Parametric ordering of complex systems

Cellular automata (CA) dynamics are ordered in terms of two global parameters, computable {\sl a priori} from the description of rules. While one of them (activity) has been used before, the second one is new; it estimates the average sensitivity of rules to small configurational changes. For two well-known families of rules, the Wolfram complexity Classes cluster satisfactorily. The observed simultaneous occurrence of sharp and smooth transitions from ordered to disordered dynamics in CA can be explained with the two-parameter diagram

Homothetic perfect fluid space-times

A brief summary of results on homotheties in General Relativity is given, including general information about space-times admitting an r-parameter group of homothetic transformations for r>2, as well as some specific results on perfect fluids. Attention is then focussed on inhomogeneous models, in particular on those with a homothetic group $H_4$ (acting multiply transitively) and $H_3$. A classification of all possible Lie algebra structures along with (local) coordinate expressions for the metric and homothetic vectors is then provided (irrespectively of the matter content), and some new perfect fluid solutions are given and briefly discussed.Comment: 27 pages, Latex file, Submitted to Class. Quantum Gra

On the absence of scalar hair for charged rotating blackholes in non minimally coupled theories

In this work we check the validity of the no scalar hair theorem in charged axisymmetric stationary black holes for a wide class of scalar tensor theories.Comment: Revtex style, 11 pages, major rivisions done, appendix added, title change

Regular Conjugacy Classes in the Weyl Group and Integrable Hierarchies

Generalized KdV hierarchies associated by Drinfeld-Sokolov reduction to grade one regular semisimple elements from non-equivalent Heisenberg subalgebras of a loop algebra \G\otimes{\bf C}[\lambda,\lambda^{-1}] are studied. The graded Heisenberg subalgebras containing such elements are labelled by the regular conjugacy classes in the Weyl group {\bf W}(\G) of the simple Lie algebra \G. A representative w\in {\bf W}(\G) of a regular conjugacy class can be lifted to an inner automorphism of \G given by $\hat w=\exp\left(2i\pi {\rm ad I_0}/m\right)$, where $I_0$ is the defining vector of an $sl_2$ subalgebra of \G.The grading is then defined by the operator $d_{m,I_0}=m\lambda {d\over d\lambda} + {\rm ad} I_0$ and any grade one regular element $\Lambda$ from the Heisenberg subalgebra associated to $[w]$ takes the form $\Lambda = (C_+ +\lambda C_-)$, where $[I_0, C_-]=-(m-1) C_-$ and $C_+$ is included in an $sl_2$ subalgebra containing $I_0$. The largest eigenvalue of ${\rm ad}I_0$ is $(m-1)$ except for some cases in $F_4$, $E_{6,7,8}$. We explain how these Lie algebraic results follow from known results and apply them to construct integrable systems.If the largest ${\rm ad} I_0$ eigenvalue is $(m-1)$, then using any grade one regular element from the Heisenberg subalgebra associated to $[w]$ we can construct a KdV system possessing the standard \W-algebra defined by $I_0$ as its second Poisson bracket algebra. For \G a classical Lie algebra, we derive pseudo-differential Lax operators for those non-principal KdV systems that can be obtained as discrete reductions of KdV systems related to $gl_n$. Non-abelian Toda systems are also considered.Comment: 44 pages, ENSLAPP-L-493/94, substantial revision, SWAT-95-77. (use OLATEX (preferred) or LATEX

Glaciovolcanic evidence for a polythermal Neogene East Antarctic Ice Sheet

A paradigm has existed for more than 30 years that the basal thermal regime of the East Antarctic Ice Sheet in Victoria Land made a fundamental transition from wet-based to cold-based either at ca. 14 Ma or after ca. 2.5 Ma. The basal thermal regime is important because it determines the potential for unstable behavior in an ice sheet. We have studied the environmental characteristics of subglacially erupted volcanic centers scattered along 800 km of the Ross Sea fl ank of the Transantarctic Mountains. The volcanoes preserve evidence for the coeval paleo-ice thicknesses and contain features diagnostic of both wet-based and cold-based ice conditions. By dating the sequences we are able to demonstrate that the basal thermal regime varied spatially and with time between ca. 12 Ma and present. It was polythermal overall and probably comprised a coarse temperature patchwork of frozen-bed and thawed-bed ice, similar to the East Antarctic Ice Sheet today. Thus, an important shift is required in the prevailing paradigm describing its temporal evolution

