On Max-Semistable Laws and Extremes for Dynamical Systems

Suppose [Formula: see text] is a measure preserving dynamical system and [Formula: see text] a measurable observable. Let [Formula: see text] denote the time series of observations on the system, and consider the maxima process [Formula: see text]. Under linear scaling of [Formula: see text] , its asymptotic statistics are usually captured by a three-parameter generalised extreme value distribution. This assumes certain regularity conditions on the measure density and the observable. We explore an alternative parametric distribution that can be used to model the extreme behaviour when the observables (or measure density) lack certain regular variation assumptions. The relevant distribution we study arises naturally as the limit for max-semistable processes. For piecewise uniformly expanding dynamical systems, we show that a max-semistable limit holds for the (linear) scaled maxima process

Refining models of crustal growth and evolution in southwestern Laurentia with paired U-Pb and Lu-Hf analyses of igneous and detrital zircon

The origin and evolution of continental crust is a fundamental and debated topic in geoscience. For over thirty years, Proterozoic crust of the southwestern United States has been a field laboratory for studying orogenic processes in the middle crust, and the growth of continental lithosphere via accretionary orogenesis. Three distinct crustal provinces are delineated based on differences in isotopic, structural, and geochronologic characteristics. To address questions about the origin of each province, this dissertation is composed of three chapters that present new U-Pb and Lu-Hf isotope analysis of plutonic, volcanic, and detrital zircon from the oldest known rocks in each crustal province in order to better understand the processes responsible for initial lithospheric formation and subsequent modification. Collectively, these chapters present a new synthesis of lithospheric formation during successive accretionary orogenic episodes that builds on three decades of prior field-based structural, metamorphic, and geochronologic studies. Major conclusions of each chapter are summarized in an extended abstract in the main body of this dissertation

Avoiding Object Misconceptions

This paper identifies and describes a number of misconceptions observed in students learning about object technology, It identifies simple, concrete, measures course designers and teachers can take to avoid these misconceptions arising. The context for this work centres on an introductory undergraduate course and a postgraduate course, Both these courses are taught by distance education. These courses both use Smalltalk as an introduction to object technology. More particularly, the undergraduate course uses Smalltalk as a first programming language. Distance education can limit the amount and speed of individual feedback that can be given in the early stages of learning. For this reason, particular attention has been paid to characterizing measures for avoiding elementary misconceptions seen in beginning learners. At the same time we also address some misconceptions observed in postgraduate students. The pedagogical issues discussed are of particular importance when devising an extended series of examples for teaching or assessment, or when designing a visual microworld to be used for teaching purposes

Synthesis, characterisation and performance of (TiO2)(0.18)(SiO2)(0.82) xerogel catalysts

The synthesis of high surface area xerogels has been achieved using the sol-gel route. Heptane washing was used during the stages of drying to minimise capillary pressures and hence preserve pore structure and maximise the surface area. SAXS data have identified that heptane washing during drying, in general, results in a preservation of the pore structure and surface areas of up to 450 m(2) g(-1). O-17 NMR showed that Ti is fully mixed into the silica network in all of the samples. XANES data confirm that reversible 4-fold Ti sites are more prevalent in samples with high surface areas, as expected. The calcined xerogels were tested for their catalytic activity using the epoxidation of cyclohexene with tert-butyl hydroperoxide (TBHP) as a test reaction, with excellent selectivities and reasonable percentage conversions. FT-IR spectroscopy has revealed that the catalytic activity is correlated with the intensity of the Si-O-Ti signal, after accounting for variations in Si-OH and Si-O-Si. The most effective catalyst was produced with heptane washing, a calcination temperature of 500 degreesC, and a heating rate of 5 degreesC min(-1)

2,3,7,8-Tetrachlorodibenzo-p-dioxin induces apoptotic cell death and cytochrome P4501A expression in developing \u3ci\u3eFundulus heteroclitus\u3c/i\u3e embryos

Fundulus heteroclitus embryos were exposed to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) during early development using nanoinjection or water bath exposure. TCDD caused developmental abnormalities that included hemorrhaging, loss of vascular integrity, edema, stunted development and death. The LC50 and LD50 of TCDD for Fundulus embryos were ~19.7 ± 9.5 pg TCDD/µl (water bath) and 0.25 ± 0.09 ng TCDD/g embryo (nanoinjection). To identify a possible cause for these developmental abnormalities we analyzed the effects of TCDD on apoptotic cell death and cytochrome P4501A (CYP1A) expression in the embryos. TCDD exposure increased apoptotic cell death in several tissues including brain, eye, gill, kidney, tail, intestine, heart, and vascular tissue. CYP1A expression was also increased in the TCDD-exposed embryos predominantly in liver, kidney, gill, heart, intestine, and in vascular tissues throughout the embryo. There was co-occurrence of TCDD-induced apoptosis and CYP1A expression in some, but not all, cell types. In addition the dose response relationships for apoptosis and mortality were similar, while CYP1A expression appeared more sensitive to TCDD induction

2,3,7,8-Tetrachlorodibenzo-p-dioxin induces apoptotic cell death and cytochrome P4501A expression in developing \u3ci\u3eFundulus heteroclitus\u3c/i\u3e embryos

