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

Almost sure convergence of maxima for chaotic dynamical systems

ArticleSuppose (f,X,ν) is a measure preserving dynamical system and ϕ:X→R is an observable with some degree of regularity. We investigate the maximum process M n :=max{X 1 ,…,X n } , where X i =ϕ∘f i is a time series of observations on the system. When M n →∞ almost surely, we establish results on the almost sure growth rate, namely the existence (or otherwise) of a sequence u n →∞ such that M n /u n →1 almost surely. The observables we consider will be functions of the distance to a distinguished point x ~ ∈X . Our results are based on the interplay between shrinking target problem estimates at x ~ and the form of the observable (in particular polynomial or logarithmic) near x ~ . We determine where such an almost sure limit exists and give examples where it does not. Our results apply to a wide class of non-uniformly hyperbolic dynamical systems, under mild assumptions on the rate of mixing, and on regularity of the invariant measure

On the predictability of extremes: Does the butterfly effect ever decrease?

This is the peer reviewed version of the following article: Sterk, A. E., Stephenson, D. B., Holland, M. P. and Mylne, K. R. (2015), On the predictability of extremes: Does the butterfly effect ever decrease?. Quarterly Journal of the Royal Meteorological Society, which has been published in final form at http://dx.doi.org/10.1002/qj.2627. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving: http://olabout.wiley.com/WileyCDA/Section/id-820227.html#termsThis study investigates whether or not predictability always decreases for more extreme events. Predictability is measured by the Mean Squared Error (MSE), estimated here from the difference of pairs of ensemble forecasts, conditioned on one of the forecast variables (the 'pseudo-observation') exceeding a threshold. Using an exchangeable linear regression model for pairs of forecast variables, we show that the MSE can be decomposed into the sum of three terms: a threshold-independent constant, a mean term that always increases with threshold, and a variance term that can either increase, decrease, or stay constant with threshold. Using the generalised Pareto distribution to model wind speed excesses over a threshold, we show that MSE always increases with threshold at sufficiently high threshold. However, MSE can be a decreasing function of threshold at lower thresholds but only if the forecasts have finite upper bounds. The methods are illustrated by application to daily wind speed forecasts for London made using the 24 member Met Office Global and Regional Ensemble Prediction System from 1 January 2009 to 31 May 2011. For this example, the mean term increases faster than the variance term decreases with increasing threshold, and so predictability decreases for more extreme events.Engineering and Physical Sciences Research Council (EPSRC)Netherlands Organisation for Scientific Research (NWO

Far-infrared and sub-millimetre imaging of HD 76582's circumstellar disc

Debris discs, the tenuous rocky and icy remnants of planet formation, are believed to be evidence for planetary systems around other stars. The JCMT/SCUBA-2 debris disc legacy survey ‘SCUBA-2 Observations of Nearby Stars’ (SONS) observed 100 nearby stars, amongst them HD 76582, for evidence of such material. Here, we present imaging observations by JCMT/SCUBA-2 and Herschel/PACS at sub-millimetre and far-infrared wavelengths, respectively. We simultaneously model the ensemble of photometric and imaging data, spanning optical to sub-millimetre wavelengths, in a self-consistent manner. At far-infrared wavelengths, we find extended emission from the circumstellar disc providing a strong constraint on the dust spatial location in the outer system, although the angular resolution is too poor to constrain the interior of the system. In the sub-millimetre, photometry at 450 and 850 µm reveals a steep fall-off that we interpret as a disc dominated by moderately sized dust grains (amin = 36 µm), perhaps indicative of a non-steady-state collisional cascade within the disc. A disc architecture of three distinct annuli, comprising an unresolved component at 20 au and outer components at 80 and 270 au, along with a very steep particle size distribution (γ = 5), is proposed to match the observations

Rediscovery of Otto Frank's contribution to science.

In the late 19th century, German physiologist Otto Frank (1865-1944) embarked on a near life-long research program of laying down the mathematical, methodological, and theoretical foundations in order to understand and define the performance of the heart and circulatory system in all their complexity. The existence of the 'Frank-Starling law' testifies to this. Two of his seminal publications have been translated into English previously, introducing Frank's research on the dynamics of the heart and the arterial pulse to a wider audience. It is likely that there are a host of other comparable achievements and publications of Frank that are still unknown to the international scientific (cardiological and physiological) community. However, their influence can still be felt and seen in modern cardiology and cardio-physiology, such as in the development of modern interactive simulating and teaching programs. We have translated and commented on ten of these papers, which can be read in parallel with the German originals. These publications show a wealth of theoretical assumptions and projections regarding the importance of the sarcomere, the development of models of contraction, thermo-dynamical considerations for muscular activity, differences between cardiac and skeletal muscles, problems related to methodology and measurement, and the first pressure-volume diagram (published 120 years ago). These topics were envisioned by Frank long before they became a focus of subsequent modern research. Nowadays, frequent measurements of pressure-volume relationships are made in research using the pressure-volume conductance catheter technique. In commenting Frank's scientific topics, we try to show how interconnected his thinking was, and thus how it enabled him to cover such a wide range of subjects. The authors regret that the following source was not mentioned. The portrait of the physiologist Otto Frank, shown on the front cover of JMCC volume 119 (June 2018), was kindly provided by the archive of University of Giessen/Germany copyright/permission: Universitätsarchiv Giessen/Germany Sign. HR A 114 a). The authors would like to apologise for any inconvenience caused

Common Carp Disrupt Ecosystem Structure and Function Through Middle-out Effects

Middle-out effects or a combination of top-down and bottom-up processes create many theoretical and empirical challenges in the realm of trophic ecology. We propose using specific autecology or species trait (i.e. behavioural) information to help explain and understand trophic dynamics that may involve complicated and nonunidirectional trophic interactions. The common carp (Cyprinus carpio) served as our model species for whole-lake observational and experimental studies; four trophic levels were measured to assess common carp-mediated middle-out effects across multiple lakes. We hypothesised that common carp could influence aquatic ecosystems through multiple pathways (i.e. abiotic and biotic foraging, early life feeding, nutrient). Both studies revealed most trophic levels were affected by common carp, highlighting strong middle-out effects likely caused by common carp foraging activities and abiotic influence (i.e. sediment resuspension). The loss of water transparency, submersed vegetation and a shift in zooplankton dynamics were the strongest effects. Trophic levels furthest from direct pathway effects were also affected (fish life history traits). The present study demonstrates that common carp can exert substantial effects on ecosystem structure and function. Species capable of middle-out effects can greatly modify communities through a variety of available pathways and are not confined to traditional top-down or bottom-up processes

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

Proof-of-Concept Study of the NOTI Chelating Platform: Preclinical Evaluation of 64Cu-Labeled Mono- and Trimeric c(RGDfK) Conjugates

Purpose We recently developed a chelating platform based on the macrocycle 1,4,7-triazacyclononane with up to three five-membered azaheterocyclic arms for the preparation of 68Ga- and 64Cu-based radiopharmaceuticals. Based on this platform, the chelator scaffold NOTI-TVA with three additional carboxylic acid groups for bioconjugation was synthesized and characterized. The primary aims of this proof-of-concept study were (1) to evaluate if trimeric radiotracers on the basis of the NOTI-TVA 6 scaffold can be developed, (2) to determine if the additional substituents for bioconjugation at the non-coordinating NH atoms of the imidazole residues of the building block NOTI influence the metal binding properties, and (3) what influence multiple targeting vectors have on the biological performance of the radiotracer. The cyclic RGDfK peptide that specifically binds to the αvß3 integrin receptor was selected as the biological model system. Procedures Two different synthetic routes for the preparation of NOTI-TVA 6 were explored. Three c(RGDfK) peptide residues were conjugated to the NOTI-TVA 6 building block by standard peptide chemistry providing the trimeric bioconjugate NOTI-TVA-c(RGDfK)3 9. Labeling of 9 with [64Cu]CuCl2 was performed manually at pH 8.2 at ambient temperature. Binding affinities of Cu-8, the Cu2+ complex of the previously described monomer NODIA-Me-c(RGDfK) 8, and the trimer Cu-9 to integrin αvß3 were determined in competitive cell binding experiments in the U-87MG cell line. The pharmacokinetics of both 64Cu-labeled conjugates [64Cu]Cu-8 and [64Cu]Cu-9 were determined by small-animal PET imaging and ex vivo biodistribution studies in mice bearing U-87MG xenografts. Results Depending on the synthetic route, NOTI-TVA 6 was obtained with an overall yield up to 58 %. The bioconjugate 9 was prepared in 41 % yield. Both conjugates [64Cu]Cu-8 and [64Cu]Cu-9 were radiolabeled quantitatively at ambient temperature in high molar activities of Am ~ 20 MBq nmol−1 in less than 5 min. Competitive inhibitory constants IC50 of c(RDGfK) 7, Cu-8, and Cu-9 were determined to be 159.5 ± 1.3 nM, 256.1 ± 2.1 nM, and 99.5 ± 1.1 nM, respectively. In small-animal experiments, both radiotracers specifically delineated αvß3 integrin-positive U-87MG tumors with low uptake in non-target organs and rapid blood clearance. The trimer [64Cu]Cu-9 showed a ~ 2.5-fold higher tumor uptake compared with the monomer [64Cu]Cu-8. Conclusions Functionalization of NOTI at the non-coordinating NH atoms of the imidazole residues for bioconjugation was straightforward and allowed the preparation of a homotrimeric RGD conjugate. After optimization of the synthesis, required building blocks to make NOTI-TVA 6 are now available on multi-gram scale. Modifications at the imidazole groups had no measurable impact on metal binding properties in vitro and in vivo suggesting that the NOTI scaffold is a promising candidate for the development of 64Cu-labeled multimeric/multifunctional radiotracers

VIS: the visible imager for Euclid

Euclid-VIS is a large format visible imager for the ESA Euclid space mission in their Cosmic Vision program, scheduled for launch in 2019. Together with the near infrared imaging within the NISP instrument it forms the basis of the weak lensing measurements of Euclid. VIS will image in a single r+i+z band from 550-900 nm over a field of view of ~0.5 deg2. By combining 4 exposures with a total of 2240 sec, VIS will reach to V=24.5 (10{\sigma}) for sources with extent ~0.3 arcsec. The image sampling is 0.1 arcsec. VIS will provide deep imaging with a tightly controlled and stable point spread function (PSF) over a wide survey area of 15000 deg2 to measure the cosmic shear from nearly 1.5 billion galaxies to high levels of accuracy, from which the cosmological parameters will be measured. In addition, VIS will also provide a legacy imaging dataset with an unprecedented combination of spatial resolution, depth and area covering most of the extra-Galactic sky. Here we will present the results of the study carried out by the Euclid Consortium during the Euclid Definition phase.Comment: 10 pages, 6 figure