SuperMassive Black Holes in Bulges

We present spatially extended gas kinematics at parsec-scale resolution for the nuclear regions of four nearby disk galaxies, and model them as rotation of a gas disk in the joint potential of the stellar bulge and a putative central black hole. The targets were selected from a larger set of long-slit spectra obtained with the Hubble Space Telescope as part of the Survey of Nearby Nuclei with STIS (SUNNS). They represents the 4 galaxies (of 24) that display symmetric gas velocity curves consistent with a rotating disk. We derive the stellar mass distribution from the STIS acquisition images adopting the stellar mass-to-light ratio normalized so as to match ground-based velocity dispersion measurements over a large aperture. Subsequently, we constrain the mass of a putative black hole by matching the gas rotation curve, following two distinct approaches. In the most general case we explore all the possible disk orientations, alternatively we constrain the gas disk orientation from the dust-lane morphology at similar radii. In the latter case the kinematic data indicate the presence of a central black hole for three of the four objects, with masses of 10^7 - 10^8 solar masses, representing up to 0.025 % of the host bulge mass. For one object (NGC2787) the kinematic data alone provide clear evidence for the presence of a central black hole even without external constraints on the disk orientation. These results illustrate directly the need to determine black-hole masses by differing methods for a large number of objects, demonstrate that the variance in black hole/bulge mass is much larger than previously claimed, and reinforce the recent finding that the black-hole mass is tightly correlated with the bulge stellar velocity dispersion.Comment: 26 pages, 11 Postscript figures, accepted for publication on Ap

General approach to the study of vacuum space-times with an isometry

In vacuum space-times the exterior derivative of a Killing vector field is a 2-form (named here as the Papapetrou field) that satisfies Maxwell's equations without electromagnetic sources. In this paper, using the algebraic structure of the Papapetrou field, we will set up a new formalism for the study of vacuum space-times with an isometry, which is suitable to investigate the connections between the isometry and the Petrov type of the space-time. This approach has some advantages, among them, it leads to a new classification of these space-times and the integrability conditions provide expressions that determine completely the Weyl curvature. These facts make the formalism useful for application to any problem or situation with an isometry and requiring the knowledge of the curvature.Comment: 24 pages, LaTeX2e, IOP style. To appear in Classical and Quantum Gravit

Mental health in UK Biobank - development, implementation and results from an online questionnaire completed by 157 366 participants: a reanalysis

Background UK Biobank is a well-characterised cohort of over 500 000 participants including genetics, environmental data and imaging. An online mental health questionnaire was designed for UK Biobank participants to expand its potential. Aims Describe the development, implementation and results of this questionnaire. Method An expert working group designed the questionnaire, using established measures where possible, and consulting a patient group. Operational criteria were agreed for defining likely disorder and risk states, including lifetime depression, mania/hypomania, generalised anxiety disorder, unusual experiences and self-harm, and current post-traumatic stress and hazardous/harmful alcohol use. Results A total of 157 366 completed online questionnaires were available by August 2017. Participants were aged 45–82 (53% were ≥65 years) and 57% women. Comparison of self-reported diagnosed mental disorder with a contemporary study shows a similar prevalence, despite respondents being of higher average socioeconomic status. Lifetime depression was a common finding, with 24% (37 434) of participants meeting criteria and current hazardous/harmful alcohol use criteria were met by 21% (32 602), whereas other criteria were met by less than 8% of the participants. There was extensive comorbidity among the syndromes. Mental disorders were associated with a high neuroticism score, adverse life events and long-term illness; addiction and bipolar affective disorder in particular were associated with measures of deprivation. Conclusions The UK Biobank questionnaire represents a very large mental health survey in itself, and the results presented here show high face validity, although caution is needed because of selection bias. Built into UK Biobank, these data intersect with other health data to offer unparalleled potential for crosscutting biomedical research involving mental health

Geometric Interpretation of the Mixed Invariants of the Riemann Spinor

Mixed invariants are used to classify the Riemann spinor in the case of Einstein-Maxwell fields and perfect fluids. In the Einstein-Maxwell case these mixed invariants provide information as to the relative orientation of the gravitational and electromagnetic principal null directions. Consideration of the perfect fluid case leads to some results about the behaviour of the Bel-Robinson tensor regarded as a quartic form on unit timelike vectors.Comment: 31 pages, AMS-LaTe

Nonstandard Drinfeld-Sokolov reduction

Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV type hierarchies is a quadruplet (\A,\Lambda, d_1, d_0), where the $d_i$ are $\Z$-gradations of a loop algebra \A and \Lambda\in \A is a semisimple element of nonzero $d_1$-grade. A new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented. The proposal relies on splitting the $d_1$-grade zero part of \A into a vector space direct sum of two subalgebras. This permits one to interpret certain Gelfand-Dickey type systems associated with a nonstandard splitting of the algebra of pseudo-differential operators in the Drinfeld-Sokolov framework.Comment: 19 pages, LaTeX fil