O princípio da Indução Finita e jogos para o ensino de funções

Pós-graduação em Matemática em Rede Nacional - IBILCE

Equações de diferenças: aplicações no ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Um rio de imagens

O presente artigo apresenta uma reflexão sobre a imagem dos rios ao longo da história da arte, a partir da pesquisa realizada por mim para a tese de doutorado “Poéticas Líquidas: a água na arte contemporânea“. Os rios são estudados tanto a partir de suas representações pictóricas de interesse histórico, como também enquanto suporte para a realização de obras de arte contemporânea. São identificadas conotações simbólicas e espirituais dos rios, como metáfora para o transcorrer da vida e para as transformações, assim como também suas questões mais terrenas, ligadas à ecologia e à sua relação com as cidades. Como reflexão final, apresento alguns trabalhos plásticos realizados por mim ao longo dos anos, que discutem a presença dos rios na vida contemporânea, a partir de proposições estéticas que refletem as conflituosas relações entre o homem e a natureza na atualidade.

Generalizations of Lie Algebras

The generalizations of Lie algebras appeared in the modern mathematics and mathematical physics. In this paper we consider recent developments and remaining open problems on the subject. Some of that developments have been influenced by lectures given by Professor Jaime Keller in his research seminar. The survey includes Lie superalgebras, color Lie algebras, Lie algebras in symmetric categories, free Lie tau-algebras, and some generalizations with non-associative enveloping algebras: tangent algebras to analytic loops, bialgebras and primitive elements, non-associative Hopf algebras.

Necessidades de saúde, políticas públicas e gênero: a perspectiva das práticas profissionais

Examina-se a relação entre políticas públicas e práticas dos profissionais, relativamente às necessidades de saúde. Em abordagem teórico-conceitual, as práticas são definidas como desempenhos permeados por determinantes técnico-cien­tíficos e sócio-históricos para a produção social de um trabalho, analisando-se suas possibilidades de mudanças culturais, éticas e políticas, para um agir crítico das desigualdades de gênero. Tomando-se a atenção integral à saúde dos homens, examina-se a relevância da distinção entre necessidades masculinas e femininas, enquanto realidades parciais não necessariamente convergentes na (re)produção daquelas desigualdades. Igualmente se examinam as práticas profissionais, como realidade parcial e distinta das políticas, estabelecendo relações não imediatas. Desenvolve-se que são obstáculos simbólicos e práticos para mudanças: a normalização biomédica redutora das necessidades, a cultura do trabalho autônomo e da abordagem individualizante das necessidades, a cultura tradicional de gênero conservando práticas desiguais para homens e mulheres e a ausência de inscrição dos direitos como parte do agir profissio­nal. Isto exige propostas específicas às práticas de saúde e às necessidades masculinas para maior convergência com as reformas das políticas.

A General Latent Class Model for Performance Evaluation of Diagnostic Tests in the Absence of a Gold Standard: An Application to Chagas Disease

We propose a new general Bayesian latent class model for evaluation of the performance of multiple diagnostic tests in situations in which no gold standard test exists based on a computationally intensive approach. The modeling represents an interesting and suitable alternative to models with complex structures that involve the general case of several conditionally independent diagnostic tests, covariates, and strata with different disease prevalences. The technique of stratifying the population according to different disease prevalence rates does not add further marked complexity to the modeling, but it makes the model more flexible and interpretable. To illustrate the general model proposed, we evaluate the performance of six diagnostic screening tests for Chagas disease considering some epidemiological variables. Serology at the time of donation (negative, positive, inconclusive) was considered as a factor of stratification in the model. The general model with stratification of the population performed better in comparison with its concurrents without stratification. The group formed by the testing laboratory Biomanguinhos FIOCRUZ-kit (c-ELISA and rec-ELISA) is the best option in the confirmation process by presenting false-negative rate of 0.0002% from the serial scheme. We are 100% sure that the donor is healthy when these two tests have negative results and he is chagasic when they have positive results.

Prominent Effect of Soil Network Heterogeneity on Microbial Invasion

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil.

