This thesis contains four articles related to mathematical aspects of Density Functional Theory. In Paper A, the theoretical justification of density methods formulated with current densities is addressed. It is shown that the set of ground-states is determined by the ensemble-representable particle and paramagnetic current density. Furthermore, it is demonstrated that the Schrödinger equation with a magnetic field is not uniquely determined by its ground-state solution. Thus, a wavefunction may be the ground-state of two different Hamiltonians, where the Hamiltonians differ by more than a gauge transformation. This implies that the particle and paramagnetic current density do not determine the potentials of the system and, consequently, no Hohenberg-Kohn theorem exists for Current Density Functional Theory formulated with the paramagnetic current density. On the other hand, by instead using the particle density as data, we show that the scalar potential in the system's Hamiltonian is determined for a fixed magnetic field. This means that the Hohenberg-Kohn theorem continues to hold in the presence of a magnetic field, if the magnetic field has been fixed. Paper B deals with N-representable density functionals that also depend on the paramagnetic current density. Here the Levy-Lieb density functional is generalized to include the paramagnetic current density. It is shown that a wavefunction exists that minimizes the "free" Hamiltonian subject to the constraints that the particle and paramagnetic current density are held fixed. Furthermore, a convex and universal current density functional is introduced and shown to equal the convex envelope of the generalized Levy-Lieb density functional. Since this functional is convex, the problem of finding the particle and paramagnetic current density that minimize the energy is related to a set of Euler-Lagrange equations. In Paper C, an N-representable Kohn-Sham approach is developed that also include the paramagnetic current density. It is demonstrated that a wavefunction exists that minimizes the kinetic energy subject to the constraint that only determinant wavefunctions are considered, as well as that the particle and paramagnetic current density are held fixed. Using this result, it is then shown that the ground-state energy can be obtained by minimizing an energy functional over all determinant wavefunctions that have finite kinetic energy. Moreover, the minimum is achieved and this determinant wavefunction gives the ground-state particle and paramagnetic current density. Lastly, Paper D addresses the issue of a Hohenberg-Kohn variational principle for Current Density Functional Theory formulated with the total current density. Under the assumption that a Hohenberg-Kohn theorem exists formulated with the total current density, it is shown that the map from particle and total current density to the vector potential enters explicitly in the energy functional to be minimized. Thus, no variational principle as that of Hohenberg and Kohn exists for density methods formulated with the total current density. / <p>QC 20140523</p>

O presente estudo analisa teorias do abuso no planejamento tributário. Inicialmente, busca-se definir e diferenciar planejamento tributário, planejamento tributário abusivo e evasão fiscal, partindo-se da premissa de que compete a cada Estado estabelecer, de forma peculiar, quais os critérios devem ser adotados para a identificação dessas figuras em seu ordenamento jurídico. Analisam-se os princípios constitucionais que podem ser ponderados no Brasil em relação a esse tema. Diante das teses que defendem a adoção, pelo Direito Tributário brasileiro, do abuso do direito, do abuso de formas, da fraude à lei e do propósito negocial, inclusive com fundamento nas experiências do Direito estrangeiro, analisa-se como tais teorias têm sido originalmente construídas, respectivamente, pela França, Alemanha, Espanha e Estados Unidos da América. Após a análise de cada uma dessas teorias estrangeiras, analisam-se os fundamentos da doutrina e jurisprudência favoráveis e contrários à sua aplicação no ordenamento tributário brasileiro, seja a partir de princípios jurídicos, de dispositivos do Código Tributário Nacional (em especial, art. 116, parágrafo único) ou mesmo do novo Código Civil (em especial, art. 187). Por fim, busca-se apresentar qual a norma atualmente vigente no Brasil para a tutela do planejamento tributário. / This study examines theories of abuse in tax planning. Initially, it defines and differentiates tax planning, tax avoidance and tax evasion, starting from the premise that is to the State to establish, in a peculiar way, in which criteria should be adopted for the identification of these figures in its legal system. It examines the constitutional principles that can be weighted in Brazil in relation to this theme. It examines the arguments that advocate the adoption of some theories by the Brazilian tax law, as abuse of law, abuse of forms, fraus legis and business purpose test. The research considers how such theories have been originally constructed, respectively, by France, Germany, Spain and the United States of America. After analyzes of each one of these foreign theories and examines the fundamentals of doctrine and court decisions that would be favorable or unfavorable for its application in the Brazilian tax planning, either from legal principles, from National Tax Code (in particular, art. 116, single paragraph) or even from the new Civil Code (in particular, art. 187). Finally, analyses which rule is currently in force in Brazil to the tax planning issues.

