Center of mass integral in canonical general relativity

For a two-surface B tending to an infinite--radius round sphere at spatial infinity, we consider the Brown--York boundary integral H_B belonging to the energy sector of the gravitational Hamiltonian. Assuming that the lapse function behaves as N \sim 1 in the limit, we find agreement between H_B and the total Arnowitt--Deser--Misner energy, an agreement first noted by Braden, Brown, Whiting, and York. However, we argue that the Arnowitt--Deser--Misner mass--aspect differs from a gauge invariant mass--aspect by a pure divergence on the unit sphere. We also examine the boundary integral H_B corresponding to the Hamiltonian generator of an asymptotic boost, in which case the lapse N \sim x^k grows like one of the asymptotically Cartesian coordinate functions. Such an integral defines the kth component of the center of mass for a Cauchy surface \Sigma bounded by B. In the large--radius limit, we find agreement between H_B and an integral introduced by Beig and O'Murchadha. Although both H_B and the Beig--O'Murchadha integral are naively divergent, they are in fact finite modulo the Hamiltonian constraint. Furthermore, we examine the relationship between H_B and a certain two--surface integral linear in the spacetime Riemann curvature tensor. Similar integrals featuring the curvature appear in works by Ashtekar and Hansen, Penrose, Goldberg, and Hayward. Within the canonical 3+1 formalism, we define gravitational energy and center--of--mass as certain moments of Riemann curvature.Comment: 52 pages, revtex4, uses amsmath and amssym

When to Censor?

Loss to follow-up is an endemic feature of time-to-event analyses that precludes observation of the event of interest. To our knowledge, in typical cohort studies with encounters occurring at regular or irregular intervals, there is no consensus on how to handle person-time between participants’ last study encounter and the point at which they meet a definition of loss to follow-up. We demonstrate, using simulation and an example, that when the event of interest is captured outside of a study encounter (e.g., in a registry), person-time should be censored when the study-defined criterion for loss to follow-up is met (e.g., 1 year after last encounter), rather than at the last study encounter. Conversely, when the event of interest must be measured within the context of a study encounter (e.g., a biomarker value), person-time should be censored at the last study encounter. An inappropriate censoring scheme has the potential to result in substantial bias that may not be easily corrected

A quasilocal calculation of tidal heating

We present a method for computing the flux of energy through a closed surface containing a gravitating system. This method, which is based on the quasilocal formalism of Brown and York, is illustrated by two applications: a calculation of (i) the energy flux, via gravitational waves, through a surface near infinity and (ii) the tidal heating in the local asymptotic frame of a body interacting with an external tidal field. The second application represents the first use of the quasilocal formalism to study a non-stationary spacetime and shows how such methods can be used to study tidal effects in isolated gravitating systems.Comment: REVTex, 4 pages, 1 typo fixed, standard sign convention adopted for the Newtonian potential, a couple of lines added to the discussion of gauge dependent term

Boundary Conditions and Quasilocal Energy in the Canonical Formulation of All 1+1 Models of Gravity

Within a first-order framework, we comprehensively examine the role played by boundary conditions in the canonical formulation of a completely general two-dimensional gravity model. Our analysis particularly elucidates the perennial themes of mass and energy. The gravity models for which our arguments are valid include theories with dynamical torsion and so-called generalized dilaton theories (GDTs). Our analysis of the canonical action principle (i) provides a rigorous correspondence between the most general first-order two-dimensional Einstein-Cartan model (ECM) and GDT and (ii) allows us to extract in a virtually simultaneous manner the ``true degrees of freedom'' for both ECMs and GDTs. For all such models, the existence of an absolutely conserved (in vacuo) quantity C is a generic feature, with (minus) C corresponding to the black-hole mass parameter in the important special cases of spherically symmetric four-dimensional general relativity and standard two-dimensional dilaton gravity. The mass C also includes (minimally coupled) matter into a ``universal mass function.'' We place particular emphasis on the (quite general) class of models within GDT possessing a Minkowski-like groundstate solution (allowing comparison between $C$ and the Arnowitt-Deser-Misner mass for such models).Comment: REVTeX, 41 pages, 2 Postscript figures, 10 macro

Beyond binary retention in HIV care: Predictors of the dynamic processes of patient engagement, disengagement, and re-entry into care in a US clinical cohort

