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591	Some Contributions to Distribution Theory and Applications Selvitella, Alessandro 11 1900 (has links) In this thesis, we present some new results in distribution theory for both discrete and continuous random variables, together with their motivating applications. We start with some results about the Multivariate Gaussian Distribution and its characterization as a maximizer of the Strichartz Estimates. Then, we present some characterizations of discrete and continuous distributions through ideas coming from optimal transportation. After this, we pass to the Simpson's Paradox and see that it is ubiquitous and it appears in Quantum Mechanics as well. We conclude with a group of results about discrete and continuous distributions invariant under symmetries, in particular invariant under the groups $A_1$, an elliptical version of $O(n)$ and $\mathbb{T}^n$. As mentioned, all the results proved in this thesis are motivated by their applications in different research areas. The applications will be thoroughly discussed. We have tried to keep each chapter self-contained and recalled results from other chapters when needed. The following is a more precise summary of the results discussed in each chapter. In chapter \ref{chapter 2}, we discuss a variational characterization of the Multivariate Normal distribution (MVN) as a maximizer of the Strichartz Estimates. Strichartz Estimates appear as a fundamental tool in the proof of wellposedness results for dispersive PDEs. With respect to the characterization of the MVN distribution as a maximizer of the entropy functional, the characterization as a maximizer of the Strichartz Estimate does not require the constraint of fixed variance. In this chapter, we compute the precise optimal constant for the whole range of Strichartz admissible exponents, discuss the connection of this problem to Restriction Theorems in Fourier analysis and give some statistical properties of the family of Gaussian Distributions which maximize the Strichartz estimates, such as Fisher Information, Index of Dispersion and Stochastic Ordering. We conclude this chapter presenting an optimization algorithm to compute numerically the maximizers. Chapter \ref{chapter 3} is devoted to the characterization of distributions by means of techniques from Optimal Transportation and the Monge-Amp\`{e}re equation. We give emphasis to methods to do statistical inference for distributions that do not possess good regularity, decay or integrability properties. For example, distributions which do not admit a finite expected value, such as the Cauchy distribution. The main tool used here is a modified version of the characteristic function (a particular case of the Fourier Transform). An important motivation to develop these tools come from Big Data analysis and in particular the Consensus Monte Carlo Algorithm. In chapter \ref{chapter 4}, we study the \emph{Simpson's Paradox}. The \emph{Simpson's Paradox} is the phenomenon that appears in some datasets, where subgroups with a common trend (say, all negative trend) show the reverse trend when they are aggregated (say, positive trend). Even if this issue has an elementary mathematical explanation, the statistical implications are deep. Basic examples appear in arithmetic, geometry, linear algebra, statistics, game theory, sociology (e.g. gender bias in the graduate school admission process) and so on and so forth. In our new results, we prove the occurrence of the \emph{Simpson's Paradox} in Quantum Mechanics. In particular, we prove that the \emph{Simpson's Paradox} occurs for solutions of the \emph{Quantum Harmonic Oscillator} both in the stationary case and in the non-stationary case. We prove that the phenomenon is not isolated and that it appears (asymptotically) in the context of the \emph{Nonlinear Schr\"{o}dinger Equation} as well. The likelihood of the \emph{Simpson's Paradox} in Quantum Mechanics and the physical implications are also discussed. Chapter \ref{chapter 5} contains some new results about distributions with symmetries. We first discuss a result on symmetric order statistics. We prove that the symmetry of any of the order statistics is equivalent to the symmetry of the underlying distribution. Then, we characterize elliptical distributions through group invariance and give some properties. Finally, we study geometric probability distributions on the torus with applications to molecular biology. In particular, we introduce a new family of distributions generated through stereographic projection, give several properties of them and compare them with the Von-Mises distribution and its multivariate extensions. / Thesis / Doctor of Philosophy (PhD) Distribution Theory Quantum Mechanics Molecular Biology Simpson's Paradox Optimal Transportation Statistical Inference Von Mises Distribution Orthogonal Group Protein Folding Problem Symmetric Order Statistics Prisoner's Dilemma Strichartz Estimates Elliptical Distributions Measure of Amalgamation Big Data Consensus Monte Carlo Algorithm Bohr Radius Quantum Harmonic Oscillator Nonlinear Schrödinger Equation Characteristic Function Optimization Algorithms Symmetric Distributions