A Bayesian Approach for Decision Making on the Identification of Genes with Different Expression Levels: An Application to Escherichia coli Bacterium Data

A common interest in gene expression data analysis is to identify from a large pool of candidate genes the genes that present significant changes in expression levels between a treatment and a control biological condition. Usually, it is done using a statistic value and a cutoff value that are used to separate the genes differentially and nondifferentially expressed. In this paper, we propose a Bayesian approach to identify genes differentially expressed calculating sequentially credibility intervals from predictive densities which are constructed using the sampled mean treatment effect from all genes in study excluding the treatment effect of genes previously identified with statistical evidence for difference. We compare our Bayesian approach with the standard ones based on the use of the t-test and modified t-tests via a simulation study, using small sample sizes which are common in gene expression data analysis. Results obtained report evidence that the proposed approach performs better than standard ones, especially for cases with mean differences and increases in treatment variance in relation to control variance. We also apply the methodologies to a well-known publicly available data set on Escherichia coli bacterium.

Automatic lumen segmentation in IVOCT images using binary morphological reconstruction

Abstract Background Atherosclerosis causes millions of deaths, annually yielding billions in expenses round the world. Intravascular Optical Coherence Tomography (IVOCT) is a medical imaging modality, which displays high resolution images of coronary cross-section. Nonetheless, quantitative information can only be obtained with segmentation; consequently, more adequate diagnostics, therapies and interventions can be provided. Since it is a relatively new modality, many different segmentation methods, available in the literature for other modalities, could be successfully applied to IVOCT images, improving accuracies and uses. Method An automatic lumen segmentation approach, based on Wavelet Transform and Mathematical Morphology, is presented. The methodology is divided into three main parts. First, the preprocessing stage attenuates and enhances undesirable and important information, respectively. Second, in the feature extraction block, wavelet is associated with an adapted version of Otsu threshold; hence, tissue information is discriminated and binarized. Finally, binary morphological reconstruction improves the binary information and constructs the binary lumen object. Results The evaluation was carried out by segmenting 290 challenging images from human and pig coronaries, and rabbit iliac arteries; the outcomes were compared with the gold standards made by experts. The resultant accuracy was obtained: True Positive (%) = 99.29 ± 2.96, False Positive (%) = 3.69 ± 2.88, False Negative (%) = 0.71 ± 2.96, Max False Positive Distance (mm) = 0.1 ± 0.07, Max False Negative Distance (mm) = 0.06 ± 0.1. Conclusions In conclusion, by segmenting a number of IVOCT images with various features, the proposed technique showed to be robust and more accurate than published studies; in addition, the method is completely automatic, providing a new tool for IVOCT segmentation.

Tuzla City (BiH): an example of geohazard induced by salt extraction

Salt deposits characterize the subsurface of Tuzla (BiH) and made it famous since the ancient times. Archeological discoveries demonstrate the presence of a Neolithic pile-dwelling settlement related to the existence of saltwater springs that contributed to make the most of the area a swampy ground. Since the Roman times, the town is reported as “the City of Salt deposits and Springs”; "tuz" is the Turkish word for salt, as the Ottomans renamed the settlement in the 15th century following their conquest of the medieval Bosnia (Donia and Fine, 1994). Natural brine springs were located everywhere and salt has been evaporated by means of hot charcoals since pre-Roman times. The ancient use of salt was just a small exploitation compared to the massive salt production carried out during the 20th century by means of classical mine methodologies and especially wild brine pumping. In the past salt extraction was practised tapping natural brine springs, while the modern technique consists in about 100 boreholes with pumps tapped to the natural underground brine runs, at an average depth of 400-500 m. The mining operation changed the hydrogeological conditions enabling the downward flow of fresh water causing additional salt dissolution. This process induced severe ground subsidence during the last 60 years reaching up to 10 meters of sinking in the most affected area. Stress and strain of the overlying rocks induced the formation of numerous fractures over a conspicuous area (3 Km2). Consequently serious damages occurred to buildings and infrastructures such as water supply system, sewage networks and power lines. Downtown urban life was compromised by the destruction of more than 2000 buildings that collapsed or needed to be demolished causing the resettlement of about 15000 inhabitants (Tatić, 1979). Recently salt extraction activities have been strongly reduced, but the underground water system is returning to his natural conditions, threatening the flooding of the most collapsed area. During the last 60 years local government developed a monitoring system of the phenomenon, collecting several data about geodetic measurements, amount of brine pumped, piezometry, lithostratigraphy, extension of the salt body and geotechnical parameters. A database was created within a scientific cooperation between the municipality of Tuzla and the city of Rotterdam (D.O.O. Mining Institute Tuzla, 2000). The scientific investigation presented in this dissertation has been financially supported by a cooperation project between the Municipality of Tuzla, The University of Bologna (CIRSA) and the Province of Ravenna. The University of Tuzla (RGGF) gave an important scientific support in particular about the geological and hydrogeological features. Subsidence damage resulting from evaporite dissolution generates substantial losses throughout the world, but the causes are only well understood in a few areas (Gutierrez et al., 2008). The subject of this study is the collapsing phenomenon occurring in Tuzla area with the aim to identify and quantify the several factors involved in the system and their correlations. Tuzla subsidence phenomenon can be defined as geohazard, which represents the consequence of an adverse combination of geological processes and ground conditions precipitated by human activity with the potential to cause harm (Rosenbaum and Culshaw, 2003). Where an hazard induces a risk to a vulnerable element, a risk management process is required. The single factors involved in the subsidence of Tuzla can be considered as hazards. The final objective of this dissertation represents a preliminary risk assessment procedure and guidelines, developed in order to quantify the buildings vulnerability in relation to the overall geohazard that affect the town. The historical available database, never fully processed, have been analyzed by means of geographic information systems and mathematical interpolators (PART I). Modern geomatic applications have been implemented to deeply investigate the most relevant hazards (PART II). In order to monitor and quantify the actual subsidence rates, geodetic GPS technologies have been implemented and 4 survey campaigns have been carried out once a year. Subsidence related fractures system has been identified by means of field surveys and mathematical interpretations of the sinking surface, called curvature analysis. The comparison of mapped and predicted fractures leaded to a better comprehension of the problem. Results confirmed the reliability of fractures identification using curvature analysis applied to sinking data instead of topographic or seismic data. Urban changes evolution has been reconstructed analyzing topographic maps and satellite imageries, identifying the most damaged areas. This part of the investigation was very important for the quantification of buildings vulnerability.

