Diego P. Ruiz

Elliptic problems with critical exponents and Hardy potentials

This paper is devoted to the existence of positive solutions of a Dirichlet problem with critical exponent and a singular potential. Under various assumption on the domain Omega, which include some kinds of unbounded domains, we prove the existence of ground states and of symmetric solutions

Characterization of electron contamination in megavoltage photon beams

The purpose of the present study is to characterize electron contamination in photon beams in different clinical situations. Variations with field size, beam modifier (tray, shaping block) and source-surface distance (SSD) were studied. Percentage depth dose measurements with and without a purging magnet and replacing the air by helium were performed to identify the two electron sources that are clearly differentiated: air and treatment head. Previous analytical methods were used to fit the measured data, exploring the validity of these models. Electrons generated in the treatment head are more energetic and more important for larger field sizes, shorter SSD, and greater depths. This difference is much more noticeable for the 18 MV beam than for the 6 MV beam. If a tray is used as beam modifier, electron contamination increases, but the energy of these electrons is similar to that of electrons coming from the treatment head. Electron contamination could be fitted to a modified exponential curve. For machine modeling in a treatment planning system, setting SSD at 90 cm for input data could reduce errors for most isocentric treatments, because they will be delivered for SSD ranging from 80 to 100 cm. For very small field sizes, air-generated electrons must be considered independently, because of their different energetic spectrum and dosimetric influence.

Finite mixture of α-stable distributions

Over the last decades, the @a-stable distribution has proved to be a very efficient model for impulsive data. In this paper, we propose an extension of stable distributions, namely mixture of @a-stable distributions to model multimodal, skewed and impulsive data. A fully Bayesian framework is presented for the estimation of the stable density parameters and the mixture parameters. As opposed to most previous work on mixture models, the model order is assumed unknown and is estimated using reversible jump Markov chain Monte Carlo. It is important to note that the Gaussian mixture model is a special case of the presented model which provides additional flexibility to model skewed and impulsive phenomena. The algorithm is tested using synthetic and real data, accurately estimating @a-stable parameters, mixture coefficients and the number of components in the mixture.

Parameter estimation of exponentially damped sinusoids using a higher order correlation-based approach

A very common problem in signal processing is parameter estimation of exponentially damped sinusoids from a finite subset of noisy observations. When the signal is contaminated with colored noise of unknown power spectral density, a cumulant-based approach provides an appropriate solution to this problem. We propose a new class of estimator, namely, a covariance-type estimator, which reduces the deterministic errors associated with imperfect estimation of higher order correlations from finite-data length. This estimator allows a higher order correlation sequence to be modeled as a damped exponential model in certain slices of the moments plane. This result shows a useful link with well-known linear-prediction-based methods, such as the minimum-norm principal-eigenvector method of Kumaresan and Tufts (1982), which can be subsequently applied to extracting frequencies and damping coefficients from the 1-D correlation sequence. This paper discusses the slices allowed in the moments plane, the uses and limitations of this estimator using multiple realizations, and a single record in a noisy environment. Monte Carlo simulations applied to standard examples are also performed, and the results are compared with the KT method and the standard biased-estimator-based approach. The comparison shows the effectiveness of the proposed estimator in terms of bias and mean-square error when the signals are contaminated with additive Gaussian noise and a single data record with short data length is available.

Modelling with mixture of symmetric stable distributions using Gibbs sampling

The stable distribution is a very useful tool to model impulsive data. In this work, a fully Bayesian mixture of symmetric stable distribution model is presented. Despite the non-existence of closed form for @a-stable distributions, the use of the product property make it possible to infer on parameters using a straightforward Gibbs sampling. This model is compared to the mixture of Gaussians model. Our proposed methodology is proved to be more robust to outliers than the mixture of Gaussians. Therefore, it is suitable to model mixture of impulsive data. Moreover, as Gaussian is a particular case of the @a-stable distribution, the proposed model is a generalization of mixture of Gaussians. Mixture of symmetric @a-stable is intensively tested in both, simulated and real data.

