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In recent years, entire industries and their participants have been affected by disruptive technologies, resulting in dramatic market changes and challenges to firm’s business logic and thus their business models (BMs). Firms from mature industries are increasingly realizing that BMs that worked successfully for years have become insufficient to stay on track in today’s “move fast and break things” economy. Firms must scrutinize the core logic that informs how they do business, which means exploring novel ways to engage customers and get them to pay. This can lead to a complete renewal of existing BMs or innovating completely new BMs.
BMs have emerged as a popular object of research within the last decade. Despite the popularity of the BM, the theoretical and empirical foundation underlying the concept is still weak. In particular, the innovation process for BMs has been developed and implemented in firms, but understanding of the mechanisms behind it is still lacking. Business model innovation (BMI) is a complex and challenging management task that requires more than just novel ideas. Systematic studies to generate a better understanding of BMI and support incumbents with appropriate concepts to improve BMI development are in short supply. Further, there is a lack of knowledge about appropriate research practices for studying BMI and generating valid data sets in order to meet expectations in both practice and academia.
This paper-based dissertation aims to contribute to research practice in the field of BM and BMI and foster better understanding of the BM concept and BMI processes in incumbent firms from mature industries. The overall dissertation presents three main results. The first result is a new perspective, or the systems thinking view, on the BM and BMI. With the systems thinking view, the fuzzy BM concept is clearly structured and a BMI framework is proposed. The second result is a new research strategy for studying BMI. After analyzing current research practice in the areas of BMs and BMI, it is obvious that there is a need for better research on BMs and BMI in terms of accuracy, transparency, and practical orientation. Thus, the action case study approach combined with abductive methodology is proposed and proven in the research setting of this thesis. The third result stems from three action case studies in incumbent firms from mature industries employed to study how BMI occurs in practice. The new insights and knowledge gained from the action case studies help to explain BMI in such industries and increase understanding of the core of these processes.
By studying these issues, the articles complied in this thesis contribute conceptually and empirically to the recently consolidated but still increasing literature on the BM and BMI. The conclusions and implications made are intended to foster further research and improve managerial practices for achieving BMI in a dramatically changing business environment.
In this thesis we use integral-field spectroscopy to detect and understand of Lyman α (Lyα) emission from high-redshift galaxies.
Intrinsically the Lyα emission at λ = 1216 Å is the strongest recombination line from galaxies. It arises from the 2p → 1s transition in hydrogen. In star-forming galaxies the line is powered by ionisation of the interstellar gas by hot O- and B- stars. Galaxies with star-formation rates of 1 - 10 Msol/year are expected to have Lyα luminosities of 42 dex - 43 dex (erg/s), corresponding to fluxes ~ -17 dex - -18 dex (erg/s/cm²) at redshifts z~3, where Lyα is easily accessible with ground-based telescopes. However, star-forming galaxies do not show these expected Lyα fluxes. Primarily this is a consequence of the high-absorption cross-section of neutral hydrogen for Lyα photons σ ~ -14 dex (cm²). Therefore, in typical interstellar environments Lyα photons have to undergo a complex radiative transfer. The exact conditions under which Lyα photons can escape a galaxy are poorly understood.
Here we present results from three observational projects. In Chapter 2, we show integral field spectroscopic observations of 14 nearby star-forming galaxies in Balmer α radiation (Hα, λ = 6562.8 Å). These observations were obtained with the Potsdam Multi Aperture Spectrophotometer at the Calar-Alto 3.5m Telescope}. Hα directly traces the intrinsic Lyα radiation field. We present Hα velocity fields and velocity dispersion maps spatially registered onto Hubble Space Telescope Lyα and Hα images. From our observations, we conjecture a causal connection between spatially resolved Hα kinematics and Lyα photometry for individual galaxies. Statistically, we find that dispersion-dominated galaxies are more likely to emit Lyα photons than galaxies where ordered gas-motions dominate. This result indicates that turbulence in actively star-forming systems favours an escape of Lyα radiation.