This thesis examines the reinvention of jihād ideology in twelfth‑century al‑Shām. In modern scholarship there is a tendency to speak of a revival of jihād in the twelfth century, but discussion of this revival has been dominated by study of the practice of jihād rather than of the ideology of jihād. This thesis addresses this imbalance by studying two twelfth‑century Damascene works: the Kitāb al‑jihād (Book of Jihād) of ʿAlī b. Ṭāhir al‑Sulamī (d. 500/1106), and the al‑Arbaʿūn ḥadīthan fī al‑ḥathth ʿala al‑jihād (Forty Hadiths for Inciting Jihād) of Abū al‑Qāsim Ibn ʿAsākir (d. 571/1176). Through discussion of these texts, this thesis sheds light on twelfth‑century perceptions of jihād by asking what their authors meant when they referred to jihād, and how their perceptions of jihād related to the broader Islamic discourse on jihād. A holistic approach is taken to these works; they are discussed not only in the context of the 'master narrative' of jihād, wherein juristic sources have been privileged over other non‑legal genres and corpora, but also in the context of the Sufi discourse of jihād al‑nafs, and the earliest traditions on jihād which thrived from the eighth century onwards on the Muslim‑Byzantine frontier. This thesis argues that both al‑Sulamī and Ibn ʿAsākir integrated elements from these different traditions of jihād in order to create models of jihād suited to their own political contexts, and that it is only in the context of a more nuanced appreciation of jihād ideology that their attempts can be properly understood. At the same time, this thesis argues against the model of the 'counter‑crusade', which holds that the revival of jihād began in earnest only in the middle of the twelfth century, by stressing that there was no delay between the arrival of the Franks and attempts to modify jihād ideology.

L'objectif de cette thèse est de fournir des bornes d'erreur pour des problèmes aux valeurs propres linéaires et non linéaires issus du calcul de structure électronique, en particulier celui de l'état fondamental avec la théorie de la fonctionnelle de la densité. Ces bornes d'erreur reposent principalement sur des estimations a posteriori. D'abord, nous étudions un phénomène de compensation d'erreur de discrétisation pour un problème linéaire aux valeurs propres, grâce à une analyse a priori de l'erreur sur l'énergie. Ensuite, nous présentons une analyse a posteriori pour le problème du laplacien aux valeurs propres discrétisé par une large classe d'éléments finis. Les bornes d'erreur proposées pour les valeurs propres simples et leurs vecteurs propres associés sont garanties, calculables et efficaces. Nous nous concentrons alors sur des problèmes aux valeurs propres non linéaires. Nous proposons des bornes d'erreur pour l'équation de Gross-Pitaevskii, valables sous des hypothèses vérifiables numériquement, et pouvant être séparées en deux composantes venant respectivement de la discrétisation et de l'algorithme itératif utilisé pour résoudre le problème non linéaire aux valeurs propres. L'équilibrage de ces composantes d'erreur permet d'optimiser les ressources numériques. Enfin, nous présentons une méthode de post-traitement pour le problème de Kohn-Sham discrétisé en ondes planes, améliorant la précision des résultats à un faible coût de calcul. Les solutions post-traitées peuvent être utilisées soit comme solutions plus précises du problème, soit pour calculer une estimation de l'erreur de discrétisation, qui n'est plus garantie, mais néanmoins proche de l'erreur. / The objective of this thesis is to provide error bounds for linear and nonlinear eigenvalue problems arising from electronic structure calculation. We focus on ground-state calculations based on Density Functional Theory, including Kohn-Sham models. Our bounds mostly rely on a posteriori error analysis. More precisely, we start by studying a phenomenon of discretization error cancellation for a simple linear eigenvalue problem, for which analytical solutions are available. The mathematical study is based on an a priori analysis for the energy error. Then, we present an a posteriori analysis for the Laplace eigenvalue problem discretized with finite elements. For simple eigenvalues of the Laplace operator and their corresponding eigenvectors , we provide guaranteed, fully computable and efficient error bounds. Thereafter, we focus on nonlinear eigenvalue problems. First, we provide an a posteriori analysis for the Gross-Pitaevskii equation. The error bounds are valid under assumptions that can be numerically checked, and can be separated in two components coming respectively from the discretization and the iterative algorithm used to solve the nonlinear eigenvalue problem. Balancing these error components allows to optimize the computational resources. Second, we present a post-processing method for the Kohn-Sham problem, which improves the accuracy of planewave computations of ground state orbitals at a low computational cost. The post-processed solutions can be used either as a more precise solution of the problem, or used for computing an estimation of the discretization error. This estimation is not guaranteed, but in practice close to the real error.

