Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

On Wald Residuals in Generalized Linear Models

A rigorous asymptotic theory for Wald residuals in generalized linear models is not yet available. The authors provide matrix formulae of order O(n(-1)), where n is the sample size, for the first two moments of these residuals. The formulae can be applied to many regression models widely used in practice. The authors suggest adjusted Wald residuals to these models with approximately zero mean and unit variance. The expressions were used to analyze a real dataset. Some simulation results indicate that the adjusted Wald residuals are better approximated by the standard normal distribution than the Wald residuals.

Simultaneous optical signal-to-noise ratio and differential group delay monitoring based on degree of polarization measurements in optical communications systems

We present a simultaneous optical signal-to-noise ratio (OSNR) and differential group delay (DGD) monitoring method based on degree of polarization (DOP) measurements in optical communications systems. For the first time in the literature (to our best knowledge), the proposed scheme is demonstrated to be able to independently and simultaneously extract OSNR and DGD values from the DOP measurements. This is possible because the OSNR is related to maximum DOP, while DGD is related to the ratio between the maximum and minimum values of DOP. We experimentally measured OSNR and DGD in the ranges from 10 to 30 dB and 0 to 90 ps for a 10 Gb/s non-return-to-zero signal. A theoretical analysis of DOP accuracy needed to measure low values of DGD and high OSNRs is carried out, showing that current polarimeter technology is capable of yielding an OSNR measurement within 1 dB accuracy, for OSNR values up to 34 dB, while DGD error is limited to 1.5% for DGD values above 10 ps. For the first time to our knowledge, the technique was demonstrated to accurately measure first-order polarization mode dispersion (PMD) in the presence of a high value of second-order PMD (as high as 2071 ps(2)). (C) 2012 Optical Society of America

ON THE CONSISTENCY OF TWISTED GENERALIZED WEYL ALGEBRAS

A twisted generalized Weyl algebra A of degree n depends on a. base algebra R, n commuting automorphisms sigma(i) of R, n central elements t(i) of R and on some additional scalar parameters. In a paper by Mazorchuk and Turowska, it is claimed that certain consistency conditions for sigma(i) and t(i) are sufficient for the algebra to be nontrivial. However, in this paper we give all example which shows that this is false. We also correct the statement by finding a new set of consistency conditions and prove that the old and new conditions together are necessary and sufficient for the base algebra R to map injectively into A. In particular they are sufficient for the algebra A to be nontrivial. We speculate that these consistency relations may play a role in other areas of mathematics, analogous to the role played by the Yang-Baxter equation in the theory of integrable systems.

A simple analysis of the influence of the solvent-induced electronic polarization on the N-15 magnetic shielding of pyridine in water

Electronic polarization induced by the interaction of a reference molecule with a liquid environment is expected to affect the magnetic shielding constants. Understanding this effect using realistic theoretical models is important for proper use of nuclear magnetic resonance in molecular characterization. In this work, we consider the pyridine molecule in water as a model system to briefly investigate this aspect. Thus, Monte Carlo simulations and quantum mechanics calculations based on the B3LYP/6-311++G (d,p) are used to analyze different aspects of the solvent effects on the N-15 magnetic shielding constant of pyridine in water. This includes in special the geometry relaxation and the electronic polarization of the solute by the solvent. The polarization effect is found to be very important, but, as expected for pyridine, the geometry relaxation contribution is essentially negligible. Using an average electrostatic model of the solvent, the magnetic shielding constant is calculated as -58.7 ppm, in good agreement with the experimental value of -56.3 ppm. The explicit inclusion of hydrogen-bonded water molecules embedded in the electrostatic field of the remaining solvent molecules gives the value of -61.8 ppm.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Bilateral subthalamic nucleus stimulation for generalized dystonia after bilateral pallidotomy

Background: Thalamotomies and pallidotomies were commonly performed before the deep brain stimulation (DBS) era. Although ablative procedures can lead to significant dystonia improvement, longer periods of analysis reveal disease progression and functional deterioration. Today, the same patients seek additional treatment possibilities. Methods: Four patients with generalized dystonia who previously had undergone bilateral pallidotomy came to our service seeking additional treatment because of dystonic symptom progression. Bilateral subthalamic nucleus DBS (B-STN-DBS) was the treatment of choice. The patients were evaluated with the BurkeFahnMarsden Dystonia Rating Scale (BFMDRS) and the Unified Dystonia Rating Scale (UDRS) before and 2 years after surgery. Results: All patients showed significant functional improvement, averaging 65.3% in BFMDRS (P = .014) and 69.2% in UDRS (P = .025). Conclusions: These results suggest that B-STN-DBS may be an interesting treatment option for generalized dystonia, even for patients who have already undergone bilateral pallidotomy. (c) 2012 Movement Disorder Society

A note on the use of the generalized odds ratio in meta-analysis of association studies involving bi- and tri-allelic polymorphisms