La comunicazione della cooperazione allo sviluppo: gli Enti Pubblici. Analisi discorsive dei Siti Web

Our research takes place in the context of a discipline kwown as Communication for Development, sited inside the field of Communication for Social Change, characterized by the use of interpersonal ad mass communication theories and tools, applyied to international development cooperation. Our study aims at pointing out a change of paradigm in this field: our object is Public Administration’s communication, therefore, what we suggest is a shift from Communication for Development, to Development Communication. The object of our study, hence, becomes the discourse itself, in its double action of representation and construction of reality. In particular, we are interested in the discourse’s tribute to the creation of a collective immagination, wich is the perspective towards which we have oriented the analysis, through a structuralist semoitics-based methodology integrated with a socio-semiotic approach. Taking into consideartion the fact that in our contemporary society (that is to say a ‘Western’ and ‘First World’ society), the internet is a crucial public space for the mediation and the management of collective immagination, we chose the web sites of Public Bodies which are dedicated to International Cooperation has our analysis corpus. This, due to their symbolic and ideologic significance, as well as for the actual political responsibility we think these web sites should have. The result of our analysis allows us to suggest some discoursive strategies used in the web sites of Public Bodies. In these sites, there is a tendency to shift the discourses around international cooperation from the ideological axis - avoiding in so doing to explicit a political statement about the causes of injustices and un-balances which lead to the necessity of a support in development (i.e. avoiding to mention values such as social justice and democracy while acknowledging socio-economical institutions which contribute to foster underdevelopment on a global scale) -, to the ethical axis, hence referring to moral values concerning the private sphere (human solidarity and charity), which is delegated mainly to non governamental associations.

Self-organising coordination systems

Many research fields are pushing the engineering of large-scale, mobile, and open systems towards the adoption of techniques inspired by self-organisation: pervasive computing, but also distributed artificial intelligence, multi-agent systems, social networks, peer-topeer and grid architectures exploit adaptive techniques to make global system properties emerge in spite of the unpredictability of interactions and behaviour. Such a trend is visible also in coordination models and languages, whenever a coordination infrastructure needs to cope with managing interactions in highly dynamic and unpredictable environments. As a consequence, self-organisation can be regarded as a feasible metaphor to define a radically new conceptual coordination framework. The resulting framework defines a novel coordination paradigm, called self-organising coordination, based on the idea of spreading coordination media over the network, and charge them with services to manage interactions based on local criteria, resulting in the emergence of desired and fruitful global coordination properties of the system. Features like topology, locality, time-reactiveness, and stochastic behaviour play a key role in both the definition of such a conceptual framework and the consequent development of self-organising coordination services. According to this framework, the thesis presents several self-organising coordination techniques developed during the PhD course, mainly concerning data distribution in tuplespace-based coordination systems. Some of these techniques have been also implemented in ReSpecT, a coordination language for tuple spaces, based on logic tuples and reactions to events occurring in a tuple space. In addition, the key role played by simulation and formal verification has been investigated, leading to analysing how automatic verification techniques like probabilistic model checking can be exploited in order to formally prove the emergence of desired behaviours when dealing with coordination approaches based on self-organisation. To this end, a concrete case study is presented and discussed.