Objectives: Studies examining engagement in HIV care often capture cross-sectional patient status to estimate retention and identify predictors of attrition, which ignore longitudinal patient care-seeking behaviors. We describe the cyclical nature of (dis)engagement and re-entry into HIV care using the state transition framework. Design: We represent the dynamic patterns of patient care-retention using five states: engaged in care, missed one, two, three, or more expected visits, and deceased. Then we describe various care-seeking behaviors in terms of transitioning from one state to another (e.g. from disengaged to engaged). This analysis includes 31 009 patients enrolled in the Center for AIDS Research Network of Integrated Systems (CNICS) in the United States from 1996 to 2014. Method: Multistate models for longitudinal data were used to identify barriers to retention and subgroups at higher risk of falling out of care. Results: The initial 2 years following primary engagement in care were a crucial time for improving retention. Patients who had not initiated antiretroviral therapy, with lower CD4+ cell counts, higher viral load, or not having an AIDS-defining illness were less likely to be retained in care. Conclusion: Beyond the individual patient characteristics typically used to characterize retention in HIV care, we identified specific periods of time and points in the care continuum associated with elevated risk of transitioning out of care. Our findings can contribute to evidence-based recommendations to enhance long-term retention in CNICS. This approach can also be applied to other cohort data to identify retention strategies tailored to each population

Comparing results from multiple imputation and dynamic marginal structural models for estimating when to start antiretroviral therapy

Optimal timing of initiating antiretroviral therapy has been a controversial topic in HIV research. Two highly publicized studies applied different analytical approaches, a dynamic marginal structural model and a multiple imputation method, to different observational databases and came up with different conclusions. Discrepancies between the two studies' results could be due to differences between patient populations, fundamental differences between statistical methods, or differences between implementation details. For example, the two studies adjusted for different covariates, compared different thresholds, and had different criteria for qualifying measurements. If both analytical approaches were applied to the same cohort holding technical details constant, would their results be similar? In this study, we applied both statistical approaches using observational data from 12,708 HIV‐infected persons throughout the USA. We held technical details constant between the two methods and then repeated analyses varying technical details to understand what impact they had on findings. We also present results applying both approaches to simulated data. Results were similar, although not identical, when technical details were held constant between the two statistical methods. Confidence intervals for the dynamic marginal structural model tended to be wider than those from the imputation approach, although this may have been due in part to additional external data used in the imputation analysis. We also consider differences in the estimands, required data, and assumptions of the two statistical methods. Our study provides insights into assessing optimal dynamic treatment regimes in the context of starting antiretroviral therapy and in more general settings

Atmospheric Heating and Wind Acceleration: Results for Cool Evolved Stars based on Proposed Processes

A chromosphere is a universal attribute of stars of spectral type later than ~F5. Evolved (K and M) giants and supergiants (including the zeta Aurigae binaries) show extended and highly turbulent chromospheres, which develop into slow massive winds. The associated continuous mass loss has a significant impact on stellar evolution, and thence on the chemical evolution of galaxies. Yet despite the fundamental importance of those winds in astrophysics, the question of their origin(s) remains unsolved. What sources heat a chromosphere? What is the role of the chromosphere in the formation of stellar winds? This chapter provides a review of the observational requirements and theoretical approaches for modeling chromospheric heating and the acceleration of winds in single cool, evolved stars and in eclipsing binary stars, including physical models that have recently been proposed. It describes the successes that have been achieved so far by invoking acoustic and MHD waves to provide a physical description of plasma heating and wind acceleration, and discusses the challenges that still remain.Comment: 46 pages, 9 figures, 1 table; modified and unedited manuscript; accepted version to appear in: Giants of Eclipse, eds. E. Griffin and T. Ake (Berlin: Springer

Estimating multiple time-fixed treatment effects using a semi-Bayes semiparametric marginal structural Cox proportional hazards regression model

Marginal structural models for time-fixed treatments fit using inverse-probability weighted estimating equations are increasingly popular. Nonetheless, the resulting effect estimates are subject to finite-sample bias when data are sparse, as is typical for large-sample procedures. Here we propose a semi-Bayes estimation approach which penalizes or shrinks the estimated model parameters to improve finite-sample performance. This approach uses simple symmetric data-augmentation priors. Limited simulation experiments indicate that the proposed approach reduces finite-sample bias and improves confidence-interval coverage when the true values lie within the central “hill” of the prior distribution. We illustrate the approach with data from a nonexperimental study of HIV treatments

Scale Vs. Conformal Invariance in the AdS/CFT Correspondence

We present two examples of non-trivial field theories which are scale invariant, but not conformally invariant. This is done by placing certain field theories, which are conformally invariant in flat space, onto curved backgrounds of a specific type. We define this using the AdS/CFT correspondence, which relates the physics of gravity in asymptotically Anti-de Sitter (AdS) spacetimes to that of a conformal field theory (CFT) in one dimension fewer. The AdS rotating (Kerr) black holes in five and seven dimensions provide us with the examples, since by the correspondence we are able to define and compute the action and stress tensor of four and six dimensional field theories residing on rotating Einstein universes, using the ``boundary counterterm'' method. The rotation breaks conformal but not scale invariance. The AdS/CFT framework is therefore a natural arena for generating such examples of non-trivial scale invariant theories which are not conformally invariant.Comment: 4 pages, RevTeX (v3: references added