The aim of this thesis is to answer the question of why rebel groups engage in conflict with each other despite sharing an identity. Previous research suggests that a shared identity should promote cooperation, but recent conflicts between rebel groups in Syria seem to suggest that shared identity can instead be a cause for rivalry. This thesis investigates this puzzle by using Pischedda’s theory on windows of opportunity and vulnerability and Hafez theory on proxidistant ideologies. The cases of the thesis are the conflicts between Ahrar Al-Sham and IS in 2014 and between Ahrar Al-Sham and the Al Nusra Front in 2017. The results indicate that shared identity does cause rivalry, and both theories receive support for their explanation of inter-rebel conflict. All three rebel groups are labeled as extremists, which supports Hafez theory that extremist groups are more likely to engage in conflict with rivals. The military strength and the possible costs of attack of the rebel groups seem to support Pischedda’s theory that rebel groups use specific windows in time to attack their rivals. There are however some problems that neither theory can explain, such as Ahrar Al-Shams friendly relationship to Al Nusra between 2014 and 2017. This thesis provide insight into the understudied field of inter-rebel conflict of War Studies by highlighting the importance of identity.

Objetivos: Determinar la efectividad del Kinesiotape en la reducción del dolor debido a la dismenorrea en jóvenes-adultas. Métodos: Se realizó un estudio experimental, tipo ensayo clínico en mujeres de la Escuela de Policías de Chorrillos y San Bartolo en Lima, Perú. El muestreo se realizó por aleatorización por bloques, se distribuyeron las 229 participantes en bloques de 6. Se tuvo un total de 36 bloques y dentro de cada bloque se eligió al azar la asignación a los grupos de intervención o de Kinesiotape y control o de Kinesiotape simulado. Se aplicó el Kinesiotape por 4-5 días al grupo intervención y al de control. Se colocaron tres bandas adhesivas de 5 cm de ancho y 12 de largo, la banda horizontal se colocó de forma directa, la banda vertical se aplicó de caudal a cefálico en la zona suprapúbica, y la última banda se aplicó de forma horizontal en la zona lumbar, a la altura de L4. El dolor menstrual y lumbar se valoró con la Escala de calificación numérica del dolor antes, 2-3 hrs después de la aplicación del método, a las 24 hrs, 48 hrs y 72 hrs respectivamente. Finalmente, se realizó la fase de intervención con una duración de 3 meses por cada integrante en donde se midió el dolor menstrual y lumbar durante su periodo menstrual. Resultados: Se evaluó la eficacia del Kinesiotape versus el Kinesiotape simulado en el dolor asociado a la dismenorrea primaria. Las diferencias entre el grupo de control e intervención con respecto al dolor menstrual fueron que en el mes 1 luego de 2-3 horas de la aplicación del Kinesiotape el dolor se redujo en -2.32 (p<0.001), en el mes 2 de -2.8 (p<0.001) y en el mes 3 de -1.3 (p<0.001). Se observó que a las 24 horas del efecto, el dolor se redujo en -2.15 (p<0.001) en el mes 1, -1.77 (p<0.001) en el mes 2 y -0.87 (p<0.001) en el mes 3. Asimismo, en el dolor lumbar se observó el efecto del Kinesiotape a las 24 horas de la aplicación en el mes 1 con una diferencia de -0.5 (p: 0.013), en el mes 2 -0.62 (p: 0.001) entre ambos grupos. Conclusiones: La aplicación del Kinesiotape es efectiva para reducir el dolor abdominal relacionado a la dismenorrea en comparación a la aplicación del Kinesiotape simulado. / Objectives: Determine the effectiveness of Kinesiotape to decrease pain due to dysmenorrhea in young adult women. Methods: An experimental study was conducted a clinical trial in women of the Police school in Chorrillos and San Bartolo in Lima, Perú. We performed a blocked randomization. The 229 participants were distributed in blocks of 6 individuals. A total of 36 blocks were taken and within each block the allocation to the intervention group and control group was chosen at random simulated. Kinesiotape was applied for 4-5 days to the intervention and control group. Three adhesive bands 5 cm wide and 12 long were placed, the horizontal band was placed directly, the vertical band was applied from flow to cephalic in the suprapubic area, and the last band was applied horizontally in the area lumbar, at the height of L4. Lumbar and menstrual pain was assessed with the Numerical Pain