Algorithmische Methoden zur Berechnung von Vierbeinfunktionen

Die vorliegende Arbeit beschäftigt sich mit derAutomatisierung von Berechnungen virtuellerStrahlungskorrekturen in perturbativen Quantenfeldtheorien.Die Berücksichtigung solcher Korrekturen aufMehrschleifen-Ebene in der Störungsreihenentwicklung istheute unabdingbar, um mit der wachsenden Präzisionexperimenteller Resultate Schritt zu halten. Im allgemeinen kinematischen Fall können heute nur dieEinschleifen-Korrekturen als theoretisch gelöst angesehenwerden -- für höhere Ordnungen liegen nur Teilergebnissevor. In Mainz sind in den letzten Jahren einige neuartigeMethoden zur Integration von Zweischleifen-Feynmandiagrammenentwickelt und im xloops-Paket in algorithmischer Formteilweise erfolgreich implementiert worden. Die verwendetenVerfahren sind eine Kombination exakter symbolischerRechenmethoden mit numerischen. DieZweischleifen-Vierbeinfunktionen stellen in diesem Rahmenein neues Kapitel dar, das durch seine große Anzahl vonfreien kinematischen Parametern einerseits leichtunüberschaubar wird und andererseits auch auf symbolischerEbene die bisherigen Anforderungen übersteigt. Sie sind ausexperimenteller Sicht aber für manche Streuprozesse vongroßem Interesse. In dieser Arbeit wurde, basierend auf einer Idee von DirkKreimer, ein Verfahren untersucht, welches die skalarenVierbeinfunktionen auf Zweischleifen-Niveau ganz ohneRandbedingungen an den Parameterraum zu integrierenversucht. Die Struktur der nach vier Residuenintegrationenauftretenden Terme konnte dabei weitgehend geklärt und dieKomplexität der auftretenden Ausdrücke soweit verkleinertwerden, dass sie von heutigen Rechnern darstellbar sind.Allerdings ist man noch nicht bei einer vollständigautomatisierten Implementierung angelangt. All dies ist dasThema von Kapitel 2. Die Weiterentwicklung von xloops über Zweibeinfunktionenhinaus erschien aus vielfältigen Gründen allerdings nichtmehr sinnvoll. Im Rahmen dieser Arbeit wurde daher einradikaler Bruch vollzogen und zusammen mit C. Bauer und A.Frink eine Programmbibliothek entworfen, die als Vehikel fürsymbolische Manipulationen dient und es uns ermöglicht,übliche symbolische Sprachen wie Maple durch C++ zuersetzen. Im dritten Kapitel wird auf die Gründeeingegangen, warum diese Umstellung sinnvoll ist, und dabeidie Bibliothek GiNaC vorgestellt. Im vierten Kapitel werdenDetails der Implementierung dann im Einzelnen vorgestelltund im fünften wird sie auf ihre Praxistauglichkeituntersucht. Anhang A bietet eine Übersicht über dieverwendeten Hilfsmittel komplexer Analysis und Anhang Bbeschreibt ein bewährtes numerisches Instrument.

