Learning dependent sources using mixtures of Dirichlet: applications on hyperspectral unmixing

This paper is an elaboration of the DECA algorithm [1] to blindly unmix hyperspectral data. The underlying mixing model is linear, meaning that each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. The proposed method, as DECA, is tailored to highly mixed mixtures in which the geometric based approaches fail to identify the simplex of minimum volume enclosing the observed spectral vectors. We resort then to a statitistical framework, where the abundance fractions are modeled as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely non-negativity and constant sum. With respect to DECA, we introduce two improvements: 1) the number of Dirichlet modes are inferred based on the minimum description length (MDL) principle; 2) The generalized expectation maximization (GEM) algorithm we adopt to infer the model parameters is improved by using alternating minimization and augmented Lagrangian methods to compute the mixing matrix. The effectiveness of the proposed algorithm is illustrated with simulated and read data.

Geometric picture of generalized-CP and Higgs-family transformations in the two-Higgs-doublet model

In the two-Higgs-doublet model (THDM), generalized-CP transformations (phi(i) -> X-ij phi(*)(j) where X is unitary) and unitary Higgs-family transformations (phi(i) -> U-ij phi(j)) have recently been examined in a series of papers. In terms of gauge-invariant bilinear functions of the Higgs fields phi(i), the Higgs-family transformations and the generalized-CP transformations possess a simple geometric description. Namely, these transformations correspond in the space of scalar-field bilinears to proper and improper rotations, respectively. In this formalism, recent results relating generalized CP transformations with Higgs-family transformations have a clear geometric interpretation. We will review what is known regarding THDM symmetries, as well as derive new results concerning those symmetries, namely how they can be interpreted geometrically as applications of several CP transformations.

The influence of geometric factors on the wall shear stress distribution in realistic human coronary arteries

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para a obtenção do grau de Mestre em Engenharia Biomédica. A presente dissertação foi desenvolvida no Erasmus Medical Center em Roterdão, Holanda