Subsectional-polynomial E-pulse synthesis and application to radar target discrimination

A new family of extinction-pulses (E-pulses), called subsectional-polynomial E-pulses, is presented. This new type of E-pulse is constructed by choosing polynomials of degree Q as subsectional basis-functions in the E-pulse expansion. The main feature of this family of E-pulses is that the waveforms are continuous and smooth. Several topics concerning the E-pulse technique are investigated, such as: insensitivity to the exact number of natural modes present in the target response; aspect-angle independence; and effects of additive white Gaussian noise. Numerical results, using the response of a thin cylinder and a sphere, show that the subsectional-polynomial E-pulses improve the results obtained using subsectional-rectangular E-pulses. >

Application of a methodology for categorizing and differentiating urban soundscapes using acoustical descriptors and semantic-differential attributes

A subjective and physical categorization of an ambient sound is the first step to evaluate the soundscape and provides a basis for designing or adapting this ambient sound to match peoples expectations. For this reason, the main goal of this work is to develop a categorization and differentiation analysis of soundscapes on the basis of acoustical and perceptual variables. A hierarchical cluster analysis, using 15 semantic-differential attributes and acoustical descriptors to include an equivalent sound-pressure level, maximum-minimum sound-pressure level, impulsiveness of the sound-pressure level, sound-pressure level time course, and spectral composition, was conducted to classify soundscapes into different typologies. This analysis identified 15 different soundscape typologies. Furthermore, based on a discriminant analysis the acoustical descriptors, the crest factor (impulsiveness of the sound-pressure level), and the sound level at 125 Hz were found to be the acoustical variables with the highest impact in the differentiation of the recognized types of soundscapes. Finally, to determine how the different soundscape typologies differed from each other, both subjectively and acoustically, a study was performed.

A neural network based model for urban noise prediction.

Noise is a global problem. In 1972 the World Health Organization (WHO) classified noise as a pollutant. Since then, most industrialized countries have enacted laws and local regulations to prevent and reduce acoustic environmental pollution. A further aim is to alert people to the dangers of this type of pollution. In this context, urban planners need to have tools that allow them to evaluate the degree of acoustic pollution. Scientists in many countries have modeled urban noise, using a wide range of approaches, but their results have not been as good as expected. This paper describes a model developed for the prediction of environmental urban noise using Soft Computing techniques, namely Artificial Neural Networks (ANN). The model is based on the analysis of variables regarded as influential by experts in the field and was applied to data collected on different types of streets. The results were compared to those obtained with other models. The study found that the ANN system was able to predict urban noise with greater accuracy, and thus, was an improvement over those models. The principal component analysis (PCA) was also used to try to simplify the model. Although there was a slight decline in the accuracy of the results, the values obtained were also quite acceptable.

Using Recorded Sound Spectra Profile as Input Data for Real-Time Short-Term Urban Road-Traffic-Flow Estimation

Road traffic has a heavy impact on the urban sound environment, constituting the main source of noise and widely dominating its spectral composition. In this context, our research investigates the use of recorded sound spectra as input data for the development of real-time short-term road traffic flow estimation models. For this, a series of models based on the use of Multilayer Perceptron Neural Networks, multiple linear regression, and the Fisher linear discriminant were implemented to estimate road traffic flow as well as to classify it according to the composition of heavy vehicles and motorcycles/mopeds. In view of the results, the use of the 50-400 Hz and 1-2.5 kHz frequency ranges as input variables in multilayer perceptron-based models successfully estimated urban road traffic flow with an average percentage of explained variance equal to 86%, while the classification of the urban road traffic flow gave an average success rate of 96.1%.

A tool for urban soundscape evaluation applying Support Vector Machines for developing a soundscape classification model

To ensure appropriate soundscape management in urban environments, the urban-planning authorities need a range of tools that enable such a task to be performed. An essential step during the management of urban areas from a sound standpoint should be the evaluation of the soundscape in such an area. In this sense, it has been widely acknowledged that a subjective and acoustical categorization of a soundscape is the first step to evaluate it, providing a basis for designing or adapting it to match peoples expectations as well. In this sense, this work proposes a model for automatic classification of urban soundscapes. This model is intended for the automatic classification of urban soundscapes based on underlying acoustical and perceptual criteria. Thus, this classification model is proposed to be used as a tool for a comprehensive urban soundscape evaluation. Because of the great complexity associated with the problem, two machine learning techniques, Support Vector Machines (SVM) and Support Vector Machines trained with Sequential Minimal Optimization (SMO), are implemented in developing model classification. The results indicate that the SMO model outperforms the SVM model in the specific task of soundscape classification. With the implementation of the SMO algorithm, the classification model achieves an outstanding performance (91.3% of instances correctly classified).