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Determining the optimal grid resolution for topographic analysis on an airborne lidar dataset
(2019)

Digital elevation models (DEMs) are a gridded representation of the surface of the Earth and typically contain uncertainties due to data collection and processing. Slope and aspect estimates on a DEM contain errors and uncertainties inherited from the representation of a continuous surface as a grid (referred to as truncation error; TE) and from any DEM uncertainty. We analyze in detail the impacts of TE and propagated elevation uncertainty (PEU) on slope and aspect.
Using synthetic data as a control, we define functions to quantify both TE and PEU for arbitrary grids. We then develop a quality metric which captures the combined impact of both TE and PEU on the calculation of topographic metrics. Our quality metric allows us to examine the spatial patterns of error and uncertainty in topographic metrics and to compare calculations on DEMs of different sizes and accuracies.
Using lidar data with point density of ∼10 pts m−2 covering Santa Cruz Island in southern California, we are able to generate DEMs and uncertainty estimates at several grid resolutions. Slope (aspect) errors on the 1 m dataset are on average 0.3∘ (0.9∘) from TE and 5.5∘ (14.5∘) from PEU. We calculate an optimal DEM resolution for our SCI lidar dataset of 4 m that minimizes the error bounds on topographic metric calculations due to the combined influence of TE and PEU for both slope and aspect calculations over the entire SCI. Average slope (aspect) errors from the 4 m DEM are 0.25∘ (0.75∘) from TE and 5∘ (12.5∘) from PEU. While the smallest grid resolution possible from the high-density SCI lidar is not necessarily optimal for calculating topographic metrics, high point-density data are essential for measuring DEM uncertainty across a range of resolutions.

Determining the optimal grid resolution for topographic analysis on an airborne lidar dataset
(2019)

The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequences "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means.
The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.

The advances in modern geodetic techniques such as the global navigation satellite system (GNSS) and synthetic aperture radar (SAR) provide surface deformation measurements with an unprecedented accuracy and temporal and spatial resolutions even at most remote volcanoes on Earth. Modelling of the high-quality geodetic data is crucial for understanding the underlying physics of volcano deformation processes. Among various approaches, mathematical models are the most effective for establishing a quantitative link between the surface displacements and the shape and strength of deformation sources. Advancing the geodetic data analyses and hence, the knowledge on the Earth’s interior processes, demands sophisticated and efficient deformation modelling approaches. Yet the majority of these models rely on simplistic assumptions for deformation source geometries and ignore complexities such as the Earth’s surface topography and interactions between multiple sources.
This thesis addresses this problem in the context of analytical and numerical volcano deformation modelling. In the first part, new analytical solutions for triangular dislocations (TDs) in uniform infinite and semi-infinite elastic media have been developed. Through a comprehensive investigation, the locations and causes of artefact singularities and numerical instabilities associated with TDs have been determined and these long-standing drawbacks have been addressed thoroughly. This approach has then been extended to rectangular dislocations (RDs) with full rotational degrees of freedom. Using this solution in a configuration of three orthogonal RDs a compound dislocation model (CDM) has been developed. The CDM can represent generalized volumetric and planar deformation sources efficiently. Thus, the CDM is relevant for rapid inversions in early warning systems and can also be used for detailed deformation analyses. In order to account for complex source geometries and realistic topography in the deformation models, in this thesis the boundary element method (BEM) has been applied to the new solutions for TDs. In this scheme, complex surfaces are simulated as a continuous mesh of TDs that may possess any displacement or stress boundary conditions in the BEM calculations. In the second part of this thesis, the developed modelling techniques have been applied to five different real-world deformation scenarios. As the first and second case studies the deformation sources associated with the 2015 Calbuco eruption and 2013–2016 Copahue inflation period have been constrained by using the CDM. The highly anisotropic source geometries in these two cases highlight the importance of using generalized deformation models such as the CDM, for geodetic data inversions. The other three case studies in this thesis involve high-resolution dislocation models and BEM calculations. As the third case, the 2013 pre-explosive inflation of Volcán de Colima has been simulated by using two ellipsoidal cavities, which locate zones of pressurization in the volcano’s lava dome. The fourth case study, which serves as an example for volcanotectonics interactions, the 3-D kinematics of an active ring-fault at Tendürek volcano has been investigated through modelling displacement time series over the 2003–2010 time period. As the fifth example, the deformation sources associated with North Korea’s underground nuclear test in September 2017 have been constrained. These examples demonstrate the advancement and increasing level of complexity and the general applicability of the developed dislocation modelling techniques.
This thesis establishes a unified framework for rapid and high-resolution dislocation modelling, which in addition to volcano deformations can also be applied to tectonic and humanmade deformations.

