Higher-order variational problems of Herglotz type

We obtain a generalized Euler–Lagrange differential equation and transversality optimality conditions for Herglotz-type higher-order variational problems. Illustrative examples of the new results are given.

Beyond the Cosmological Principle

Simplifying the Einstein field equation by assuming the cosmological principle yields a set of differential equations which governs the dynamics of the universe as described in the cosmological standard model. The cosmological principle assumes the space appears the same everywhere and in every direction and moreover, the principle has earned its position as a fundamental assumption in cosmology by being compatible with the observations of the 20th century. It was not until the current century when observations in cosmological scales showed significant deviation from isotropy and homogeneity implying the violation of the principle. Among these observations are the inconsistency between local and non-local Hubble parameter evaluations, baryon acoustic features of the Lyman-α forest and the anomalies of the cosmic microwave background radiation. As a consequence, cosmological models beyond the cosmological principle have been studied vastly; after all, the principle is a hypothesis and as such should frequently be tested as any other assumption in physics. In this thesis, the effects of inhomogeneity and anisotropy, arising as a consequence of discarding the cosmological principle, is investigated. The geometry and matter content of the universe becomes more cumbersome and the resulting effects on the Einstein field equation is introduced. The cosmological standard model and its issues, both fundamental and observational are presented. Particular interest is given to the local Hubble parameter, supernova explosion, baryon acoustic oscillation, and cosmic microwave background observations and the cosmological constant problems. Explored and proposed resolutions emerging by violating the cosmological principle are reviewed. This thesis is concluded by a summary and outlook of the included research papers.

Elmar Schwinger: Literarische Erziehung und Gymnasium. Zur Entwicklung des bayerischen Gymnasiums in der Ära Niethammer/Thiersch. Mit einem Geleitwort von A. Reble. (Würzburger Arbeiten zur Erziehungswissenschaft. Bd. 18.) Bad Heilbrunn: Klinkhardt 1988 [Rezension]

Rezension von: Elmar Schwinger: Literarische Erziehung und Gymnasium. Zur Entwicklung des bayerischen Gymnasiums in der Ära Niethammer/Thiersch. Mit einem Geleitwort von A. Reble. (Würzburger Arbeiten zur Erziehungswissenschaft. Bd. 18.) Bad Heilbrunn: Klinkhardt 1988. 452 S.

The Principle of Proportionality in International Law

Whilst the principle of proportionality indisputably plays a crucial role in the protection of fundamental rights, it is still unclear to what extent it applies to other fields in international law. The paper therefore explores the role it plays in selected fields of public international law, beyond human rights. The examination begins in the classical domain of reprisals and in maritime boundary delimitation and continues to analyse the role played in the law of multilateral trade regulation of the World Trade Organization and in bilateral investment protection. In an attempt to explain differences in recourse to proportionality in the various fields, we develop in our conclusions a distinction between horizontal and vertical constellations of legal protection.

Investigation of un-American propaganda activities in the United States : Hearings before a Special Committee on Un-American Activities, House of Representatives, Seventy-fifth Congress, third session-Seventy-eighth Congress, second session, on H. Res. 282, to investigate (1) the extent, character, and objects of un-American propaganda activities in the United States, (2) the diffusion within the United States of subversive and un-American propaganda that is instigated from foreign countries or of a domestic origin and attacks the principle of the form of government as guaranteed by our Constitution, and (3) all other questions in relation thereto that would aid Congress in any necessary remedial legislation.

Martin Dies, chairman.

