Monodromy calculations for some differential equations

In vielen Teilgebieten der Mathematik ist es w"{u}nschenswert, die Monodromiegruppe einer homogenen linearen Differenzialgleichung zu verstehen. Es sind nur wenige analytische Methoden zur Berechnung dieser Gruppe bekannt, daher entwickeln wir im ersten Teil dieser Arbeit eine numerische Methode zur Approximation ihrer Erzeuger.rnIm zweiten Abschnitt fassen wir die Grundlagen der Theorie der Uniformisierung Riemannscher Fl"achen und die der arithmetischen Fuchsschen Gruppen zusammen. Auss erdem erkl"aren wir, wie unsere numerische Methode bei der Bestimmung von uniformisierenden Differenzialgleichungen dienlich sein kann. F"ur arithmetische Fuchssche Gruppen mit zwei Erzeugern erhalten wir lokale Daten und freie Parameter von Lam'{e} Gleichungen, welche die zugeh"origen Riemannschen Fl"achen uniformisieren. rnIm dritten Teil geben wir einen kurzen Abriss zur homologischen Spiegelsymmetrie und f"uhren die $widehat{Gamma}$-Klasse ein. Wir erkl"aren wie diese genutzt werden kann, um eine Hodge-theoretische Version der Spiegelsymmetrie f"ur torische Varit"aten zu beweisen. Daraus gewinnen wir Vermutungen "uber die Monodromiegruppe $M$ von Picard-Fuchs Gleichungen von gewissen Familien $f:mathcal{X}rightarrow bbp^1$ von $n$-dimensionalen Calabi-Yau Variet"aten. Diese besagen erstens, dass bez"uglich einer nat"urlichen Basis die Monodromiematrizen in $M$ Eintr"age aus dem K"orper $bbq(zeta(2j+1)/(2 pi i)^{2j+1},j=1,ldots,lfloor (n-1)/2 rfloor)$ haben. Und zweitens, dass sich topologische Invarianten des Spiegelpartners einer generischen Faser von $f:mathcal{X}rightarrow bbp^1$ aus einem speziellen Element von $M$ rekonstruieren lassen. Schliess lich benutzen wir die im ersten Teil entwickelten Methoden zur Verifizierung dieser Vermutungen, vornehmlich in Hinblick auf Dimension drei. Dar"uber hinaus erstellen wir eine Liste von Kandidaten topologischer Invarianten von vermutlich existierenden dreidimensionalen Calabi-Yau Variet"aten mit $h^{1,1}=1$.

Measurement of ttbar production differential cross section at \sqrt{s}=8 TeV at ATLAS

Top quark studies play an important role in the physics program of the Large Hadron Collider (LHC). The energy and luminosity reached allow the acquisition of a large amount of data especially in kinematic regions never studied before. In this thesis is presented the measurement of the ttbar production differential cross section on data collected by ATLAS in 2012 in proton proton collisions at \sqrt{s} = 8 TeV, corresponding to an integrated luminosity of 20.3 fb^{−1}. The measurement is performed for ttbar events in the semileptonic channel where the hadronically decaying top quark has a transverse momentum above 300 GeV. The hadronic top quark decay is reconstructed as a single large radius jet and identified using jet substructure properties. The final differential cross section result has been compared with several theoretical distributions obtaining a discrepancy of about the 25% between data and predictions, depending on the MC generator. Furthermore the kinematic distributions of the ttbar production process are very sensitive to the choice of the parton distribution function (PDF) set used in the simulations and could provide constraints on gluons PDF. In particular in this thesis is performed a systematic study on the PDF of the protons, varying several PDF sets and checking which one better describes the experimental distributions. The boosted techniques applied in this measurement will be fundamental in the next data taking at \sqrt{s}=13 TeV when will be produced a large amount of heavy particles with high momentum.

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.

Differential inhibition sensitivities of MET mutants to the small molecule inhibitor SU11274

Point mutations emerge as one of the rate-limiting steps in tumor response to small molecule inhibitors of protein kinases. Here we characterized the response of the MET mutated variants, V1110I, V1238I, V1206L and H1112L to the small molecule SU11274. Our results reveal a distinct inhibition pattern of the four mutations with IC(50) values for autophosphorylation inhibition ranging between 0.15 and 1.5muM. Differences were further seen on the ability of SU11274 to inhibit phosphorylation of downstream MET transducers such as AKT, ERK, PLCgamma and STAT3 and a variety of MET-dependent biological endpoints. In all the assays, H1112L was the most sensitive to SU11274, while V1206L was less affected under the used concentration range. The differences in responses to SU11274 are discussed based on a structural model of the MET kinase domain.