Rating Scale before, 2-3 hours after the application of the method, at 24 hours, 48 hours and 72 hours respectively. Finally, the intervention phase was carried out with a duration of 3 months for each member where menstrual and lumbar pain was measured during their menstrual period. Results: The efficacy of Kinesiotape vs Sham Kinesiotape in pain associated with primary dysmenorrhea was evaluated. The differences in the results between the control and intervention group with respect to menstrual pain were that in month 1 during 2-3 hours of the application of Kinesiotape the difference was -2.32 (p <0.001), in month 2 of -2.8 (p <0.001) and in month 3 of -1.3 (p <0.001). It was observed that 24 hours after the effect of Kinesiotape on the control group had a difference of -2.15 (p <0.001) in month 1, -1.77 (p <0.001) in month 2 and -0.87 (p <0.001) in month 3. Also, in lumbar pain the effect of Kinesiotape was observed 24 hours after application in month 1 with a difference of -0.5 (p: 0.013), in month 2 -0.62 (p: 0.001) between both groups Conclusions: During the intervention period with the application of Kinesiotape to the intervention group, abdominal pain related to dysmenorrhea was reduced compared to the application of simulated Kinesiotape in the control group. / Tesis

Le vaste domaine de l’amélioration cognitive traverse les applications comportementales, biochimiques et physiques. Aussi nombreuses sont les techniques que les limites de ces premières : des études de pauvre méthodologie, des pratiques éthiquement ambiguës, de faibles effets positifs, des effets secondaires significatifs, des couts financiers importants, un investissement de temps significatif, une accessibilité inégale, et encore un manque de transfert. L’objectif de cette thèse est de proposer une méthode novatrice d’intégration de l’une de ces techniques, le neurofeedback, directement dans un paradigme d’apprentissage afin d’améliorer la performance cognitive et l’apprentissage. Cette thèse propose les modalités, les fondements empiriques et des données à l’appui de ce paradigme efficace d’apprentissage ‘bouclé’. En manipulant la difficulté dans une tâche en fonction de l’activité cérébrale en temps réel, il est démontré que dans un paradigme d’apprentissage traditionnel (3-dimentional multiple object tracking), la vitesse et le degré d’apprentissage peuvent être améliorés de manière significative lorsque comparés au paradigme traditionnel ou encore à un groupe de contrôle actif. La performance améliorée demeure observée même avec un retrait du signal de rétroaction, ce qui suggère que les effets de l’entrainement amélioré sont consolidés et ne dépendent pas d’une rétroaction continue. Ensuite, cette thèse révèle comment de tels effets se produisent, en examinant les corrélés neuronaux des états de préparation et de performance à travers les conditions d’état de base et pendant la tâche, de plus qu’en fonction du résultat (réussite/échec) et de la difficulté (basse/moyenne/haute vitesse). La préparation, la performance et la charge cognitive sont mesurées via des liens robustement établis dans un contexte d’activité cérébrale fonctionnelle mesurée par l’électroencéphalographie quantitative. Il est démontré que l’ajout d’une assistance- à-la-tâche apportée par la fréquence alpha dominante est non seulement appropriée aux conditions de ce paradigme, mais influence la charge cognitive afin de favoriser un maintien du sujet dans sa zone de développement proximale, ce qui facilite l’apprentissage et améliore la performance. Ce type de paradigme d’apprentissage peut contribuer à surmonter, au minimum, un des limites fondamentales du neurofeedback et des autres techniques d’amélioration cognitive : le manque de transfert, en utilisant une méthode pouvant être intégrée directement dans le contexte dans lequel l’amélioration de la performance est souhaitée. / The domain of cognitive enhancement is vast, spanning behavioral, biochemical and physical applications. The techniques are as numerous as are the limitations: poorly conducted studies, ethically ambiguous practices, limited positive effects, significant side-effects, high financial costs, significant time investment, unequal accessibility, and lack of transfer. The purpose of this thesis is to propose a novel way of integrating one of these techniques, neurofeedback, directly into a learning context in order to enhance cognitive performance and