592	Aspects hors de l'équilibre de systèmes quantiques unidimensionnels fortement corrélés / Nonequilibrium aspects in strongly correlated one-dimensional quatum systems Collura, Mario 23 February 2012 (has links) Dans cette thèse, nous avons répondu à certaines questions ouverts dans le domaine de la dynamique hors équilibre des systèmes quantiques unidimensionnels fermés. Durant ces dernières années, les avancées dans les techniques expérimentales ont revitalisé la recherche théorique en physique de la matière condensée et dans l'optique quantique. Nous avons traité trois sujets différents et en utilisant des techniques à la fois numériques et analytiques. Dans le cadre des techniques numériques, nous avons utilisé des méthodes de diagonalisation exacte, l'algorithme du groupe de renormalisation de la matrice densité en fonction du temps (t-DMRG) et l'algorithme de Lanczos. Au début, nous avons étudié la dynamique quantique adiabatique d'un système quantique près d'un point critique. Nous avons démontré que la présence d'un potentiel de confinement modifie fortement les propriétés d'échelle de la dynamique des observables en proximité du point critique quantique. La densité d'excitations moyenne et l'excès d'énergie, après le croisement du point critique, suivent une loi algébrique en fonction de la vitesse de la trempe avec un exposant qui dépend des propriétés spatio-temporelles du potentiel. Ensuite, nous avons étudié le comportement de bosons ultra-froids dans un réseau optique incliné. En commençant par l'hamiltonien de Bose-Hubbard, dans la limite de Hard-Core bosons, nous avons développé une théorie hydrodynamique qui reproduit exactement l'évolution temporelle d'une partie des observables du système. En particulier, nous avons observé qu'une partie de bosons reste piégée, et oscille avec une fréquence qui dépend de la pente du potentiel, au contraire, une autre partie est expulsée hors de la rampe. Nous avons également analysé la dynamique du modèle de Bose-Hubbard en utilisant l'algorithme t-DMRG et l'algorithme de Lanczos. De cette façon, nous avons mis en évidence le rôle de la non-intégrabilité du modèle dans son comportement dynamique. Enfin, nous avons abordé le problème de la thermalisation dans un système quantique étendu. À partir de considérations générales, nous avons introduit la notion de profil de température hors équilibre dans une chaîne des bosons à coeur dure. Nous avons analysé la dynamique du profil de temperature et, notamment, ses propriétés d'échelle / In this thesis we have addressed some open questions on the out-of-equilibrium dynamics of closed one-dimensional quantum systems. In recent years, advances in experimental techniques have revitalized the theoretical research in condensed matter physics and quantum optics. We have treated three different subjects using both numerical and analytical techniques. As far as the numerical techniques are concerned, we have used essentially exact diagonalization methods, the adaptive time-dependent density-matrix renormalization-group algorithm (t-DMRG) and the Lanczos algorithm. At first, we studied the adiabatic quantum dynamics of a quantum system close to a critical point. We have demonstrated that the presence of a confining potential strongly affects the scaling properties of the dynamical observables near the quantum critical point. The mean excitation density and the energy excess, after the crossing of the critical point, follow an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential. After that, we have studied the behavior of ultra-cold bosons in a tilted optical lattice. Starting with the Bose-Hubbard Hamiltonian, in the limit of Hard-Core bosons, we have developed a hydrodynamic theory that exactly reproduces the temporal evolution of some of the observables of the system. In particular, it was observed that part of the boson density remains trapped, and oscillates with a frequency that depends on the slope of the potential, whereas the remaining packet part is expelled out of the ramp. We have also analyzed the dynamics of the Bose-Hubbard model using the tDMRG algorithm and the Lanczos algorithm. In this way we have highlighted the role of the non-integrability of the model on its dynamical behavior. Finally, we have addressed the issue of thermalization in an extended quantum system. Starting from quite general considerations, we have introduced the notion of out-of-equilibrium temperature profile in a chain of Hard-Core bosons. We have analyzed the dynamics of the temperature profile and especially its scaling properties Mécanique quantique Phénomènes critiques quantiques Transitions de phase quantiques Théorie d'échelle Dynamique adiabatique Mécanisme de Kibble-Zurek Densité de défauts Modèle XY quantique Modèle de Bose-Hubbard Intrication quantique Entropie Bosons ultra-froids Oscillations de Bloch Auto-piégeage Thermalisation quantique Profil de température quantique Quantum mechanics Quantum critical phenomena Quantum phase transitions Scaling theory Adiabatic dynamics Kibble-Zurek mechanism Defect density Quantum XY model Quantum Bose-Hubbard model Entanglement Entropy Ultra-cold bosons Bloch oscillations Self-trapping Quantum thermalization Quantum temperature profile 535.15 530.41 530.12
