Two-loop self-energy diagrams worked out with NDIM

In this work we calculate two two-loop massless Feynman integrals pertaining to self-energy diagrams using NDIM (Negative Dimensional Integration Method). We show that the answer we get is 36-fold degenerate. We then consider special cases of exponents for propagators and the outcoming results compared with known ones obtained via traditional methods.

Loop Integrals in Three Outstanding Gauges: Feynman, Light-Cone, and Coulomb

We apply the negative dimensional integration method (NDIM) to three outstanding gauges: Feynman, light-cone, and Coulomb gauges. Our aim is to show that NDIM is a very suitable technique to deal with loop integrals, regardless of which gauge choice that originated them. In the Feynman gauge we perform scalar two-loop four-point massless integrals; in the light-cone gauge we calculate scalar two-loop integrals contributing to two-point functions without any kind of prescriptions, since NDIM can abandon such devices - this calculation is the first test of our prescriptionless method beyond one-loop order; and finally, for the Coulomb gauge we consider a four-propagator massless loop integral, in the split-dimensional regularization context. © 2001 Academic Press.

First results for the Coulomb gauge integrals using NDIM

The Coulomb gauge has at least two advantages over other gauge choices in that bound states between quarks and studies of confinement are easier to understand in this gauge. However, perturbative calculations, namely Feynman loop integrations, are not well defined (there are the so-called energy integrals) even within the context of dimensional regularization. Leibbrandt and Williams proposed a possible cure to such a problem by splitting the space-time dimension into D = ω + ρ, i.e., introducing a specific parameter ρ to regulate the energy integrals. The aim of our work is to apply the negative dimensional integration method (NDIM) to the Coulomb gauge integrals using the recipe of split-dimension parameters and present complete results - finite and divergent parts - to the one- and two-loop level for arbitrary exponents of the propagators and dimension.

Integração em dimensões negativas em calibres covariantes e não-covariantes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cálculos de integrais de Feynman em teorias de campos

Pós-graduação em Física - IFT

Determination of viral load and integration status of HPV 16 in normal and LSIL exfoliated cervical cells

L’intégration du génome du virus papilloma humain (VPH) a été reconnu jusqu’`a récemment comme étant un événnement fréquent mais pourtant tardif dans la progression de la maladie du col de l’utérus. La perspective temporelle vient, pourtant, d’être mise au défi par la détection de formes intégrées de VPH dans les tissus normaux et dans les lésions prénéoplasiques. Notre objectif était de déterminer la charge virale de VPH-16 et son état physique dans une série de 220 échantillons provenant de cols uterins normaux et avec des lésions de bas-grade. La technique quantitative de PCR en temps réel, méthode Taqman, nous a permis de quantifier le nombre de copies des gènes E6, E2, et de la B-globine, permettant ainsi l’évaluation de la charge virale et le ratio de E6/E2 pour chaque spécimen. Le ratio E6/E2 de 1.2 ou plus était suggestif d’intégration. Par la suite, le site d’intégration du VPH dans le génome humain a été déterminé par la téchnique de RS-PCR. La charge virale moyenne était de 57.5±324.6 copies d'ADN par cellule et le ratio E6/E2 a évalué neuf échantillons avec des formes d’HPV intégrées. Ces intégrants ont été amplifiés par RS-PCR, suivi de séquençage, et l’homologie des amplicons a été déterminée par le programme BLAST de NCBI afin d’identifier les jonctions virales-humaines. On a réussi `a identifier les jonctions humaines-virales pour le contrôle positif, c'est-à-dire les cellules SiHa, pourtant nous n’avons pas detecté d’intégration par la technique de RS-PCR dans les échantillons de cellules cervicales exfoliées provenant de tissus normaux et de lésions de bas-grade. Le VPH-16 est rarement intégré dans les spécimens de jeunes patientes.

