Elementary properties of Modular curves and Modular forms

Lo scopo di questa tesi è introdurre in breve le prime proprietà delle curve modulari e delle forme modulari, per poi mostrarne alcune applicazioni archetipiche. Per farlo, dopo aver richiamato alcune nozioni utili nel primo capitolo, sviluppiamo, nel secondo capitolo, la teoria di base delle curve modulari compatte come superfici di Riemann, calcolandone il genere nel caso dei sottogruppi principali di congruenza. Dunque, nel terzo capitolo, dopo un estesa trattazione dell'esempio delle forme modulari rispetto al gruppo modulare, viene calcolata la dimensione degli spazi delle forme intere e delle forme cuspidali rispetto a un sottogruppo di indice finito del gruppo modulare. Questo capitolo si conclude con tre esempi di applicazione della teoria esposta, tra i quali spiccano la dimostrazione del Grande Teorema di Picard e del Teorema dei quattro quadrati di Jacobi.

Serology of paracoccidioidomycosis. II. Correlation between class-specific antibodies and clinical forms of the disease

Untreated and previously treated patients with paracoccidioidomycosis were studied for: (i) serum levels of total IgG, IgM and IgA immunoglobulins, by radial immunodiffusion and Paracoccidioides brasiliensis (Pb) antibodies, by indirect immunofluorescence; (ii) correlation between their levels with the clinical forms of the disease; (iii) correlation between the serum titres obtained by tube precipitin with those of anti-Pb IgG, IgM and IgA. In the untreated group, serum IgG levels were significantly increased in patients with the more systemic forms of the disease, especially the acute progressive form. Serum IgA levels were significantly increased in all patients with no statistical difference between clinical forms. Serum IgM levels were normal in all patients. Anti-Pb IgG, IgA and IgM were detected in 97·5%, 32·5% and 45·0% of all cases, respectively. There was a sharp tendency towards higher levels of anti-Pb IgG among those with the acute progressive form (83·4%) in relation to the chronic, more localized forms, mixed form (68·0%) and isolated organic form (55·5%). In the untreated and previously treated group sera, there was positive correlation between the level of anti-Pb IgG and positivity for the tube precipitin test, suggesting that the precipitin-type antibodies are of the IgG class. Broadly, the present data demonstrate a polyclonal activation of the humoral immune system in paracoccidioidomycosis, with a positive relationship between serological results and severity of the disease. © 1984.

A dictionary of modular threefolds

The thesis deals with the modularity conjecture for three-dimensional Calabi-Yau varieties. This is a generalization of the work of A. Wiles and others on modularity of elliptic curves. Modularity connects the number of points on varieties with coefficients of certain modular forms. In chapter 1 we collect the basics on arithmetic on Calabi-Yau manifolds, including general modularity results and strategies for modularity proofs. In chapters 2, 3, 4 and 5 we investigate examples of modular Calabi-Yau threefolds, including all examples occurring in the literature and many new ones. Double octics, i.e. Double coverings of projective 3-space branched along an octic surface, are studied in detail. In chapter 6 we deal with examples connected with the same modular forms. According to the Tate conjecture there should be correspondences between them. Many correspondences are constructed explicitly. We finish by formulating conjectures on the occurring newforms, especially their levels. In the appendices we compile tables of coefficients of weight 2 and weight 4 newforms and many examples of double octics.

Comparison of growth traits between abundant and uncommon forms of a non-native vine, Dolichandra unguis-cati (Bignoniaceae) in Australia

Cat’s claw creeper vine, Dolichandra unguis-cati (L.) Lohmann (syn. Macfadyena unguis-cati (L.) Gentry) (Bignoniaceae), is a major environmental weed in Australia. Two distinct forms of this weed (‘long’ and ‘short’ pod), with differences in leaf morphology and fruit size, occur in Australia. The long pod form has only been reported in less than fifteen localities in the whole of south-east Queensland, while the short pod form is widely distributed in Queensland and New South Wales. This study sought to compare growth traits such as specific leaf area, relative growth rate, stem length, shoot/root ratio, tuber biomass and branching architecture between these forms. These traits were monitored under glasshouse conditions over a period of 18 months. Short pod exhibited higher values of relative growth rates, stem length, number of tubers and specific leaf area than long pod, but only after 10 months of plant growth. Prior to this, long and short pod did not differ significantly. Higher values for these traits have been described as characteristics of successful colonizers. Results from this study could partly explain why the short pod form is more widely distributed in Australia while long pod is confined to a few localities.

