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 $h^{1,1}=1$.

Stima della variabilità intra-annuale del regime dei deflussi idrici superficiali in bacini non strumentati

La curva di durata di lungo periodo (POR) è uno strumento grafico molto efficace che mette in evidenza la relazione fra intensità e frequenza delle portate osservate in un determinato intervallo temporale. Essa è ricavata dall'idrogramma dei deflussi, ma presenta il problema della perdita di informazioni relative alla variabilità annuale e stagionali delle portate. Per tal motivo si è reso necessario l'utilizzo di due nuove interpretazioni delle curve di durate: le curve di durata annuali (alle quali può essere associato il concetto di percentile e quindi di probabilità di superamento di un particolare valore di portata) e le curve a base stagionale. La costruzione di tali curve, come nel caso delle POR complessive, è ostacolata dall'insufficienza di dati di portata, per cui sono utilizzate, a tale scopo, procedure di stima basate sulla regionalizzazione dei deflussi. Tra di esse è stato analizzata la tecnica geostatistica del Top-kriging applicata all'indice TND che sintetizza l'intera curva (Pugliese et al., 2014) nella ricostruzione, in cross-validazione, delle curve di durata annuali e stagionali di 182 bacini della regione sud-orientale degli Stati Uniti.

Stabilizing molecular self-assemblies via on-surface reactions

Für die Realisierung zukünftiger Technologien, wie z.B. molekulare Elektronik, werden Strategien benötigt, um funktionale Strukturen direkt auf Oberflächen zu erzeugen. Für die Bewältigung dieser Aufgabe ist die molekulare Selbstanordnung ein äußerst vielversprechender Bottom-up-Ansatz. Hierbei ist eine der größten Herausforderungen das Zusammenspiel aus intramolekularer Wechselwirkung und der Wechselwirkung zwischen Substrat und Molekülen in ein Gleichgewicht zu bringen. Da jedoch die wirkenden Kräfte der molekularen Selbstanordnung ausschließlich reversibler Natur sind, ist eine langfristige Stabilität fragwürdig. Somit ist die kovalente Verknüpfung der gebildeten Strukturen durch Reaktionen direkt auf der Oberfläche unerlässlich, um die Stabilität der Strukturen weiter zu erhöhen. Hierzu stellt die vorliegende Arbeit eine ausführliche Studie zu molekularer Selbstanordnung und der zielgerichteten Modifikation ebensolcher Strukturen dar. Durch den Einsatz von hochauflösender Rasterkraftmikroskopie im Ultrahochvakuum, welche es erlaubt einzelne Moleküle auf Nichtleitern abzubilden, wurde der maßgebliche Einfluss von Ankerfunktionalitäten auf den Prozess der molekularen Selbstanordnung gezeigt. Des Weiteren konnte die Stabilität der selbst angeordneten Strukturen durch neue Oberflächenreaktionskonzepte entschieden verbessert werden. Der Einfluss von Ankerfunktionen, die elektrostatische Wechselwirkung zwischen Molekül und Substrat vermitteln, auf den Strukturbildungsprozess der molekularen Selbstanordnung wird eingehend durch den Vergleich eines aromatischen Moleküls und seines vierfach chlorierten Derivates gezeigt. Für diese beiden Moleküle wurde ein deutlich unterschiedliches Verhalten der Selbstanordnung beobachtet. Es wird gezeigt, dass die Fähigkeit zur Bildung selbst angeordneter, stabiler Inseln entscheidend durch die Substituenten und die Abmessungen des Moleküls beeinflusst wird. Auch wird in dieser Arbeit die erste photochemische Reaktion organischer Moleküle auf einem Isolator gezeigt. Qualitative und quantitative Ergebnisse liefern ein detailliertes Bild darüber, wie die Abmessungen des Substratgitters die Richtung der Reaktion gezielt beeinflussen. Des Weiteren wird ein allgemeines Konzept zur selektiven Stabilisierung selbstangeordneter Molekülstrukturen durch den kontrollierten Transfer von Elektronen präsentiert. Durch die gezielte Steuerung der Menge an Dotierungsatomen wird die Desorptionstemperatur der molekularen Inseln signifikant erhöht und das Desorptionsverhalten der Inseln entschieden verändert. Diese Arbeit präsentiert somit erfolgreich durchgeführte Strategien um den Prozess der molekularen Selbstanordnung zu steuern, sowie entscheidende Mechanismen um die Stabilisierung und Modifizierung von selbst angeordneten Strukturen zu gewährleisten.