Not only massive stars can power Lyα radiation, but also non-thermal emission from an accreting super-massive black hole in the galaxy centre. If a galaxy harbours such an active galactic nucleus, the rate of hydrogen-ionising photons can be more than 1000 times higher than that of a typical star-forming galaxy. This radiation can potentially ionise large regions well outside the main stellar body of galaxies. Therefore, it is expected that the neutral hydrogen from these circum-galactic regions shines fluorescently in Lyα. Circum-galactic gas plays a crucial role in galaxy formation. It may act as a reservoir for fuelling star formation, and it is also subject to feedback processes that expel galactic material. If Lyα emission from this circum-galactic medium (CGM) was detected, these important processes could be studied in-situ around high-z galaxies. In Chapter 3, we show observations of five radio-quiet quasars with PMAS to search for possible extended CGM emission in the Lyα line. However, in four of the five objects, we find no significant traces of this emission. In the fifth object, there is evidence for a weak and spatially quite compact Lyα excess at several kpc outside the nucleus. The faintness of these structures is consistent with the idea that radio-quiet quasars typically reside in dark matter haloes of modest masses. While we were not able to detect Lyα CGM emission, our upper limits provide constraints for the new generation of IFS instruments at 8--10m class telescopes.
The Multi Unit Spectroscopic Explorer (MUSE) at ESOs Very Large Telescopeis such an unique instrument. One of the main motivating drivers in its construction was the use as a survey instrument for Lyα emitting galaxies at high-z. Currently, we are conducting such a survey that will cover a total area of ~100 square arcminutes with 1 hour exposures for each 1 square arcminute MUSE pointing. As a first result from this survey we present in Chapter 5 a catalogue of 831 emission-line selected galaxies from a 22.2 square arcminute region in the Chandra Deep Field South. In order to construct the catalogue, we developed and implemented a novel source detection algorithm -- LSDCat -- based on matched filtering for line emission in 3D spectroscopic datasets (Chapter 4). Our catalogue contains 237 Lyα emitting galaxies in the redshift range 3 ≲ z ≲ 6. Only four of those previously had spectroscopic redshifts in the literature. We conclude this thesis with an outlook on the construction of a Lyα luminosity function based on this unique sample (Chapter 6).
The current study investigates an interaction between numbers and physical size (i.e. size congruity) in visual search. In three experiments, participants had to detect a physically large (or small) target item among physically small (or large) distractors in a search task comprising single-digit numbers. The relative numerical size of the digits was varied, such that the target item was either among the numerically large or small numbers in the search display and the relation between numerical and physical size was either congruent or incongruent. Perceptual differences of the stimuli were controlled by a condition in which participants had to search for a differently coloured target item with the same physical size and by the usage of LCD-style numbers that were matched in visual similarity by shape transformations. The results of all three experiments consistently revealed that detecting a physically large target item is significantly faster when the numerical size of the target item is large as well (congruent), compared to when it is small (incongruent). This novel finding of a size congruity effect in visual search demonstrates an interaction between numerical and physical size in an experimental setting beyond typically used binary comparison tasks, and provides important new evidence for the notion of shared cognitive codes for numbers and sensorimotor magnitudes. Theoretical consequences for recent models on attention, magnitude representation and their interactions are discussed.
Over the past ~40 years, several attempts were made to reintroduce Eurasian lynx to suitable habitat within their former distribution range in Western Europe. In general, limited numbers of individuals have been released to establish new populations. To evaluate the effects of reintroductions on the genetic status of lynx populations we used 12 microsatellite loci to study lynx populations in the Bohemian–Bavarian and Vosges–Palatinian forests. Compared with autochthonous lynx populations, these two reintroduced populations displayed reduced genetic diversity, particularly the Vosges–Palatinian population. Our genetic data provide further evidence to support the status of ‘endangered’ and ‘critically endangered’ for the Bohemian–Bavarian and Vosges–Palatinian populations, respectively. Regarding conservation management, we highlight the need to limit poaching, and advocate additional translocations to bolster genetic variability.
