The Carter Constant for Inclined Orbits About a Massive Kerr Black Hole: I. circular orbits

In an extreme binary black hole system, an orbit will increase its angle of inclination (i) as it evolves in Kerr spacetime. We focus our attention on the behaviour of the Carter constant (Q) for near-polar orbits; and develop an analysis that is independent of and complements radiation reaction models. For a Schwarzschild black hole, the polar orbits represent the abutment between the prograde and retrograde orbits at which Q is at its maximum value for given values of latus rectum (l) and eccentricity (e). The introduction of spin (S = |J|/M2) to the massive black hole causes this boundary, or abutment, to be moved towards greater orbital inclination; thus it no longer cleanly separates prograde and retrograde orbits. To characterise the abutment of a Kerr black hole (KBH), we first investigated the last stable orbit (LSO) of a test-particle about a KBH, and then extended this work to general orbits. To develop a better understanding of the evolution of Q we developed analytical formulae for Q in terms of l, e, and S to describe elliptical orbits at the abutment, polar orbits, and last stable orbits (LSO). By knowing the analytical form of dQ/dl at the abutment, we were able to test a 2PN flux equation for Q. We also used these formulae to numerically calculate the di/dl of hypothetical circular orbits that evolve along the abutment. From these values we have determined that di/dl = -(122.7S - 36S^3)l^-11/2 -(63/2 S + 35/4 S^3) l^-9/2 -15/2 S l^-7/2 -9/2 S l^-5/2. Thus the abutment becomes an important analytical and numerical laboratory for studying the evolution of Q and i in Kerr spacetime and for testing current and future radiation back-reaction models for near-polar retrograde orbits.Comment: 51 pages, 8 figures, accepted by Classical and Quantum Gravity on September 22nd, 201

Fundamentals of Anesthesiology for Spaceflight

During future space exploration missions, the risk of medical events requiring surgery is significant, and will likely rely on anesthetic techniques. Available options during spaceflight include local, regional (nerve block) and general anesthesia. No actual invasive anesthesia was ever performed on humans in space or immediately after landing, and the safe delivery of such advanced medical care in this context is challenging. In the first section of this review, Human adaptation to the space environment is detailed, with a focus on the cardiovascular system, along with a discussion regarding which medical conditions may arise. The second part of the study focuses on discussing the extensive list of challenges associated with delivering an anesthetic procedure in space or on a foreign planetary surface. They schematically fall into two categories: missing technologies (generation of intravenous fluid, specific medical equipment, preservation of drugs…) and missing knowledge (human physiology in partial gravity, use of vasopressors, cardiovascular tolerance of general anesthesia and blood loss, choice of the most appropriate anesthetic technique, medical training). Future space exploration mis¬sions will push back the limits of human expe¬rience in maintaining health and performance of crew members in extreme settings. After more than five decades of research, our understanding of human physiology in weightlessness is advanced. Despite a number of challenges, the safe delivery of an anesthetic procedure on previously healthy individuals and given our current knowledge and technologies remains risky but could be possible even by non-anesthesiologists, and should not represent a showstopper for future space exploration missions

Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension

We consider the long time, large scale behavior of the Wigner transform W_\eps(t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile, Bernardin, and Olla to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile, Olla, and Spohn. In the present paper we prove that in the unpinned case there exists $\gamma_0>0$ such that for any $\gamma\in(0,\gamma_0]$ the weak limit of W_\eps(t/\eps^{3/2\gamma},x/\eps^{\gamma},k), as \eps\ll1, satisfies a one dimensional fractional heat equation $\partial_t W(t,x)=-\hat c(-\partial_x^2)^{3/4}W(t,x)$ with $\hat c>0$. In the pinned case an analogous result can be claimed for W_\eps(t/\eps^{2\gamma},x/\eps^{\gamma},k) but the limit satisfies then the usual heat equation

Towards Intelligent Databases

This article is a presentation of the objectives and techniques of deductive databases. The deductive approach to databases aims at extending with intensional definitions other database paradigms that describe applications extensionaUy. We first show how constructive specifications can be expressed with deduction rules, and how normative conditions can be defined using integrity constraints. We outline the principles of bottom-up and top-down query answering procedures and present the techniques used for integrity checking. We then argue that it is often desirable to manage with a database system not only database applications, but also specifications of system components. We present such meta-level specifications and discuss their advantages over conventional approaches

