Asymptotic expansions close to the singularity in Gowdy spacetimes

We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In an article by Grubisic and Moncrief, a formal expansion of solutions in the direction toward the singularity was proposed. Later, Kichenassamy and Rendall constructed a family of real analytic solutions with the maximum number of free functions and the desired asymptotics at the singularity. The condition of real analyticity was subsequently removed by Rendall. In an article by the author, it was shown that one can put a condition on initial data that leads to asymptotic expansions. In this article, we show the following. By fixing a point in hyperbolic space, we can consider the hyperbolic distance from this point to the solution at a given spacetime point. If we fix a spatial point for the solution, it is enough to put conditions on the rate at which the hyperbolic distance tends to infinity as time tends to the singularity in order to conclude that there are smooth expansions in a neighbourhood of the given spatial point.Comment: 18 pages, no figure

On Gowdy vacuum spacetimes

By Fuchsian techniques, a large family of Gowdy vacuum spacetimes have been constructed for which one has detailed control over the asymptotic behaviour. In this paper we formulate a condition on initial data yielding the same form of asymptotics.Comment: 28 pages, no figure

Reward is not Necessary: How to Create a Compositional Self-Preserving Agent for Life-Long Learning

We introduce a physiological model-based agent as proof-of-principle that it is possible to define a flexible self-preserving system that does not use a reward signal or reward-maximization as an objective. We achieve this by introducing the Self-Preserving Agent (SPA) with a physiological structure where the system can get trapped in an absorbing state if the agent does not solve and execute goal-directed polices. Our agent is defined using new class of Bellman equations called Operator Bellman Equations (OBEs), for encoding jointly non-stationary non-Markovian tasks formalized as a Temporal Goal Markov Decision Process (TGMDP). OBEs produce optimal goal-conditioned spatiotemporal transition operators that map an initial state-time to the final state-times of a policy used to complete a goal, and can also be used to forecast future states in multiple dynamic physiological state-spaces. SPA is equipped with an intrinsic motivation function called the valence function, which quantifies the changes in empowerment (the channel capacity of a transition operator) after following a policy. Because empowerment is a function of a transition operator, there is a natural synergism between empowerment and OBEs: the OBEs create hierarchical transition operators, and the valence function can evaluate hierarchical empowerment change defined on these operators. The valence function can then be used for goal selection, wherein the agent chooses a policy sequence that realizes goal states which produce maximum empowerment gain. In doing so, the agent will seek freedom and avoid internal death-states that undermine its ability to control both external and internal states in the future, thereby exhibiting the capacity of predictive and anticipatory self-preservation. We also compare SPA to Multi-objective RL, and discuss its capacity for symbolic reasoning and life-long learning.Comment: 54 page

An Analysis of Stock Market Performance:The Dow Jones Industrial Average and the Three Top Performing Lodging Firma: 1982-1988

In their dialogue - An Analysis of Stock Market Performance: The Dow Jones Industrial Average and the Three Top Performing Lodging Firms 1982 – 1988 - by N. H. Ringstrom, Professor and Elisa S. Moncarz, Associate Professor, School of Hospitality Management at Florida International University, Professors Ringstrom and Moncarz state at the outset: “An interesting comparison can be made between the Dow Jones lndustrial Average and the three top performing, publicly held lodging firms which had $100 million or more in annual lodging revenues. The authors provide that analytical comparison with Prime Motor Inns Inc., the Marriott Corporation, and Hilton Hotels Corporation.” “Based on a criterion of size, only those with$100 million in annual lodging revenues or more resulted in the inclusion of the following six major hotel firms: Prime Motor Inns, Inc., Marriott Corporation, Hilton Hotels Corporation, Ramada Inc., Holiday Corporation and La Quinta Motor Inns, Inc.,” say Professors Ringstrom and Moncarz in framing this discussion with its underpinnings in the years 1982 to 1988. The article looks at each company’s fiscal and Dow Jones performance for the years in question, and presents a detailed analysis of said performance. Graphic analysis is included. It helps to have a fairly vigorous knowledge of stock market and fiscal examination criteria to digest this material. The Ringstrom and Moncarz analysis of Prime Motor Inns Incorporated occupies the first 7 pages of this article in and of itself. Marriot Corporation also occupies a prominent position in this discussion. “Marriott, a giant in the hospitality industry, is huge and continuing to grow. Its 1987 sales were more than $6.5 billion, and its employees numbered over 200,000 individuals, which place Marriott among the 10 largest private employers in the country,” Ringstrom and Moncarz parse Marriott’s influence as a significant financial player. “The firm has a fantastic history of growth over the past 60 years, starting in May 1927 with a nine-seat A & W Root Beer stand in Washington, D.C.,” offer the authors in initialing Marriot’s portion of the discussion with a brief history lesson. The Marriot firm was officially incorporated as Hot Shoppes Inc. in 1929. As the thesis statement for the discussion suggests the performance of these huge, hospitality giants is compared and contrasted directly to the Dow Jones Industrial Average performance. Reasons and empirical data are offered by the authors to explain the distinctions. It would be difficult to explain those distinctions without delving deeply into corporate financial history and the authors willingly do so in an effort to help you understand the growth, as well as some of the setbacks of these hospitality based juggernauts. Ringstrom and Moncarz conclude the article with an extensive overview and analysis of the Hilton Hotels Corporation performance for the period outlined. It may well be the most fiscally dynamic of the firms presented for your perusal. “It is interesting to note that Hilton Hotels Corporation maintained a very strong financial position with relatively little debt during the years 1982-1988…the highest among all companies in the study,” the authors paint

