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 $B(G)$.

Evolutionary tendencies in flowers of Marantaceae with special reference to the style movement mechanism

One of the quickest plant movements ever known is made by the ´explosive´ style in Marantaceae in the service of secondary pollen presentation – herewith showing a striking apomorphy to the sister Cannaceae that might be of high evolutionary consequence. Though known already since the beginning of the 19th century the underlying mechanism of the movement has hitherto not been clarified. The present study reports about the biomechanics of the style-staminode complex and the hydraulic principles of the movement. For the first time it is shown by experiment that in Maranta noctiflora through longitudinal growth of the maturing style in the ´straitjacket´ of the hooded staminode both the hold of the style prior to its release and its tensioning for the movement are brought about. The longer the style grows in relation to the enclosing hooded staminode the more does its capacity for curling up for pollen transfer increase. Hereby I distinguish between the ´basic tension´ that a growing style builds up anyway, even when the hooded staminode is removed beforehand, and the ´induced tension´ which comes about only under the pressure of a ´too short´ hooded staminode and which enables the movement. The results of these investigations are discussed in view of previous interpretations ranging from possible biomechanical to electrophysiological mechanisms. To understand furthermore by which means the style gives way to the strong bending movement without suffering outwardly visible damage I examined its anatomical structure in several genera for its mechanical and hydraulic properties and for the determination of the entire curvature after release. The actual bending part contains tubulate cells whose walls are extraordinarily porous and large longitudinal intercellular spaces. SEM indicates the starting points of cell-wall loosening in primary walls and lysis of middle lamellae - probably through an intense pectinase activity in the maturing style. Fluorescence pictures of macerated and living style-tissue confirm cell-wall perforations that do apparently connect neighbouring cells, which leads to an extremely permeable parenchyma. The ´water-body´ can be shifted from central to dorsal cell layers to support the bending. The geometrical form of the curvature is determined by the vascular bundles. I conclude that the style in Marantaceae contains no ´antagonistic´ motile tissues as in Mimosa or Dionaea. Instead, through self-maceration it develops to a ´hydraulic tissue´ which carries out an irreversible movement through a sudden reshaping. To ascertain the evolutionary consequence of this apomorphic pollination mechanism the diversity and systematic value of hooded staminodes are examined. For this hooded staminodes of 24 genera are sorted according to a minimalistic selection of shape characters and eight morphological types are abstracted from the resulting groups. These types are mapped onto an already available maximally parsimonious tree comprising five major clades. An amazing correspondence is found between the morphological types and the clades; several sister-relationships are confirmed and in cases of uncertain position possible evolutionary pathways, such as convergence, dispersal or re-migration, are discussed, as well as the great evolutionary tendencies for the entire family in which – at least as regards the shape of hooded staminodes – there is obviously a tendency from complicated to strongly simplified forms. It suggests itself that such simplifying derivations may very likely have taken place as adaptations to pollinating animals about which at present too little is known. The value of morphological characters in relation to modern phylogenetic analysis is discussed and conditions for the selection of morphological characters valuable for a systematic grouping are proposed. Altogether, in view of the evolutionary success of Marantaceae compared with Cannaceae the movement mechanism of the style-staminode complex can safely be considered a key innovation within the order Zingiberales.

Evolutionary tendencies in African Marantaceae

Die Marantaceae (550 Arten) sind eine weltweit verbreitete Familie von Stauden und Lianen aus dem Unterwuchs tropischer Tieflandregenwälder. Der morphologisch-ökologische Vergleich des basal abzweigenden Sarcophrynium-Astes mit dem in abgeleiteter Position stehenden Marantochloa-Ast, soll beispielhaft evolutionäre Muster in der Familie beleuchten. So wird in der Doktorarbeit zum ersten Mal ein Überblick über die Blütenbiologie und Phylogenie von rund 30 der 40 afrikanischen Marantaceae Arten präsentiert. Die Analysen basieren auf Daten von drei mehrmonatigen Feldaufenthalten in Gabun jeweils zwischen September und Januar. Vier Blütentypen werden beschrieben, die jeweils mit einer spezifischen Bestäubergilde verbunden sind (kleine, mittlere, große Bienen bzw. Vögel). Bestäubungsexperimente belegen, dass 18 Arten selbstkompatibel, aber nur zwei Arten autogam sind, also keine Bestäubungsvermittler benötigen. Der Fruchtansatz ist generell gering (10 -30 %). Die komplexe Synorganisation der Blüte ermöglicht in den Marantaceae einen explosiven Bestäubungsmechanismus. Um dessen ökologische Funktionalität zu verstehen, werden die Blüten von 66 Arten, alle wichtigen Äste der Marantaceae abdeckend, unter einem morphologisch-funktionalen Gesichtspunkt untersucht. Es gibt große Übereinstimmungen zwischen allen untersuchten Arten im Zusammenspiel (Synorganisation) der wichtigsten Bauelemente (Griffel, Kapuzenblatt, Schwielenblatt), die eine präzise Pollenübertragung ermöglichen. Basierend auf Daten von nrDNA (ITS, 5S) und cpDNA (trnL-F) wird für ein nahezu komplettes Artenspektrum die Phylogenie der zwei afrikanischen Äste erstellt. Hierauf werden morphologische und ökologische Merkmale sowie geographischer Verbreitungsmuster nach dem Parsimonieprinzip rekonstruiert, um so deren evolutionäre Bedeutung für die Marantaceae abschätzen zu können. Die Ergebnisse weisen auf die Beteiligung einer Vielzahl verschiedener Artbildungsfaktoren hin.