This dissertation combines field and geochemical observations and analyses with numerical modeling to understand the formation of vein-hosted Sn-W ore in the Panasqueira deposit of Portugal, which is among the ten largest worldwide. The deposit is located above a granite body that is altered by magmatic-hydrothermal fluids in its upper part (greisen). These fluids are thought to be the source of metals, but that was still under debate. The goal of this study is to determine the composition and temperature of hydrothermal fluids at Panasqueira, and with that information to construct a numerical model of the hydrothermal system. The focus is on analysis of the minerals tourmaline and white mica, which formed during mineralization and are widespread throughout the deposit. Tourmaline occurs mainly in alteration zones around mineralized veins and is less abundant in the vein margins. White mica is more widespread. It is abundant in vein margins as well as alteration zones, and also occurs in the granite greisen. The laboratory work involved in-situ microanalysis of major- and trace elements in tourmaline and white mica, and boron-isotope analysis in both minerals by secondary ion mass spectrometry (SIMS).
The boron-isotope composition of tourmaline and white mica suggests a magmatic source. Comparison of hydrothermally-altered and unaltered rocks from drill cores shows that the ore metals (W, Sn, Cu, and Zn) and As, F, Li, Rb, and Cs were introduced during the alteration. Most of these elements are also enriched in tourmaline and mica, which confirms their potential value as exploration guides to Sn-W ores elsewhere.
The thermal evolution of the hydrothermal system was estimated by B-isotope exchange thermometry and the Ti-in-quartz method. Both methods yielded similar temperatures for the early hydrothermal phase: 430° to 460°C for B-isotopes and 503° ± 24°C for Ti-in-quartz. Mineral pairs from a late fault zone yield significantly lower median temperatures of 250°C. The combined results of thermometry with variations in chemical and B-isotope composition of tourmaline and mica suggest that a similar magmatic-hydrothermal fluid was active at all stages of mineralization. Mineralization in the late stage shows the same B-isotope composition as in the main stage despite a ca. 250°C cooling, which supports a multiple injection model of magmatic-hydrothermal fluids.
Two-dimensional numerical simulations of convection in a multiphase NaCl hydrothermal system were conducted: (a) in order to test a new approach (lower dimensional elements) for flow through fractures and faults and (b) in order to identify conditions for horizontal fluid flow as observed in the flat-lying veins at Panasqueira. The results show that fluid flow over an intrusion (heat and fluid source) develops a horizontal component if there is sufficient fracture connectivity. Late, steep fault zones have been identified in the deposit area, which locally contain low-temperature Zn-Pb mineralization. The model results confirm that the presence of subvertical faults with enhanced permeability play a crucial role in the ascent of magmatic fluids to the surface and the recharge of meteoric waters. Finally, our model results suggest that recharge of meteoric fluids and mixing processes may be important at later stages, while flow of magmatic fluids dominate the early stages of the hydrothermal fluid circulation.