We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic Kuramoto-Daido phase model as well as demonstrate the effect in limit-cycle relaxational Rayleigh oscillators. Such a regime extends the notion of splay state from a uniform distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of an inhomogeneous distribution. The characteristic and most peculiar property of self-consistent partial synchrony is the difference between the frequency of single units and that of the macroscopic field.
BACKGROUND: The etiology of low back pain (LBP), one of the most prevalent and costly diseases of our time, is accepted to be multi-causal, placing functional factors in the focus of research. Thereby, pain models suggest a centrally controlled strategy of trunk stiffening in LBP. However, supporting biomechanical evidence is mostly limited to static measurements during maximum voluntary contractions (MVC), probably influenced by psychological factors in LBP. Alternatively, repeated findings indicate that the neuromuscular efficiency (NME), characterized by the strength-to-activation relationship (SAR), of lower back muscles is impaired in LBP. Therefore, a dynamic SAR protocol, consisting of normalized trunk muscle activation recordings during submaximal loads (SMVC) seems to be relevant. This thesis aimed to investigate the influence of LBP on the NME and activation pattern of trunk muscles during dynamic trunk extensions.
METHODS: The SAR protocol consisted of an initial MVC reference trial (MVC1), followed by SMVCs at 20, 40, 60 and 80% of MVC1 load. An isokinetic trunk dynamometer (Con-Trex TP, ROM: 45° flexion to 10° extension, velocity: 45°/s) and a trunk surface EMG setup (myon, up to 12 leads) was used. Extension torque output [Nm] and muscular activation [V] were assessed in all trials. Finally, another MVC trial was performed (MVC2) for reliability analysis. For SAR evaluation the SMVC trial values were normalized [%MVC1] and compared inter- and intra-individually.
The methodical validity of the approach was tested in an isometric SAR single-case pilot study (S1a: N = 2, female LBP patient vs. healthy male). In addition, the validity of the MVC reference method was verified by comparing different contraction modes (S1b: N = 17, healthy individuals). Next, the isokinetic protocol was validated in terms of content for its applicability to display known physiological differences between sexes in a cross-sectional study (S2: each n = 25 healthy males/females). Finally, the influence of acute pain on NME was investigated longitudinally by comparing N = 8 acute LBP patients with the retest after remission of pain (S3). The SAR analysis focused on normalized agonistic extensor activation and abdominal and synergistic extensor co-activation (t-tests, ANOVA, α = .05) as well as on reliability of MVC1/2 outcomes.
RESULTS: During the methodological validation of the protocol (S1a), the isometric SAR was found to be descriptively different between individuals. Whereas torque output was highest during eccentric MVC, no relevant difference in peak EMG activation was found between contraction modes (S1b). The isokinetic SAR sex comparison (S2), though showing no significant overall effects, revealed higher normalized extensor activation at moderate submaximal loads in females (13 ± 4%), primarily caused by pronounced thoracic activation. Similarly, co-activation analysis resulted in significantly higher antagonistic activation at moderate loads compared to males (33 ± 9%). During intra-individual analysis of SAR in LBP patients (S3), a significant effect of pain status on the SAR has been identified, manifesting as increased normalized EMG activation of extensors during acute LBP (11 ± 8%) particularly at high load. Abdominal co-activation tended to be elevated (27 ± 11%) just as the thoracic extensor parts seemed to take over proportions of lumbar activation. All together, the M. erector spinae behaviour during the SAR protocol was rather linear with the tendency to rise exponentially during high loads. For the level of normalized EMG activation during SMVCs, a clear increasing trend from healthy males to females over to non-acute and acute LBP patients was discovered. This was associated by elevated antagonistic activation and a shift of synergistic towards lumbar extensor activation. The MVC data revealed overall good reliability, with clearly higher variability during acute LBP.
