Blind hyperspectral unmixing

Hyperspectral unmixing methods aim at the decomposition of a hyperspectral image into a collection endmember signatures, i.e., the radiance or reflectance of the materials present in the scene, and the correspondent abundance fractions at each pixel in the image. This paper introduces a new unmixing method termed dependent component analysis (DECA). This method is blind and fully automatic and it overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical based approaches. DECA is based on the linear mixture model, i.e., each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. These abundances are modeled as mixtures of Dirichlet densities, thus enforcing the non-negativity and constant sum constraints, imposed by the acquisition process. The endmembers signatures are inferred by a generalized expectation-maximization (GEM) type algorithm. The paper illustrates the effectiveness of DECA on synthetic and real hyperspectral images.

Hyperspectral unmixing algorithm via dependent component analysis

This paper introduces a new method to blindly unmix hyperspectral data, termed dependent component analysis (DECA). This method decomposes a hyperspectral images into a collection of reflectance (or radiance) spectra of the materials present in the scene (endmember signatures) and the corresponding abundance fractions at each pixel. DECA assumes that each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. These abudances 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. The mixing matrix is inferred by a generalized expectation-maximization (GEM) type algorithm. This method overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical based approaches. The effectiveness of the proposed method is illustrated using simulated data based on U.S.G.S. laboratory spectra and real hyperspectral data collected by the AVIRIS sensor over Cuprite, Nevada.

From weak Allee effect to no Allee effect in Richards’ growth models

Population dynamics have been attracting interest since many years. Among the considered models, the Richards’ equations remain one of the most popular to describe biological growth processes. On the other hand, Allee effect is currently a major focus of ecological research, which occurs when positive density dependence dominates at low densities. In this chapter, we propose the dynamical study of classes of functions based on Richards’ models describing the existence or not of Allee effect. We investigate bifurcation structures in generalized Richards’ functions and we look for the conditions in the (β, r) parameter plane for the existence of a weak Allee effect region. We show that the existence of this region is related with the existence of a dovetail structure. When the Allee limit varies, the weak Allee effect region disappears when the dovetail structure also disappears. Consequently, we deduce the transition from the weak Allee effect to no Allee effect to this family of functions. To support our analysis, we present fold and flip bifurcation curves and numerical simulations of several bifurcation diagrams.

Iberian peninsula ecosystem carbon fluxes: a model-data integration study

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia do Ambiente pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Osteoporotic hip fractures: Bisphosphonates sales and observed turning point in trend. A population-based retrospective study

The aim is to examine the temporal trends of hip fracture incidence in Portugal by sex and age groups, and explore the relation with anti-osteoporotic medication. From the National Hospital Discharge Database, we selected from 1st January 2000 to 31st December 2008, 77,083 hospital admissions (77.4% women) caused by osteoporotic hip fractures (low energy, patients over 49 years-age), with diagnosis codes 820.x of ICD 9-CM. The 2001 Portuguese population was used as standard to calculate direct age-standardized incidence rates (ASIR) (100,000 inhabitants). Generalized additive and linear models were used to evaluate and quantify temporal trends of age specific rates (AR), by sex. We identified 2003 as a turning point in the trend of ASIR of hip fractures in women. After 2003, the ASIR in women decreased on average by 10.3 cases/100,000 inhabitants, 95% CI (− 15.7 to − 4.8), per 100,000 anti-osteoporotic medication packages sold. For women aged 65–69 and 75–79 we identified the same turning point. However, for women aged over 80, the year 2004 marked a change in the trend, from an increase to a decrease. Among the population aged 70–74 a linear decrease of incidence rate (95% CI) was observed in both sexes, higher for women: − 28.0% (− 36.2 to − 19.5) change vs − 18.8%, (− 32.6 to − 2.3). The abrupt turning point in the trend of ASIR of hip fractures in women is compatible with an intervention, such as a medication. The trends were different according to gender and age group, but compatible with the pattern of bisphosphonates sales.

Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

NEPHROTOXICITY ATTRIBUTED TO MEGLUMINE ANTIMONIATE (GLUCANTIME) IN THE TREATMENT OF GENERALIZED CUTANEOUS LEISHMANIASIS

Background: Pentavalent antimonials have became of basic importance for the treatment of leishmaniasis. Their most severe side effects have been reported to be increased hepatic enzyme levels and electrocardiographic abnormalities. Nephrotoxicity has been rarely related. Observations: We report a case of generalized cutaneous leishmaniasis involving a 50-year old male patient who was submitted to treatment with meglumine antimoniate (Glucantime). He developed acute renal failure (ARF) due to acute tubular necrosis (ATN), followed by death after receiving a total of 53 ampoules of Glucantime. Conclusions: The treatment with Glucantime was responsible by ARF diagnosed in this patient. The previous urine osmolarity and serum creatinine levels were normal and the autopsy showed ATN. It should be pointed out if ARF may also be explained by massive deposits of immunocomplexes by leishmania antibodies and antigens due to the antigenic break by the antimonial compound, since our patient presented countless lesions covering the entire tegument, similar to the Hexheimer phenomenon, but at the autopsy no glomerular alterations were seen.