Principle and prejudice : attitudes toward ethnic minorities in Quebec

L’intégration des nouveaux immigrants pose un défi, et ce, particulièrement dans les nations infra-étatiques. En effet, les citoyens vivant dans ces contextes ont davantage tendance à percevoir les immigrants comme de potentielles menaces politiques et culturelles. Cependant, les différents groupes ethniques et religieux minoritaires ne représentent pas tous le même degré de menace. Cette étude cherche à déterminer si les citoyens francophones québécois perçoivent différemment les différents groupes ethniques et religieux minoritaires, et s’ils entretiennent des attitudes plus négatives envers ces groupes, comparativement aux autres Canadiens. Dans la mesure où ces attitudes négatives existent, l’étude cherche à comprendre si ces dernières sont basées principalement sur des préjugés raciaux ou sur des inquiétudes culturelles. Se fondant sur des données nationales et provinciales, les résultats démontrent que les francophones Québécois sont plus négatifs envers les minorités religieuses que les autres canadiens mais pas envers les minorités raciales, et que ces attitudes négatives sont fondées principalement sur une inquiétude liée la laïcité et à la sécurité culturelle. L’antipathie envers certaines minorités observée au sein de la majorité francophone au Québec semble donc être dirigée envers des groupes spécifiques, et se fondent sur des principes de nature davantage culturelle que raciale.

Maximum Principle for Elliptic and Parabolic Equations

Nel primo capitolo si riporta il principio del massimo per operatori ellittici. Sarà considerato, in un primo momento, l'operatore di Laplace e, successivamente, gli operatori ellittici del secondo ordine, per i quali si dimostrerà anche il principio del massimo di Hopf. Nel secondo capitolo si affronta il principio del massimo per operatori parabolici e lo si utilizza per dimostrare l'unicità delle soluzioni di problemi ai valori al contorno.

Principle and prejudice : attitudes toward ethnic minorities in Quebec

L’intégration des nouveaux immigrants pose un défi, et ce, particulièrement dans les nations infra-étatiques. En effet, les citoyens vivant dans ces contextes ont davantage tendance à percevoir les immigrants comme de potentielles menaces politiques et culturelles. Cependant, les différents groupes ethniques et religieux minoritaires ne représentent pas tous le même degré de menace. Cette étude cherche à déterminer si les citoyens francophones québécois perçoivent différemment les différents groupes ethniques et religieux minoritaires, et s’ils entretiennent des attitudes plus négatives envers ces groupes, comparativement aux autres Canadiens. Dans la mesure où ces attitudes négatives existent, l’étude cherche à comprendre si ces dernières sont basées principalement sur des préjugés raciaux ou sur des inquiétudes culturelles. Se fondant sur des données nationales et provinciales, les résultats démontrent que les francophones Québécois sont plus négatifs envers les minorités religieuses que les autres canadiens mais pas envers les minorités raciales, et que ces attitudes négatives sont fondées principalement sur une inquiétude liée la laïcité et à la sécurité culturelle. L’antipathie envers certaines minorités observée au sein de la majorité francophone au Québec semble donc être dirigée envers des groupes spécifiques, et se fondent sur des principes de nature davantage culturelle que raciale.

Variational mean-field approach to the double-exchange model

It has been recently shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a richer variety of first- and second-order transitions than previously anticipated, and that such transitions are consistent with the magnetic properties of manganites. Here we present a thorough discussion of the variational mean-field approach that leads to these results. We also show that the effect of the Berry phase turns out to be crucial to produce first-order paramagnetic-ferromagnetic transitions near half filling with transition temperatures compatible with the experimental situation. The computation relies on two crucial facts: the use of a mean-field ansatz that retains the complexity of a system of electrons with off-diagonal disorder, not fully taken into account by the mean-field techniques, and the small but significant antiferromagnetic superexchange interaction between the localized spins.