Computing Gowdy spacetimes via spectral evolution in future and past directions

We consider a system of nonlinear wave equations with constraints that arises from the Einstein equations of general relativity and describes the geometry of the so-called Gowdy symmetric spacetimes on T3. We introduce two numerical methods, which are based on pseudo-spectral approximation. The first approach relies on marching in the future time-like direction and toward the coordinate singularity t=0. The second approach is designed from asymptotic formulas that are available near this singularity; it evolves the solutions in the past timelike direction from "final" data given at t=0. This backward method relies a novel nonlinear transformation, which allows us to reduce the nonlinear source terms to simple quadratic products of the unknown variables. Numerical experiments are presented in various regimes, including cases where "spiky" structures are observed as the coordinate singularity is approached. The proposed backward strategy leads to a robust numerical method which allows us to accurately simulate the long-time behavior of a large class of Gowdy spacetimes.Comment: 19 pages, 12 figure

Stress Alters Rates and Types of Loss of Heterozygosity in Candida albicans

Genetic diversity is often generated during adaptation to stress, and in eukaryotes some of this diversity is thought to arise via recombination and reassortment of alleles during meiosis. Candida albicans, the most prevalent pathogen of humans, has no known meiotic cycle, and yet it is a heterozygous diploid that undergoes mitotic recombination during somatic growth. It has been shown that clinical isolates as well as strains passaged once through a mammalian host undergo increased levels of recombination. Here, we tested the hypothesis that stress conditions increase rates of mitotic recombination in C. albicans, which is measured as loss of heterozygosity (LOH) at specific loci. We show that LOH rates are elevated during in vitro exposure to oxidative stress, heat stress, and antifungal drugs. In addition, an increase in stress severity correlated well with increased LOH rates. LOH events can arise through local recombination, through homozygosis of longer tracts of chromosome arms, or by whole-chromosome homozygosis. Chromosome arm homozygosis was most prevalent in cultures grown under conventional lab conditions. Importantly, exposure to different stress conditions affected the levels of different types of LOH events, with oxidative stress causing increased recombination, while fluconazole and high temperature caused increases in events involving whole chromosomes. Thus, C. albicans generates increased amounts and different types of genetic diversity in response to a range of stress conditions, a process that we term “stress-induced LOH” that arises either by elevating rates of recombination and/or by increasing rates of chromosome missegregation

Cosmic No Hair for Collapsing Universes

It is shown that all contracting, spatially homogeneous, orthogonal Bianchi cosmologies that are sourced by an ultra-stiff fluid with an arbitrary and, in general, varying equation of state asymptote to the spatially flat and isotropic universe in the neighbourhood of the big crunch singularity. This result is employed to investigate the asymptotic dynamics of a collapsing Bianchi type IX universe sourced by a scalar field rolling down a steep, negative exponential potential. A toroidally compactified version of M*-theory that leads to such a potential is discussed and it is shown that the isotropic attractor solution for a collapsing Bianchi type IX universe is supersymmetric when interpreted in an eleven-dimensional context.Comment: Extended discussion to include Kantowski-Sachs universe. In press, Classical and Quantum Gravit

The problem of a self-gravitating scalar field with positive cosmological constant

We study the Einstein-scalar field system with positive cosmological constant and spherically symmetric characteristic initial data given on a truncated null cone. We prove well-posedness, global existence and exponential decay in (Bondi) time, for small data. From this, it follows that initial data close enough to de Sitter data evolves to a causally geodesically complete spacetime (with boundary), which approaches a region of de Sitter asymptotically at an exponential rate; this is a non-linear stability result for de Sitter within the class under consideration, as well as a realization of the cosmic no-hair conjecture.We thank Pedro Girao, Marc Mars, Alan Rendall, Jorge Silva and Raul Vera for useful discussions. This work was supported by projects PTDC/MAT/108921/2008 and CERN/FP/116377/2010, and by CMAT, Universidade do Minho, and CAMSDG, Instituto Superior Tecnico, through FCT plurianual funding. AA thanks the Mathematics Department of Instituto Superior Tecnico (Lisbon), where this work was done, and the International Erwin Schrodinger Institute (Vienna), where the workshop "Dynamics of General Relativity: Analytical and Numerical Approaches" took place, for hospitality, and FCT for grant SFRH/BD/48658/2008

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra