3,063 research outputs found
Generation of measures on the torus with good sequences of integers
Let be a strictly increasing sequence of positive
integers and denote . We say
is good if for every real the limit exists. By the Riesz representation theorem, a sequence
is good iff for every real the sequence possesses an
asymptotic distribution modulo 1. Another characterization of a good sequence
follows from the spectral theorem: the sequence is good iff in any
probability measure preserving system the limit exists in -norm for .
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
on the torus can be. In this first paper on the subject, we investigate the
case of a single irrational . We show that if is a good set then
for every irrational the limit measure must be a
continuous Borel probability measure. Using random methods, we show that the
limit measure can be any measure which is absolutely
continuous with respect to the Haar-Lebesgue probability measure on the torus.
On the other hand, if is the uniform probability measure supported on the
Cantor set, there are some irrational so that for no good sequence
can we have the limit measure equal . We leave open the
question whether for any continuous Borel probability measure on the
torus there is an irrational and a good sequence so that
.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
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
Factors associated with genetic testing distress in patients tested for Lynch Syndrome or Hereditary Breast and Ovarian Cancer Syndrome
Evaluation of flight foods under hypokinetic conditions, part 2, chapters 4 and 5
Effects of weightlessness on body temperature and heart rate determined by 56 day bed rest stud
Development of a stochastic computational fluid dynamics approach for offshore wind farms
In this paper, a method for stochastic analysis of an offshore wind farm using computational fluid dynamics (CFD) is proposed. An existing offshore wind farm is modelled using a steady-state CFD solver at several deterministic input ranges and an approximation model is trained on the CFD results. The approximation model is then used in a Monte-Carlo analysis to build joint probability distributions for values of interest within the wind farm. The results are compared with real measurements obtained from the existing wind farm to quantify the accuracy of the predictions. It is shown that this method works well for the relatively simple problem considered in this study and has potential to be used in more complex situations where an existing analytical method is either insufficient or unable to make a good prediction
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
Impact of mismatch repair (MMR) genetic test result on perceived cancer risk and cancer screening
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
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