Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

A produção de educação nos Açores: a nota de matemática

Tese de Doutoramento, Ciências Económicas e Empresariais (Desenvolvimento Económico e Social e Economia Pública), 16 de Janeiro de 2014, Universidade dos Açores.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Models with three Higgs doublets in the triplet representations of A(4) or S-4

We consider the quark sector of theories containing three scalar SU(2)(L) doublets in the triplet representation of A(4) (or S-4) and three generations of quarks in arbitrary A(4) (or S-4) representations. We show that for all possible choices of quark field representations and for all possible alignments of the Higgs vacuum expectation values that can constitute global minima of the scalar potential, it is not possible to obtain simultaneously nonvanishing quark masses and a nonvanishing CP-violating phase in the Cabibbo-Kobayashi-Maskawa quark mixing matrix. As a result, in this minimal form, models with three scalar fields in the triplet representation of A(4) or S-4 cannot be extended to the quark sector in a way consistent with experiment. DOI: 10.1103/PhysRevD.87.055010.

Five models for lepton mixing

We produce five flavour models for the lepton sector. All five models fit perfectly well - at the 1 sigma level - the existing data on the neutrino mass-squared differences and on the lepton mixing angles. The models are based on the type I seesaw mechanism, on a Z(2) symmetry for each lepton flavour, and either on a (spontaneously broken) symmetry under the interchange of two lepton flavours or on a (spontaneously broken) CP symmetry incorporating that interchange - or on both symmetries simultaneously. Each model makes definite predictions both for the scale of the neutrino masses and for the phase delta in lepton mixing; the fifth model also predicts a correlation between the lepton mixing angles theta(12) and theta(23).

Neutrino masses and mixing in A(4) models with three Higgs doublets

We study neutrino masses and mixing in the context of flavor models with A(4) symmetry, three scalar doublets in the triplet representation, and three lepton families. We show that there is no representation assignment that yields a dimension-5 mass operator consistent with experiment. We then consider a type-I seesaw with three heavy right-handed neutrinos, explaining in detail why it fails, and allowing us to show that agreement with the present neutrino oscillation data can be recovered with the inclusion of dimension-3 heavy neutrino mass terms that break softly the A(4) symmetry.

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A similarity measure for music signals

One of the goals in the field of Music Information Retrieval is to obtain a measure of similarity between two musical recordings. Such a measure is at the core of automatic classification, query, and retrieval systems, which have become a necessity due to the ever increasing availability and size of musical databases. This paper proposes a method for calculating a similarity distance between two music signals. The method extracts a set of features from the audio recordings, models the features, and determines the distance between models. While further work is needed, preliminary results show that the proposed method has the potential to be used as a similarity measure for musical signals.

Automatic vehicle detection and classification

This paper presents a proposal for an automatic vehicle detection and classification (AVDC) system. The proposed AVDC should classify vehicles accordingly to the Portuguese legislation (vehicle height over the first axel and number of axels), and should also support profile based classification. The AVDC should also fulfill the needs of the Portuguese motorway operator, Brisa. For the classification based on the profile we propose:he use of Eigenprofiles, a technique based on Principal Components Analysis. The system should also support multi-lane free flow for future integration in this kind of environments.

Classification and staging of chronic liver disease from multimodal data

Chronic liver disease (CLD) is most of the time an asymptomatic, progressive, and ultimately potentially fatal disease. In this study, an automatic hierarchical procedure to stage CLD using ultrasound images, laboratory tests, and clinical records are described. The first stage of the proposed method, called clinical based classifier (CBC), discriminates healthy from pathologic conditions. When nonhealthy conditions are detected, the method refines the results in three exclusive pathologies in a hierarchical basis: 1) chronic hepatitis; 2) compensated cirrhosis; and 3) decompensated cirrhosis. The features used as well as the classifiers (Bayes, Parzen, support vector machine, and k-nearest neighbor) are optimally selected for each stage. A large multimodal feature database was specifically built for this study containing 30 chronic hepatitis cases, 34 compensated cirrhosis cases, and 36 decompensated cirrhosis cases, all validated after histopathologic analysis by liver biopsy. The CBC classification scheme outperformed the nonhierachical one against all scheme, achieving an overall accuracy of 98.67% for the normal detector, 87.45% for the chronic hepatitis detector, and 95.71% for the cirrhosis detector.