Survival of the fittest: Herausforderungen an den Fremdenverkehr im Zeichen des global change

Der Globale Wandel ist im Begriff, den Tourismus zu verändern. Die Wechselwirkung von Tourismus und Klimawandel sind beidseitiger Art. Die vorliegende Arbeit zeigt Möglichkeiten der Adaption und einen wandelbaren Fremdenverkehr. Eine Übersicht der gängigen Tourismusmodelle stellt den Stand der Forschung dar. Der Fremdenverkehr ist durch drei Faktoren massiv geprägt: Die Nachfrage und Motivation, die Reisemittler und Veranstalter sowie das Destinationsangebot. Bei der Motivation wirken Motiv und Anreiz Motivationspsychologisch betrachtet auf die Reiseentscheidung deren Grundlage verarbeitete Informationen sind. Reisemittler und Veranstalter haben einen großen Einfluss auf Entscheidungsprozesse. Neue IuK Technologien haben deren Arbeit grundlegend verändert. Das Tourismusangebot wird stark durch die naturräumlichen Gegebenheiten sowie das politische System bestimmt. Überlebenswichtig für die Destination ist die evolutionstheoretisch etrachtete Fitnessmaximierung also Adaption und Wandel, um sich an geänderte Rahmenbedingungen anpassen zu können. Gerade im Bereich des Klimawandels müssen Maßnahmen ergriffen werden. Aber auch die Marktsättigung gerade in Verbindung mit der aktuellen Finanzkrise wirkt besonders schwer auf die Destination. Eine hohes Innovationsvermögen, Trendscanning und der Zusammenschluss in flexiblen Netzwerkclustern können einen Kundenmehrwert erzeugen. Die Fitnessmaximierung ist somit Überlebensziel der Destination und führt zur Kundenzufriedenheit die im Sättigungsmarkt alleinig Wachstum generieren kann.

Aspects of poriferan (Suberites domuncula) apoptosis and innate immune system and evolutionary implications

Survivin, a unique member of the family of inhibitors of apoptosis (IAP) proteins, orchestrates intracellular pathways during cell division and apoptosis. Its central regulatory function in vertebrate molecular pathways as mitotic regulator and inhibitor of apoptotic cell death has major implications for tumor cell proliferation and viability, and has inspired several approaches that target survivin for cancer therapy. Analyses in early-branching Metazoa so far propose an exclusive role of survivin as a chromosomal passenger protein, whereas only later during evolution the second, complementary antiapoptotic function might have arisen, concurrent with increased organismal complexity. To lift the veil on the ancestral function(s) of this key regulatory molecule, a survivin homologue of the phylogenetically oldest extant metazoan taxon (phylum Porifera) was identified and functionally characterized. SURVL of the demosponge Suberites domuncula shares significant similarities with its metazoan homologues, ranging from conserved exon/intron structures to the presence of localization signal and protein-interaction domains, characteristic of IAP proteins. Whereas sponge tissue displayed a very low steady-state level, SURVL expression was significantly up-regulated in rapidly proliferating primmorph cells. In addition, challenge of sponge tissue and primmorphs with cadmium and the lipopeptide Pam3Cys-Ser-(Lys)4 stimulated SURVL expression, concurrent with the expression of newly discovered poriferan caspases (CASL and CASL2). Complementary functional analyses in transfected HEK-293 revealed that heterologous expression of poriferan survivin in human cells not only promotes cell proliferation but also augments resistance to cadmium-induced cell death. Taken together, these results demonstrate both a deep evolutionary conserved and fundamental dual role of survivin, and an equally conserved central position of this key regulatory molecule in interconnected pathways of cell cycle and apoptosis. Additionally, SDCASL, SDCASL2, and SDTILRc (TIR-LRR containing protein) may represent new components of the innate defense sentinel in sponges. SDCASL and SDCASL2 are two new caspase-homolog proteins with a singular structure. In addition to their CASc domains, SDCASL and SDCASL2 feature a small prodomain NH2-terminal (effector caspases) and a remarkably long COOH-terminal domain containing one or several functional double stranded RNA binding domains (dsrm). This new caspase prototype can characterize a caspase specialization coupling pathogen sensing and apoptosis, and could represent a very efficient defense mechanism. SDTILRc encompasses also a unique combination of domains: several leucine rich repeats (LRR) and a Toll/IL-1 receptor (TIR) domain. This unusual domain association may correspond to a new family of intracellular sensing protein, forming a subclass of pattern recognition receptors (PRR).