learning. This thesis provides the framework, empirical foundations, and supporting evidence for a highly efficient ‘closed-loop’ learning paradigm. By manipulating task difficulty based on a measure of cognitive load within a classic learning scenario (3-dimentional multiple object tracking) using real-time brain activity, results demonstrate that over 10 sessions, speed and degree of learning can be substantially improved compared with a classic learning system or an active sham-control group. Superior performance persists even once the feedback signal is removed, which suggests that the effects of enhanced training are consolidated and do not rely on continued feedback. Next, this thesis examines how these effects occur, exploring the neural correlates of the states of preparedness and performance across baseline and task conditions, further examining correlates related to trial results (correct/incorrect) and task difficulty (slow/medium/fast speeds). Cognitive preparedness, performance and load are measured using well-established relationships between real-time quantified brain activity as measured by quantitative electroencephalography. It is shown that the addition of neurofeedback-based task assistance based on peak alpha frequency is appropriate to task conditions and manages to influence cognitive load, keeping the subject in the zone of proximal development more often, facilitating learning and improving performance. This type of learning paradigm could contribute to overcoming at least one of the fundamental limitations of neurofeedback and other cognitive enhancement techniques : a lack of observable transfer effects, by utilizing a method that can be directly integrated into the context in which improved performance is sought.

The Kohn-Sham density functional theory (KS-DFT) finds an approximate solution for the many-electron problem for the ground state energy and density by solving the self-consistent one-electron Schr\"{o}dinger equations. KS-DFT would be an exact theory if we could find the precise form of exchange-correlation energy $(E_{xc})$. However, this would not be computationally feasible. The density functional approximations (DFAs) are designed to be exact in the limit of uniform densities. They require a parametrization of the correlation energy per electron $(\varepsilon_c)$ of the uniform electron gas (UEG). These DFAs take the parametrizations of correlation energy as their input since the exact analytical form of $\varepsilon_c$ is still unknown. Almost all the DFAs of higher rungs of Jacob's ladder employ an additional function on top of $\varepsilon_c$ for approximating their correlation energy. Exchange energies in these DFAs are also approximated by applying an enhancement factor to the exchange energy per electron of the UEG. Exchange-correlation energy is the glue that holds the atoms and molecules together. The correlation energy is an important part of ``nature's glue" that binds one atom to another, and it changes significantly when the bonding of the molecule changes. It is a measure of the effect of Coulomb repulsion due to electronic mutual avoidance and is necessarily negative. We compared three parametrizations of the correlation energy per electron of the uniform electron gas to the original and the corrected density parameter interpolation (DPI), which is almost independent of QMC input, and with the recent QMC of Spink \textit{et al.}, which extends the Ceperley-Alder results to fractional spin polarization and higher densities or smaller Seitz radius $r_s$. These three parametrizations are Perdew-Zunger or PZ 1981, Vosko-Wilk-Nusair or VWN 1980, and Perdew-Wang or PW 1992. The three parametrizations (especially the sophisticated PW92) are closer to the constraint satisfying DPI and are very close to the high-density limit rather than the QMC results of Spink \textit{et al.