Abstract Background The generalized odds ratio (GOR) was recently suggested as a genetic model-free measure for association studies. However, its properties were not extensively investigated. We used Monte Carlo simulations to investigate type-I error rates, power and bias in both effect size and between-study variance estimates of meta-analyses using the GOR as a summary effect, and compared these results to those obtained by usual approaches of model specification. We further applied the GOR in a real meta-analysis of three genome-wide association studies in Alzheimer's disease. Findings For bi-allelic polymorphisms, the GOR performs virtually identical to a standard multiplicative model of analysis (e.g. per-allele odds ratio) for variants acting multiplicatively, but augments slightly the power to detect variants with a dominant mode of action, while reducing the probability to detect recessive variants. Although there were differences among the GOR and usual approaches in terms of bias and type-I error rates, both simulation- and real data-based results provided little indication that these differences will be substantial in practice for meta-analyses involving bi-allelic polymorphisms. However, the use of the GOR may be slightly more powerful for the synthesis of data from tri-allelic variants, particularly when susceptibility alleles are less common in the populations (≤10%). This gain in power may depend on knowledge of the direction of the effects. Conclusions For the synthesis of data from bi-allelic variants, the GOR may be regarded as a multiplicative-like model of analysis. The use of the GOR may be slightly more powerful in the tri-allelic case, particularly when susceptibility alleles are less common in the populations.

Generalized soluble groups of finite co-central rank

Eine Gruppe G hat endlichen Prüferrang (bzw. Ko-zentralrang) kleiner gleich r, wenn für jede endlich erzeugte Gruppe H gilt: H (bzw. H modulo seinem Zentrum) ist r-erzeugbar. In der vorliegenden Arbeit werden, soweit möglich, die bekannten Sätze über Gruppen von endlichem Prüferrang (kurz X-Gruppen), auf die wesentlich größere Klasse der Gruppen mit endlichem Ko-zentralrang (kurz R-Gruppen) verallgemeinert.Für lokal nilpotente R-Gruppen, welche torsionsfrei oder p-Gruppen sind, wird gezeigt, dass die Zentrumsfaktorgruppe eine X-Gruppe sein muss. Es folgt, dass Hyperzentralität und lokale Nilpotenz für R-Gruppen identische Bediungungen sind. Analog hierzu sind R-Gruppen genau dann lokal auflösbar, wenn sie hyperabelsch sind. Zentral für die Strukturtheorie hyperabelscher R-Gruppen ist die Tatsache, dass solche Gruppen eine aufsteigende Normalreihe abelscher X-Gruppen besitzen. Es wird eine Sylowtheorie für periodische hyperabelsche R-Gruppen entwickelt. Für torsionsfreie hyperabelsche R-Gruppen wird deren Auflösbarkeit bewiesen. Des weiteren sind lokal endliche R-Gruppen fast hyperabelsch. Für R-Gruppen fallen sehr große Gruppenklassen mit den fast hyperabelschen Gruppen zusammen. Hierzu wird der Begriff der Sektionsüberdeckung eingeführt und gezeigt, dass R-Gruppen mit fast hyperabelscher Sektionsüberdeckung fast hyperabelsch sind.

Cosmological perturbations in generalized theories of gravity

The first part of the thesis concerns the study of inflation in the context of a theory of gravity called "Induced Gravity" in which the gravitational coupling varies in time according to the dynamics of the very same scalar field (the "inflaton") driving inflation, while taking on the value measured today since the end of inflation. Through the analytical and numerical analysis of scalar and tensor cosmological perturbations we show that the model leads to consistent predictions for a broad variety of symmetry-breaking inflaton's potentials, once that a dimensionless parameter entering into the action is properly constrained. We also discuss the average expansion of the Universe after inflation (when the inflaton undergoes coherent oscillations about the minimum of its potential) and determine the effective equation of state. Finally, we analyze the resonant and perturbative decay of the inflaton during (p)reheating. The second part is devoted to the study of a proposal for a quantum theory of gravity dubbed "Horava-Lifshitz (HL) Gravity" which relies on power-counting renormalizability while explicitly breaking Lorentz invariance. We test a pair of variants of the theory ("projectable" and "non-projectable") on a cosmological background and with the inclusion of scalar field matter. By inspecting the quadratic action for the linear scalar cosmological perturbations we determine the actual number of propagating degrees of freedom and realize that the theory, being endowed with less symmetries than General Relativity, does admit an extra gravitational degree of freedom which is potentially unstable. More specifically, we conclude that in the case of projectable HL Gravity the extra mode is either a ghost or a tachyon, whereas in the case of non-projectable HL Gravity the extra mode can be made well-behaved for suitable choices of a pair of free dimensionless parameters and, moreover, turns out to decouple from the low-energy Physics.