ATP-binding cassette (ABC) transporters are present in all kingdoms of life and enable active transport of various different molecules across biological membranes. They all share an overall architecture of two lipophilic transmembrane spanning domains (TMDs) traversing the membrane and two hydrophilic nucleotide binding domains (NBDs) usually lacking sequence identity. The multiplicity in transported molecules is accompanied by extreme diversity in TMDs. Human mitochondria harbor four ABC transporters, namely ABCB6, ABCB7, ABCB8 and ABCB10 with functional homologues in yeast and plants. Except the ones found in Rickettsiae and related bacteria mitochondrial ABC transporters are absent in bacteria. In addition to converting energy mitochondria are important platforms for biosynthesizing various cofactors as iron sulfur clusters, molybdenum cofactor (Moco) or heme. ABCB7 (Atm1 in yeast) has been shown to connect mitochondrial with cytosolic iron sulfur cluster assembly by exporting a yet unknown sulfur containing molecule. In addition, TMDs of Atm1 display a glutathione binding pocket accessible from the matrix which has been identified in all ABCB7-like transporters and also exists in a bacterial ABC transporter homologue of Atm1 in Novosphingobium aromaticivorans. In addition, ATM3, a plant mitochondrial homologous ABC transporter to human ABCB7, has been associated with biosynthesizing Moco.
In this study we used the α-proteobacterium Rhodobacter capsulatus as a model organism to characterize mitochondrial ABC transporter homologues. R. capsulatus contains two homologues to mitochondrial ABC transporters with the corresponding gene loci rcc03139 and rcc02305. They share 38 to 47 % sequence identities to human mitochondrial ABC transporters ABCB8/ABCB10 and ABCB7/ABCB6, respectively. We created interposon mutants lacking either rcc03139 or rcc02305, analyzed the physiological effects on R. capsulatus and compared the findings especially to eukaryotic deletion studies. A viable bacterial double mutant strain lacking both mitochondrial ABC transporters was constructed to investigate possible overlapping functions. Both R. capsulatus single mutants showed a severe accumulation of intracellular reactive oxygen species (ROS) in comparison to ∆nifDK which revealed to be additive in the double mutant. In the proteome of ∆rcc03139I abundancies of tetrapyrrole related proteins were significantly increased in comparison to the proteome of parental strain, which was further validated by reduced amounts of tetrapyrrole intermediates in ∆rcc03139. In contrast, in ∆rcc02305I total glutathione (GSH) was elevated when endogenous GSH biosynthesis was inhibited. In conjunction with proteomic studies we uncovered misbalanced sulfur distribution in ∆rcc02305I. Furthermore, strains lacking Rcc02305 accumulated cyclic pyranopterin monophosphate (cPMP), an intermediate of Moco biosynthesis, as it was already shown for the deletion strain of the eukaryotic counterpart ATM3 in plants. In contrast single mutant strain Δrcc03139I neither accumulated cPMP nor glutathione.
Bioinformatic analysis of the amino acid sequence of Rcc02305 revealed a pyridoxal 5´phosphate (PLP) binding site which overlaps with Walker A within the NBDs of Rcc02305 and other ABCB7-like transporters. The PLP cofactor is well studied in C-DES (L-cysteine/cystine lyase from Synechocystis) for persulfide production and in L-cysteine desulfurases such as IscS and NFS1 for its role in formation of protein-bound persulfides. Based on our findings we are able to propose a new modality for the transport of the sulfur containing molecule: first of all, the transporter produces a highly reactive persulfide which is then subsequently trapped by glutathione polysulfide, already bound within the binding pocket in TMDs. Walker A becomes accessible for ATP and after hydrolysis the mixed polysulfide is released.
Based on our studies we are convinced that both mitochondrial ABC transporter homologues fulfil distinct roles in R. capsulatus: Rcc02305 is a representative of Atm1/ABCB7-like transporters and important for proper sulfur distribution by exporting persulfides. In contrast Rcc03139 is a representative of ABCB6/ABCB10 related transporters and involved in biosynthesizing tetrapyrroles.