Proteomic characterization of the multiple forms of the PLAs from the venom of the social wasp Polybia paulista

The phospholipases A(1) (PLA(1)s) from the venom of the social wasp Polybia paulista occur as a mixture of different molecular forms. To characterize the molecular origin of these structural differences, an experimental strategy was planned combining the isolation of the pool of PLAs from the wasp venom with proteomic approaches by using 2-D, MALDI-TOF-TOF MS and classical protocols of protein chemistry, which included N- and C-terminal sequencing. The existence of an intact form of PLA(1) and seven truncated forms was identified, apparently originating from controlled proteolysis of the intact protein; in addition to this, four of these truncated forms also presented carbohydrates attached to their molecules. Some of these forms are immunoreactive to specific-IgE, while others are not. These observations permit to raise the hypothesis that naturally occurring proteolysis of PLA(1), combined with protein glycosylation may create a series of different molecular forms of these proteins, with different levels of allergenicity. Two forms of PLA(2)s, apparently related to each other, were also identified; however, it was not possible to determine the molecular origin of the differences between both forms, except that one of them was glycosylated. None of these forms were immunoreactive to human specific IgE.

Close relationship between diameters at 30cm height and at breast height (DBH)

This paper proposes the establishment of a second diameter measuring standard at 30cm shoot extension ('diam30') as input variable for allometric biomass estimation of small and mid-sized plant shoots. This diameter standard is better suited than the diameter at breast height (DBH, i.e. diameter at 1.30m shoot extension) for adequate characterization of plant dimensions in low bushy vegetation or in primary forest undergrowth. The relationships between both diameter standards are established based on a dataset of 8645 tree, liana and palm shoots in secondary and primary forests of central Amazonia (ranging from 1-150mm dbh). Dbh can be predicted from the diam(30) with high precision, the error introduced by diameter transformation is only 2-3% for trees and palms, and 5% for lianas. This is well acceptable for most field study purposes. Relationships deviate slightly from linearity and differ between growth forms. Relationships were markedly similar for different vegetation types (low secondary regrowth vs. primary forests), soils, and selected genera or species. This points to a general validity and applicability of diameter transformations for other field studies. This study provides researchers with a tool for the allometric estimation of biomass in low or structurally heterogeneous vegetation. Rather than applying a uniform diameter standard, the measuring position which best represents the respective plant can be decided on shoot-by-shoot. Plant diameters measured at 30cm height can be transformed to dbh for subsequent allometric biomass estimation. We recommend the use of these diameter transformations only for plants extending well beyond the theoretical minimum shoot length (i.e., >2m height). This study also prepares the ground for the comparability and compatability of future allometric equations specifically developed for small- to mid-sized vegetation components (i.e., bushes, undergrowth) which are based on the diam(30) measuring standard.

Comparative clinical study of different multiplex real time PCR strategies for the simultaneous differential diagnosis between extrapulmonary tuberculosis and focal complications of brucellosis

Background: Both brucellosis and tuberculosis are chronic-debilitating systemic granulomatous diseases with a high incidence in many countries in Africa, Central and South America, the Middle East and the Indian subcontinent. Certain focal complications of brucellosis and extrapulmonary tuberculosis are very difficult to differentiate clinically, biologically and radiologically. As the conventional microbiological methods for the diagnosis of the two diseases have many limitations, as well as being time-consuming, multiplex real time PCR (M RT-PCR) could be a promising and practical approach to hasten the differential diagnosis and improve prognosis. Methodology/Principal Findings: We designed a SYBR Green single-tube multiplex real-time PCR protocol targeting bcsp31 and the IS711 sequence detecting all pathogenic species and biovars of Brucella genus, the IS6110 sequence detecting Mycobacterium genus, and the intergenic region senX3-regX3 specifically detecting Mycobacterium tuberculosis complex. The diagnostic yield of the M RT-PCR with the three pairs of resultant amplicons was then analyzed in 91 clinical samples corresponding to 30 patients with focal complications of brucellosis, 24 patients with extrapulmonary tuberculosis, and 36 patients (Control Group) with different infectious, autoimmune or neoplastic diseases. Thirty-five patients had vertebral osteomyelitis, 21 subacute or chronic meningitis or meningoencephalitis, 13 liver or splenic abscess, eight orchiepididymitis, seven subacute or chronic arthritis, and the remaining seven samples were from different locations. Of the three pairs of amplicons (senX3-regX3+ bcsp3, senX3-regX3+ IS711 and IS6110+ IS711) only senX3-regX3+ IS711 was 100% specific for both the Brucella genus and M. tuberculosis complex. For all the clinical samples studied, the overall sensitivity, specificity, and positive and negative predictive values of the M RT-PCR assay were 89.1%, 100%, 85.7% and 100%, respectively, with an accuracy of 93.4%, (95% CI, 88.3—96.5%). Conclusions/Significance: In this study, a M RT-PCR strategy with species-specific primers based on senX3-regX3+IS711 sequences proved to be a sensitive and specific test, useful for the highly efficient detection of M. tuberculosis and Brucella spp in very different clinical samples. It thus represents an advance in the differential diagnosis between some forms of extrapulmonary tuberculosis and focal complications of brucellosis.

Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Relationship between deadbeat and pole-placement discrete-time PID controllers

This paper considers PID control in terms of its implementation by means of an ARMA plant model. Two controller actions are considered, namely pole placement and deadbeat, both being applied via a PID structure for the adaptive real-time control of an industrial level system. As well as looking at two controller types separately, a comparison is made between the forms and it is shown how, under certain circumstances, the two forms can be seen to be identical. It is shown how the pole-placement PID form does not in fact realise an action which is equivalent to the deadbeat controller, when all closed-loop poles are chosen to be at the origin of the z-plane.

Proteomic characterization of the multiple forms of the PLAs from the venom of the social wasp Polybia paulista