DISCUSSION: The present thesis demonstrates that the NME of lower back muscles is impaired in LBP patients, especially during an acute pain episode. A new dynamic protocol has been developed that makes it possible to display the underlying SAR using normalized trunk muscle EMG during submaximal isokinetic loads. The protocol shows promise as a biomechanical tool for diagnostic analysis of NME in LBP patients and monitoring of rehabilitation progress. Furthermore, reliability not of maximum strength but rather of peak EMG of MVC measurements seems to be decreased in LBP patients. Meanwhile, the findings of this thesis largely substantiate the assumptions made by the recently presented ‘motor adaptation to pain’ model, suggesting a pain-related intra- and intermuscular activation redistribution affecting movement and stiffness of the trunk. Further research is needed to distinguish the grade of NME impairment between LBP subgroups.
This dissertation examines the impact of the type of referring expression on the acquisition of word order variation in German-speaking preschoolers. A puzzle in the area of language acquisition concerns the production-comprehension asymmetry for non-canonical sentences like "Den Affen fängt die Kuh." (“The monkey, the cow chases.”), that is, preschoolers usually have difficulties in accurately understanding non-canonical sentences approximately until age six (e.g., Dittmar et al., 2008) although they produce non-canonical sentences already around age three (e.g., Poeppel & Wexler, 1993; Weissenborn, 1990). This dissertation investigated the production and comprehension of non-canonical sentences to address this issue.
Three corpus analyses were conducted to investigate the impact of givenness, topic status and the type of referring expression on word order in the spontaneous speech of two- to four-year-olds and the child-directed speech produced by their mothers. The positioning of the direct object in ditransitive sentences was examined; in particular, sentences in which the direct object occurred before or after the indirect object in the sentence-medial positions and sentences in which it occurred in the sentence-initial position. The results reveal similar ordering patterns for children and adults. Word order variation was to a large extent predictable from the type of referring expression, especially with respect to the word order involving the sentence-medial positions. Information structure (e.g., topic status) had an additional impact only on word order variation that involved the sentence-initial position.
Two comprehension experiments were conducted to investigate whether the type of referring expression and topic status influences the comprehension of non-canonical transitive sentences in four- and five-year-olds. In the first experiment, the topic status of the one of the sentential arguments was established via a preceding context sentence, and in the second experiment, the type of referring expression for the sentential arguments was additionally manipulated by using either a full lexical noun phrase (NP) or a personal pronoun. The results demonstrate that children’s comprehension of non-canonical sentences improved when the topic argument was realized as a personal pronoun and this improvement was independent of the grammatical role of the arguments. However, children’s comprehension was not improved when the topic argument was realized as a lexical NP.
In sum, the results of both production and comprehension studies support the view that referring expressions may be seen as a sentence-level cue to word order and to the information status of the sentential arguments. The results highlight the important role of the type of referring expression on the acquisition of word order variation and indicate that the production-comprehension asymmetry is reduced when the type of referring expression is considered.
Optical biosensors based on porous silicon were fabricated by metal assisted chemical etching. Thereby double layered porous silicon structures were obtained consisting of porous pillars with large pores on top of a porous silicon layer with smaller pores. These structures showed a similar sensing performance in comparison to electrochemically produced porous silicon interferometric sensors.
This article explores a recent performance of excerpts from T.S. Eliot’s Four Quartets (1935/36–1942) entitled Engaging Eliot: Four Quartets in Word, Color, and Sound as an example of live poetry. In this context, Eliot’s poem can be analysed as an auditory artefact that interacts strongly with other oral performances (welcome addresses and artists’ conversations), as well as with the musical performance of Christopher Theofanidis’s quintet “At the Still Point” at the end of the opening of Engaging Eliot. The event served as an introduction to a 13-day art exhibition and engaged in a re-evaluation of Eliot’s poem after 9/11: while its first part emphasises the connection between Eliot’s poem and Christian doctrine, its second part – especially the combination of poetry reading and musical performance – highlights the philosophical and spiritual dimensions of Four Quartets.
TripleA is a workshop series founded by linguists from the University of Tübingen and the University of Potsdam. Its aim is to provide a forum for semanticists doing fieldwork on understudied languages, and its focus is on languages from Africa, Asia, Australia and Oceania. The second TripleA workshop was held at the University of Potsdam, June 3-5, 2015.