The natural abundance of Coiled Coil (CC) motifs in cytoskeleton and extracellular matrix proteins suggests that CCs play an important role as passive (structural) and active (regulatory) mechanical building blocks. CCs are self-assembled superhelical structures consisting of 2-7 α-helices. Self-assembly is driven by hydrophobic and ionic interactions, while the helix propensity of the individual helices contributes additional stability to the structure. As a direct result of this simple sequence-structure relationship, CCs serve as templates for protein design and sequences with a pre-defined thermodynamic stability have been synthesized de novo. Despite this quickly increasing knowledge and the vast number of possible CC applications, the mechanical function of CCs has been largely overlooked and little is known about how different CC design parameters determine the mechanical stability of CCs. Once available, this knowledge will open up new applications for CCs as nanomechanical building blocks, e.g. in biomaterials and nanobiotechnology.
With the goal of shedding light on the sequence-structure-mechanics relationship of CCs, a well-characterized heterodimeric CC was utilized as a model system. The sequence of this model system was systematically modified to investigate how different design parameters affect the CC response when the force is applied to opposing termini in a shear geometry or separated in a zipper-like fashion from the same termini (unzip geometry). The force was applied using an atomic force microscope set-up and dynamic single-molecule force spectroscopy was performed to determine the rupture forces and energy landscape properties of the CC heterodimers under study. Using force as a denaturant, CC chain separation is initiated by helix uncoiling from the force application points. In the shear geometry, this allows uncoiling-assisted sliding parallel to the force vector or dissociation perpendicular to the force vector. Both competing processes involve the opening of stabilizing hydrophobic (and ionic) interactions. Also in the unzip geometry, helix uncoiling precedes the rupture of hydrophobic contacts.
In a first series of experiments, the focus was placed on canonical modifications in the hydrophobic core and the helix propensity. Using the shear geometry, it was shown that both a reduced core packing and helix propensity lower the thermodynamic and mechanical stability of the CC; however, with different effects on the energy landscape of the system. A less tightly packed hydrophobic core increases the distance to the transition state, with only a small effect on the barrier height. This originates from a more dynamic and less tightly packed core, which provides more degrees of freedom to respond to the applied force in the direction of the force vector. In contrast, a reduced helix propensity decreases both the distance to the transition state and the barrier height. The helices are ‘easier’ to unfold and the remaining structure is less thermodynamically stable so that dissociation perpendicular to the force axis can occur at smaller deformations.
Having elucidated how canonical sequence modifications influence CC mechanics, the pulling geometry was investigated in the next step. Using one and the same sequence, the force application points were exchanged and two different shear and one unzipping geometry were compared. It was shown that the pulling geometry determines the mechanical stability of the CC. Different rupture forces were observed in the different shear as well as in the unzipping geometries, suggesting that chain separation follows different pathways on the energy landscape. Whereas the difference between CC shearing and unzipping was anticipated and has also been observed for other biological structures, the observed difference for the two shear geometries was less expected. It can be explained with the structural asymmetry of the CC heterodimer. It is proposed that the direction of the α-helices, the different local helix propensities and the position of a polar asparagine in the hydrophobic core are responsible for the observed difference in the chain separation pathways. In combination, these factors are considered to influence the interplay between processes parallel and perpendicular to the force axis.
To obtain more detailed insights into the role of helix stability, helical turns were reinforced locally using artificial constraints in the form of covalent and dynamic ‘staples’. A covalent staple bridges to adjacent helical turns, thus protecting them against uncoiling. The staple was inserted directly at the point of force application in one helix or in the same terminus of the other helix, which did not experience the force directly. It was shown that preventing helix uncoiling at the point of force application reduces the distance to the transition state while slightly increasing the barrier height. This confirms that helix uncoiling is critically important for CC chain separation. When inserted into the second helix, this stabilizing effect is transferred across the hydrophobic core and protects the force-loaded turns against uncoiling. If both helices were stapled, no additional increase in mechanical stability was observed. When replacing the covalent staple with a dynamic metal-coordination bond, a smaller decrease in the distance to the transition was observed, suggesting that the staple opens up while the CC is under load.
Using fluorinated amino acids as another type of non-natural modification, it was investigated how the enhanced hydrophobicity and the altered packing at the interface influences CC mechanics. The fluorinated amino acid was inserted into one central heptad of one or both α-helices. It was shown that this substitution destabilized the CC thermodynamically and mechanically. Specifically, the barrier height was decreased and the distance to the transition state increased. This suggests that a possible stabilizing effect of the increased hydrophobicity is overruled by a disturbed packing, which originates from a bad fit of the fluorinated amino acid into the local environment. This in turn increases the flexibility at the interface, as also observed for the hydrophobic core substitution described above. In combination, this confirms that the arrangement of the hydrophobic side chains is an additional crucial factor determining the mechanical stability of CCs.
In conclusion, this work shows that knowledge of the thermodynamic stability alone is not sufficient to predict the mechanical stability of CCs. It is the interplay between helix propensity and hydrophobic core packing that defines the sequence-structure-mechanics relationship. In combination, both parameters determine the relative contribution of processes parallel and perpendicular to the force axis, i.e. helix uncoiling and uncoiling-assisted sliding as well as dissociation. This new mechanistic knowledge provides insight into the mechanical function of CCs in tissues and opens up the road for designing CCs with pre-defined mechanical properties. The library of mechanically characterized CCs developed in this work is a powerful starting point for a wide spectrum of applications, ranging from molecular force sensors to mechanosensitive crosslinks in protein nanostructures and synthetic extracellular matrix mimics.