A Study of Elliptical Last Stable Orbits About a Massive Kerr Black Hole

The last stable orbit (LSO) of a compact object (CO) is an important boundary condition when performing numerical analysis of orbit evolution. Although the LSO is already well understood for the case where a test-particle is in an elliptical orbit around a Schwarzschild black hole (SBH) and for the case of a circular orbit about a Kerr black hole (KBH) of normalised spin, S (|J|/M^2, where J is the spin angular momentum of the KBH); it is worthwhile to extend our knowledge to include elliptical orbits about a KBH. This extension helps to lay the foundation for a better understanding of gravitational wave (GW) emission. The mathematical developments described in this work sprang from the use of an effective potential (V) derived from the Kerr metric, which encapsulates the Lense-Thirring precession. That allowed us to develop a new form of analytical expression to calculate the LSO Radius for circular orbits (R_LSO) of arbitrary KBH spin. We were then able to construct a numerical method to calculate the latus rectum (l_LSO) for an elliptical LSO. Abstract Formulae for E^2 (square of normalised orbital energy) and L^2 (square of normalised orbital angular momentum) in terms of eccentricity, e, and latus rectum, l, were previously developed by others for elliptical orbits around an SBH and then extended to the KBH case; we used these results to generalise our analytical l_LSO equations to elliptical orbits. LSO data calculated from our analytical equations and numerical procedures, and those previously published, are then compared and found to be in excellent agreement.Comment: 42 pages, 9 figures, accepted for publication in Classical and Quantum Gravit

Quantifying the impact of AI recommendations with explanations on prescription decision making

The influence of AI recommendations on physician behaviour remains poorly characterised. We assess how clinicians' decisions may be influenced by additional information more broadly, and how this influence can be modified by either the source of the information (human peers or AI) and the presence or absence of an AI explanation (XAI, here using simple feature importance). We used a modified between-subjects design where intensive care doctors (N=86) were presented on a computer for each of 16 trials with a patient case and prompted to prescribe continuous values for two drugs. We used a multi-factorial experimental design with four arms, where each clinician experienced all four arms on different subsets of our 24 patients. The four arms were (i) baseline (control), (ii) peer human clinician scenario showing what doses had been prescribed by other doctors, (iii) AI suggestion and (iv) XAI suggestion. We found that additional information (peer, AI or XAI) had a strong influence on prescriptions (significantly for AI, not so for peers) but simple XAI did not have higher influence than AI alone. There was no correlation between attitudes to AI or clinical experience on the AI-supported decisions and nor was there correlation between what doctors self-reported about how useful they found the XAI and whether the XAI actually influenced their prescriptions. Our findings suggest that the marginal impact of simple XAI was low in this setting and we also cast doubt on the utility of self-reports as a valid metric for assessing XAI in clinical experts

Sepsis biomarkers and diagnostic tools with a focus on machine learning.

Over the last years, there have been advances in the use of data-driven techniques to improve the definition, early recognition, subtypes characterisation, prognostication and treatment personalisation of sepsis. Some of those involve the discovery or evaluation of biomarkers or digital signatures of sepsis or sepsis sub-phenotypes. It is hoped that their identification may improve timeliness and accuracy of diagnosis, suggest physiological pathways and therapeutic targets, inform targeted recruitment into clinical trials, and optimise clinical management. Given the complexities of the sepsis response, panels of biomarkers or models combining biomarkers and clinical data are necessary, as well as specific data analysis methods, which broadly fall under the scope of machine learning. This narrative review gives a brief overview of the main machine learning techniques (mainly in the realms of supervised and unsupervised methods) and published applications that have been used to create sepsis diagnostic tools and identify biomarkers

Nonequilibrium dynamics of a stochastic model of anomalous heat transport

We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math. Theor. 42 (2009) 025001], we have studied the stationary state of this system with fixed boundary conditions, finding analytical exact expressions for the temperature profile and the heat current in the thermodynamic (continuum) limit. In this paper we extend the analysis to the evolution of the covariance matrix and to generic boundary conditions. Our main purpose is to construct a hydrodynamic description of the relaxation to the stationary state, starting from the exact equations governing the evolution of the correlation matrix. We identify and adiabatically eliminate the fast variables, arriving at a continuity equation for the temperature profile T(y,t), complemented by an ordinary equation that accounts for the evolution in the bulk. Altogether, we find that the evolution of T(y,t) is the result of fractional diffusion.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica