Generation of measures on the torus with good sequences of integers

Let $S= (s_1<s_2<\dots)$ be a strictly increasing sequence of positive integers and denote $\mathbf{e}(\beta)=\mathrm{e}^{2\pi i \beta}$. We say $S$ is good if for every real $\alpha$ the limit $\lim_N \frac1N\sum_{n\le N} \mathbf{e}(s_n\alpha)$ exists. By the Riesz representation theorem, a sequence $S$ is good iff for every real $\alpha$ the sequence $(s_n\alpha)$ possesses an asymptotic distribution modulo 1. Another characterization of a good sequence follows from the spectral theorem: the sequence $S$ is good iff in any probability measure preserving system $(X,\mathbf{m},T)$ the limit $\lim_N \frac1N\sum_{n\le N}f\left(T^{s_n}x\right)$ exists in $L^2$-norm for $f\in L^2(X)$. Of these three characterization of a good set, the one about limit measures is the most suitable for us, and we are interested in finding out what the limit measure $\mu_{S,\alpha}= \lim_N\frac1N\sum_{n\le N} \delta_{s_n\alpha}$ on the torus can be. In this first paper on the subject, we investigate the case of a single irrational $\alpha$. We show that if $S$ is a good set then for every irrational $\alpha$ the limit measure $\mu_{S,\alpha}$ must be a continuous Borel probability measure. Using random methods, we show that the limit measure $\mu_{S,\alpha}$ can be any measure which is absolutely continuous with respect to the Haar-Lebesgue probability measure on the torus. On the other hand, if $\nu$ is the uniform probability measure supported on the Cantor set, there are some irrational $\alpha$ so that for no good sequence $S$ can we have the limit measure $\mu_{S,\alpha}$ equal $\nu$. We leave open the question whether for any continuous Borel probability measure $\nu$ on the torus there is an irrational $\alpha$ and a good sequence $S$ so that $\mu_{S,\alpha}=\nu$.Comment: 44 page

Using conditional kernel density estimation for wind power density forecasting

Of the various renewable energy resources, wind power is widely recognized as one of the most promising. The management of wind farms and electricity systems can benefit greatly from the availability of estimates of the probability distribution of wind power generation. However, most research has focused on point forecasting of wind power. In this paper, we develop an approach to producing density forecasts for the wind power generated at individual wind farms. Our interest is in intraday data and prediction from 1 to 72 hours ahead. We model wind power in terms of wind speed and wind direction. In this framework, there are two key uncertainties. First, there is the inherent uncertainty in wind speed and direction, and we model this using a bivariate VARMA-GARCH (vector autoregressive moving average-generalized autoregressive conditional heteroscedastic) model, with a Student t distribution, in the Cartesian space of wind speed and direction. Second, there is the stochastic nature of the relationship of wind power to wind speed (described by the power curve), and to wind direction. We model this using conditional kernel density (CKD) estimation, which enables a nonparametric modeling of the conditional density of wind power. Using Monte Carlo simulation of the VARMA-GARCH model and CKD estimation, density forecasts of wind speed and direction are converted to wind power density forecasts. Our work is novel in several respects: previous wind power studies have not modeled a stochastic power curve; to accommodate time evolution in the power curve, we incorporate a time decay factor within the CKD method; and the CKD method is conditional on a density, rather than a single value. The new approach is evaluated using datasets from four Greek wind farms

A kernel extension to handle missing data

An extension for univariate kernels that deals with missing values is proposed. These extended kernels are shown to be valid Mercer kernels and can adapt to many types of variables, such as categorical or continuous. The proposed kernels are tested against standard RBF kernels in a variety of benchmark problems showing different amounts of missing values and variable types. Our experimental results are very satisfactory, because they usually yield slight to much better improvements over those achieved with standard methods.Postprint (author’s final draft

The Roles of Large Top Predators in Coastal Ecosystems: New Insights from Long Term Ecological Research

During recent human history, human activities such as overhunting and habitat destruction have severely impacted many large top predator populations around the world. Studies from a variety of ecosystems show that loss or diminishment of top predator populations can have serious consequences for population and community dynamics and ecosystem stability. However, there are relatively few studies of the roles of large top predators in coastal ecosystems, so that we do not yet completely understand what could happen to coastal areas if large top predators are extirpated or significantly reduced in number. This lack of knowledge is surprising given that coastal areas around the globe are highly valued and densely populated by humans, and thus coastal large top predator populations frequently come into conflict with coastal human populations. This paper reviews what is known about the ecological roles of large top predators in coastal systems and presents a synthesis of recent work from three coastal eastern US Long Term Ecological Research (LTER) sites where long-term studies reveal what appear to be common themes relating to the roles of large top predators in coastal systems. We discuss three specific themes: (1) large top predators acting as mobile links between disparate habitats, (2) large top predators potentially affecting nutrient and biogeochemical dynamics through localized behaviors, and (3) individual specialization of large top predator behaviors. We also discuss how research within the LTER network has led to enhanced understanding of the ecological roles of coastal large top predators. Highlighting this work is intended to encourage further investigation of the roles of large top predators across diverse coastal aquatic habitats and to better inform researchers and ecosystem managers about the importance of large top predators for coastal ecosystem health and stability

The uses and functions of ageing celebrity war reporters

This article starts from the premise that recognition of professional authority and celebrity status depends on the embodiment and performance of field-specific dispositional practices: there’s no such thing as a natural, though we often talk about journalistic instinct as something someone simply has or doesn’t have. Next, we have little control over how we are perceived by peers and publics, and what we think are active positioning or subjectifying practices are in fact, after Bourdieu, revelations of already-determined delegation. The upshot is that two journalists can arrive at diametrically opposed judgements on the basis of observation of the same actions of a colleague, and as individuals we are blithely hypocritical in forming (or reciting) evaluations of the professional identity of celebrities. Nowhere is this starker than in the discourse of age-appropriate behaviour, which this paper addresses using the examples of ‘star’ war reporters John Simpson, Kate Adie and Martin Bell. A certain rough-around-the-edges irreverence is central to dispositional authenticity amongst war correspondents, and for ageing hacks this incorporates gendered attitudes to sex and alcohol as well as indifference to protocol. And yet perceived age-inappropriate sexual behaviour is also used to undermine professional integrity, and the paper ends by outlining the phenomenological context that makes possible this effortless switching between amoral and moralising recognition by peers and audiences alike

Asymptotic normality of the Parzen-Rosenblatt density estimator for strongly mixing random fields

We prove the asymptotic normality of the kernel density estimator (introduced by Rosenblatt (1956) and Parzen (1962)) in the context of stationary strongly mixing random fields. Our approach is based on the Lindeberg's method rather than on Bernstein's small-block-large-block technique and coupling arguments widely used in previous works on nonparametric estimation for spatial processes. Our method allows us to consider only minimal conditions on the bandwidth parameter and provides a simple criterion on the (non-uniform) strong mixing coefficients which do not depend on the bandwith.Comment: 16 page

Venus Express radio occultation observed by PRIDE

Context. Radio occultation is a technique used to study planetary atmospheres by means of the refraction and absorption of a spacecraft carrier signal through the atmosphere of the celestial body of interest, as detected from a ground station on Earth. This technique is usually employed by the deep space tracking and communication facilities (e.g., NASA's Deep Space Network (DSN), ESA's Estrack). Aims. We want to characterize the capabilities of the Planetary Radio Interferometry and Doppler Experiment (PRIDE) technique for radio occultation experiments, using radio telescopes equipped with Very Long Baseline Interferometry (VLBI) instrumentation. Methods. We conducted a test with ESA's Venus Express (VEX), to evaluate the performance of the PRIDE technique for this particular application. We explain in detail the data processing pipeline of radio occultation experiments with PRIDE, based on the collection of so-called open-loop Doppler data with VLBI stations, and perform an error propagation analysis of the technique. Results. With the VEX test case and the corresponding error analysis, we have demonstrated that the PRIDE setup and processing pipeline is suited for radio occultation experiments of planetary bodies. The noise budget of the open-loop Doppler data collected with PRIDE indicated that the uncertainties in the derived density and temperature profiles remain within the range of uncertainties reported in previous Venus' studies. Open-loop Doppler data can probe deeper layers of thick atmospheres, such as that of Venus, when compared to closed-loop Doppler data. Furthermore, PRIDE through the VLBI networks around the world, provides a wide coverage and range of large antenna dishes, that can be used for this type of experiments

A window of opportunity for abatacept in RA: is disease duration an independent predictor of low disease activity/remission in clinical practice?

The objective of the study was to examine whether disease duration independently predicts treatment response among biologic-naive patients with rheumatoid arthritis (RA) initiating abatacept in clinical practice. Using the Corrona RA registry (February 2006-January 2015), biologic-naive patients with RA initiating abatacept with 12-month (+/-3 months) follow-up and assessment of disease activity (Clinical Disease Activity Index [CDAI]) at initiation and at 12 months were identified. The primary outcome was mean change in CDAI (DeltaCDAI) from baseline to 12 months. Secondary outcomes at 12 months included achievement of low disease activity (LDA; CDAI 10 years, n = 79). Increased disease duration was associated with older age (p = 0.047), and the median number of prior conventional disease-modifying antirheumatic drugs used was lowest in the 0- to 2-year duration group (p \u3c 0.001). Mean DeltaCDAI (SE) ranged from -10.22 (1.19) for 0-2 years to -4.63 (1.38) for \u3e 10 years. In adjusted analyses, shorter disease duration was significantly associated with greater mean DeltaCDAI (p = 0.015) and greater likelihood of achieving LDA (p = 0.048). In biologic-naive patients with RA initiating abatacept, earlier disease (shorter disease duration) was associated with greater DeltaCDAI and likelihood of achieving LDA