended analysis for 2 × 2 crossover trials with baseline measurements.

In many two-period, two-treatment (2 × 2) crossover trials, for each subject, a continuous response of interest is measured before and after administration of the assigned treatment within each period. The resulting data are typically used to test a null hypothesis involving the true difference in treatment response means. We show that the power achieved by different statistical approaches is greatly influenced by (i) the 'structure' of the variance-covariance matrix of the vector of within-subject responses and (ii) how the baseline (i.e., pre-treatment) responses are accounted for in the analysis. For (ii), we compare different approaches including ignoring one or both period baselines, using a common change from baseline analysis (which we advise against), using functions of one or both baselines as period-specific or period-invariant covariates, and doing joint modeling of the post-baseline and baseline responses with corresponding mean constraints for the latter. Based on theoretical arguments and simulation-based type I error rate and power properties, we recommend an analysis of covariance approach that uses the within-subject difference in treatment responses as the dependent variable and the corresponding difference in baseline responses as a covariate. Data from three clinical trials are used to illustrate the main points.

The mutual-information-based variance–covariance approach: an application to operational risk aggregation in Chinese banking

Most advanced measurement approaches cannot simultaneously capture the overall dependence between operational risk components and be easy to use and understand. This paper proposes a mutual information-based variance covariance approach that is able to capture the overall correlation and is also highly tractable. Specifically, we replace the linear correlation coefficient with the global correlation coefficient in the framework of the variance-covariance approach. Originating from the theory of mutual information, the global correlation coefficient is able to capture both linear and nonlinear correlation relationships. The value-at-risk (VaR) of each individual risk component is calculated; these VaRs are then aggregated by using the global correlation coefficient. In empirical analysis, the proposed approach is employed to aggregate the operational risk of Chinese banking across business lines, based on the most comprehensive (to the best of our knowledge) operational risk data set. After an overall comparison with results from other correlation assumptions and the actual capital allocation of Chinese banking in 2013, we conclude that the actual capital allocation in China at present is not effective, and the aggregate VaR calculated from our approach is more reasonable.

Reconstructing static spherically symmetric metrics in general relativity

We present a general method to reconstruct static spherically symmetric metrics in general relativity based on the $1+1+2$ covariant approach. This method allows a more complete exploration of the properties of these metrics in the case of a generic fluid and in the presence of a scalar field. A number of new exact solutions are reconstructed in these cases.

QED radiative effects in the processes of exclusive photon electroproduction from polarized protons with the next-to-leading accuracy

Radiative effects in the electroproduction of photons in polarized $ep$ scattering are calculated with next-to-leading-order accuracy. The contributions of loops and two-photon emission are presented in analytical form. The covariant approach of Bardin and Shumeiko is used to extract the infrared divergence. All contributions to the radiative correction are presented in the form of the correction to the leptonic tensor thus allowing for further applications in other experiments, e.g., deep inelastic scattering. The radiative corrections to the cross sections and polarization asymmetries are analyzed numerically for the kinematical conditions of the current measurement at Jefferson Lab. Specific attention is paid to analyzing kinematical conditions for the process with a large radiative effect when the momenta of two photons in the final state are collinear with the momenta of the initial and final electrons, respectively.

Covariant approaches to superconformal blocks

We develop techniques for computing superconformal blocks in 4d superconformal field theories. First we study the super-Casimir differential equation, deriving simple new expressions for superconformal blocks for 4-point functions containing chiral operators in theories with N-extended supersymmetry. We also reproduce these results by extending the "shadow formalism" of Ferrara, Gatto, Grillo, and Parisi to supersymmetric theories, where superconformal blocks can be represented as superspace integrals of three-point functions multiplied by shadow three-point functions.

(Anti-)de Sitter Superfluid with Spherical Symmetry

The thermodynamics of spherically symmetric region of a general relativistic superfluid is discussed in the context of (Anti-)de Sitter geometry. Also the covariant energy tensor is obtained through a covariant statistic mechanical approach.

A comparison of two stochastic model updating methods using the DLR AIRMOD test structure

The problem of stochastic model updating is addressed by means of the application of two methods (covariance and interval model updating) to the DLR AIRMOD structure which is repeatedly disassembled and reassembled to provide a database of modal variability due to uncertainty in joint and support stiffnesses and masses of cables and screws. The covariance method is based on an assumption of small uncertainty and implemented at each step of an iterative approach by forward propagation of uncertain parameters using a multivariate normal distribution. The interval approach is based on a Kriging meta-model, thereby providing a very efficient surrogate to replace the expensive full finite element model. This allows a mapping from multiple output measurements to define a hypercube bounded by intervals of parameter uncertainty. It is shown that the measured data is fully enclosed by the hyper-ellipses and hypercubes of the covariance and interval methods respectively. As expected, the interval method is found to be more conservative than the covariance approach but still provides useful estimates without restriction by any assumption of probability distribution.

Techniques of applying wavelet de-noising into a combined model for short-term load forecasting

Electrical load time series are non-stationary and highly noisy because a variety of factors affect electrical markets. The direct forecasting of electrical load with noisy data is usually subject to large errors. This paper proposes a novel approach for short-term load forecasting (STLF) by applying wavelet de-noising in a combined model that is a hybrid of the seasonal autoregressive integrated moving average model (SARIMA) and neural networks. The process of the proposed approach first decomposes the historical data into an approximate part associated with low frequency and a detailed part associated with high frequencies via a wavelet transform. A SARIMA and a back propagation neural network (BPNN) are then established by the low-frequency signal to forecast the future value. Finally, the short-term load is forecasted by combining the prediction values of SARIMA and BPNN, and the weights of the combination are determined using a variance–covariance approach. To evaluate the performance of the proposed approach, the electricity load data in New South Wales, Australia, are used as an illustrative example. A comparison of the results with other models shows that the proposed model can effectively improve the forecasting accuracy.