593	Renormalization in Field Theories Söderberg, Alexander January 2015 (has links) Several different approaches to renormalization are studied. The Callan-Symanzik equation is derived and we study its beta functions. An effective potential for the Coleman-Weinberg model is studied to find that the beta function is positive and that spontaneous symmetry breaking will occur if we expand around the classical field. Lastly we renormalize a non-abelian gaugetheory to find that the beta function in QCD is negative. renormalization in field theories renormalization quantum field theories quantum field theory quantum mechanics quantum physics quantum physics mechanics field theory theory theories fields field regularization dimensional regularization dimensional perturbative perturbative renormalization wilsonian approach wilsonian approach momentum cutoff momentum cutoff callan symanzik equation callan symanzik equation coleman weinberg model potential effective coleman-weinberg potential beta function beta non abelian gauge non abelian gauge theory non abelian gauge theories qed quantum electrodynamics electrodynamics qcd quantum chromodynamics chromodynamics
594	Twentieth-century poetry and science : science in the poetry of Hugh MacDiarmid, Judith Wright, Edwin Morgan, and Miroslav Holub Gibson, Donald January 2015 (has links) The aim of this thesis is to arrive at a characterisation of twentieth century poetry and science by means of a detailed study of the work of four poets who engaged extensively with science and whose writing lives spanned the greater part of the period. The study of science in the work of the four chosen poets, Hugh MacDiarmid (1892 – 1978), Judith Wright (1915 – 2000), Edwin Morgan (1920 – 2010), and Miroslav Holub (1923 – 1998), is preceded by a literature survey and an initial theoretical chapter. This initial part of the thesis outlines the interdisciplinary history of the academic subject of poetry and science, addressing, amongst other things, the challenges presented by the episodes known as the ‘two cultures' and the ‘science wars'. Seeking to offer a perspective on poetry and science more aligned to scientific materialism than is typical in the interdiscipline, a systemic challenge to Thomas Kuhn's The Structure of Scientific Revolutions (1962) is put forward in the first chapter. Additionally, the founding work of poetry and science, I. A. Richards's Science and Poetry (1926), is assessed both in the context in which it was written, and from a contemporary viewpoint; and, as one way to understand science in poetry, a theory of the creative misreading of science is developed, loosely based on Harold Bloom's The Anxiety of Influence (1973). The detailed study of science in poetry commences in Chapter II with Hugh MacDiarmid's late work in English, dating from his period on the Shetland Island of Whalsay (1933 – 1941). The thesis in this chapter is that this work can be seen as a radical integration of poetry and science; this concept is considered in a variety of ways including through a computational model, originally suggested by Robert Crawford. The Australian poet Judith Wright, the subject of Chapter III, is less well known to poetry and science, but a detailed engagement with physics can be identified, including her use of four-dimensional imagery, which has considerable support from background evidence. Biology in her poetry is also studied in the light of recent work by John Holmes. In Chapter IV, science in the poetry of Edwin Morgan is discussed in terms of its origin and development, from the perspective of the mythologised science in his science fiction poetry, and from the ‘hard' technological perspective of his computer poems. Morgan's work is cast in relief by readings which are against the grain of some but not all of his published comments. The thesis rounds on its theme of materialism with the fifth and final chapter which studies the work of Miroslav Holub, a poet and practising scientist in communist-era Prague. Holub's work, it is argued, represents a rare and important literary expression of scientific materialism. The focus on materialism in the thesis is not mechanistic, nor exclusive of the domain of the imagination; instead it frames the contrast between the original science and the transformed poetic version. The thesis is drawn together in a short conclusion. 821.009
595	Field Theoretic Lagrangian From Off-shell Supermultiplet Gauge Quotients Katona, Gregory 01 January 2013 (has links) Recent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a node-pair transformtion between fermionic bosonic component fields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge-quotients by supersymmetric images of other Adinkras, and the correlated building of field theoretic worldline Lagrangians to accommodate both classical and quantum venues. We find Ref [40], that such gauge quotients do not yield other stand alone or "proper" Adinkras as afore sighted, nor can they be decomposed into supermultiplet sums, but are rather a connected "Adinkraic network". Their iteration, analogous to Weyl's construction for producing all finite-dimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discrete-graph and continuous-field variables, the links of which feature distinct, supersymmetric Lagrangian templates. Collectively, these Adiankraic series air new symbolic genera for equation to phase moments in Feynman path integrals. Guided in this light, we proceed by constructing Lagrangians actions for the N = 3 supermultiplet YI /(iDI X) for I = 1, 2, 3, where YI and X are