Picard-Fuchs equations of dimensionally regulated Feynman integrals

Zusammenfassung In der vorliegenden Arbeit besch¨aftige ich mich mit Differentialgleichungen von Feynman– Integralen. Ein Feynman–Integral h¨angt von einem Dimensionsparameter D ab und kann f¨ur ganzzahlige Dimension als projektives Integral dargestellt werden. Dies ist die sogenannte Feynman–Parameter Darstellung. In Abh¨angigkeit der Dimension kann ein solches Integral divergieren. Als Funktion in D erh¨alt man eine meromorphe Funktion auf ganz C. Ein divergentes Integral kann also durch eine Laurent–Reihe ersetzt werden und dessen Koeffizienten r¨ucken in das Zentrum des Interesses. Diese Vorgehensweise wird als dimensionale Regularisierung bezeichnet. Alle Terme einer solchen Laurent–Reihe eines Feynman–Integrals sind Perioden im Sinne von Kontsevich und Zagier. Ich beschreibe eine neue Methode zur Berechnung von Differentialgleichungen von Feynman– Integralen. ¨ Ublicherweise verwendet man hierzu die sogenannten ”integration by parts” (IBP)– Identit¨aten. Die neue Methode verwendet die Theorie der Picard–Fuchs–Differentialgleichungen. Im Falle projektiver oder quasi–projektiver Variet¨aten basiert die Berechnung einer solchen Differentialgleichung auf der sogenannten Griffiths–Dwork–Reduktion. Zun¨achst beschreibe ich die Methode f¨ur feste, ganzzahlige Dimension. Nach geeigneter Verschiebung der Dimension erh¨alt man direkt eine Periode und somit eine Picard–Fuchs–Differentialgleichung. Diese ist inhomogen, da das Integrationsgebiet einen Rand besitzt und daher nur einen relativen Zykel darstellt. Mit Hilfe von dimensionalen Rekurrenzrelationen, die auf Tarasov zur¨uckgehen, kann in einem zweiten Schritt die L¨osung in der urspr¨unglichen Dimension bestimmt werden. Ich beschreibe außerdem eine Methode, die auf der Griffiths–Dwork–Reduktion basiert, um die Differentialgleichung direkt f¨ur beliebige Dimension zu berechnen. Diese Methode ist allgemein g¨ultig und erspart Dimensionswechsel. Ein Erfolg der Methode h¨angt von der M¨oglichkeit ab, große Systeme von linearen Gleichungen zu l¨osen. Ich gebe Beispiele von Integralen von Graphen mit zwei und drei Schleifen. Tarasov gibt eine Basis von Integralen an, die Graphen mit zwei Schleifen und zwei externen Kanten bestimmen. Ich bestimme Differentialgleichungen der Integrale dieser Basis. Als wichtigstes Beispiel berechne ich die Differentialgleichung des sogenannten Sunrise–Graphen mit zwei Schleifen im allgemeinen Fall beliebiger Massen. Diese ist f¨ur spezielle Werte von D eine inhomogene Picard–Fuchs–Gleichung einer Familie elliptischer Kurven. Der Sunrise–Graph ist besonders interessant, weil eine analytische L¨osung erst mit dieser Methode gefunden werden konnte, und weil dies der einfachste Graph ist, dessen Master–Integrale nicht durch Polylogarithmen gegeben sind. Ich gebe außerdem ein Beispiel eines Graphen mit drei Schleifen. Hier taucht die Picard–Fuchs–Gleichung einer Familie von K3–Fl¨achen auf.

BCJ-relations in quantum field theory

BCJ-relations have a series of important consequences in Quantum FieldrnTheory and in Gravity. In QFT, one can use BCJ-relations to reduce thernnumber of independent colour-ordered partial amplitudes and to relate nonplanarrnand planar diagrams in loop calculations. In addition, one can usernBCJ-numerators to construct gravity scattering amplitudes through a squaringrn procedure. For these reasons, it is important to nd a prescription tornobtain BCJ-numerators without requiring a diagram by diagram approach.rnIn this thesis, after introducing some basic concepts needed for the discussion,rnI will examine the existing diagrammatic prescriptions to obtainrnBCJ-numerators. Subsequently, I will present an algorithm to construct anrneective Yang-Mills Lagrangian which automatically produces kinematic numeratorsrnsatisfying BCJ-relations. A discussion on the kinematic algebrarnfound through scattering equations will then be presented as a way to xrnnon-uniqueness problems in the algorithm.