Troposphere Calibration Techniques for Deep Space Probe Tracking

Ground-based Earth troposphere calibration systems play an important role in planetary exploration, especially to carry out radio science experiments aimed at the estimation of planetary gravity fields. In these experiments, the main observable is the spacecraft (S/C) range rate, measured from the Doppler shift of an electromagnetic wave transmitted from ground, received by the spacecraft and coherently retransmitted back to ground. If the solar corona and interplanetary plasma noise is already removed from Doppler data, the Earth troposphere remains one of the main error sources in tracking observables. Current Earth media calibration systems at NASA’s Deep Space Network (DSN) stations are based upon a combination of weather data and multidirectional, dual frequency GPS measurements acquired at each station complex. In order to support Cassini’s cruise radio science experiments, a new generation of media calibration systems were developed, driven by the need to achieve the goal of an end-to-end Allan deviation of the radio link in the order of 3×〖10〗^(-15) at 1000 s integration time. The future ESA’s Bepi Colombo mission to Mercury carries scientific instrumentation for radio science experiments (a Ka-band transponder and a three-axis accelerometer) which, in combination with the S/C telecommunication system (a X/X/Ka transponder) will provide the most advanced tracking system ever flown on an interplanetary probe. Current error budget for MORE (Mercury Orbiter Radioscience Experiment) allows the residual uncalibrated troposphere to contribute with a value of 8×〖10〗^(-15) to the two-way Allan deviation at 1000 s integration time. The current standard ESA/ESTRACK calibration system is based on a combination of surface meteorological measurements and mathematical algorithms, capable to reconstruct the Earth troposphere path delay, leaving an uncalibrated component of about 1-2% of the total delay. In order to satisfy the stringent MORE requirements, the short time-scale variations of the Earth troposphere water vapor content must be calibrated at ESA deep space antennas (DSA) with more precise and stable instruments (microwave radiometers). In parallel to this high performance instruments, ESA ground stations should be upgraded to media calibration systems at least capable to calibrate both troposphere path delay components (dry and wet) at sub-centimetre level, in order to reduce S/C navigation uncertainties. The natural choice is to provide a continuous troposphere calibration by processing GNSS data acquired at each complex by dual frequency receivers already installed for station location purposes. The work presented here outlines the troposphere calibration technique to support both Deep Space probe navigation and radio science experiments. After an introduction to deep space tracking techniques, observables and error sources, in Chapter 2 the troposphere path delay is widely investigated, reporting the estimation techniques and the state of the art of the ESA and NASA troposphere calibrations. Chapter 3 deals with an analysis of the status and the performances of the NASA Advanced Media Calibration (AMC) system referred to the Cassini data analysis. Chapter 4 describes the current release of a developed GNSS software (S/W) to estimate the troposphere calibration to be used for ESA S/C navigation purposes. During the development phase of the S/W a test campaign has been undertaken in order to evaluate the S/W performances. A description of the campaign and the main results are reported in Chapter 5. Chapter 6 presents a preliminary analysis of microwave radiometers to be used to support radio science experiments. The analysis has been carried out considering radiometric measurements of the ESA/ESTEC instruments installed in Cabauw (NL) and compared with the requirements of MORE. Finally, Chapter 7 summarizes the results obtained and defines some key technical aspects to be evaluated and taken into account for the development phase of future instrumentation.

Ein inverses Problem für die degeneriert parabolische Richardsgleichung

In der vorliegenden Arbeit werden zwei physikalischeFließexperimente an Vliesstoffen untersucht, die dazu dienensollen, unbekannte hydraulische Parameter des Materials, wiez. B. die Diffusivitäts- oder Leitfähigkeitsfunktion, ausMeßdaten zu identifizieren. Die physikalische undmathematische Modellierung dieser Experimente führt auf einCauchy-Dirichlet-Problem mit freiem Rand für die degeneriertparabolische Richardsgleichung in derSättigungsformulierung, das sogenannte direkte Problem. Ausder Kenntnis des freien Randes dieses Problems soll dernichtlineare Diffusivitätskoeffizient derDifferentialgleichung rekonstruiert werden. Für diesesinverse Problem stellen wir einOutput-Least-Squares-Funktional auf und verwenden zu dessenMinimierung iterative Regularisierungsverfahren wie dasLevenberg-Marquardt-Verfahren und die IRGN-Methode basierendauf einer Parametrisierung des Koeffizientenraumes durchquadratische B-Splines. Für das direkte Problem beweisen wirunter anderem Existenz und Eindeutigkeit der Lösung desCauchy-Dirichlet-Problems sowie die Existenz des freienRandes. Anschließend führen wir formal die Ableitung desfreien Randes nach dem Koeffizienten, die wir für dasnumerische Rekonstruktionsverfahren benötigen, auf einlinear degeneriert parabolisches Randwertproblem zurück.Wir erläutern die numerische Umsetzung und Implementierungunseres Rekonstruktionsverfahrens und stellen abschließendRekonstruktionsergebnisse bezüglich synthetischer Daten vor.