}. These DFAs suffer from self-interaction error (SIE) which arises due to an imperfect cancellation of self-Hartree energy by self-exchange-correlation energy of a single fully occupied orbital. The self-interaction correction (SIC) method introduced by Perdew and Zunger (PZ) in 1981 to remove the SIE encounters a size-extensivity problem when applied to the Kohn-Sham (KS) orbitals. Hence, we make use of Fermi L\"owdin orbitals (FLO) for applying the PZ-SIC to the density functional approximations (DFAs). FLOs are the unitary transformation of the KS orbitals localized at the Fermi orbital descriptor (FOD) positions and then orthonormalized using L\"owdin's symmetric method. The PZ-SIC makes any approximation exact only in the region of one-electron density and no correction if applied to the exact functional. But it spoils the slowly varying (in space) limits of the uncorrected approximate functionals, where those functionals are right by construction. Hence, scaling of PZ-SIC is required such that it remains intact in the region of one-electron density and scales down in the region of many-electron densities. The PZ-SIC improves the performance of DFAs for the properties that involve significant SIE, as in stretched bond situations, but overcorrects for equilibrium properties where SIE is insignificant. This overcorrection is often reduced by LSIC, local scaling of the PZ-SIC to the local spin density approximation (LSDA). We propose a new scaling factor to use in an LSIC-like approach that satisfies an additional important constraint: the correct coefficient of Z in the asymptotic expansion of the $E_{xc}$ for atoms of atomic number Z, which is neglected by LSIC. LSIC and LSIC+ are scaled by functions of the iso-orbital indicator $z_{\sigma}$ that distinguishes one-electron regions from many-electron regions. LSIC+ applied to LSDA works better than LSDA-LSIC and the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA) and gives comparable results to the strongly constrained and appropriately normed (SCAN) meta-GGA in predicting the total energies of atoms, atomization energies, barrier heights, ionization potentials, electron affinities, and bond-length of molecules. LSDA-LSIC and LSDA-LSIC+ both fail to predict interaction energies involving weaker bonds, in sharp contrast to their earlier successes. It is found that more than one set of localized SIC orbitals can yield a nearly degenerate energetic description of the same multiple covalent bonds, suggesting that a consistent chemical interpretation of the localized orbitals requires a new way to choose their Fermi orbital descriptors. A spurious correction to the exact functional would be found unless the self-Hartree and exact self-exchange-correlation terms of the PZ-SIC energy density were expressed in the same gauge. Therefore, LSIC and LSIC+ are applied only to LSDA since only LSDA has the exchange-correlation (xc) energy density in the gauge of the Hartree energy density. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can be applied to approximate functionals. The use of this compliance function guarantees that scaled-down self-interaction correction (sdSIC) will make no spurious non-zero correction to the exact functional and transforms the xc energy density into the Hartree gauge. We start from the interior scaling of PZ-SIC and end at exterior scaling after the gauge transformation. SCAN-sdSIC evaluated on SCAN-SIC total and localized orbital densities is applied to the highly accurate SCAN functional, which is already much better than LSDA. Hence, the predictive power of SCAN-sdSIC is much better, even though it is scaled by $z_\sigma$ too. It provides good results for several ground state properties discussed here, including the interaction energy of weakly bonded systems. SCAN-sdSIC leads to an acceptable description of many equilibrium properties, including the dissociation energies of weak bonds. However, sdSIC fails to produce the correct asymptotic behavior $-\frac{1}{r}$ of xc potential. The xc potential as seen by the outermost electron will be $\frac{-X_{HO}^{sd}}{r}$ where HO labels the highest occupied orbital and hence doesn't guarantee a good description of charge transfer. The optimal SIC that remains to be developed might be PZ-SIC evaluated on complex Fermi-L\"owdin orbitals (with nodeless orbital densities) and Fermi orbital descriptors chosen to minimize a measure of the inhomogeneity of the orbital densities. / Physics

We have expanded the capabilities of the ab initio tight-binding molecular dynamics package FIREBALL to include calculations of optical properties. Basic zero order approximation is based on transitions between Kohn-Sham states. Corrections for electron-electron interactions are based on time dependant density functional theory (TDDFT). Consistent with the FIREBALL approach, we use precalculated integrals and approximations to make the program faster.

published_or_final_version / Architecture / Master / Master of Architecture