Applications of elliptic functions to solve differential equations

In questa tesi si mostrano alcune applicazioni degli integrali ellittici nella meccanica Hamiltoniana, allo scopo di risolvere i sistemi integrabili. Vengono descritte le funzioni ellittiche, in particolare la funzione ellittica di Weierstrass, ed elenchiamo i tipi di integrali ellittici costruendoli dalle funzioni di Weierstrass. Dopo aver considerato le basi della meccanica Hamiltoniana ed il teorema di Arnold Liouville, studiamo un esempio preso dal libro di Moser-Integrable Hamiltonian Systems and Spectral Theory, dove si prendono in considerazione i sistemi integrabili lungo la geodetica di un'ellissoide, e il sistema di Von Neumann. In particolare vediamo che nel caso n=2 abbiamo un integrale ellittico.

Local pain and spreading hyperalgesia induced by intramuscular injection of nerve growth factor are not reduced by local anesthesia of the muscle

Injections with local anesthesia for therapeutic and diagnostic purposes are common clinical practice. This double-blind placebo controlled study explores the rational of local anesthetic blocks for the detection of muscle pain as the primary generator in spreading hyperalgesic conditions.

Impact of Bone Harvesting Techniques on Cell Viability and the Release of Growth Factors of Autografts

Background: Autogenous bone grafts obtained by different harvesting techniques behave differently during the process of graft consolidation; the underlying reasons are however not fully understood. One theory is that harvesting techniques have an impact on the number and activity of the transplanted cells which contribute to the process of graft consolidation. Materials and Methods: To test this assumption, porcine bone grafts were harvested with four different surgical procedures: bone mill, piezosurgery, bone drilling (bone slurry), and bone scraper. After determining cell viability, the release of molecules affecting bone formation and resorption was assessed by reverse transcription polymerase chain reaction and immunoassay. The mitogenic and osteogenic activity of the conditioned media was evaluated in a bioassay with isolated bone cells. Results: Cell viability and the release of molecules affecting bone formation were higher in samples harvested by bone mill and bone scraper when compared with samples prepared by bone drilling and piezosurgery. The harvesting procedure also affected gene expression, for example, bone mill and bone scraper samples revealed significantly higher expression of growth factors such as bone morphogenetic protein-2 and vascular endothelial growth factor compared with the two other modalities. Receptor activator of nuclear factor kappa B ligand expression was lowest in bone scraper samples. Conclusion: These data can provide a scientific basis to better understand the impact of harvesting techniques on the number and activity of transplanted cells, which might contribute to the therapeutic outcome of the augmentation procedure.

Tradeoffs associated with constitutive and induced plant resistance against herbivory

Several prominent hypotheses have been posed to explain the immense variability among plant species in defense against herbivores. A major concept in the evolutionary ecology of plant defenses is that tradeoffs of defense strategies are likely to generate and maintain species diversity. In particular, tradeoffs between constitutive and induced resistance and tradeoffs relating these strategies to growth and competitive ability have been predicted. We performed three independent experiments on 58 plant species from 15 different plant families to address these hypotheses in a phylogenetic framework. Because evolutionary tradeoffs may be altered by human-imposed artificial selection, we used 18 wild plant species and 40 cultivated garden-plant species. Across all 58 plant species, we demonstrate a tradeoff between constitutive and induced resistance, which was robust to accounting for phylogenetic history of the species. Moreover, the tradeoff was driven by wild species and was not evident for cultivated species. In addition, we demonstrate that more competitive species—but not fast growing ones—had lower constitutive but higher induced resistance. Thus, our multispecies experiments indicate that the competition–defense tradeoff holds for constitutive resistance and is complemented by a positive relationship of competitive ability with induced resistance. We conclude that the studied genetically determined tradeoffs are indeed likely to play an important role in shaping the high diversity observed among plant species in resistance against herbivores and in life history traits.