Evolutionary genetics of lactase persistence in Eurasian human populations

Although ability to digest lactose generally declines after weaning in all mammals, in some human populations it persists also in adult individuals, a condition named lactase persistence (LP). Studies on the prevalence of the LP phenotype in worldwide human populations have shown that the frequency of this trait is highly variable in different ethnic groups, appearing to be positively correlated with the importance of milk in the diet. In particular, several single-nucleotide polymorphisms (SNPs) in the proximity of the LCT gene have been proved to be associated with LP. Nevertheless, few studies have till now analyzed genetic variation underlying LP in a wide set of Eurasian populations and, especially, in the Italian one. In the present study, we thus typed 40 SNPs surrounding the LCT gene in more than 1,000 samples from Italian and Arabic peninsulas to investigate patterns of LP-related genetic diversity in two regions which have played a pivotal role in the recent human evolutionary history according to their geographical position and historical/archaeological records. Our results underline a high and complex variability of the explored genomic region in both studied populations. In particular, a clear diversification of Northern Italian groups from the rest of the peninsula, was observed, with the formers being genetically more similar to Northern European populations than to Southern Italians. These observation are consistent with known decreasing pattern of LP from Northern to Southern Italy and suggest the possibility of an independent evolution of LP-associated genotypes in Northern Italy. A similar scenario was observed in the Arabian peninsula, with Dhofari Arabs from Southern Oman and Yemeni clustering together with respect to Arabs from Northern Oman and the subgroup of Omanis of Asian origin which appeared instead to be genetically closer to Europeans than to the rest of Arabic groups.

On differential operators of Calabi-Yau type

This thesis is devoted to the study of Picard-Fuchs operators associated to one-parameter families of $n$-dimensional Calabi-Yau manifolds whose solutions are integrals of $(n,0)$-forms over locally constant $n$-cycles. Assuming additional conditions on these families, we describe algebraic properties of these operators which leads to the purely algebraic notion of operators of CY-type. rnMoreover, we present an explicit way to construct CY-type operators which have a linearly rigid monodromy tuple. Therefore, we first usernthe translation of the existence algorithm by N. Katz for rigid local systems to the level of tuples of matrices which was established by M. Dettweiler and S. Reiter. An appropriate translation to the level of differential operators yields families which contain operators of CY-type. rnConsidering additional operations, we are also able to construct special CY-type operators of degree four which have a non-linearly rigid monodromy tuple. This provides both previously known and new examples.

Evolutionary epigenetics of modern human populations

Epigenetic variability is a new mechanism for the study of human microevolution, because it creates both phenotypic diversity within an individual and within population. This mechanism constitutes an important reservoir for adaptation in response to new stimuli and recent studies have demonstrated that selective pressures shape not only the genetic code but also DNA methylation profiles. The aim of this thesis is the study of the role of DNA methylation changes in human adaptive processes, considering the Italian peninsula and macro-geographical areas. A whole-genome analysis of DNA methylation profile across the Italian penisula identified some genes whose methylation levels differ between individuals of different Italian districts (South, Centre and North of Italy). These genes are involved in nitrogen compound metabolism and genes involved in pathogens response. Considering individuals with different macro-geographical origins (individuals of Asians, European and African ancestry) more significant DMRs (differentially methylated regions) were identified and are located in genes involved in glucoronidation, in immune response as well as in cell comunication processes. A "profile" of each ancestry (African, Asian and European) was described. Moreover a deepen analysis of three candidate genes (KRTCAP3, MAD1L and BRSK2) in a cohort of individuals of different countries (Morocco, Nigeria, China and Philippines) living in Bologna, was performed in order to explore genetic and epigenetic diversity. Moreover this thesis have paved the way for the application of DNA methylation for the study of hystorical remains and in particular for the age-estimation of individuals starting from biological samples (such as teeth or blood). Noteworthy, a mathematical model that considered methylation values of DNA extracted from cementum and pulp of living individuals can estimate chronological age with high accuracy (median absolute difference between age estimated from DNA methylation and chronological age was 1.2 years).

