Radiation reaction in the 2.5PN waveform from inspiralling binaries in circular orbits

In this Comment we compute the contributions of the radiation reaction force in the 2.5 post-Newtonian (PN) gravitational wave polarizations for compact binaries in circular orbits. (i) We point out and correct an inconsistency in the derivation of Arun, Blanchet, Iyer, and Qusailah. (ii) We prove that all contributions from radiation reaction in the 2.5PN waveform are actually negligible since they can be absorbed into a modification of the orbital phase at the 5PN order.Comment: 7 pages, no figures, submitted to CQ

Empathy and the Right to Be an Exception: What LLMs Can and Cannot Do

Advances in the performance of large language models (LLMs) have led some researchers to propose the emergence of theory of mind (ToM) in artificial intelligence (AI). LLMs can attribute beliefs, desires, intentions, and emotions, and they will improve in their accuracy. Rather than employing the characteristically human method of empathy, they learn to attribute mental states by recognizing linguistic patterns in a dataset that typically do not include that individual. We ask whether LLMs' inability to empathize precludes them from honoring an individual's right to be an exception, that is, from making assessments of character and predictions of behavior that reflect appropriate sensitivity to a person's individuality. Can LLMs seriously consider an individual's claim that their case is different based on internal mental states like beliefs, desires, and intentions, or are they limited to judging that case based on its similarities to others? We propose that the method of empathy has special significance for honoring the right to be an exception that is distinct from the value of predictive accuracy, at which LLMs excel. We conclude by considering whether using empathy to consider exceptional cases has intrinsic or merely practical value and we introduce conceptual and empirical avenues for advancing this investigation

Evolution systems for non-linear perturbations of background geometries

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised background geometry approach, for systems where there is non-trivial a priori knowledge about the spacetime under study. The background three-geometry and associated connection are used to express the ADM evolution equations in terms of physical non-linear deviations from that background. Expressing the equations in first order form leads naturally to a system closely linked to the Einstein-Christoffel system, introduced by Anderson and York, and sharing its hyperbolicity properties. We illustrate the drastic alteration of the source structure of the equations, and discuss why this is likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in Physical Review

Identification of WNT/β-CATENIN Signaling Pathway Components in Human Cumulus Cells

Signaling via the conserved WNT/β-CATENIN pathway controls diverse developmental processes. To explore its potential role in the ovary, we investigated the expression of WNTs, frizzled (FZD) receptors and other pathway components in human cumulus cells obtained from oocytes collected for in vitro fertilization. Proteins were detected in cultured cells using immunofluorescence microscopy. Protein–protein interactions were analyzed by means of immunoprecipitation. WNT2, FZD2, FZD3 and FZD9 were identified but WNT1, WNT4 and FZD4 were not detected. WNT2 is co-expressed with FZD2, FZD3 and FZD9. Co-immunoprecipitation using WNT2 antibody demonstrated that WNT2 interacts with both FZD3 and FZD9, but only FZD9 antibody precipitated WNT2. We also identified DVL (disheveled), AXIN, GSK-3β (glycogen synthase kinase-3β) and β-CATENIN. β-CATENIN is concentrated in the plasma membranes. DVL co-localizes with FZD9 and AXIN in the membranes, but GSK-3β has little co-localization with AXIN and β-CATENIN. Interestingly, β-CATENIN is highly co-localized with FZD9 and AXIN. CDH1 (E-cadherin) was also detected in the plasma membranes and cytoplasm, co-localized with β-CATENIN, and CDH1 antibody precipitated β-CATENIN. The results suggest that WNT2 could act through its receptor FZD9 to regulate the β-CATENIN pathway in cumulus cells, recruiting β-CATENIN into plasma membranes and promoting the formation of adherens junctions involving CDH1

Hyperboloidal evolution of test fields in three spatial dimensions

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on compactification at null infinity in hyperboloidal scri fixing coordinates. We report numerical tests for the particular example of a scalar wave equation on Minkowski and Schwarzschild backgrounds. We address issues related to the implementation of the hyperboloidal approach for the Einstein equations, such as nonlinear source functions, matching, and evaluation of formally singular terms at null infinity.Comment: 10 pages, 8 figure

Evaluation of Sanders Associates proposal of 6/12/63 and general comments

This memorandum discusses a proposal for funding to do research on the heating of thermonuclear fuels to ignition temperatures by means of intense focused laser radiation. Technical comments are provided as to the proposal

Einstein boundary conditions for the 3+1 Einstein equations

In the 3+1 framework of the Einstein equations for the case of vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the normal to the boundary surface of the initial-boundary value problem. Such conditions take the form of evolution equations along (as opposed to across) the boundary for certain components of the extrinsic curvature and for certain space-derivatives of the intrinsic metric. We argue that, in general, such boundary conditions do not follow necessarily from the evolution equations and the initial data, but need to be imposed on the boundary values of the fundamental variables. Using the Einstein-Christoffel formulation, which is strongly hyperbolic, we show how three of the boundary equations should be used to prescribe the values of some incoming characteristic fields. Additionally, we show that the fourth one imposes conditions on some outgoing fields.Comment: Revtex 4, 6 pages, text and references added, typos corrected, to appear in Phys. Rev.

Laser Fusion: The First Ten Years 1962-1972

This account of the beginning of the program on laser fusion at Livermore in 1962, and its subsequent development during the decade ending in 1972, was originally prepared as a contribution to the January 1991 symposium 'Achievements in Physics' honoring Professor Keith Brueckner upon his retirement from the University of San Diego at La Jolla. It is a personal recollection of work at Livermore from my vantage point as its scientific leader, and of events elsewhere that I thought significant. This period was one of rapid growth in which the technology of high-power short-pulse lasers needed to drive the implosion of thermonuclear fuel to the temperature and density needed for ignition was developed, and in which the physics of the interaction of intense light with plasmas was explored both theoretically and experimentally

Assessment of the safety of US nuclear weapons and related nuclear test requirements: A post-Bush Initiative update

The Nuclear Weapons Reduction Initiative announced by President Bush on September 27, 1991, is described herein as set forth in Defense Secretary Cheney`s Nuclear Arsenal Reduction Order issued September 28, 1991. The implications of the Bush Initiative for improved nuclear weapons safety are assessed in response to a request by US Senators Harkin, Kennedy, and Wirth to the Lawrence Livermore National Laboratory that the author prepare such an assessment. The author provides an estimate of the number of nuclear tests needed to accomplish a variety of specified warhead safety upgrades, then uses the results of this estimate to answer three questions posed by the Senators. These questions concern pit reuse and the number of nuclear tests needed for specified safety upgrades of those ballistic missiles not scheduled for retirement, namely the Minuteman III, C4, and D5 missiles