RNA interference screening identifies a novel role for autocrine fibroblast growth factor signaling in neuroblastoma chemoresistance

Chemotherapeutic drug resistance is one of the major causes for treatment failure in high-risk neuroblastoma (NB), the most common extra cranial solid tumor in children. Poor prognosis is typically associated with MYCN amplification. Here, we utilized a loss-of-function kinome-wide RNA interference screen to identify genes that cause cisplatin sensitization. We identified fibroblast growth factor receptor 2 (FGFR2) as an important determinant of cisplatin resistance. Pharmacological inhibition of FGFR2 confirmed the importance of this kinase in NB chemoresistance. Silencing of FGFR2 sensitized NB cells to cisplatin-induced apoptosis, which was regulated by the downregulation of the anti-apoptotic proteins BCL2 and BCLX(L). Mechanistically, FGFR2 was shown to activate protein kinase C-δ to induce BCL2 expression. FGFR2, as well as the ligand fibroblast growth factor-2, were consistently expressed in primary NB and NB cell lines, indicating the presence of an autocrine loop. Expression analysis revealed that FGFR2 correlates with MYCN amplification and with advanced stage disease, demonstrating the clinical relevance of FGFR2 in NB. These findings suggest a novel role for FGFR2 in chemoresistance and provide a rational to combine pharmacological inhibitors against FGFR2 with chemotherapeutic agents for the treatment of NB.Oncogene advance online publication, 1 October 2012; doi:10.1038/onc.2012.416.

An in vivo study of a growth-factor enhanced, cell free, two-layered collagen-tricalcium phosphate in deep osteochondral defects

Focal osteochondral defects are still a challenging problem in joint surgery. We have developed a two-layered implant consisting of a basal porous beta-tricalcium phosphate (TCP) for bone reconstruction and a superficial fibrous collagen type I/III layer for cartilage regeneration. Fifty-four osteochondral defects in the trochlear groove of 27 Göttinger Minipigs were created and either left untreated, treated with the implant alone, or the implant augmented with an additional growth factor mixture, which was assumed to stimulate cell and tissue differentiation. Follow-up was 6, 12 and 52 weeks with n=6 for each group. The repair tissue was evaluated for its gross appearance and biomechanical properties. Histological sections were semi-quantitatively scored for their histomorphological structure. Treatment with the two-layered implant improved defect filling and subchondral bone repair at 6 and 12 weeks follow-up. The TCP was replaced by cancellous bone at 52 weeks. Cartilage repair tissue mainly consisted of fibrocartilage and showed a moderate cell density up to the joint surface. Growth factor treatment improved the mechanical and histomorphological properties of the cartilage repair tissue at 12, but not at 52 weeks postoperatively. In conclusion, the two-layered collagen-TCP implant augmented with chondroinductive growth factors seems a promising new option for the treatment of deep osteochondral defects in joint surgery.

Mixture Cure Survival Models with Dependent Censoring

A number of authors have studies the mixture survival model to analyze survival data with nonnegligible cure fractions. A key assumption made by these authors is the independence between the survival time and the censoring time. To our knowledge, no one has studies the mixture cure model in the presence of dependent censoring. To account for such dependence, we propose a more general cure model which allows for dependent censoring. In particular, we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time using a class of Archimedean copula models. Within this framework, we consider the parameter estimation, the cure detection, and the two-sample comparison of latency distribution in the presence of dependent censoring when a proportion of patients is deemed cured. Large sample results using the martingale theory are obtained. We applied the proposed methodologies to the SEER prostate cancer data.