Fundulus heteroclitus embryos were exposed to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) during early development using nanoinjection or water bath exposure. TCDD caused developmental abnormalities that included hemorrhaging, loss of vascular integrity, edema, stunted development and death. The LC50 and LD50 of TCDD for Fundulus embryos were ~19.7 ± 9.5 pg TCDD/µl (water bath) and 0.25 ± 0.09 ng TCDD/g embryo (nanoinjection). To identify a possible cause for these developmental abnormalities we analyzed the effects of TCDD on apoptotic cell death and cytochrome P4501A (CYP1A) expression in the embryos. TCDD exposure increased apoptotic cell death in several tissues including brain, eye, gill, kidney, tail, intestine, heart, and vascular tissue. CYP1A expression was also increased in the TCDD-exposed embryos predominantly in liver, kidney, gill, heart, intestine, and in vascular tissues throughout the embryo. There was co-occurrence of TCDD-induced apoptosis and CYP1A expression in some, but not all, cell types. In addition the dose response relationships for apoptosis and mortality were similar, while CYP1A expression appeared more sensitive to TCDD induction

Extreme value laws in dynamical systems under physical observables

Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by large values attained by the observable along orbits of the system. Based on this theory, the so-called block maximum method is often used in applications for statistical prediction of large value occurrences. In this method, one performs inference for the parameters of the Generalised Extreme Value (GEV) distribution, using maxima over blocks of regularly sampled observations along an orbit of the system. The observables studied so far in the theory are expressed as functions of the distance with respect to a point, which is assumed to be a density point of the system's invariant measure. However, this is not the structure of the observables typically encountered in physical applications, such as windspeed or vorticity in atmospheric models. In this paper we consider extreme value limit laws for observables which are not functions of the distance from a density point of the dynamical system. In such cases, the limit laws are no longer determined by the functional form of the observable and the dimension of the invariant measure: they also depend on the specific geometry of the underlying attractor and of the observable's level sets. We present a collection of analytical and numerical results, starting with a toral hyperbolic automorphism as a simple template to illustrate the main ideas. We then formulate our main results for a uniformly hyperbolic system, the solenoid map. We also discuss non-uniformly hyperbolic examples of maps (H\'enon and Lozi maps) and of flows (the Lorenz63 and Lorenz84 models). Our purpose is to outline the main ideas and to highlight several serious problems found in the numerical estimation of the limit laws

Patients with Diabetes and Significant Epicardial Coronary Artery Disease have Increased Systolic Left Ventricular Apical Rotation and Rotation Rate at Rest

Objective The purpose of this study was to determine whether resting myocardial deformation and rotation may be altered in diabetic patients with significant epicardial coronary artery disease (CAD) with normal left ventricular ejection fraction. Design A prospective observational study. Setting Diagnosis of epicardial CAD in patients with diabetes. Patients and Methods Eighty-four patients with diabetes suspected of epicardial CAD scheduled for cardiac catheterization had a resting echocardiogram performed prior to their procedure. Echocardiographic measurements were compared between patients with and without significant epicardial CAD as determined by cardiac catheterization. Main Outcome Measures Measurement of longitudinal strain, strain rate, apical rotation, and rotation rate, using speckle tracking echocardiography. Results Eighty-four patients were studied, 39 (46.4%) of whom had significant epicardial CAD. Global peak systolic apical rotation was significantly increased (14.9 ± 5.1 vs. 11.0 ± 4.8 degrees, P < 0.001) in patients with epicardial CAD along with faster peak systolic apical rotation rate (90.4 ± 29 vs. 68.1 ± 22.2 degrees/sec, P < 0.001). These findings were further confirmed through multivariate logistic regression analysis (global peak systolic apical rotation OR = 1.17, P = 0.004 and peak systolic apical rotation rate OR = 1.05, P < 0.001). Conclusions Patients with diabetes with significant epicardial CAD and normal LVEF exhibit an increase in peak systolic apical counterclockwise rotation and rotation rate detected by echocardiography, suggesting that significant epicardial CAD and its associated myocardial effects in patients with diabetes may be detected noninvasively at rest

The HD 163296 Circumstellar Disk in Scattered Light: Evidence of Time-Variable Self-Shadowing

We present the first multicolor view of the scattered light disk of the Herbig Ae star HD 163296, based on coronagraphic observations from the Hubble Space Telescope Advanced Camera for Surveys (HST ACS). Radial profile fits of the surface brightness along the disk's semimajor axis indicate that the disk is not continuously flared, and extends to ~540 AU. The disk's color (V − I) = 1.1 at a radial distance of 3.5'' is redder than the observed stellar color (V − I) = 0.15. This red disk color might be indicative of either an evolution in the grain size distribution (i.e., grain growth) and/or composition, both of which would be consistent with the observed nonflared geometry of the outer disk. We also identify a single ansa morphological structure in our F435W ACS data, which is absent from earlier epoch F606W and F814W ACS data, but corresponds to one of the two ansae observed in archival HST Space Telescope Imaging Spectrograph (STIS) coronagraphic data. Following transformation to similar bandpasses, we find that the scattered light disk of HD 163296 is 1 mag arcsec^(−2) fainter at 3.5'' in the STIS data than in the ACS data. Moreover, variations are seen in (1) the visibility of the ansa(e) structures, (2) the relative surface brightness of the ansa(e) structures, and (3) the (known) intrinsic polarization of the system. These results indicate that the scattered light from the HD 163296 disk is variable. We speculate that the inner disk wall, which Sitko et al. suggests has a variable scale height as diagnosed by near-IR SED variability, induces variable self-shadowing of the outer disk. We further speculate that the observed surface brightness variability of the ansa(e) structures may indicate that the inner disk wall is azimuthally asymmetric