Differential cell cycle and proliferation marker expression in ductal pancreatic adenocarcinoma and pancreatic intraepithelial neoplasia (PanIN)

Pancreatic cancer is an aggressive tumour following a multistep progression model through precursors called pancreatic intraepithelial neoplasia (PanIN). Identification of reliable prognostic markers would help in improving survival. The aim of this study was to investigate the role as well as the prognostic significance of different cell cycle and proliferation markers, namely p21, p27, p53 and Ki-67, in pancreatic carcinogenesis.

Oropharyngeal lesions and cervical lymphadenopathy: syphilis is a differential diagnosis that is still relevant

Syphilis (lues), a chronic infectious disease caused by Treponema pallidum, has been increasing in incidence during the last few years. Therefore, while clinically it is often not suspected, syphilis is increasingly becoming a differential diagnosis in routine pathology.

Differential activation of the lateral premotor cortex during action observation

Background Action observation leads to neural activation of the human premotor cortex. This study examined how the level of motor expertise (expert vs. novice) in ballroom dancing and the visual viewpoint (internal vs. external viewpoint) influence this activation within different parts of this area of the brain. Results Sixteen dance experts and 16 novices observed ballroom dance videos from internal or external viewpoints while lying in a functional magnetic resonance imaging scanner. A conjunction analysis of all observation conditions showed that action observation activated distinct networks of premotor, parietal, and cerebellar structures. Experts revealed increased activation in the ventral premotor cortex compared to novices. An internal viewpoint led to higher activation of the dorsal premotor cortex. Conclusions The present results suggest that the ventral and dorsal premotor cortex adopt differential roles during action observation depending on the level of motor expertise and the viewpoint.

In vivo nuclear translocation of mineralocorticoid and glucocorticoid receptors in rat kidney: differential effect of corticosteroids along the distal tubule

Aldosterone and corticosterone bind to mineralocorticoid (MR) and glucocorticoid receptors (GR), which, upon ligand binding, are thought to translocate to the cell nucleus to act as transcription factors. Mineralocorticoid selectivity is achieved by the 11β-hydroxysteroid dehydrogenase type 2 (11β-HSD2) that inactivates 11β-hydroxy glucocorticoids. High expression levels of 11β-HSD2 characterize the aldosterone-sensitive distal nephron (ASDN), which comprises the segment-specific cells of late distal convoluted tubule (DCT2), connecting tubule (CNT), and collecting duct (CD). We used MR- and GR-specific antibodies to study localization and regulation of MR and GR in kidneys of rats with altered plasma aldosterone and corticosterone levels. In control rats, MR and GR were found in cell nuclei of thick ascending limb (TAL), DCT, CNT, CD cells, and intercalated cells (IC). GR was also abundant in cell nuclei and the subapical compartment of proximal tubule (PT) cells. Dietary NaCl loading, which lowers plasma aldosterone, caused a selective removal of GR from cell nuclei of 11β-HSD2-positive ASDN. The nuclear localization of MR was unaffected. Adrenalectomy (ADX) resulted in removal of MR and GR from the cell nuclei of all epithelial cells. Aldosterone replacement rapidly relocated the receptors in the cell nuclei. In ASDN cells, low-dose corticosterone replacement caused nuclear localization of MR, but not of GR. The GR was redistributed to the nucleus only in PT, TAL, early DCT, and IC that express no or very little 11β-HSD2. In ASDN cells, nuclear GR localization was only achieved when corticosterone was replaced at high doses. Thus ligand-induced nuclear translocation of MR and GR are part of MR and GR regulation in the kidney and show remarkable segment- and cell type-specific characteristics. Differential regulation of MR and GR may alter the level of heterodimerization of the receptors and hence may contribute to the complexity of corticosteroid effects on ASDN function.

Differential roles for endothelial ICAM-1, ICAM-2, and VCAM-1 in shear-resistant T cell arrest, polarization, and directed crawling on blood-brain barrier endothelium

Endothelial ICAM-1 and ICAM-2 were shown to be essential for T cell diapedesis across the blood-brain barrier (BBB) in vitro under static conditions. Crawling of T cells prior to diapedesis was only recently revealed to occur preferentially against the direction of blood flow on the endothelial surface of inflamed brain microvessels in vivo. Using live cell-imaging techniques, we prove that Th1 memory/effector T cells predominantly crawl against the direction of flow on the surface of BBB endothelium in vitro. Analysis of T cell interaction with wild-type, ICAM-1-deficient, ICAM-2-deficient, or ICAM-1 and ICAM-2 double-deficient primary mouse brain microvascular endothelial cells under physiological flow conditions allowed us to dissect the individual contributions of endothelial ICAM-1, ICAM-2, and VCAM-1 to shear-resistant T cell arrest, polarization, and crawling. Although T cell arrest was mediated by endothelial ICAM-1 and VCAM-1, T cell polarization and crawling were mediated by endothelial ICAM-1 and ICAM-2 but not by endothelial VCAM-1. Therefore, our data delineate a sequential involvement of endothelial ICAM-1 and VCAM-1 in mediating shear-resistant T cell arrest, followed by endothelial ICAM-1 and ICAM-2 in mediating T cell crawling to sites permissive for diapedesis across BBB endothelium.