Intangible and tangible heritage

‘Intangible and tangible heritage – a topology of culture in contexts of faith’ presents a conceptual framework which could enable heritage professionals to approach cul-tural heritage in a more holistic understanding. My work emphasizes opportunities for a re-combination – in conceptual and practical terms – of two recently divided heritage typologies: the so-called ‘intangible’ and ‘tangible’ heritage. In arguing that the above division cannot be maintained when observing the dynamic construction and re-affirmation processes of heritage and identity, and further, that this division is a risk to the preservation of the heritage of humankind, I will emphasize that it is important to halt and redirect the progressing divergence of the two fields. This is particularly necessary in the context of UNESCO, which is the driving force behind this conceptual separation. rnTo achieve a conceptual recombination I propose to approach heritage by means of topologies instead of typologies. In topological analysis the researcher’s focus shifts from heritage expressions towards ideas or concepts of heritage, which are defined as logos localised in place, topos, and are proposed to be analysed by means of semiotic phenomenology. Finally, I describe the findings of a topological analysis conducted for a particular heritage concept: the Umayyad Mosque in Damascus.

First-principles studies of boron nanostructures

Boron is an 'electron deficient' element which has a rather fascinating chemical versatility. In the solid state, the elemental boron has neither a pure covalent nor a pure metallic character. As a result, its vast structural dimensionally and peculiar bonding features hold a unique place among other elements in the periodic table. In order to understand and properly describe these unusual bonding features, a detailed and systematic theoretical study is needed. In this work, I will show that some of the qualitative features of boron nanostructures, including clusters, sheets and nanotubes can easily be extracted from the results of first principles calculations based on density functional theory. Specifically, the size-dependent evolution of topological structures and bonding characteristics of boron clusters, Bn will be discussed. Based on the scenario observed in the boron clusters, the unique properties of boron sheets and boron nanotubes will be described. Moreover, the ballistic electron transport in single-walled carbon nanotubes will be considered. It is expected that the theoretical results obtained in the present thesis will initiate further studies on boron nanostructures, which will be helpful in understanding, designing and realizing boron-based nanoscale devices.

Development of room temperature operating single electron transistor using FIB etching and deposition technology

The single-electron transistor (SET) is one of the best candidates for future nano electronic circuits because of its ultralow power consumption, small size and unique functionality. SET devices operate on the principle of Coulomb blockade, which is more prominent at dimensions of a few nano meters. Typically, the SET device consists of two capacitively coupled ultra-small tunnel junctions with a nano island between them. In order to observe the Coulomb blockade effects in a SET device the charging energy of the device has to be greater that the thermal energy. This condition limits the operation of most of the existing SET devices to cryogenic temperatures. Room temperature operation of SET devices requires sub-10nm nano-islands due to the inverse dependence of charging energy on the radius of the conducting nano-island. Fabrication of sub-10nm structures using lithography processes is still a technological challenge. In the present investigation, Focused Ion Beam based etch and deposition technology is used to fabricate single electron transistors devices operating at room temperature. The SET device incorporates an array of tungsten nano-islands with an average diameter of 8nm. The fabricated devices are characterized at room temperature and clear Coulomb blockade and Coulomb oscillations are observed. An improvement in the resolution limitation of the FIB etching process is demonstrated by optimizing the thickness of the active layer. SET devices with structural and topological variation are developed to explore their impact on the behavior of the device. The threshold voltage of the device was minimized to ~500mV by minimizing the source-drain gap of the device to 17nm. Vertical source and drain terminals are fabricated to realize single-dot based SET device. A unique process flow is developed to fabricate Si dot based SET devices for better gate controllability in the device characteristic. The device vi parameters of the fabricated devices are extracted by using a conductance model. Finally, characteristic of these devices are validated with the simulated data from theoretical modeling.

Structural model of the CopA copper ATPase of Enterococcus hirae based on chemical cross-linking

The CopA copper ATPase of Enterococcus hirae belongs to the family of heavy metal pumping CPx-type ATPases and shares 43% sequence similarity with the human Menkes and Wilson copper ATPases. Due to a lack of suitable protein crystals, only partial three-dimensional structures have so far been obtained for this family of ion pumps. We present a structural model of CopA derived by combining topological information obtained by intramolecular cross-linking with molecular modeling. Purified CopA was cross-linked with different bivalent reagents, followed by tryptic digestion and identification of cross-linked peptides by mass spectrometry. The structural proximity of tryptic fragments provided information about the structural arrangement of the hydrophilic protein domains, which was integrated into a three-dimensional model of CopA. Comparative modeling of CopA was guided by the sequence similarity to the calcium ATPase of the sarcoplasmic reticulum, Serca1, for which detailed structures are available. In addition, known partial structures of CPx-ATPase homologous to CopA were used as modeling templates. A docking approach was used to predict the orientation of the heavy metal binding domain of CopA relative to the core structure, which was verified by distance constraints derived from cross-links. The overall structural model of CopA resembles the Serca1 structure, but reveals distinctive features of CPx-type ATPases. A prominent feature is the positioning of the heavy metal binding domain. It features an orientation of the Cu binding ligands which is appropriate for the interaction with Cu-loaded metallochaperones in solution. Moreover, a novel model of the architecture of the intramembranous Cu binding sites could be derived.