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

Reticulados modulares em espaços euclidianos

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

Integrative Musterbildung kranialer Strukturen

Form und Gestalt kraniofazialer Strukturen sind primär beeinflusst durch die inhärente Integration der unterschiedlichsten Funktionssysteme und externer selektiver Einflüsse. Die Variabilität der Schädel-Morphe ist ein Indikator für solche Einflussfaktoren und damit ein idealer Gegenstand für vergleichende Analysen morphogenetischer Formbildung. Zur Ermittlung morphologisch-adaptiver Trends und Muster wurden sowohl Hypothesen zur morphologischen Differenziertheit als auch zu Korrelationen zwischen modularen Schädelkompartimenten (fazial, neurokranial, basikranial) untersucht. Zusätzlich wurden aus Schichtröntgenaufnahmen (CT) virtuelle Modelle rekonstruiert, welche die Interpretation der statistischen Befunde unterstützen sollten. Zur Berechnung der Gestaltunterschiede wurden mittels eines mechanischen Gelenkarm-Messgerätes (MicroScribe-G2) max. 85 ektokraniale Messpunkte (Landmarks) bzw. dreidimensionale Koordinaten an ca. 520 Schädeln von fünf rezenten Gattungen der Überfamilie Hominoidea (Hylobates, Pongo, Gorilla, Pan und Homo) akquiriert. Aus dem Datensatz wurden geometrische Störfaktoren (Größe, Translation, Rotation) mathematisch eliminiert und die verbleibenden Residuale bzw. ‚Gestalt-Variablen‘ diversen multivariat-statistischen Verfahren unterzogen (Faktoren, Cluster-, Regressions- und Korrelationsanalysen sowie statistische Tests). Die angewandten Methoden erhalten die geometrische Information der Untersuchungsobjekte über alle Analyseschritte hinweg und werden unter der Bezeichnung „Geometric Morphometrics (GMM)“ als aktueller Ansatz der Morphometrie zusammengefasst. Für die unterschiedlichen Fragestellungen wurden spezifische Datensätze generiert. Es konnten diverse morphologische Trends und adaptive Muster mit Hilfe der Synthese statistischer Methoden und computer-basierter Rekonstruktionen aus den generierten Datensätzen ermittelt werden. Außerdem war es möglich, präzise zu rekonstruieren, welche kranialen Strukturen innerhalb der Stichprobe miteinander wechselwirken, einzigartige Variabilitäten repräsentieren oder eher homogen gestaltet sind. Die vorliegenden Befunde lassen erkennen, dass Fazial- und Neurokranium am stärksten miteinander korrelieren, während das Basikranium geringe Abhängigkeiten in Bezug auf Gesichts- oder Hirnschädelveränderungen zeigte. Das Basikranium erweist sich zudem bei den nicht-menschlichen Hominoidea und über alle Analysen hinweg als konservative und evolutiv-persistente Struktur mit dem geringsten Veränderungs-Potential. Juvenile Individuen zeigen eine hohe Affinität zueinander und zu Formen mit einem kleinem Gesichts- und großem Hirnschädel. Während das Kranium des rezenten Menschen primär von Enkephalisation und fazialer Retraktion (Orthognathisierung) dominiert ist und somit eine einzigartige Gestalt aufweist, zeigt sich der Kauapparat als maßgeblich formbildendes Kompartiment bei den nicht-menschlichen Formen. Die Verbindung von GMM mit den interaktiven Möglichkeiten computergenerierter Modelle erwies sich als valides Werkzeug zur Erfassung der aufgeworfenen Fragestellungen. Die Interpretation der Befunde ist durch massive Interkorrelationen der untersuchten Strukturen und der statistisch-mathematischen Prozeduren als hoch komplex zu kennzeichnen. Die Studie präsentiert einen innovativen Ansatz der modernen Morphometrie, welcher für zukünftige Untersuchungen im Bereich der kraniofazialen Gestaltanalyse ausgebaut werden könnte. Dabei verspricht die Verknüpfung mit ‚klassischen’ und modernen Zugängen (z. B. Molekularbiologie) gesteigerte Erkenntnismöglichkeiten für künftige morphometrische Fragestellungen.

Adjoint modular Galois representations and their Selmer groups

In the last 15 years, many class number formulas and main conjectures have been proven. Here, we discuss such formulas on the Selmer groups of the three-dimensional adjoint representation ad(φ) of a two-dimensional modular Galois representation φ. We start with the p-adic Galois representation φ0 of a modular elliptic curve E and present a formula expressing in terms of L(1, ad(φ0)) the intersection number of the elliptic curve E and the complementary abelian variety inside the Jacobian of the modular curve. Then we explain how one can deduce a formula for the order of the Selmer group Sel(ad(φ0)) from the proof of Wiles of the Shimura–Taniyama conjecture. After that, we generalize the formula in an Iwasawa theoretic setting of one and two variables. Here the first variable, T, is the weight variable of the universal p-ordinary Hecke algebra, and the second variable is the cyclotomic variable S. In the one-variable case, we let φ denote the p-ordinary Galois representation with values in GL2(Zp[[T]]) lifting φ0, and the characteristic power series of the Selmer group Sel(ad(φ)) is given by a p-adic L-function interpolating L(1, ad(φk)) for weight k + 2 specialization φk of φ. In the two-variable case, we state a main conjecture on the characteristic power series in Zp[[T, S]] of Sel(ad(φ) ⊗ ν−1), where ν is the universal cyclotomic character with values in Zp[[S]]. Finally, we describe our recent results toward the proof of the conjecture and a possible strategy of proving the main conjecture using p-adic Siegel modular forms.

Computational aspects of modular parametrizations of elliptic curves

Thesis (Ph.D.)--University of Washington, 2016-06