A new micro/mesoporous hybrid clay nanocomposite prepared from kaolinite clay, Carica papaya seeds, and ZnCl2 via calcination in an inert atmosphere is presented. Regardless of the synthesis temperature, the specific surface area of the nanocomposite material is between ≈150 and 300 m2/g. The material contains both micro- and mesopores in roughly equal amounts. X-ray diffraction, infrared spectroscopy, and solid-state nuclear magnetic resonance spectroscopy suggest the formation of several new bonds in the materials upon reaction of the precursors, thus confirming the formation of a new hybrid material. Thermogravimetric analysis/differential thermal analysis and elemental analysis confirm the presence of carbonaceous matter. The new composite is stable up to 900 °C and is an efficient adsorbent for the removal of a water micropollutant, 4-nitrophenol, and a pathogen, E. coli, from an aqueous medium, suggesting applications in water remediation are feasible.

Synchronization – the adjustment of rhythms among coupled self-oscillatory systems – is a fascinating dynamical phenomenon found in many biological, social, and technical systems.
The present thesis deals with synchronization in finite ensembles of weakly coupled self-sustained oscillators with distributed frequencies.
The standard model for the description of this collective phenomenon is the Kuramoto model – partly due to its analytical tractability in the thermodynamic limit of infinitely many oscillators. Similar to a phase transition in the thermodynamic limit, an order parameter indicates the transition from incoherence to a partially synchronized state. In the latter, a part of the oscillators rotates at a common frequency. In the finite case, fluctuations occur, originating from the quenched noise of the finite natural frequency sample.
We study intermediate ensembles of a few hundred oscillators in which fluctuations are comparably strong but which also allow for a comparison to frequency distributions in the infinite limit.
First, we define an alternative order parameter for the indication of a collective mode in the finite case. Then we test the dependence of the degree of synchronization and the mean rotation frequency of the collective mode on different characteristics for different coupling strengths.
We find, first numerically, that the degree of synchronization depends strongly on the form (quantified by kurtosis) of the natural frequency sample and the rotation frequency of the collective mode depends on the asymmetry (quantified by skewness) of the sample. Both findings are verified in the infinite limit.
With these findings, we better understand and generalize observations of other authors. A bit aside of the general line of thoughts, we find an analytical expression for the volume contraction in phase space.
The second part of this thesis concentrates on an ordering effect of the finite-size fluctuations. In the infinite limit, the oscillators are separated into coherent and incoherent thus ordered and disordered oscillators. In finite ensembles, finite-size fluctuations can generate additional order among the asynchronous oscillators. The basic principle – noise-induced synchronization – is known from several recent papers. Among coupled oscillators, phases are pushed together by the order parameter fluctuations, as we on the one hand show directly and on the other hand quantify with a synchronization measure from directed statistics between pairs of passive oscillators.
We determine the dependence of this synchronization measure from the ratio of pairwise natural frequency difference and variance of the order parameter fluctuations. We find a good agreement with a simple analytical model, in which we replace the deterministic fluctuations of the order parameter by white noise.