Parameter-free extraction of the functional network topology from intracranial EEG recordings: a time-resolved study of graph properties in focal onset seizures

Rationale: Focal onset epileptic seizures are due to abnormal interactions between distributed brain areas. By estimating the cross-correlation matrix of multi-site intra-cerebral EEG recordings (iEEG), one can quantify these interactions. To assess the topology of the underlying functional network, the binary connectivity matrix has to be derived from the cross-correlation matrix by use of a threshold. Classically, a unique threshold is used that constrains the topology [1]. Our method aims to set the threshold in a data-driven way by separating genuine from random cross-correlation. We compare our approach to the fixed threshold method and study the dynamics of the functional topology. Methods: We investigate the iEEG of patients suffering from focal onset seizures who underwent evaluation for the possibility of surgery. The equal-time cross-correlation matrices are evaluated using a sliding time window. We then compare 3 approaches assessing the corresponding binary networks. For each time window: * Our parameter-free method derives from the cross-correlation strength matrix (CCS)[2]. It aims at disentangling genuine from random correlations (due to finite length and varying frequency content of the signals). In practice, a threshold is evaluated for each pair of channels independently, in a data-driven way. * The fixed mean degree (FMD) uses a unique threshold on the whole connectivity matrix so as to ensure a user defined mean degree. * The varying mean degree (VMD) uses the mean degree of the CCS network to set a unique threshold for the entire connectivity matrix. * Finally, the connectivity (c), connectedness (given by k, the number of disconnected sub-networks), mean global and local efficiencies (Eg, El, resp.) are computed from FMD, CCS, VMD, and their corresponding random and lattice networks. Results: Compared to FMD and VMD, CCS networks present: *topologies that are different in terms of c, k, Eg and El. *from the pre-ictal to the ictal and then post-ictal period, topological features time courses that are more stable within a period, and more contrasted from one period to the next. For CCS, pre-ictal connectivity is low, increases to a high level during the seizure, then decreases at offset. k shows a ‘‘U-curve’’ underlining the synchronization of all electrodes during the seizure. Eg and El time courses fluctuate between the corresponding random and lattice networks values in a reproducible manner. Conclusions: The definition of a data-driven threshold provides new insights into the topology of the epileptic functional networks.

A Simple Algorithm for Unique Representation of Chemical Structures - Cyclic/ Acyclic Functionalized Achiral Hydrocarbons

An algorithm, based on ‘vertex priority values’ has been proposed to uniquely sequence and represent connectivity matrix of chemical structures of cyclic/ acyclic functionalized achiral hydrocarbons and their derivatives. In this method ‘vertex priority values’ have been assigned in terms of atomic weights, subgraph lengths, loops, and heteroatom contents. Subsequently the terminal vertices have been considered upon completing the sequencing of the core vertices. This approach provides a multilayered connectivity graph, which can be put to use in comparing two or more structures or parts thereof for any given purpose. Furthermore the basic vertex connection tables generated here are useful in the computation of characteristic matrices/ topological indices, automorphism groups, and in storing, sorting and retrieving of chemical structures from databases.

The Topology of Auditory and Visual Perception, Linguistic Communication, and Interactive Written Discourse

In this article, it is shown that IWD incorporates topological perceptual characteristics of both spoken and written language, and it is argued that these characteristics should not be ignored or given up when synchronous textual CMC is technologically developed and upgraded.

Spin ladders and quantum simulators for Tomonaga–Luttinger liquids

Magnetic insulators have proven to be usable as quantum simulators for itinerant interacting quantum systems. In particular the compound (C5H12N)2CuBr4 (for short: (Hpip)2CuBr4) was shown to be a remarkable realization of a Tomonaga–Luttinger liquid (TLL) and allowed us to quantitatively test the TLL theory. Substitution weakly disorders this class of compounds and thus allows us to use them to tackle questions pertaining to the effect of disorder in TLL as well, such as that of the formation of the Bose glass. In this paper we present, as a first step in this direction, a study of the properties of the related (Hpip)2CuCl4 compound. We determine the exchange couplings and compute the temperature and magnetic field dependence of the specific heat, using a finite temperature density matrix renormalization group procedure. Comparison with the measured specific heat at zero magnetic field confirms the exchange parameters and Hamiltonian for the (Hpip)2CuCl4 compound, giving the basis needed to begin studying the disorder effects.