Z,E-Diene sind ein häufig auftretendes Strukturmerkmal in Naturstoffen. Aus diesem Grund ist die einfache Darstellung dieser Struktureinheit von großen Interesse in der organischen Chemie.
Das erste Ziel der vorliegenden Arbeit war daher die Weiterentwicklung der Ringschlussmetathese-/ baseninduzierten Ringöffnungs-/ Veresterungssequenz (RBRV-Sequenz) zur Synthese von (2Z,4E)-Diencarbonsäureethylestern ausgehend von Butenoaten. Dazu wurde zunächst die RBRV-Sequenz optimiert. Diese aus drei Schritten bestehende Sequenz konnte in einem Eintopf-Verfahren angewendet werden. Die Ringschlussmetathese gelang mit einer Katalysatorbeladung von 1 mol% des GRUBBS-Katalysators der zweiten Generation in Dichlormethan. Für die baseninduzierte Ringöffnung des β,γ-ungesättigten δ Valerolactons wurde NaHMDS verwendet. Die Alkylierung der Carboxylatspezies gelang mit dem MEERWEIN-Reagenz. Die Anwendbarkeit der Sequenz wurde für verschiedene Substrate demonstriert.
Die Erweiterung der Methode auf α-substituierte Butenoate unterlag starken Einschränkungen. So konnte der Zugang für α Hydroxyderivate realisiert werden. Bei der Anwendung der RBRV-Sequenz auf die α-substituierten Butenoate wurde festgestellt, dass diese sich nur in moderaten Ausbeuten umsetzen ließen und zudem nicht selektiv zu den (2E,4E)-konfigurierten α-substituierten-Dienestern reagierten.
Der Einsatz von Eninen unter den Standardbedingungen der RBRV-Sequenz gelang nicht. Erst nach Modifizierung der Sequenz (höhere Katalysatorbeladung, Wechsel des Lösungsmittels) konnten die [3]Dendralen-Produkte in geringen Ausbeuten erhalten werden.
Im zweiten Teil der Arbeit wurde der Einsatz von (2Z,4E)-Diencarbonsäureethylestern in der Totalsynthese von Naturstoffen untersucht. Dazu wurden zunächst die Transformationsmöglichkeiten der Ester geprüft. Es konnte gezeigt werden, dass sich (2Z,4E)-Diencarbonsäureethylester insbesondere zur Synthese von (2Z,4E)-Aldehyden sowie zum Aufbau der (3Z,5E)-Dien-1-in-Struktur eignen.
Anhand dieser Ergebnisse wurde im Anschluss die RBRV-Sequenz in der Totalsynthese eingesetzt. Dazu wurde zunächst der (2Z,4E)-Dienester Microsphaerodiolin in seiner ersten Totalsynthese auf drei verschiedene Routen hergestellt. Im Anschluss wurden sechs verschiedene Polyacetylene mit einer (3Z,5E)-Dien-1-in-Einheit hergestellt. Schlüsselschritte in ihrer Synthese waren immer die RBRV-Sequenz zum Aufbau der Z,E-Dien-Einheit, die Transformation des Esters in ein terminales Alkin sowie die CADIOT-CHODKIEWICZ-Kupplung zum Aufbau unsymmetrischer Polyine. Alle sechs Polyacetylene wurden zum ersten Mal in einer Totalsynthese synthetisiert. Drei Polyacetylene wurden ausgehend von (S)-Butantriol enantiomerenrein dargestellt. Anhand ihrer Drehwerte konnte eine Revision der von YAO und Mitarbeitern vorgenommen Zuordnung der Absolutkonfiguration der Naturstoffe vorgenommen werden.