Unmixing hyperspectral data: independent and dependent component analysis

The development of high spatial resolution airborne and spaceborne sensors has improved the capability of ground-based data collection in the fields of agriculture, geography, geology, mineral identification, detection [2, 3], and classification [4–8]. The signal read by the sensor from a given spatial element of resolution and at a given spectral band is a mixing of components originated by the constituent substances, termed endmembers, located at that element of resolution. This chapter addresses hyperspectral unmixing, which is the decomposition of the pixel spectra into a collection of constituent spectra, or spectral signatures, and their corresponding fractional abundances indicating the proportion of each endmember present in the pixel [9, 10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. The linear mixing model holds when the mixing scale is macroscopic [13]. The nonlinear model holds when the mixing scale is microscopic (i.e., intimate mixtures) [14, 15]. The linear model assumes negligible interaction among distinct endmembers [16, 17]. The nonlinear model assumes that incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [18]. Under the linear mixing model and assuming that the number of endmembers and their spectral signatures are known, hyperspectral unmixing is a linear problem, which can be addressed, for example, under the maximum likelihood setup [19], the constrained least-squares approach [20], the spectral signature matching [21], the spectral angle mapper [22], and the subspace projection methods [20, 23, 24]. Orthogonal subspace projection [23] reduces the data dimensionality, suppresses undesired spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel onto a subspace that is orthogonal to the undesired signatures. As shown in Settle [19], the orthogonal subspace projection technique is equivalent to the maximum likelihood estimator. This projection technique was extended by three unconstrained least-squares approaches [24] (signature space orthogonal projection, oblique subspace projection, target signature space orthogonal projection). Other works using maximum a posteriori probability (MAP) framework [25] and projection pursuit [26, 27] have also been applied to hyperspectral data. In most cases the number of endmembers and their signatures are not known. Independent component analysis (ICA) is an unsupervised source separation process that has been applied with success to blind source separation, to feature extraction, and to unsupervised recognition [28, 29]. ICA consists in finding a linear decomposition of observed data yielding statistically independent components. Given that hyperspectral data are, in given circumstances, linear mixtures, ICA comes to mind as a possible tool to unmix this class of data. In fact, the application of ICA to hyperspectral data has been proposed in reference 30, where endmember signatures are treated as sources and the mixing matrix is composed by the abundance fractions, and in references 9, 25, and 31–38, where sources are the abundance fractions of each endmember. In the first approach, we face two problems: (1) The number of samples are limited to the number of channels and (2) the process of pixel selection, playing the role of mixed sources, is not straightforward. In the second approach, ICA is based on the assumption of mutually independent sources, which is not the case of hyperspectral data, since the sum of the abundance fractions is constant, implying dependence among abundances. This dependence compromises ICA applicability to hyperspectral images. In addition, hyperspectral data are immersed in noise, which degrades the ICA performance. IFA [39] was introduced as a method for recovering independent hidden sources from their observed noisy mixtures. IFA implements two steps. First, source densities and noise covariance are estimated from the observed data by maximum likelihood. Second, sources are reconstructed by an optimal nonlinear estimator. Although IFA is a well-suited technique to unmix independent sources under noisy observations, the dependence among abundance fractions in hyperspectral imagery compromises, as in the ICA case, the IFA performance. Considering the linear mixing model, hyperspectral observations are in a simplex whose vertices correspond to the endmembers. Several approaches [40–43] have exploited this geometric feature of hyperspectral mixtures [42]. Minimum volume transform (MVT) algorithm [43] determines the simplex of minimum volume containing the data. The MVT-type approaches are complex from the computational point of view. Usually, these algorithms first find the convex hull defined by the observed data and then fit a minimum volume simplex to it. Aiming at a lower computational complexity, some algorithms such as the vertex component analysis (VCA) [44], the pixel purity index (PPI) [42], and the N-FINDR [45] still find the minimum volume simplex containing the data cloud, but they assume the presence in the data of at least one pure pixel of each endmember. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. Hyperspectral sensors collects spatial images over many narrow contiguous bands, yielding large amounts of data. For this reason, very often, the processing of hyperspectral data, included unmixing, is preceded by a dimensionality reduction step to reduce computational complexity and to improve the signal-to-noise ratio (SNR). Principal component analysis (PCA) [46], maximum noise fraction (MNF) [47], and singular value decomposition (SVD) [48] are three well-known projection techniques widely used in remote sensing in general and in unmixing in particular. The newly introduced method [49] exploits the structure of hyperspectral mixtures, namely the fact that spectral vectors are nonnegative. The computational complexity associated with these techniques is an obstacle to real-time implementations. To overcome this problem, band selection [50] and non-statistical [51] algorithms have been introduced. This chapter addresses hyperspectral data source dependence and its impact on ICA and IFA performances. The study consider simulated and real data and is based on mutual information minimization. Hyperspectral observations are described by a generative model. This model takes into account the degradation mechanisms normally found in hyperspectral applications—namely, signature variability [52–54], abundance constraints, topography modulation, and system noise. The computation of mutual information is based on fitting mixtures of Gaussians (MOG) to data. The MOG parameters (number of components, means, covariances, and weights) are inferred using the minimum description length (MDL) based algorithm [55]. We study the behavior of the mutual information as a function of the unmixing matrix. The conclusion is that the unmixing matrix minimizing the mutual information might be very far from the true one. Nevertheless, some abundance fractions might be well separated, mainly in the presence of strong signature variability, a large number of endmembers, and high SNR. We end this chapter by sketching a new methodology to blindly unmix hyperspectral data, where abundance fractions are modeled as a mixture of Dirichlet sources. This model enforces positivity and constant sum sources (full additivity) constraints. The mixing matrix is inferred by an expectation-maximization (EM)-type algorithm. This approach is in the vein of references 39 and 56, replacing independent sources represented by MOG with mixture of Dirichlet sources. Compared with the geometric-based approaches, the advantage of this model is that there is no need to have pure pixels in the observations. The chapter is organized as follows. Section 6.2 presents a spectral radiance model and formulates the spectral unmixing as a linear problem accounting for abundance constraints, signature variability, topography modulation, and system noise. Section 6.3 presents a brief resume of ICA and IFA algorithms. Section 6.4 illustrates the performance of IFA and of some well-known ICA algorithms with experimental data. Section 6.5 studies the ICA and IFA limitations in unmixing hyperspectral data. Section 6.6 presents results of ICA based on real data. Section 6.7 describes the new blind unmixing scheme and some illustrative examples. Section 6.8 concludes with some remarks.