Variational and learning models for image and time series inverse problems

Inverse problems are at the core of many challenging applications. Variational and learning models provide estimated solutions of inverse problems as the outcome of specific reconstruction maps. In the variational approach, the result of the reconstruction map is the solution of a regularized minimization problem encoding information on the acquisition process and prior knowledge on the solution. In the learning approach, the reconstruction map is a parametric function whose parameters are identified by solving a minimization problem depending on a large set of data. In this thesis, we go beyond this apparent dichotomy between variational and learning models and we show they can be harmoniously merged in unified hybrid frameworks preserving their main advantages. We develop several highly efficient methods based on both these model-driven and data-driven strategies, for which we provide a detailed convergence analysis. The arising algorithms are applied to solve inverse problems involving images and time series. For each task, we show the proposed schemes improve the performances of many other existing methods in terms of both computational burden and quality of the solution. In the first part, we focus on gradient-based regularized variational models which are shown to be effective for segmentation purposes and thermal and medical image enhancement. We consider gradient sparsity-promoting regularized models for which we develop different strategies to estimate the regularization strength. Furthermore, we introduce a novel gradient-based Plug-and-Play convergent scheme considering a deep learning based denoiser trained on the gradient domain. In the second part, we address the tasks of natural image deblurring, image and video super resolution microscopy and positioning time series prediction, through deep learning based methods. We boost the performances of supervised, such as trained convolutional and recurrent networks, and unsupervised deep learning strategies, such as Deep Image Prior, by penalizing the losses with handcrafted regularization terms.

Hierarchical active inference for cognitive architectures

This thesis explores the methods based on the free energy principle and active inference for modelling cognition. Active inference is an emerging framework for designing intelligent agents where psychological processes are cast in terms of Bayesian inference. Here, I appeal to it to test the design of a set of cognitive architectures, via simulation. These architectures are defined in terms of generative models where an agent executes a task under the assumption that all cognitive processes aspire to the same objective: the minimization of variational free energy. Chapter 1 introduces the free energy principle and its assumptions about self-organizing systems. Chapter 2 describes how from the mechanics of self-organization can emerge a minimal form of cognition able to achieve autopoiesis. In chapter 3 I present the method of how I formalize generative models for action and perception. The architectures proposed allow providing a more biologically plausible account of more complex cognitive processing that entails deep temporal features. I then present three simulation studies that aim to show different aspects of cognition, their associated behavior and the underlying neural dynamics. In chapter 4, the first study proposes an architecture that represents the visuomotor system for the encoding of actions during action observation, understanding and imitation. In chapter 5, the generative model is extended and is lesioned to simulate brain damage and neuropsychological patterns observed in apraxic patients. In chapter 6, the third study proposes an architecture for cognitive control and the modulation of attention for action selection. At last, I argue how active inference can provide a formal account of information processing in the brain and how the adaptive capabilities of the simulated agents are a mere consequence of the architecture of the generative models. Cognitive processing, then, becomes an emergent property of the minimization of variational free energy.

Inside standard and hyperspectral low-dose CT variational imaging: parameter identification and material decomposition

The main contribution of this thesis is the proposal of novel strategies for the selection of parameters arising in variational models employed for the solution of inverse problems with data corrupted by Poisson noise. In light of the importance of using a significantly small dose of X-rays in Computed Tomography (CT), and its need of using advanced techniques to reconstruct the objects due to the high level of noise in the data, we will focus on parameter selection principles especially for low photon-counts, i.e. low dose Computed Tomography. For completeness, since such strategies can be adopted for various scenarios where the noise in the data typically follows a Poisson distribution, we will show their performance for other applications such as photography, astronomical and microscopy imaging. More specifically, in the first part of the thesis we will focus on low dose CT data corrupted only by Poisson noise by extending automatic selection strategies designed for Gaussian noise and improving the few existing ones for Poisson. The new approaches will show to outperform the state-of-the-art competitors especially in the low-counting regime. Moreover, we will propose to extend the best performing strategy to the hard task of multi-parameter selection showing promising results. Finally, in the last part of the thesis, we will introduce the problem of material decomposition for hyperspectral CT, which data encodes information of how different materials in the target attenuate X-rays in different ways according to the specific energy. We will conduct a preliminary comparative study to obtain accurate material decomposition starting from few noisy projection data.