Transverse Vibrations in Beams Supported by a Piece-Wise Homogeneous Visco- Elastic Foundation

Transversal vibrations induced by a load moving uniformly along an infinite beam resting on a piece-wise homogeneous visco-elastic foundation are studied. Special attention is paid to the additional vibrations, conventionally referred to as transition radiations, which arise as the point load traverses the place of foundation discontinuity. The governing equations of the problem are solved by the normalmode analysis. The solution is expressed in a form of infinite sum of orthogonal natural modes multiplied by the generalized coordinate of displacement. The natural frequencies are obtained numerically exploiting the concept of the global dynamic stiffness matrix. This ensures that the frequencies obtained are exact. The methodology has restrictions neither on velocity nor on damping. The approach looks simple, though, the numerical expression of the results is not straightforward. A general procedure for numerical implementation is presented and verified. To illustrate the utility of the methodology parametric optimization is presented and influence of the load mass is studied. The results obtained have direct application in analysis of railway track vibrations induced by high-speed trains when passing regions with significantly different foundation stiffness.

Fractional Order Junctions

Gottfried Leibniz generalized the derivation and integration, extending the operators from integer up to real, or even complex, orders. It is presently recognized that the resulting models capture long term memory effects difficult to describe by classical tools. Leon Chua generalized the set of lumped electrical elements that provide the building blocks in mathematical models. His proposal of the memristor and of higher order elements broadened the scope of variables and relationships embedded in the development of models. This paper follows the two directions and proposes a new logical step, by generalizing the concept of junction. Classical junctions interconnect system elements using simple algebraic restrictions. Nevertheless, this simplistic approach may be misleading in the presence of unexpected dynamical phenomena and requires including additional “parasitic” elements. The novel γ-junction includes, as special cases, the standard series and parallel connections and allows a new degree of freedom when building models. The proposal motivates the search for experimental and real world manifestations of the abstract conjectures.

Multidimensional Scaling Visualization using Parametric Similarity Indices

In this paper, we apply multidimensional scaling (MDS) and parametric similarity indices (PSI) in the analysis of complex systems (CS). Each CS is viewed as a dynamical system, exhibiting an output time-series to be interpreted as a manifestation of its behavior. We start by adopting a sliding window to sample the original data into several consecutive time periods. Second, we define a given PSI for tracking pieces of data. We then compare the windows for different values of the parameter, and we generate the corresponding MDS maps of ‘points’. Third, we use Procrustes analysis to linearly transform the MDS charts for maximum superposition and to build a global MDS map of “shapes”. This final plot captures the time evolution of the phenomena and is sensitive to the PSI adopted. The generalized correlation, the Minkowski distance and four entropy-based indices are tested. The proposed approach is applied to the Dow Jones Industrial Average stock market index and the Europe Brent Spot Price FOB time-series.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Pustulose Generalizada Exantemática Aguda Associada ao Diltiazem

Acute generalized exanthematous pustulosis (AGEP) usually presents with the acute appearance of oedematous and erythematous lesions, on which multiple sterile pustules appear, associated with fever. Almost 90% of cases are associated with drugs, with antibiotics (penicillins and macrolides) being the most frequent causative agents. We describe a 36-year-old female patient, which started diltiazem 120mg/day for hypertension. After 6 days of therapy, multiple erythematous and oedematous lesions appeared, with associated multiple small non-follicular pustules. Oral corticosteroids were started, with progressive and complete improvement. Patch-tests were performed, which revealed positivity for diltiazem. Although a rare entity, AGEP must be considered in cases of acute eruptions with disseminated pustules and fever. The use of patch tests in this disease may be useful as positive reactions are frequent.

Entropy Analysis of Industrial Accident Data Series

Complex industrial plants exhibit multiple interactions among smaller parts and with human operators. Failure in one part can propagate across subsystem boundaries causing a serious disaster. This paper analyzes the industrial accident data series in the perspective of dynamical systems. First, we process real world data and show that the statistics of the number of fatalities reveal features that are well described by power law (PL) distributions. For early years, the data reveal double PL behavior, while, for more recent time periods, a single PL fits better into the experimental data. Second, we analyze the entropy of the data series statistics over time. Third, we use the Kullback–Leibler divergence to compare the empirical data and multidimensional scaling (MDS) techniques for data analysis and visualization. Entropy-based analysis is adopted to assess complexity, having the advantage of yielding a single parameter to express relationships between the data. The classical and the generalized (fractional) entropy and Kullback–Leibler divergence are used. The generalized measures allow a clear identification of patterns embedded in the data.