Data mining framework for fatty liver disease classification in ultrasound: a hybrid feature extraction paradigm

PURPOSE: Fatty liver disease (FLD) is an increasing prevalent disease that can be reversed if detected early. Ultrasound is the safest and ubiquitous method for identifying FLD. Since expert sonographers are required to accurately interpret the liver ultrasound images, lack of the same will result in interobserver variability. For more objective interpretation, high accuracy, and quick second opinions, computer aided diagnostic (CAD) techniques may be exploited. The purpose of this work is to develop one such CAD technique for accurate classification of normal livers and abnormal livers affected by FLD. METHODS: In this paper, the authors present a CAD technique (called Symtosis) that uses a novel combination of significant features based on the texture, wavelet transform, and higher order spectra of the liver ultrasound images in various supervised learning-based classifiers in order to determine parameters that classify normal and FLD-affected abnormal livers. RESULTS: On evaluating the proposed technique on a database of 58 abnormal and 42 normal liver ultrasound images, the authors were able to achieve a high classification accuracy of 93.3% using the decision tree classifier. CONCLUSIONS: This high accuracy added to the completely automated classification procedure makes the authors' proposed technique highly suitable for clinical deployment and usage.

The usefulness of ultrasound in the classification of chronic liver disease

Chronic Liver Disease is a progressive, most of the time asymptomatic, and potentially fatal disease. In this paper, a semi-automatic procedure to stage this disease is proposed based on ultrasound liver images, clinical and laboratorial data. In the core of the algorithm two classifiers are used: a k nearest neighbor and a Support Vector Machine, with different kernels. The classifiers were trained with the proposed multi-modal feature set and the results obtained were compared with the laboratorial and clinical feature set. The results showed that using ultrasound based features, in association with laboratorial and clinical features, improve the classification accuracy. The support vector machine, polynomial kernel, outperformed the others classifiers in every class studied. For the Normal class we achieved 100% accuracy, for the chronic hepatitis with cirrhosis 73.08%, for compensated cirrhosis 59.26% and for decompensated cirrhosis 91.67%.

Chronic liver disease staging classification based on ultrasound, clinical and laboratorial data

In this work the identification and diagnosis of various stages of chronic liver disease is addressed. The classification results of a support vector machine, a decision tree and a k-nearest neighbor classifier are compared. Ultrasound image intensity and textural features are jointly used with clinical and laboratorial data in the staging process. The classifiers training is performed by using a population of 97 patients at six different stages of chronic liver disease and a leave-one-out cross-validation strategy. The best results are obtained using the support vector machine with a radial-basis kernel, with 73.20% of overall accuracy. The good performance of the method is a promising indicator that it can be used, in a non invasive way, to provide reliable information about the chronic liver disease staging.

Diffuse liver disease classification from ultrasound surface characterization, clinical and laboratorial data

In this work liver contour is semi-automatically segmented and quantified in order to help the identification and diagnosis of diffuse liver disease. The features extracted from the liver contour are jointly used with clinical and laboratorial data in the staging process. The classification results of a support vector machine, a Bayesian and a k-nearest neighbor classifier are compared. A population of 88 patients at five different stages of diffuse liver disease and a leave-one-out cross-validation strategy are used in the classification process. The best results are obtained using the k-nearest neighbor classifier, with an overall accuracy of 80.68%. The good performance of the proposed method shows a reliable indicator that can improve the information in the staging of diffuse liver disease.

Fatty liver characterization and classification by ultrasound

Steatosis, also known as fatty liver, corresponds to an abnormal retention of lipids within the hepatic cells and reflects an impairment of the normal processes of synthesis and elimination of fat. Several causes may lead to this condition, namely obesity, diabetes, or alcoholism. In this paper an automatic classification algorithm is proposed for the diagnosis of the liver steatosis from ultrasound images. The features are selected in order to catch the same characteristics used by the physicians in the diagnosis of the disease based on visual inspection of the ultrasound images. The algorithm, designed in a Bayesian framework, computes two images: i) a despeckled one, containing the anatomic and echogenic information of the liver, and ii) an image containing only the speckle used to compute the textural features. These images are computed from the estimated RF signal generated by the ultrasound probe where the dynamic range compression performed by the equipment is taken into account. A Bayes classifier, trained with data manually classified by expert clinicians and used as ground truth, reaches an overall accuracy of 95% and a 100% of sensitivity. The main novelties of the method are the estimations of the RF and speckle images which make it possible to accurately compute textural features of the liver parenchyma relevant for the diagnosis.