Extracting evolutionary information from the spectral decomposition of early-type galaxies.

Holding the major share of stellar mass in galaxies and being also old and passively evolving, early-type galaxies (ETGs) are the primary probes in investigating these various evolution scenarios, as well as being useful means to provide insights on cosmological parameters. In this thesis work I focused specifically on ETGs and on their capability in constraining galaxy formation and evolution; in particular, the principal aims were to derive some of the ETGs evolutionary parameters, such as age, metallicity and star formation history (SFH) and to study their age-redshift and mass-age relations. In order to infer galaxy physical parameters, I used the public code STARLIGHT: this program provides a best fit to the observed spectrum from a combination of many theoretical models defined in user-made libraries. the comparison between the output and input light-weighted ages shows a good agreement starting from SNRs of ∼ 10, with a bias of ∼ 2.2% and a dispersion 3%. Furthermore, also metallicities and SFHs are well reproduced. In the second part of the thesis I performed an analysis on real data, starting from Sloan Digital Sky Survey (SDSS) spectra. I found that galaxies get older with cosmic time and with increasing mass (for a fixed redshift bin); absolute light-weighted ages, instead, result independent from the fitting parameters or the synthetic models used. Metallicities, instead, are very similar from each other and clearly consistent with the ones derived from the Lick indices. The predicted SFH indicates the presence of a double burst of star formation. Velocity dispersions and extinctiona are also well constrained, following the expected behaviours. As a further step, I also fitted single SDSS spectra (with SNR∼ 20), to verify that stacked spectra gave the same results without introducing any bias: this is an important check, if one wants to apply the method at higher z, where stacked spectra are necessary to increase the SNR. Our upcoming aim is to adopt this approach also on galaxy spectra obtained from higher redshift Surveys, such as BOSS (z ∼ 0.5), zCOSMOS (z 1), K20 (z ∼ 1), GMASS (z ∼ 1.5) and, eventually, Euclid (z 2). Indeed, I am currently carrying on a preliminary study to estabilish the applicability of the method to lower resolution, as well as higher redshift (z 2) spectra, just like the Euclid ones.

Data sanitization in a clearing system for public transport operators

In this work we will discuss about a project started by the Emilia-Romagna Regional Government regarding the manage of the public transport. In particular we will perform a data mining analysis on the data-set of this project. After introducing the Weka software used to make our analysis, we will discover the most useful data mining techniques and algorithms; and we will show how these results can be used to violate the privacy of the same public transport operators. At the end, despite is off topic of this work, we will spend also a few words about how it's possible to prevent this kind of attack.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

La prova penale nelle indagini difensive. Analisi comparata degli strumenti processuali concessi alla difesa nei sistemi italiano e statunitense.

L’elaborato si occupa di fare il punto in materia di indagini difensive a tre lustri dall’entrata in vigore della legge n. 397/2000, epilogo di un lungo processo evolutivo che ha visto da un lato, una gestazione faticosa e travagliata, dall’altro, un prodotto normativo accolto dagli operatori in un contesto di scetticismo generale. In un panorama normativo e giurisprudenziale in continua evoluzione, i paradigmi dettati dagli artt. 24 e 111 della Costituzione, in tema di diritto alla difesa e di formazione della prova penale secondo il principio del contraddittorio tra le parti, in condizioni di parità, richiedono che il sistema giustizia offra sia all’indagato che all’imputato sufficienti strumenti difensivi. Tenuto conto delle diversità che caratterizzano naturalmente i ruoli dell’accusa e della difesa che impongono asimmetrie genetiche inevitabili, l’obiettivo della ricerca consiste nella disamina degli strumenti idonei a garantire il diritto alla prova della difesa in ogni stato e grado del procedimento, nel tentativo di realizzare compiutamente il principio di parità accusa - difesa nel processo penale. La ricerca si dipana attraverso tre direttrici: l’analisi dello statuto sulle investigazioni difensive nella sua evoluzione storica sino ai giorni nostri, lo studio della prova penale nel sistema americano e, infine, in alcune considerazioni finali espresse in chiave comparatistica. Le suggestioni proposte sono caratterizzate da un denominatore comune, ovvero dal presupposto che per contraddire è necessario conoscere e che solo per tale via sia possibile, finalmente, riconoscere il diritto di difendersi indagando.