Der Bittergeschmack warnt den Organismus vor potentiell verdorbener oder giftiger Nahrung und ist somit ein wichtiger Kontrollmechanismus. Die initiale Detektion der zahlreich vorkommenden Bitterstoffe erfolgt bei der Maus durch 35 Bitterrezeptoren (Tas2rs), die sich im Zungengewebe befinden. Die Geschmacksinformation wird anschließend von der Zunge über das periphere (PNS) ins zentrale Nervensystem (ZNS) geleitet, wo deren Verarbeitung stattfindet. Die Verarbeitung der Geschmacksinformation konnte bislang nicht gänzlich aufgeklärt werden. Neue Studien deuten auf eine Expression von Tas2rs auch im PNS und ZNS entlang der Geschmacksbahn hin. Über Vorkommen und Aufgaben dieser Rezeptoren bzw. Rezeptorzellen im Nervensystem ist bislang wenig bekannt.
Im Rahmen dieser Arbeit wurde die Tas2r-Expression in verschiedenen Mausmodellen untersucht, Tas2r-exprimierende Zellen identifiziert und deren Funktionen bei der Übertragung der Geschmacksinformationen analysiert. Im Zuge der Expressionsanalysen mittels qRT-PCR konnte die Expression von 25 der 35 bekannten Bittergeschmacksrezeptoren im zentralen Nervensystem der Maus nachgewiesen werden. Die Expressionsmuster im PNS sowie im ZNS lassen darüber hinaus Vermutungen zu Funktionen in verschiedenen Bereichen des Nervensystems zu. Basierend auf den Ergebnissen der Expressionsanalysen war es möglich, stark exprimierte Tas2rs mittels In-situ-Hybridisierung in verschiedenen Zelltypen zu visualisieren. Des Weiteren konnten immunhistochemische Färbungen unter Verwendung eines genetisch modifizierten Mausmodells die Ergebnisse der Expressionsanalysen bestätigen. Sie zeigten eine Expression von Tas2rs, am Beispiel des Tas2r131-Rezeptors, in cholinergen, dopaminergen, GABAergen, noradrenergen und glycinerg-angesteuerten Projektionsneuronen sowie in Interneuronen. Die Ergebnisse der vorliegenden Arbeit zeigen daher erstmals das Vorkommen von Tas2rs in verschiedenen neuronalen Zelltypen in weiten Teilen des ZNS. Dies lässt den Schluss zu, dass Tas2r-exprimierende Zellen potentiell multiple Funktionen innehaben. Anhand von Verhaltensexperimenten in genetisch modifizierten Mäusen wurde die mögliche Funktion von Tas2r131-exprimierenden Neuronen (Tas2r131-Neurone) bei der Geschmackswahrnehmung untersucht. Die Ergebnisse weisen auf eine Beteiligung von Tas2r131-Neuronen an der Signalweiterleitung bzw. -verarbeitung der Geschmacksinformation für eine Auswahl von Bittersubstanzen hin. Die Analysen zeigen darüber hinaus, dass Tas2r131-Neuronen nicht an der Geschmackswahrnehmung anderer Bitterstoffe sowie Geschmacksstimuli anderer Qualitäten (süß, umami, sauer, salzig), beteiligt sind. Eine spezifische „Tas2r131-Bittergeschmacksbahn“, die mit anderen potentiellen „Bitterbahnen“ teils unabhängige, teils überlappende Signalwege bzw. Verarbeitungsbereiche besitzt, bildet eine mögliche zelluläre Grundlage zur Unterscheidung von Bitterstoffen. Die im Rahmen dieser Arbeit entstandene Hypothese einer potentiellen Diskriminierung von Bitterstoffen soll daher in weiterführenden Studien durch die Etablierung eines Verhaltenstest mit Mäusen geprüft werden.
Beyond the Crystal-Image
(2016)
Zu Hause
(2016)
The cytoskeleton is an essential component of living cells. It is composed of different types of protein filaments that form complex, dynamically rearranging, and interconnected networks. The cytoskeleton serves a multitude of cellular functions which further depend on the cell context. In animal cells, the cytoskeleton prominently shapes the cell's mechanical properties and movement. In plant cells, in contrast, the presence of a rigid cell wall as well as their larger sizes highlight the role of the cytoskeleton in long-distance intracellular transport. As it provides the basis for cell growth and biomass production, cytoskeletal transport in plant cells is of direct environmental and economical relevance. However, while knowledge about the molecular details of the cytoskeletal transport is growing rapidly, the organizational principles that shape these processes on a whole-cell level remain elusive.