108 Sn studied with intermediate-energy Coulomb excitation

In dieser Arbeit wurde der instabile, Neutronenarme Kern 108Sn mit Hilfe der Coulomb-Anregung bei intermediaeren Energien in inverser Kinematik studiert. Diese Methode wurde bisher zur Untersuchung der ersten angeregten 2+ Zustaende und deren E2 Zerfallsraten in Kernen mit Kernladungszahl Z< 30 angewendet. 108Sn ist somit der Kern mit der groeßten Kernladungszahl, bei dem diese Studien bisher stattfanden. Das Ziel dieses Experiments war die Messung der unbekannten reduzierten Uebergangswahrscheinlichkeit B(E2,0+ -> 2+). Der B(E2)-Wert von 0.230(57) e2b2 wurde relativ zu dem bekannten Wert des Isotops 112Sn bestimmt. Das Experiment wurde an der GSI Darmstadt mit Hilfe des RISING Detektors und des Fragmentseperators (FRS) durchgefuehrt. Sekundaere Strahlen (108Sn, 112Sn) mit einer Energie von ca. 150 MeV pro Nukleon wurden auf ein 386 mg/cm2 dickes 197Au Target geschossen. Die Projektilfragmente wurden mit Hilfe des Fragmentseparators selektiert und identifiziert. Zur Selektion des Reaktionskanals und zur Bestimmung des Winkels der gestreuten Fragmente wurde das Teilchenteleskop CATE, das sich hinter dem Target befand, verwendet. Gammastrahlung, die in Koinzidenz mit den Projektilrestkernen emittiert wurde, wurde in den Germanium-Cluster Detektoren des RISING Detektors nachgewiesen. Der gemessene B(E2,0+ -> 2+)-Wert von 108Sn ist in Uebereinstimmung mit neueren Schalenmodellrechnungen, die auf realistischen effektiven Wechselwirkungen basieren und im Rahmen eines verallgemeinerten Seniorit¨ats-Schemas erklaert werden.

Polarization in heavy quark decays

In this thesis I concentrate on the angular correlations in top quark decays and their next--to--leading order (NLO) QCD corrections. I also discuss the leading--order (LO) angular correlations in unpolarized and polarized hyperon decays. In the first part of the thesis I calculate the angular correlation between the top quark spin and the momentum of decay products in the rest frame decay of a polarized top quark into a charged Higgs boson and a bottom quark in Two-Higgs-Doublet-Models: $t(uparrow)rightarrow b+H^{+}$. The decay rate in this process is split into an angular independent part (unpolarized) and an angular dependent part (polar correlation). I provide closed form formulae for the ${mathcal O}(alpha_{s})$ radiative corrections to the unpolarized and the polar correlation functions for $m_{b}neq 0$ and $m_{b}=0$. The results for the unpolarized rate agree with the existing results in the literature. The results for the polarized correlations are new. I found that, for certain values of $tanbeta$, the ${mathcal O}(alpha_s)$ radiative corrections to the unpolarized, polarized rates, and the asymmetry parameter can become quite large. In the second part I concentrate on the semileptonic rest frame decay of a polarized top quark into a bottom quark and a lepton pair: $t(uparrow) to X_b + ell^+ + nu_ell$. I analyze the angular correlations between the top quark spin and the momenta of the decay products in two different helicity coordinate systems: system 1a with the $z$--axis along the charged lepton momentum, and system 3a with the $z$--axis along the neutrino momentum. The decay rate then splits into an angular independent part (unpolarized), a polar angle dependent part (polar correlation) and an azimuthal angle dependent part (azimuthal correlation). I present closed form expressions for the ${mathcal O}(alpha_{s})$ radiative corrections to the unpolarized part and the polar and azimuthal correlations in system 1a and 3a for $m_{b}neq 0$ and $m_{b}=0$. For the unpolarized part and the polar correlation I agree with existing results. My results for the azimuthal correlations are new. In system 1a I found that the azimuthal correlation vanishes in the leading order as a consequence of the $(V-A)$ nature of the Standard Model current. The ${mathcal O}(alpha_{s})$ radiative corrections to the azimuthal correlation in system 1a are very small (around 0.24% relative to the unpolarized LO rate). In system 3a the azimuthal correlation does not vanish at LO. The ${mathcal O}(alpha_{s})$ radiative corrections decreases the LO azimuthal asymmetry by around 1%. In the last part I turn to the angular distribution in semileptonic hyperon decays. Using the helicity method I derive complete formulas for the leading order joint angular decay distributions occurring in semileptonic hyperon decays including lepton mass and polarization effects. Compared to the traditional covariant calculation the helicity method allows one to organize the calculation of the angular decay distributions in a very compact and efficient way. This is demonstrated by the specific example of the polarized hyperon decay $Xi^0(uparrow) to Sigma^+ + l^- + bar{nu}_l$ ,($l^-=e^-, mu^-$) followed by the nonleptonic decay $Sigma^+ to p + pi^0$, which is described by a five--fold angular decay distribution.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.