standard, Salam-Strathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external background (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory responses, some of which are found to be surprisingly controlled by the golden ratio, [phi] = 1.61803, Ref [52]. It is further determined that these Lagrangians allow an N = 3 - > 4 supersymmetric extension to the Chiral-Chiral and Chiral-twistedChiral multiplet, while a subset admits two inequivalent such extensions. In a natural proiii gression, a continuum of observably and usefully inequivalent, finite-dimensional off-shell representations of worldline N = 4 extended supersymmetry are explored, that are variate from one another but in the value of a tuning parameter, Ref [53]. Their dynamics turns out to be nontrivial already when restricting to just bilinear Lagrangians. In particular, we find a 34-parameter family of bilinear Lagrangians that couple two differently tuned supermultiplets to each other and to external magnetic fluxes, where the explicit parameter dependence is unremovable by any field redefinition and is therefore observable. This offers the evaluation of X-phase sensitive, off-shell path integrals with promising correlations to group product decompositions and to deriving source emergences of higher-order background flux-forms on 2-dimensional manifolds, the stacks of which comprise space-time volumes. Application to nonlinear sigma models would naturally follow, having potential use in M- and F- string theories. Supersymmetry superspace supermultiplet adinkra automata adiankraic tensor product decomposition group theoretic lorentz group su(2) so(3) gauge quotient isomorphism surjective bijective image mapping indefinite adiankraic network sequence super poincare group haag lopuszanski sohnius theorem string theory m theory f theory nonlinear sigma model (numerical) algebraic geometry algebraic paradigms worldsheet worldsheet stacks supersymmetric lagrangians ansatz templates super potentials quantum mechanics field theory fermionic bosonic (super) zeeman background flux fields supergravity superfields young tableaux susy tableaux controlled chaos supercharge continuum chiral chiral twisted chiral Physics
596	Electrostaticanalisys the Ras active site Khan, Abdul Kareem 05 March 2009 (has links) La preorganització electrostàtica del centre actiu s'ha postulat com el mecanisme genèric de l'acció dels enzims. Així, alguns residus "estratègics" es disposarien per catalitzar reaccions interaccionant en una forma més forta amb l'estat de transició, baixant d'aquesta manera el valor de l'energia dactivació g cat. S'ha proposat que aquesta preorientació electrostática s'hauria de poder mostrar analitzant l'estabilitat electrostàtica de residus individuals en el centre actiu.Ras es una proteïna essencial de senyalització i actúa com un interruptor cel.lular. Les característiques estructurals de Ras en el seu estat actiu (ON) són diferents de les que té a l'estat inactiu (OFF). En aquesta tesi es duu a terme una anàlisi exhaustiva de l'estabilitat dels residus del centre actiu deRas en l'estat actiu i inactiu. / The electrostatic preorganization of the active site has been put forward as the general framework of action of enzymes. Thus, enzymes would position "strategic" residues in such a way to be prepared to catalyze reactions byinteracting in a stronger way with the transition state, in this way decreasing the activation energy g cat for the catalytic process. It has been proposed thatsuch electrostatic preorientation should be shown by analyzing the electrostatic stability of individual residues in the active site.Ras protein is an essential signaling molecule and functions as a switch in thecell. The structural features of the Ras protein in its active state (ON state) are different than those in its inactive state (OFF state). In this thesis, an exhaustive analysis of the stability of residues in the active and inactive Ras active site is performed. dinàmica centre actiu relacions d'estructura activitat preorganització reorganització estat de transició estat actiu estabilitat electrostàtica interacción proteïna-proteïna test de ranks de Wilcoxon P-loop G1 motif HVR metastability RMSD substrate assisted catalysis sequence alignment beta sheet helix Z-test wilcoxon rank test protein-protein interactions electrostatic stability active state dynamics signal transduction electrostatic stabilization ras effectors guanine exchange factor GTPase-activating proteins quantum mechanics/molecular PDLD/S-LRA X-ray crystallography solvation energy free energy perturbation statistical analysis GTP hydrolysis guanosine diphosphate guanosine triphosphate computer simulation thermodynamics protein conformation electrostatics interruptor II interruptor I llaç P motiu G1 HVR (regions altament variables) metaestabilita RMSD catàlisi assistida pel substrat aliniament de seqüència fulla beta hèlix test Z transducció del senyal estabilització electrostàtica efectors de ras factor de bescamvi de guanina proteïnes activadores de l'activitat mecànica quàntica/mecànica PDLD/S-LRA cristalografia de raigs X energia de solvatació perturbació de l'energia lliure anàlisi estadística hidròlisi de GTP difosfat de guanosina trifosfat de guanosina simulació computacional termodinàmica conformació proteïca electrostàtica switch-I switch-II 537 576

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