On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q . It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P ^ be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process n √ (P ^ −P) under random projections, conditional on P ^ .

Variability of daily winter wind speed distribution over Northern Europe during the past millennium in regional and global climate simulations

We analyse the variability of the probability distribution of daily wind speed in wintertime over Northern and Central Europe in a series of global and regional climate simulations covering the last centuries, and in reanalysis products covering approximately the last 60 years. The focus of the study lies on identifying the link of the variations in the wind speed distribution to the regional near-surface temperature, to the meridional temperature gradient and to the North Atlantic Oscillation. Our main result is that the link between the daily wind distribution and the regional climate drivers is strongly model dependent. The global models tend to behave similarly, although they show some discrepancies. The two regional models also tend to behave similarly to each other, but surprisingly the results derived from each regional model strongly deviates from the results derived from its driving global model. In addition, considering multi-centennial timescales, we find in two global simulations a long-term tendency for the probability distribution of daily wind speed to widen through the last centuries. The cause for this widening is likely the effect of the deforestation prescribed in these simulations. We conclude that no clear systematic relationship between the mean temperature, the temperature gradient and/or the North Atlantic Oscillation, with the daily wind speed statistics can be inferred from these simulations. The understand- ing of past and future changes in the distribution of wind speeds, and thus of wind speed extremes, will require a detailed analysis of the representation of the interaction between large-scale and small-scale dynamics.

Projector Model for Efficient List-Mode Reconstruction in PET Scanners with Parallel Planar Detectors

We have developed a new projector model specifically tailored for fast list-mode tomographic reconstructions in Positron emission tomography (PET) scanners with parallel planar detectors. The model provides an accurate estimation of the probability distribution of coincidence events defined by pairs of scintillating crystals. This distribution is parameterized with 2D elliptical Gaussian functions defined in planes perpendicular to the main axis of the tube of response (TOR). The parameters of these Gaussian functions have been obtained by fitting Monte Carlo simulations that include positron range, acolinearity of gamma rays, as well as detector attenuation and scatter effects. The proposed model has been applied efficiently to list-mode reconstruction algorithms. Evaluation with Monte Carlo simulations over a rotating high resolution PET scanner indicates that this model allows to obtain better recovery to noise ratio in OSEM (ordered-subsets, expectation-maximization) reconstruction, if compared to list-mode reconstruction with symmetric circular Gaussian TOR model, and histogram-based OSEM with precalculated system matrix using Monte Carlo simulated models and symmetries.

Modelled spatial and seasonal distribution of Blue Whiting (Micromesistius poutassou) larvae in the North-East Atlantic (1951 to 2005)

Blue whiting (Micromesistius poutassou, http://www.marinespecies.org/aphia.php?p=taxdetails&id=126439) is a small mesopelagic planktivorous gadoid found throughout the North-East Atlantic. This data contains the results of a model-based analysis of larvae captured by the Continuous Plankton Recorder (CPR) during the period 1951-2005. The observations are analysed using Generalised Additive Models (GAMs) of the the spatial, seasonal and interannual variation in the occurrence of larvae. The best fitting model is chosen using the Aikaike Information Criteria (AIC). The probability of occurrence in the continous plankton recorder is then normalised and converted to a probability distribution function in space (UTM projection Zone 28) and season (day of year). The best fitting model splits the distribution into two separate spawning grounds north and south of a dividing line at 53 N. The probability distribution is therefore normalised in these two regions (ie the space-time integral over each of the two regions is 1). The modelled outputs are on a UTM Zone 28 grid: however, for convenience, the latitude ("lat") and longitude ("lon") of each of these grid points are also included as a variable in the NetCDF file. The assignment of each grid point to either the Northern or Southern component (defined here as north/south of 53 N), is also included as a further variable ("component"). Finally, the day of year ("doy") is stored as the number of days elapsed from and included January 1 (ie doy=1 on January 1) - the year is thereafter divided into 180 grid points.

First year qualifying report: neural networks for extracting wind vectors from satellite scatterometer data

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about km800, carrying a C-band scatterometer. A scatterometer measures the amount of radar back scatter generated by small ripples on the ocean surface induced by instantaneous local winds. Operational methods that extract wind vectors from satellite scatterometer data are based on the local inversion of a forward model, mapping scatterometer observations to wind vectors, by the minimisation of a cost function in the scatterometer measurement space.par This report uses mixture density networks, a principled method for modelling conditional probability density functions, to model the joint probability distribution of the wind vectors given the satellite scatterometer measurements in a single cell (the `inverse' problem). The complexity of the mapping and the structure of the conditional probability density function are investigated by varying the number of units in the hidden layer of the multi-layer perceptron and the number of kernels in the Gaussian mixture model of the mixture density network respectively. The optimal model for networks trained per trace has twenty hidden units and four kernels. Further investigation shows that models trained with incidence angle as an input have results comparable to those models trained by trace. A hybrid mixture density network that incorporates geophysical knowledge of the problem confirms other results that the conditional probability distribution is dominantly bimodal.par The wind retrieval results improve on previous work at Aston, but do not match other neural network techniques that use spatial information in the inputs, which is to be expected given the ambiguity of the inverse problem. Current work uses the local inverse model for autonomous ambiguity removal in a principled Bayesian framework. Future directions in which these models may be improved are given.