Método de integração em dimensão negativa em teoria quântica de campos

This work is a review of the Negative Dimension Integration Method as a powerful tool for the computation of the radiative corrections present in Quantum Field Perturbation Theory. This method is applicable in the context of Dimensional Regularization and it provides exact solutions for Feynman integrals with both dimensional parameter and propagator exponents generalized. These solutions are presentedintheformoflinearcombinationsofhypergeometricfunctionswhosedomains of convergence are related to the analytic structure of the Feynman Integral. Each solution is connected to the others trough analytic continuations. Besides presenting and discussing the general algorithm of the method in a detailed way, we offer concrete applications to scalar one-loop and two-loop integrals as well as to the one-loop renormalizationofQuantumElectrodynamics (QED)

Ruin Theory with Excess of Loss Reinsurance and Reinstatements

The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical Cramer-Lundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin probability is both the solution of a partial integro-differential equation and the fixed point of a contractive integral operator. We exploit the latter representation to develop and implement a recursive algorithm for numerical approximation of the ruin probability that involves high-dimensional integration. Furthermore we study the behavior of the finite-time ruin probability under various levels of initial surplus and security loadings and compare the efficiency of the numerical algorithm with the computational alternative of stochastic simulation of the risk process. (C) 2011 Elsevier Inc. All rights reserved.

Quasi-Interpolation von Funktionen und Anwendungen auf Potentialprobleme

Ausgangspunkt der Dissertation ist ein von V. Maz'ya entwickeltes Verfahren, eine gegebene Funktion f : Rn ! R durch eine Linearkombination fh radialer glatter exponentiell fallender Basisfunktionen zu approximieren, die im Gegensatz zu den Splines lediglich eine näherungsweise Zerlegung der Eins bilden und somit ein für h ! 0 nicht konvergentes Verfahren definieren. Dieses Verfahren wurde unter dem Namen Approximate Approximations bekannt. Es zeigt sich jedoch, dass diese fehlende Konvergenz für die Praxis nicht relevant ist, da der Fehler zwischen f und der Approximation fh über gewisse Parameter unterhalb der Maschinengenauigkeit heutiger Rechner eingestellt werden kann. Darüber hinaus besitzt das Verfahren große Vorteile bei der numerischen Lösung von Cauchy-Problemen der Form Lu = f mit einem geeigneten linearen partiellen Differentialoperator L im Rn. Approximiert man die rechte Seite f durch fh, so lassen sich in vielen Fällen explizite Formeln für die entsprechenden approximativen Volumenpotentiale uh angeben, die nur noch eine eindimensionale Integration (z.B. die Errorfunktion) enthalten. Zur numerischen Lösung von Randwertproblemen ist das von Maz'ya entwickelte Verfahren bisher noch nicht genutzt worden, mit Ausnahme heuristischer bzw. experimenteller Betrachtungen zur sogenannten Randpunktmethode. Hier setzt die Dissertation ein. Auf der Grundlage radialer Basisfunktionen wird ein neues Approximationsverfahren entwickelt, welches die Vorzüge der von Maz'ya für Cauchy-Probleme entwickelten Methode auf die numerische Lösung von Randwertproblemen überträgt. Dabei werden stellvertretend das innere Dirichlet-Problem für die Laplace-Gleichung und für die Stokes-Gleichungen im R2 behandelt, wobei für jeden der einzelnen Approximationsschritte Konvergenzuntersuchungen durchgeführt und Fehlerabschätzungen angegeben werden.

General massive one-loop off-shell three-point functions

In this work we compute the most general massive one-loop off-shell three-point vertex in D-dimensions, where the masses, external momenta and exponents of propagators are arbitrary. This follows our previous paper in which we have calculated several new hypergeometric series representations for massless and massive (with equal masses) scalar one-loop three-point functions, in the negative dimensional approach.

Prescriptionless light-cone integrals

Perturbative quantum gauge field theory as seen within the perspective of physical gauge choices such as the light-cone gauge entails the emergence of troublesome poles of the type (k · n)-α in the Feynman integrals. These come from the boson field propagator, where α = 1, 2, ⋯ and nμ is the external arbitrary four-vector that defines the gauge proper. This becomes an additional hurdle in the computation of Feynman diagrams, since any graph containing internal boson lines will inevitably produce integrands with denominators bearing the characteristic gauge-fixing factor. How one deals with them has been the subject of research over decades, and several prescriptions have been suggested and tried in the course of time, with failures and successes. However, a more recent development at this fronteer which applies the negative dimensional technique to compute light-cone Feynman integrals shows that we can altogether dispense with prescriptions to perform the calculations. An additional bonus comes to us attached to this new technique, in that not only it renders the light-cone prescriptionless but, by the very nature of it, it can also dispense with decomposition formulas or partial fractioning tricks used in the standard approach to separate pole products of the type (k · n)-α[(k - p) · n]-β (β = 1, 2, ⋯). In this work we demonstrate how all this can be done.