Variational Quantum Splines: Moving Beyond Linearity for Quantum Activation Functions

Activation functions within neural networks play a crucial role in Deep Learning since they allow to learn complex and non-trivial patterns in the data. However, the ability to approximate non-linear functions is a significant limitation when implementing neural networks in a quantum computer to solve typical machine learning tasks. The main burden lies in the unitarity constraint of quantum operators, which forbids non-linearity and poses a considerable obstacle to developing such non-linear functions in a quantum setting. Nevertheless, several attempts have been made to tackle the realization of the quantum activation function in the literature. Recently, the idea of the QSplines has been proposed to approximate a non-linear activation function by implementing the quantum version of the spline functions. Yet, QSplines suffers from various drawbacks. Firstly, the final function estimation requires a post-processing step; thus, the value of the activation function is not available directly as a quantum state. Secondly, QSplines need many error-corrected qubits and a very long quantum circuits to be executed. These constraints do not allow the adoption of the QSplines on near-term quantum devices and limit their generalization capabilities. This thesis aims to overcome these limitations by leveraging hybrid quantum-classical computation. In particular, a few different methods for Variational Quantum Splines are proposed and implemented, to pave the way for the development of complete quantum activation functions and unlock the full potential of quantum neural networks in the field of quantum machine learning.

Characterization Of Morphology And Composition Of Inorganic Fillers In Dental Alginates.

Energy dispersive X-ray spectroscopy microanalysis (EDX), scanning electron microscopy (SEM), and Archimedes' Principle were used to determine the characteristics of inorganic filler particles in five dental alginates, including Cavex ColorChange (C), Hydrogum 5 (H5), Hydrogum (H), Orthoprint (O), and Jeltrate Plus (JP). The different alginate powders (0.5 mg) were fixed on plastic stubs (n = 5) and sputter coated with carbon for EDX analysis, then coated with gold, and observed using SEM. Volume fractions were determined by weighing a sample of each material in water before and after calcining at 450(°)C for 3 h. The alginate materials were mainly composed of silicon (Si) by weight (C-81.59%, H-79.89%, O-78.87%, H5-77.95%, JP-66.88%, wt). The filler fractions in volume (vt) were as follows: H5-84.85%, JP-74.76%, H-70.03%, O-68.31%, and C-56.10%. The tested materials demonstrated important differences in the inorganic elemental composition, filler fraction, and particle morphology.

Volumetric Capnography For The Evaluation Of Chronic Airways Diseases.

Obstructive lung diseases of different etiologies present with progressive peripheral airway involvement. The peripheral airways, known as the silent lung zone, are not adequately evaluated with conventional function tests. The principle of gas washout has been used to detect pulmonary ventilation inhomogeneity and to estimate the location of the underlying disease process. Volumetric capnography (VC) analyzes the pattern of CO2 elimination as a function of expired volume. To measure normalized phase 3 slopes with VC in patients with non-cystic fibrosis bronchiectasis (NCB) and in bronchitic patients with chronic obstructive pulmonary disease (COPD) in order to compare the slopes obtained for the groups. NCB and severe COPD were enrolled sequentially from an outpatient clinic (Hospital of the State University of Campinas). A control group was established for the NCB group, paired by sex and age. All subjects performed spirometry, VC, and the 6-Minute Walk Test (6MWT). Two comparisons were made: NCB group versus its control group, and NCB group versus COPD group. The project was approved by the ethical committee of the institution. Statistical tests used were Wilcoxon or Student's t-test; P<0.05 was considered to be a statistically significant difference. Concerning the NCB group (N=20) versus the control group (N=20), significant differences were found in body mass index and in several functional variables (spirometric, VC, 6MWT) with worse results observed in the NCB group. In the comparison between the COPD group (N=20) versus the NCB group, although patients with COPD had worse spirometric and 6MWT values, the capnographic variables mean phase 2 slope (Slp2), mean phase 3 slope normalized by the mean expiratory volume, or mean phase 3 slope normalized by the end-tidal CO2 concentration were similar. These findings may indicate that the gas elimination curves are not sensitive enough to monitor the severity of structural abnormalities. The role of normalized phase 3 slope may be worth exploring as a more sensitive index of small airway disease, even though it may not be equally sensitive in discriminating the severity of the alterations.