Multi-valued control problems and mixture density network

We have proposed a novel robust inversion-based neurocontroller that searches for the optimal control law by sampling from the estimated Gaussian distribution of the inverse plant model. However, for problems involving the prediction of continuous variables, a Gaussian model approximation provides only a very limited description of the properties of the inverse model. This is usually the case for problems in which the mapping to be learned is multi-valued or involves hysteritic transfer characteristics. This often arises in the solution of inverse plant models. In order to obtain a complete description of the inverse model, a more general multicomponent distributions must be modeled. In this paper we test whether our proposed sampling approach can be used when considering an arbitrary conditional probability distributions. These arbitrary distributions will be modeled by a mixture density network. Importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The effectiveness of the importance sampling from an arbitrary conditional probability distribution will be demonstrated using a simple single input single output static nonlinear system with hysteretic characteristics in the inverse plant model.

A pragmatic Bayesian approach to wind field retrieval

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about 800 km, carrying a C-band scatterometer. A scatterometer measures the amount of backscatter microwave radiation reflected by small ripples on the ocean surface induced by sea-surface winds, and so provides instantaneous snap-shots of wind flow over large areas of the ocean surface, known as wind fields. Inherent in the physics of the observation process is an ambiguity in wind direction; the scatterometer cannot distinguish if the wind is blowing toward or away from the sensor device. This ambiguity implies that there is a one-to-many mapping between scatterometer data and wind direction. Current operational methods for wind field retrieval are based on the retrieval of wind vectors from satellite scatterometer data, followed by a disambiguation and filtering process that is reliant on numerical weather prediction models. The wind vectors are retrieved by the local inversion of a forward model, mapping scatterometer observations to wind vectors, and minimising a cost function in scatterometer measurement space. This thesis applies a pragmatic Bayesian solution to the problem. The likelihood is a combination of conditional probability distributions for the local wind vectors given the scatterometer data. The prior distribution is a vector Gaussian process that provides the geophysical consistency for the wind field. The wind vectors are retrieved directly from the scatterometer data by using mixture density networks, a principled method to model multi-modal conditional probability density functions. The complexity of the mapping and the structure of the conditional probability density function are investigated. A hybrid mixture density network, that incorporates the knowledge that the conditional probability distribution of the observation process is predominantly bi-modal, is developed. The optimal model, which generalises across a swathe of scatterometer readings, is better on key performance measures than the current operational model. Wind field retrieval is approached from three perspectives. The first is a non-autonomous method that confirms the validity of the model by retrieving the correct wind field 99% of the time from a test set of 575 wind fields. The second technique takes the maximum a posteriori probability wind field retrieved from the posterior distribution as the prediction. For the third technique, Markov Chain Monte Carlo (MCMC) techniques were employed to estimate the mass associated with significant modes of the posterior distribution, and make predictions based on the mode with the greatest mass associated with it. General methods for sampling from multi-modal distributions were benchmarked against a specific MCMC transition kernel designed for this problem. It was shown that the general methods were unsuitable for this application due to computational expense. On a test set of 100 wind fields the MAP estimate correctly retrieved 72 wind fields, whilst the sampling method correctly retrieved 73 wind fields.

Calculation of non-Gaussian statistics and bit error rate degradation due to pulse-to-pulse interaction

We develop a theoretical method to calculate jitter statistics of interacting solitons. Applying this approach, we have derived the non-Gaussian probability density function and calculated the bit-error rate as a function of noise level, initial separation and phase difference between solitons.

Intellect Sensing of Neural Network that Trained to Classify Complex Signals

An experimental comparison of information features used by neural network is performed. The sensing method was used. Suboptimal classifier agreeable to the gaussian model of the training data was used as a probe. Neural nets with architectures of perceptron and feedforward net with one hidden layer were used. The experiments were carried out with spatial ultrasonic data, which are used for car’s passenger safety system neural controller learning. In this paper we show that a neural network doesn’t fully make use of gaussian components, which are first two moment coefficients of probability distribution. On the contrary, the network can find more complicated regularities inside data vectors and thus shows better results than suboptimal classifier. The parallel connection of suboptimal classifier improves work of modular neural network whereas its connection to the network input improves the specialization effect during training.

Unifractality and multifractality in the Italian stock market

Tests for random walk behaviour in the Italian stock market are presented, based on an investigation of the fractal properties of the log return series for the Mibtel index. The random walk hypothesis is evaluated against alternatives accommodating either unifractality or multifractality. Critical values for the test statistics are generated using Monte Carlo simulations of random Gaussian innovations. Evidence is reported of multifractality, and the departure from random walk behaviour is statistically significant on standard criteria. The observed pattern is attributed primarily to fat tails in the return probability distribution, associated with volatility clustering in returns measured over various time scales. © 2009 Elsevier Inc. All rights reserved.