Pólos no gauge do cone de luz e o método de covariantização

Pós-graduação em Física - IFT

Likelihood-Based Inference for Partially Observed Multi-Type Markov Branching Processes

Thesis (Ph.D.)--University of Washington, 2016-08

Cryo-negative staining: advantages and applications for three-dimensional electron microscopy of biological macromolecules

Les échantillons biologiques ne s?arrangent pas toujours en objets ordonnés (cristaux 2D ou hélices) nécessaires pour la microscopie électronique ni en cristaux 3D parfaitement ordonnés pour la cristallographie rayons X alors que de nombreux spécimens sont tout simplement trop << gros D pour la spectroscopie NMR. C?est pour ces raisons que l?analyse de particules isolées par la cryo-microscopie électronique est devenue une technique de plus en plus importante pour déterminer la structure de macromolécules. Néanmoins, le faible rapport signal-sur-bruit ainsi que la forte sensibilité des échantillons biologiques natifs face au faisceau électronique restent deux parmi les facteurs limitant la résolution. La cryo-coloration négative est une technique récemment développée permettant l?observation des échantillons biologiques avec le microscope électronique. Ils sont observés à l?état vitrifié et à basse température, en présence d?un colorant (molybdate d?ammonium). Les avantages de la cryo-coloration négative sont étudiés dans ce travail. Les résultats obtenus révèlent que les problèmes majeurs peuvent êtres évités par l?utilisation de cette nouvelle technique. Les échantillons sont représentés fidèlement avec un SNR 10 fois plus important que dans le cas des échantillons dans l?eau. De plus, la comparaison de données obtenues après de multiples expositions montre que les dégâts liés au faisceau électronique sont réduits considérablement. D?autre part, les résultats exposés mettent en évidence que la technique est idéale pour l?analyse à haute résolution de macromolécules biologiques. La solution vitrifiée de molybdate d?ammonium entourant l?échantillon n?empêche pas l?accès à la structure interne de la protéine. Finalement, plusieurs exemples d?application démontrent les avantages de cette technique nouvellement développée.<br/><br/>Many biological specimens do not arrange themselves in ordered assemblies (tubular or flat 2D crystals) suitable for electron crystallography, nor in perfectly ordered 3D crystals for X-ray diffraction; many other are simply too large to be approached by NMR spectroscopy. Therefore, single-particles analysis has become a progressively more important technique for structural determination of large isolated macromolecules by cryo-electron microscopy. Nevertheless, the low signal-to-noise ratio and the high electron-beam sensitivity of biological samples remain two main resolution-limiting factors, when the specimens are observed in their native state. Cryo-negative staining is a recently developed technique that allows the study of biological samples with the electron microscope. The samples are observed at low temperature, in the vitrified state, but in presence of a stain (ammonium molybdate). In the present work, the advantages of this novel technique are investigated: it is shown that cryo-negative staining can generally overcome most of the problems encountered with cryo-electron microscopy of vitrified native suspension of biological particles. The specimens are faithfully represented with a 10-times higher SNR than in the case of unstained samples. Beam-damage is found to be considerably reduced by comparison of multiple-exposure series of both stained and unstained samples. The present report also demonstrates that cryo-negative staining is capable of high- resolution analysis of biological macromolecules. The vitrified stain solution surrounding the sample does not forbid the access to the interna1 features (ie. the secondary structure) of a protein. This finding is of direct interest for the structural biologist trying to combine electron microscopy and X-ray data. developed electron microscopy technique. Finally, several application examples demonstrate the advantages of this newly

Structures and negative thermal expansion properties of the one-dimensional cyanides, CuCN, AgCN and AuCN

The behaviour of the lattice parameters of HTCuCN (high-temperature form), AgCN and AuCN have been investigated as a function of temperature over the temperature range 90–490 K. All materials show one-dimensional negative thermal expansion (NTE) along the ––(M––CN)–– chain direction c (ac(HT-CuCN) ¼32.1 10–6 K1, ac(AgCN)¼23.910–6 K1 and ac(AuCN) ¼9.3106 K1 over the temperature range 90–490 K). The origin of this behaviour has been studied using RMC modelling of Bragg and total neutron diffraction data from AgCN and AuCN at 10 and 300 K. These analyses yield details of the local motions within the chains responsible for NTE. The low-temperature form of CuCN, LT-CuCN, has been studied using single-crystal X-ray diffraction. In this form of CuCN, wavelike distortions of the ––(Cu––CN)–– chains occur in the static structure, which are reminiscent of the motions seen in the RMC modelling of AgCN and AuCN, which are responsible for the NTE behaviour.