A didactic sequence of elementary geometric optics Informed by history and philosophy of science

The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic processwithout a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the teaching and learning process in mathematics but has been used in other disciplinary fields. It will be used in this work in order to clear up the main obstacles in the teachinglearning process of geometric optics. We proceed to argue that since Newton’s approach to optics, in his Book I of Opticks, is independent of the corpuscular or undulatory nature of light, it is the most suitable for a constructivist learning environment. However, Newton’s theory must be subject to a proper didactic transposition to help overcome the referred alternative concepts. Then is described our didactic transposition in order to create knowledge to be taught using a dialogical process between students’ previous knowledge, history of optics and the desired outcomes on geometrical optics in an elementary pre-service teacher training course. Finally, we use the scheme-facet structure of knowledge both to analyse and discuss our results as well as to illuminate shortcomings that must be addressed in our next stage of the inquiry.

The sum-of-the-parts method: An international application

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Implementação de um modelo de geometric semantic genetic programming para aplicação naval

Recaí sob a responsabilidade da Marinha Portuguesa a gestão da Zona Económica Exclusiva de Portugal, assegurando a sua segurança da mesma face a atividades criminosas. Para auxiliar a tarefa, é utilizado o sistema Oversee, utilizado para monitorizar a posição de todas as embarcações presentes na área afeta, permitindo a rápida intervenção da Marinha Portuguesa quando e onde necessário. No entanto, o sistema necessita de transmissões periódicas constantes originadas nas embarcações para operar corretamente – casos as transmissões sejam interrompidas, deliberada ou acidentalmente, o sistema deixa de conseguir localizar embarcações, dificultando a intervenção da Marinha. A fim de colmatar esta falha, é proposto adicionar ao sistema Oversee a capacidade de prever as posições futuras de uma embarcação com base no seu trajeto até à cessação das transmissões. Tendo em conta os grandes volumes de dados gerados pelo sistema (históricos de posições), a área de Inteligência Artificial apresenta uma possível solução para este problema. Atendendo às necessidades de resposta rápida do problema abordado, o algoritmo de Geometric Semantic Genetic Programming baseado em referências de Vanneschi et al. apresenta-se como uma possível solução, tendo já produzido bons resultados em problemas semelhantes. O presente trabalho de tese pretende integrar o algoritmo de Geometric Semantic Genetic Programming desenvolvido com o sistema Oversee, a fim de lhe conceder capacidades preditivas. Adicionalmente, será realizado um processo de análise de desempenho a fim de determinar qual a ideal parametrização do algoritmo. Pretende-se com esta tese fornecer à Marinha Portuguesa uma ferramenta capaz de auxiliar o controlo da Zona Económica Exclusiva Portuguesa, permitindo a correta intervenção da Marinha em casos onde o atual sistema não conseguiria determinar a correta posição da embarcação em questão.

Integration of geometric consistency contributory factors in three-leg junctions collision prediction models of Portuguese two-lane national highways

This paper aims at developing a collision prediction model for three-leg junctions located in national roads (NR) in Northern Portugal. The focus is to identify factors that contribute for collision type crashes in those locations, mainly factors related to road geometric consistency, since literature is scarce on those, and to research the impact of three modeling methods: generalized estimating equations, random-effects negative binomial models and random-parameters negative binomial models, on the factors of those models. The database used included data published between 2008 and 2010 of 177 three-leg junctions. It was split in three groups of contributing factors which were tested sequentially for each of the adopted models: at first only traffic, then, traffic and the geometric characteristics of the junctions within their area of influence; and, lastly, factors which show the difference between the geometric characteristics of the segments boarding the junctionsâ area of influence and the segment included in that area were added. The choice of the best modeling technique was supported by the result of a cross validation made to ascertain the best model for the three sets of researched contributing factors. The models fitted with random-parameters negative binomial models had the best performance in the process. In the best models obtained for every modeling technique, the characteristics of the road environment, including proxy measures for the geometric consistency, along with traffic volume, contribute significantly to the number of collisions. Both the variables concerning junctions and the various national highway segments in their area of influence, as well as variations from those characteristics concerning roadway segments which border the already mentioned area of influence have proven their relevance and, therefore, there is a rightful need to incorporate the effect of geometric consistency in the three-leg junctions safety studies.