An Estimation of Distribution Algorithm with Intelligent Local Search for Rule-based Nurse Rostering

This paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse's assignment. The main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. Unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, i.e. we are able to identify building blocks directly. The overall approach learns by building a probabilistic model, i.e. an estimation of the probability distribution of individual nurse-rule pairs that are used to construct schedules. The local search processor (i.e. the ant-miner) reinforces nurse-rule pairs that receive higher rewards. A challenging real world nurse rostering problem is used as the test problem. Computational results show that the proposed approach outperforms most existing approaches. It is suggested that the learning methodologies suggested in this paper may be applied to other scheduling problems where schedules are built systematically according to specific rules.

An Estimation of Distribution Algorithm with Intelligent Local Search for Rule-based Nurse Rostering

This paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse's assignment. The main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. Unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, i.e. we are able to identify building blocks directly. The overall approach learns by building a probabilistic model, i.e. an estimation of the probability distribution of individual nurse-rule pairs that are used to construct schedules. The local search processor (i.e. the ant-miner) reinforces nurse-rule pairs that receive higher rewards. A challenging real world nurse rostering problem is used as the test problem. Computational results show that the proposed approach outperforms most existing approaches. It is suggested that the learning methodologies suggested in this paper may be applied to other scheduling problems where schedules are built systematically according to specific rules.

Analysis of slip distribution of large earthquakes oriented to tsunamigenesis characterisation

The present thesis focuses on the on-fault slip distribution of large earthquakes in the framework of tsunami hazard assessment and tsunami warning improvement. It is widely known that ruptures on seismic faults are strongly heterogeneous. In the case of tsunamigenic earthquakes, the slip heterogeneity strongly influences the spatial distribution of the largest tsunami effects along the nearest coastlines. Unfortunately, after an earthquake occurs, the so-called finite-fault models (FFM) describing the coseismic on-fault slip pattern becomes available over time scales that are incompatible with early tsunami warning purposes, especially in the near field. Our work aims to characterize the slip heterogeneity in a fast, but still suitable way. Using finite-fault models to build a starting dataset of seismic events, the characteristics of the fault planes are studied with respect to the magnitude. The patterns of the slip distribution on the rupture plane, analysed with a cluster identification algorithm, reveal a preferential single-asperity representation that can be approximated by a two-dimensional Gaussian slip distribution (2D GD). The goodness of the 2D GD model is compared to other distributions used in literature and its ability to represent the slip heterogeneity in the form of the main asperity is proven. The magnitude dependence of the 2D GD parameters is investigated and turns out to be of primary importance from an early warning perspective. The Gaussian model is applied to the 16 September 2015 Illapel, Chile, earthquake and used to compute early tsunami predictions that are satisfactorily compared with the available observations. The fast computation of the 2D GD and its suitability in representing the slip complexity of the seismic source make it a useful tool for the tsunami early warning assessments, especially for what concerns the near field.

Metodologia para a suavização de dados biomecanicos por função não parametrica ponderada local robusta

Universidade Estadual de Campinas. Faculdade de Educação Física

Turbulence in collisionless plasmas: statistical analysis from numerical simulations with pressure anisotropy

In recent years, we have experienced increasing interest in the understanding of the physical properties of collisionless plasmas, mostly because of the large number of astrophysical environments (e. g. the intracluster medium (ICM)) containing magnetic fields that are strong enough to be coupled with the ionized gas and characterized by densities sufficiently low to prevent the pressure isotropization with respect to the magnetic line direction. Under these conditions, a new class of kinetic instabilities arises, such as firehose and mirror instabilities, which have been studied extensively in the literature. Their role in the turbulence evolution and cascade process in the presence of pressure anisotropy, however, is still unclear. In this work, we present the first statistical analysis of turbulence in collisionless plasmas using three-dimensional numerical simulations and solving double-isothermal magnetohydrodynamic equations with the Chew-Goldberger-Low laws closure (CGL-MHD). We study models with different initial conditions to account for the firehose and mirror instabilities and to obtain different turbulent regimes. We found that the CGL-MHD subsonic and supersonic turbulences show small differences compared to the MHD models in most cases. However, in the regimes of strong kinetic instabilities, the statistics, i.e. the probability distribution functions (PDFs) of density and velocity, are very different. In subsonic models, the instabilities cause an increase in the dispersion of density, while the dispersion of velocity is increased by a large factor in some cases. Moreover, the spectra of density and velocity show increased power at small scales explained by the high growth rate of the instabilities. Finally, we calculated the structure functions of velocity and density fluctuations in the local reference frame defined by the direction of magnetic lines. The results indicate that in some cases the instabilities significantly increase the anisotropy of fluctuations. These results, even though preliminary and restricted to very specific conditions, show that the physical properties of turbulence in collisionless plasmas, as those found in the ICM, may be very different from what has been largely believed.