A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observed for each individual. A particular case of FDA is when the observed functions are density functions, that are also an example of infinite dimensional compositional data. In this work we compare several methods for dimensionality reduction for this particular type of data: functional principal components analysis (PCA) with or without a previous data transformation and multidimensional scaling (MDS) for diferent inter-densities distances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (households income distributions)

Modeling and Classifying Breast Tissue Density in Mammograms

We present a new approach to model and classify breast parenchymal tissue. Given a mammogram, first, we will discover the distribution of the different tissue densities in an unsupervised manner, and second, we will use this tissue distribution to perform the classification. We achieve this using a classifier based on local descriptors and probabilistic Latent Semantic Analysis (pLSA), a generative model from the statistical text literature. We studied the influence of different descriptors like texture and SIFT features at the classification stage showing that textons outperform SIFT in all cases. Moreover we demonstrate that pLSA automatically extracts meaningful latent aspects generating a compact tissue representation based on their densities, useful for discriminating on mammogram classification. We show the results of tissue classification over the MIAS and DDSM datasets. We compare our method with approaches that classified these same datasets showing a better performance of our proposal

A Novel Breast Tissue Density Classification Methodology

It has been shown that the accuracy of mammographic abnormality detection methods is strongly dependent on the breast tissue characteristics, where a dense breast drastically reduces detection sensitivity. In addition, breast tissue density is widely accepted to be an important risk indicator for the development of breast cancer. Here, we describe the development of an automatic breast tissue classification methodology, which can be summarized in a number of distinct steps: 1) the segmentation of the breast area into fatty versus dense mammographic tissue; 2) the extraction of morphological and texture features from the segmented breast areas; and 3) the use of a Bayesian combination of a number of classifiers. The evaluation, based on a large number of cases from two different mammographic data sets, shows a strong correlation ( and 0.67 for the two data sets) between automatic and expert-based Breast Imaging Reporting and Data System mammographic density assessment

Automatic classification of breast density

A recent trend in digital mammography is computer-aided diagnosis systems, which are computerised tools designed to assist radiologists. Most of these systems are used for the automatic detection of abnormalities. However, recent studies have shown that their sensitivity is significantly decreased as the density of the breast increases. This dependence is method specific. In this paper we propose a new approach to the classification of mammographic images according to their breast parenchymal density. Our classification uses information extracted from segmentation results and is based on the underlying breast tissue texture. Classification performance was based on a large set of digitised mammograms. Evaluation involves different classifiers and uses a leave-one-out methodology. Results demonstrate the feasibility of estimating breast density using image processing and analysis techniques

Partial disjoint path for multi-layer protection in GMPLS networks

In this paper, different recovery methods applied at different network layers and time scales are used in order to enhance the network reliability. Each layer deploys its own fault management methods. However, current recovery methods are applied to only a specific layer. New protection schemes, based on the proposed partial disjoint path algorithm, are defined in order to avoid protection duplications in a multi-layer scenario. The new protection schemes also encompass shared segment backup computation and shared risk link group identification. A complete set of experiments proves the efficiency of the proposed methods in relation with previous ones, in terms of resources used to protect the network, the failure recovery time and the request rejection ratio

Partial Diff pdf

Exam questions and solutions in PDF

MA167exam00pdf

Exam questions and solutions in PDF

MA167exam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

Partial Diff

Exam questions and solutions in LaTex

Applications of Partial Differentiation

Exercises and solutions for an applications of partial differentiation course. Diagrams for the questions are all together in the support.zip file, as .eps files

Partial Differentiation

Exercises and solutions about partial differentiation.

Exercise and Training at Altitudes: Physiological Effects and Protocols

An increase in altitude leads to a proportional fall in the barometric pressure, and a decrease in atmospheric oxygen pressure, producing hypobaric hypoxia that affects, in different degrees, all body organs, systems and functions. The chronically reduced partial pressure of oxygen causes that individuals adapt and adjust to physiological stress. These adaptations are modulated by many factors, including the degree of hypoxia related to altitude, time of exposure, exercise intensity and individual conditions. It has been established that exposure to high altitude is an environmental stressor that elicits a response that contributes to many adjustments and adaptations that influence exercise capacity and endurance performance. These adaptations include in crease in hemoglobin concentration, ventilation, capillary density and tissue myoglobin concentration. However, a negative effect in strength and power is related to a decrease in muscle fiber size and body mass due to the decrease in the training intensity. Many researches aim at establishing how training or living at high altitudes affects performance in athletes. Training methods, such as living in high altitudes training low, and training high-living in low altitudes have been used to research the changes in the physical condition in athletes and how the physiological adaptations to hypoxia can enhanceperformance at sea level. This review analyzes the literature related to altitude training focused on how physiological adaptations to hypoxic environments influence performance, and which protocols are most frequently used to train in high altitudes.

Partial decentralization as a safeguard against favoritism

In this paper I investigate the optimal level of decentralization of tasks for the provision of a local public good. I enrich the well-known trade-off between internalization of spillovers (that favors centralization) and accountability (that favors decentralization) by considering that public goods are produced through multiple tasks. This adds an additional institutional setting, partial decentralization, to the classical choice between full decentralization and full centralization. The main results are that partial decentralization is optimal when both the variance of exogenous shocks to electorate’s utility is large and the electorate expects high performance from politicians. I also show that the optimal institutional setting depends on the degree of substitutability / complementarity between tasks. In particular, I show that a large degree of substitutability between tasks makes favoritism more likely, which increases the desirability of partial decentralization as a safeguard against favoritism.

Partial scalar invariance and observed differences across gender in a reasoning test battery

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