Echocardiographic assessment of the different left ventricular geometric patterns in hypertensive patients

OBJECTIVE: To identiy left ventricular geometric patterns in hypertensive patients on echocardiography, and to correlate those patterns with casual blood pressure measurements and with the parameters obtained on a 24-hour ambulatory blood pressure monitoring. METHODS: We studied sixty hypertensive patients, grouped according to the Joint National Committee stages of hypertension.. Using the single- and two-dimensional Doppler Echocardiography, we analyzed the left ventricular mass and the geometric patterns through the correlation of left ventricular mass index and relative wall thickness. On ambulatory blood pressure monitoring we assessed the means and pressure loads in the different geometric patterns detected on echocardiography RESULTS: We identified three left ventricular geometric patterns: 1) concentric hypertrophy, in 25% of the patients; 2) concentric remodeling, in 25%; and 3) normal geometry, in 50%. Casual systolic blood pressure was higher in the group with concentric hypertrophy than in the other groups (p=0.001). Mean systolic pressure in the 24h, daytime and nighttime periods was also higher in patients with concentric hypertrophy, as compared to the other groups (p=0.003, p=0.004 and p=0.007). Daytime systolic load and nighttime diastolic load were higher in patients with concentric hypertrophy ( p=0.004 and p=0.01, respectively). CONCLUSIONS: Left ventricular geometric patterns show significant correlation with casual systolic blood pressure, and with means and pressure loads on ambulatory blood pressure monitoring.

Distribution of cardiac geometric patterns on echocardiography in essential hypertension. Impact of two criteria of stratification

PURPOSE: To evaluate 2 left ventricular mass index (LVMI) normality criteria for the prevalence of left ventricular geometric patterns in a hypertensive population ( HT ) . METHODS: 544 essential hypertensive patients, were evaluated by echocardiography, and different left ventricular hypertrophy criteria were applied: 1 - classic : men - 134 g/m² and women - 110 g/m² ; 2- obtained from the 95th percentil of LVMI from a normotensive population (NT). RESULTS: The prevalence of 4 left ventricular geometric patterns, respectively for criteria 1 and 2, were: normal geometry - 47.7% and 39.3%; concentric remodelying - 25.4% and 14.3%; concentric hypertrophy - 18.4% and 27.7% and excentric hypertrophy - 8.8% and 16.7%, which confered abnormal geometry to 52.6% and 60.7% of hypertensive. The comparative analysis between NT and normal geometry hypertensive group according to criteria 1, detected significative stuctural differences,"( *p < 0.05):LVMI- 78.4 ± 1.50 vs 85.9 ±0.95 g/m² *; posterior wall thickness -8.5 ± 0.1 vs 8.9 ± 0.05 mm*; left atrium - 33.3 ± 0.41 vs 34.7 ± 0.30 mm *. With criteria 2, significative structural differences between the 2 groups were not observed. CONCLUSION: The use of a reference population based criteria, increased the abnormal left ventricular geometry prevalence in hypertensive patients and seemed more appropriate for left ventricular hypertrophy detection and risk stratification.

Geometric distortion correction in EPI at ultra high field

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2012

Shape and size variations of Aegla uruguayana (Anomura, Aeglidae) under laboratory conditions: A geometric morphometric approach to the growth

Crustacean growth studies typically use modal analysis rather than focusing on the growth of individuals. In the present work, we use geometric morphometrics to determine how organism shape and size varies during the life of the freshwater crab, Aegla uruguayana Schmitt, 1942. A total of 66 individuals from diverse life cycle stages were examined daily and each exuvia was recorded. Digital images of the dorsal region of the cephalothorax were obtained for each exuvia and were subsequently used to record landmark configurations. Moult increment and intermoult period were estimated for each crab. Differences in shape between crabs of different sizes (allometry) and sexes (sexual dimorphism; SD) were observed. Allometry was registered among specimens; however, SD was not statistically significant between crabs of a given size. The intermoult period increased as size increased, but the moult frequency was similar between the sexes. Regarding ontogeny, juveniles had short and blunt rostrum, robust forehead region, and narrow cephalothorax. Unlike juveniles crabs, adults presented a well-defined anterior and posterior cephalothorax region. The rostrum was long and stylised and the forehead narrow. Geometric morphometric methods were highly effective for the analysis of aeglid-individual- growth and avoided excessive handling of individuals through exuvia analysis.

Geometric tools to determine the hyperbolicity of limit cycles

"Vegeu el resum a l'inici del document del fitxer adjunt."

Equilibrium play and best response to (Stated) beliefs in constant sum games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.

Euclidean geometric invariant of framed knots in manifolds

We present an invariant of a three dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. An important feature of our work is that we are not using any nontrivial representation of the manifold fundamental group or knot group.