Differential expression of the bone and the liver tissue non-specific alkaline phosphatase isoforms in brain tissues

The enzyme tissue non-specific alkaline phosphatase (TNAP) belongs to the ectophosphatase family. It is present in large amounts in bone in which it plays a role in mineralization but little is known about its function in other tissues. Arguments are accumulating for its involvement in the brain, in particular in view of the neurological symptoms accompanying human TNAP deficiencies. We have previously shown, by histochemistry, alkaline phosphatase (AP) activity in monkey brain vessels and parenchyma in which AP exhibits specific patterns. Here, we clearly attribute this activity to TNAP expression rather than to other APs in primates (human and marmoset) and in rodents (rat and mouse). We have not found any brain-specific transcripts but our data demonstrate that neuronal and endothelial cells exclusively express the bone TNAP transcript in all species tested, except in mouse neurons in which liver TNAP transcripts have also been detected. Moreover, we highlight the developmental regulation of TNAP expression; this also acts during neuronal differentiation. Our study should help to characterize the regulation of the expression of this ectophosphatase in various cell types of the central nervous system.

Differential response of Human Bone Marrow Stromal Cells to either TGF-β1 or to rhGDF-5

Cell therapy along with growth factor injection is currently widely investigated to restore the intervertebral disc. However, there is increasing evidence that transplanted unconditioned bone marrow-derived stromal cells (BMSCs) cannot thrive in the intervertebral disc "niche". Moreover, uncertainty exists with respect to the cell phenotype that would be suitable to inject. The intervertebral disc cell phenotype only recently has been started to be characterised using transcriptomics profiling. Recent findings suggest that cytokeratin 19 (KRT-19) could be used as a potential candidate marker for the intervertebral disc, or more specifically the nucleus pulposus cell (NPC) phenotype. We present in vitro cell culture data using alginate bead culture of primary human BMSCs exposed to the standard chondrogenic stimulus, transforming growth factor beta-1 (TGF-β), the growth and differentiation factor 5 and/or bovine NPCs to induce a potential "discogenic" pathway. Chondrogenic induction via TGF-β pathway provoked down-regulation of KRT-19 gene expression in four out of five donors after 18 days of culture, whereas KRT-19 expression remained unchanged in the "discogenic" groups. In addition, the ratio of aggrecan/collagen II gene expression showed a remarkable difference (of at least 3 magnitudes) between the chondrogenic stimulus (low ratio) and the discogenic stimulus (high ratio). Therefore, KRT-19 and aggrecan/collagen II ratio may be potential markers to distinguish chondrogenic from "discogenic" differentiation.

Impact of differential P450c17 phosphorylation by cAMP stimulation and by starvation conditions on enzyme activities and androgen production in NCI-H295R cells

CYP17A1 plays a pivotal role in the biosynthesis of androgens in the adrenals and the gonads. Although this enzyme catalyzes two different reactions on one single active site, its specific activities are regulated independently. Although the 17alpha-hydroxylase activity is rather constant and regulated by gene expression, the 17,20-lyase activity varies significantly with the amount of cofactors or by protein phosphorylation. cAMP increases CYP17A1 expression, P450c17 phosphorylation, and androgen production. However, the exact mechanism(s) and the specific regulators of CYP17A1 remain unknown. Therefore, we studied the regulation of adrenal androgen biosynthesis in human adrenal H295R cells focusing on CYP17A1. We analyzed androgen production and P450c17 activities in H295R cells grown under normal and serum-free conditions and/or after stimulation with 8-bromoadenosine-cAMP. H295R cells grown in starvation medium produced more androgens and had decreased HSD3B2 expression and activity but increased P450c17-17,20-lyase activity and serine phosphorylation. Although starvation increased serine phosphorylation of P450c17 specifically, cAMP stimulation enhanced threonine phosphorylation exclusively. Time-course experiments revealed that a short cAMP stimulation augmented threonine phosphorylation of P450c17 but did not increase 17,20-lyase activity. By contrast, long cAMP stimulation increased androgen production through increased P450c17 activities by enhancing CYP17A1 gene expression. We conclude that serum withdrawal shifts steroidogenesis of H295R cells towards androgen production, providing a suitable model for detailed studies of androgen regulation. In addition, our study shows that starvation and cAMP stimulation regulate P450c17 phosphorylation differentially and that an increase in P450c17 phosphorylation does not necessarily lead to enhanced enzyme activity and androgen production.