This thesis is devoted to the following question: How does the complex architecture of the plant cytoskeleton relate to its transport functionality? The answer requires a systems level perspective of plant cytoskeletal structure and transport. To this end, I combined state-of-the-art confocal microscopy, quantitative digital image analysis, and mathematically powerful, intuitively accessible graph-theoretical approaches.
This thesis summarizes five of my publications that shed light on the plant cytoskeleton as a transportation network: (1) I developed network-based frameworks for accurate, automated quantification of cytoskeletal structures, applicable in, e.g., genetic or chemical screens; (2) I showed that the actin cytoskeleton displays properties of efficient transport networks, hinting at its biological design principles; (3) Using multi-objective optimization, I demonstrated that different plant cell types sustain cytoskeletal networks with cell-type specific and near-optimal organization; (4) By investigating actual transport of organelles through the cell, I showed that properties of the actin cytoskeleton are predictive of organelle flow and provided quantitative evidence for a coordination of transport at a cellular level; (5) I devised a robust, optimization-based method to identify individual cytoskeletal filaments from a given network representation, allowing the investigation of single filament properties in the network context. The developed methods were made publicly available as open-source software tools.
Altogether, my findings and proposed frameworks provide quantitative, system-level insights into intracellular transport in living cells. Despite my focus on the plant cytoskeleton, the established combination of experimental and theoretical approaches is readily applicable to different organisms. Despite the necessity of detailed molecular studies, only a complementary, systemic perspective, as presented here, enables both understanding of cytoskeletal function in its evolutionary context as well as its future technological control and utilization.
It is "scientific folklore" coming from physical heuristics that solutions to the heat equation on a Riemannian manifold can be represented by a path integral. However, the problem with such path integrals is that they are notoriously ill-defined. One way to make them rigorous (which is often applied in physics) is finite-dimensional approximation, or time-slicing approximation: Given a fine partition of the time interval into small subintervals, one restricts the integration domain to paths that are geodesic on each subinterval of the partition. These finite-dimensional integrals are well-defined, and the (infinite-dimensional) path integral then is defined as the limit of these (suitably normalized) integrals, as the mesh of the partition tends to zero.
In this thesis, we show that indeed, solutions to the heat equation on a general compact Riemannian manifold with boundary are given by such time-slicing path integrals. Here we consider the heat equation for general Laplace type operators, acting on sections of a vector bundle. We also obtain similar results for the heat kernel, although in this case, one has to restrict to metrics satisfying a certain smoothness condition at the boundary. One of the most important manipulations one would like to do with path integrals is taking their asymptotic expansions; in the case of the heat kernel, this is the short time asymptotic expansion. In order to use time-slicing approximation here, one needs the approximation to be uniform in the time parameter. We show that this is possible by giving strong error estimates.
Finally, we apply these results to obtain short time asymptotic expansions of the heat kernel also in degenerate cases (i.e. at the cut locus). Furthermore, our results allow to relate the asymptotic expansion of the heat kernel to a formal asymptotic expansion of the infinite-dimensional path integral, which gives relations between geometric quantities on the manifold and on the loop space. In particular, we show that the lowest order term in the asymptotic expansion of the heat kernel is essentially given by the Fredholm determinant of the Hessian of the energy functional. We also investigate how this relates to the zeta-regularized determinant of the Jacobi operator along minimizing geodesics.
Солярис как процесс
(2016)
Werben für sich selbst
(2016)
I. Einführung
II. Schädliche traditionelle Praktiken in
der UN-Frauenrechtskonvention
III. Einfluss der CEDAW-Konzeption auf
die Entwicklung des Konzepts und
dessen Verankerung in regionalen
Menschenrechtsinstrumenten
IV. Fallstudie: Strukturelle Parallelen von
FGM/C, männlicher Genitalbeschneidung
und operativen Eingriffen an
intersexuellen Kindern
V. Reformansätze