The Hamiltonian formulation of General Relativity: myths and reality

A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in "Gravitation: An Introduction to Current Research" (1962) 227] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i-iii) have been shown to be incorrect in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric $g_{\mu\nu}$ to lapse and shift functions and the three-metric $g_{km}$, which is not canonical. This proves that point (iv) is incorrect. Points (i-iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein's theory itself.Comment: References are added and updated, Introduction is extended, Subsection 3.5 is added, 83 pages; corresponds to the published versio

Acute biphenotypic leukaemia: immunophenotypic and cytogenetic analysis

The incidence of acute biphenotypic leukaemia has ranged from less than 1% to almost 50% in various reports in the literature. This wide variability may be attributed to a number of reasons including lack of consistent diagnostic criteria, use of various panels of antibodies, and the failure to recognize the lack of lineage specificity of some of the antibodies used. The morphology, cytochemistry, immunophenotype and cytogenetics of acute biphenotypic leukaemias from our institution were studied. The diagnostic criteria took into consideration the morphology of the analysed cells, light scatter characteristics, and evaluation of antibody fluorescence histograms in determining whether the aberrant marker expression was arising from leukaemic blasts or differentiated bone marrow elements. Fifty-two of 746 cases (7%) fulfilled our criteria for acute biphenotypic leukaemias. These included 30 cases of acute lymphoblastic leukaemia (ALL) expressing myeloid antigens, 21 cases of acute myelogenous leukaemia (AML) expressing lymphoid markers, and one case of ALL expressing both B- and T-cell associated antigens. The acute biphenotypic leukaemia cases consisted of four major immunophenotypic subgroups: CD2± AML (11), CD19± AML (8), CD13 and/or CD33± ALL (24), CD11b± ALL (5) and others (4). Chromosomal analysis was carried out in 42/52 of the acute biphenotypic leukaemia cases; a clonal abnormality was found in 31 of these 42 cases. This study highlights the problems encountered in the diagnosis of acute biphenotypic leukaemia, some of which may be reponsible for the wide variation in the reported incidence of this leukaemia. We suggest that the use of strict, uniform diagnostic criteria may help in establishing a more consistent approach towards diagnosis of this leukaemic entity. We also suggest that biphenotypic leukaemia is comprised of biologically different groups of leukaemia based on immunophenotypic and cytogenetic findings.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73301/1/j.1365-2141.1993.tb03024.x.pd

Can Current Moisture Responses Predict Soil CO2 Efflux Under Altered Precipitation Regimes? A Synthesis of Manipulation Experiments

As a key component of the carbon cycle, soil CO2 efflux (SCE) is being increasingly studied to improve our mechanistic understanding of this important carbon flux. Predicting ecosystem responses to climate change often depends on extrapolation of current relationships between ecosystem processes and their climatic drivers to conditions not yet experienced by the ecosystem. This raises the question to what extent these relationships remain unaltered beyond the current climatic window for which observations are available to constrain the relationships. Here, we evaluate whether current responses of SCE to fluctuations in soil temperature and soil water content can be used to predict SCE under altered rainfall patterns. Of the 58 experiments for which we gathered SCE data, 20 were discarded because either too few data were available, or inconsistencies precluded their incorporation in the analyses. The 38 remaining experiments were used to test the hypothesis that a model parameterized with data from the control plots (using soil temperature and water content as predictor variables) could adequately predict SCE measured in the manipulated treatment. Only for seven of these 38 experiments, this hypothesis was rejected. Importantly, these were the experiments with the most reliable datasets, i.e., those providing high-frequency measurements of SCE. Accordingly, regression tree analysis demonstrated that measurement frequency was crucial; our hypothesis could be rejected only for experiments with measurement intervals of less than 11 days, and was not rejected for any of the 24 experiments with larger measurement intervals. This highlights the importance of high-frequency measurements when studying effects of altered precipitation on SCE, probably because infrequent measurement schemes have insufficient capacity to detect shifts in the climate-dependencies of SCE. We strongly recommend that future experiments focus more strongly on establishing response functions across a broader range of precipitation regimes and soil moisture conditions. Such experiments should make accurate measurements of water availability, they require high-frequency SCE measurements and they should consider both instantaneous responses and the potential legacy effects of climate extremes. This is important, because we demonstrated that at least for some ecosystems, current moisture responses cannot be extrapolated to predict SCE under altered rainfall

Guidelines and considerations for designing field experiments simulating precipitation extremes in forest ecosystems

1. Precipitation regimes are changing in response to climate change, yet understanding of how forest ecosystems respond to extreme droughts and pluvials remains incomplete. As future precipitation extremes will likely fall outside the range of historical variability, precipitation manipulation experiments (PMEs) are critical to advancing knowledge about potential ecosystem responses. However, few PMEs have been conducted in forests compared to short‐statured ecosystems, and forest PMEs have unique design requirements and constraints. Moreover, past forest PMEs have lacked coordination, limiting cross‐site comparisons. Here, we review and synthesize approaches, challenges, and opportunities for conducting PMEs in forests, with the goal of guiding design decisions, while maximizing the potential for coordination. 2. We reviewed 63 forest PMEs at 70 sites world‐wide. Workshops, meetings, and communications with experimentalists were used to generate and build consensus around approaches for addressing the key challenges and enhancing coordination. 3. Past forest PMEs employed a variety of study designs related to treatment level, replication, plot and infrastructure characteristics, and measurement approaches. Important considerations for establishing new forest PMEs include: selecting appropriate treatment levels to reach ecological thresholds; balancing cost, logistical complexity, and effectiveness in infrastructure design; and preventing unintended water subsidies. Response variables in forest PMEs were organized into three broad tiers reflecting increasing complexity and resource intensiveness, with the first tier representing a recommended core set of common measurements. 4. Differences in site conditions combined with unique research questions of experimentalists necessitate careful adaptation of guidelines for forest PMEs to balance local objectives with coordination among experiments. We advocate adoption of a common framework for coordinating forest PME design to enhance cross‐site comparability and advance fundamental knowledge about the response and sensitivity of diverse forest ecosystems to precipitation extremes.New Hampshire Agricultural Experiment Station, Grant/Award Number: NH00071-M; Northern States Research Cooperative, Grant/Award Number: 14-DG-11242307- 142; National Science Foundation Long-Term Ecological Research, Grant/Award Number: 1637685; USDA Forest Service; University of New Hampshire; NASA, Grant/Award Number: NNX14AD31G; USDA National Institute of Food and Agriculture McIntire- Stennis Project, Grant/Award Number: NH00071-M; U.S. Department of Energy; Office of Science’s Terrestrial Ecosystem Science program; Pacific Northwest National Labs’ LDRD program; MSCA-IF 2015; EU-Horizon2020 program; NSF’s Research Coordination Network Progra

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58×10-8, Ω0V<6.35×10-8, and Ω0S<1.08×10-7 at a reference frequency f0=25 Hz. © 2018 American Physical Society

Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)

[no abstract available