Electron transport through catechol-functionalized molecular rods

The charge transport properties of a catechol-type dithiol-terminated oligo-phenylene-ethynylene was investigated by cyclic voltammetry (CV) and by the scanning tunnelling microscopy break junction technique (STM-BJ). Single molecule charge transport experiments demonstrated the existence of high and low conductance regions. The junction conductance is rather weakly dependent on the redox state of the bridging molecule. However, a distinct dependence of junction formation probability and of relative stretching distances of the catechol- and quinone-type molecular junctions is observed. Substitution of the central catechol ring with alkoxy-moieties and the combination with a topological analysis of possible π-electron pathways through the respective molecular skeletons lead to a working hypothesis, which could rationalize the experimentally observed conductance characteristics of the redox-active nanojunctions.

Heterotic T-folds with a small number of neutral moduli

We discuss non-geometric supersymmetric heterotic string models in D=4, in the framework of the free fermionic construction. We perform a systematic scan of models with four a priori left-right asymmetric Z2 projections and shifts. We analyze some 220 models, identifying 18 inequivalent classes and addressing variants generated by discrete torsions. They do not contain geometrical or trivial neutral moduli, apart from the dilaton. However, we show the existence of flat directions in the form of exactly marginal deformations and identify patterns of symmetry breaking where product gauge groups, realized at level one, are broken to their diagonal at higher level. We also describe an “inverse Gepner map” from Heterotic to Type II models that could be used, in certain non geometric settings, to define “effective” topological invariants.

MQN-Mapplet: Visualization of Chemical Space with Interactive Maps of DrugBank, ChEMBL, PubChem, GDB-11, and GDB-13

The MQN-mapplet is a Java application giving access to the structure of small molecules in large databases via color-coded maps of their chemical space. These maps are projections from a 42-dimensional property space defined by 42 integer value descriptors called molecular quantum numbers (MQN), which count different categories of atoms, bonds, polar groups, and topological features and categorize molecules by size, rigidity, and polarity. Despite its simplicity, MQN-space is relevant to biological activities. The MQN-mapplet allows localization of any molecule on the color-coded images, visualization of the molecules, and identification of analogs as neighbors on the MQN-map or in the original 42-dimensional MQN-space. No query molecule is necessary to start the exploration, which may be particularly attractive for nonchemists. To our knowledge, this type of interactive exploration tool is unprecedented for very large databases such as PubChem and GDB-13 (almost one billion molecules). The application is freely available for download at www.gdb.unibe.ch.

In situ dehydration behavior of veszelyite (Cu,Zn)2Zn(PO4)(OH)3·2H2O: A single-crystal X-ray study

The rare mixed copper-zinc phosphate mineral veszelyite (Cu,Zn)2Zn(PO4)(OH)3·2H2O space group P21/c, a = 7.5096(2), b = 10.2281(2), c = 9.8258(2) Å, β = 103.3040(10)°, V = 734.45(3) Å3 was investigated by in situ temperature-dependent single-crystal X-ray structure refinements. The atomic arrangement of veszelyite consists of an alternation of octahedral and tetrahedral sheets. The Jahn-Teller distorted CuO6 octahedra form sheets with eight-membered rings. The tetrahedral sheet composed of PO4 and ZnO3(OH) tetrahedra shows strong topological similarities to that of cavansite, gismondine, and kipushite.Diffraction data of a sample from Zdravo Vrelo, near Kreševo (Bosnia and Herzegovina) have been measured in steps of 25 up to 225 °C. Hydrogen positions and the hydrogen-bond system were determined experimentally from the structure refinements of data collected up to 125 °C. At 200 °C, the hydrogen-bonding scheme was inferred from bond-valence calculations and donor-acceptor distances. The hydrogen-bond system connects the tetrahedral sheet to the octahedral sheet and also braces the Cu sheet.At 150 °C, the H2O molecule at H2O2 was released and the Cu coordination (Cu1 and Cu2) decreased from originally six- to fivefold. Cu1 has a square planar coordination by four OH groups and an elongate distance to O3, whereas Cu2 has the Jahn-Teller characteristic elongate bond to H2O1. The unit-cell volume decreased 7% from originally 734.45(3) to 686.4(4) Å3 leading to a formula with 1 H2O pfu. The new phase observed above 150 °C is characterized by an increase of the c axis and a shortening of the b axis. The bending of T-O-T angles causes an increasing elliptical shape of the eight-membered rings in the tetrahedral and octahedral sheets. Moreover a rearrangement of the hydrogen-bond system was observed.At 225 °C, the structure degrades to an X-ray amorphous residual due to release of the last H2O molecule at H2O1. The stronger Jahn-Teller distortion of Cu1 relative to Cu2 suggests that Cu1 is fully occupied by Cu, whereas Cu2 bears significant Zn. H2O1 is the fifth ligand of Cu2. Zn at Cu2 is not favorable to adopt planar fourfold coordination. Thus, if the last water molecule is expelled the structure is destabilized.This study contributes to understanding the dehydration mechanism and thermal stability of supergene minerals characterized by Jahn-Teller distorted octahedra with mixed Cu, Zn occupancy.