Establishment of murine cell lines by constitutive and conditional immortalization

Mouse cell lines were immortalized by introduction of specific immortalizing genes. Embryonic and adult animals and an embryonal stem cell line were used as a source of primary cells. The immortalizing genes were either introduced by DNA transfection or by ecotropic retrovirus transduction. Fibroblasts were obtained by expression of SV40 virus large T antigen (TAg). The properties of the resulting fibroblast cell lines were reproducible, independent of the donor mouse strains employed and the cells showed no transformed properties in vitro and did not form tumors in vivo. Endothelial cell lines were generated by Polyoma virus middle T antigen expression in primary embryonal cells. These cell lines consistently expressed relevant endothelial cell surface markers. Since the expression of the immortalizing genes was expected to strongly influence the cellular characteristics fibroblastoid cells were reversibly immortalized by using a vector that allows conditional expression of the TAg. Under inducing conditions, these cells exhibited properties that were highly similar to the properties of constitutively immortalized cells. In the absence of TAg expression, cell proliferation stops. Cell growth is resumed when TAg expression is restored. Gene expression profiling indicates that TAg influences the expression levels of more than 1000 genes that are involved in diverse cellular processes. The data show that conditionally immortalized cell lines have several advantageous properties over constitutively immortalized cells.

Compensatory growth in moose and its relationship to sex, longevity, intraspecific competition, and senescence

Individual life history theory is largely focused on understanding the extent to which various phenotypes of an organism are adaptive and whether they represent life history trade-offs. Compensatory growth (CG) is increasingly appreciated as a phenotype of interest to evolutionary ecologists. CG or catch-up growth involves the ability of an organism to grow at a faster-than-normal rate following periods of under-nutrition once conditions subsequently improve. Here, I examine CG in a population of moose (Alces alces) living on Isle Royale, a remote island in Lake Superior, North America. I gained insights about CG from measurements of skeletal remains of 841 moose born throughout a 52-year period. In particular, I compared the length of the metatarsal bone (ML) with several skull measurements. While ML is an index of growth while the moose is in utero and during the first year or two of life, a moose skull continues to grow until a moose is approximately 5 years of age. Because of these differences, the strength of correlation between ML and skull measurements, for a group of moose (say female moose) is an indication of that group’s capacity for CG. Using this logic, I conducted analyses whose results suggest that the capacity for CG did not differ between sexes, between individuals born during periods of high and low population densities, or between individuals exhibiting signs of senescence and those that do not. The analysis did however suggest that long-lived individuals had a greater capacity for CG than short-lived individuals. These results suggest that CG in moose is an adaptive trait and might not be associated with life history trade-offs.

COMBUSTION INITIATION BY ELECTRICAL-DISCHARGE-INDUCED PLASMA IN LEAN AND DILUTE METHANE-AIR MIXTURE: EXPERIMENTAL AND MODELING INVESTIGATION

This dissertation represents experimental and numerical investigations of combustion initiation trigged by electrical-discharge-induced plasma within lean and dilute methane air mixture. This research topic is of interest due to its potential to further promote the understanding and prediction of spark ignition quality in high efficiency gasoline engines, which operate with lean and dilute fuel-air mixture. It is specified in this dissertation that the plasma to flame transition is the key process during the spark ignition event, yet it is also the most complicated and least understood procedure. Therefore the investigation is focused on the overlapped periods when plasma and flame both exists in the system. Experimental study is divided into two parts. Experiments in Part I focuses on the flame kernel resulting from the electrical discharge. A number of external factors are found to affect the growth of the flame kernel, resulting in complex correlations between discharge and flame kernel. Heat loss from the flame kernel to code ambient is found to be a dominant factor that quenches the flame kernel. Another experimental focus is on the plasma channel. Electrical discharges into gases induce intense and highly transient plasma. Detailed observation of the size and contents of the discharge-induced plasma channel is performed. Given the complex correlation and the multi-discipline physical/chemical processes involved in the plasma-flame transition, the modeling principle is taken to reproduce detailed transitions numerically with minimum analytical assumptions. Detailed measurement obtained from experimental work facilitates the more accurate description of initial reaction conditions. The novel and unique spark source considering both energy and species deposition is defined in a justified manner, which is the key feature of this Ignition by Plasma (IBP) model. The results of numerical simulation are intuitive and the potential of numerical simulation to better resolve the complex spark ignition mechanism is presented. Meanwhile, imperfections of the IBP model and numerical simulation have been specified and will address future attentions.