TY - THES
AB - In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations.
The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,
and thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics.
We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration
function on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss
the implications on persistence for periodic data sets.
AU - Osang, Georg F
ID - 9056
SN - 2663-337X
TI - Multi-cover persistence and Delaunay mosaics
ER -
TY - THES
AB - Most real-world flows are multiphase, yet we know little about them compared to their single-phase counterparts. Multiphase flows are more difficult to investigate as their dynamics occur in large parameter space and involve complex phenomena such as preferential concentration, turbulence modulation, non-Newtonian rheology, etc. Over the last few decades, experiments in particle-laden flows have taken a back seat in favour of ever-improving computational resources. However, computers are still not powerful enough to simulate a real-world fluid with millions of finite-size particles. Experiments are essential not only because they offer a reliable way to investigate real-world multiphase flows but also because they serve to validate numerical studies and steer the research in a relevant direction. In this work, we have experimentally investigated particle-laden flows in pipes, and in particular, examined the effect of particles on the laminar-turbulent transition and the drag scaling in turbulent flows.
For particle-laden pipe flows, an earlier study [Matas et al., 2003] reported how the sub-critical (i.e., hysteretic) transition that occurs via localised turbulent structures called puffs is affected by the addition of particles. In this study, in addition to this known transition, we found a super-critical transition to a globally fluctuating state with increasing particle concentration. At the same time, the Newtonian-type transition via puffs is delayed to larger Reynolds numbers. At an even higher concentration, only the globally fluctuating state is found. The dynamics of particle-laden flows are hence determined by two competing instabilities that give rise to three flow regimes: Newtonian-type turbulence at low, a particle-induced globally fluctuating state at high, and a coexistence state at intermediate concentrations.
The effect of particles on turbulent drag is ambiguous, with studies reporting drag reduction, no net change, and even drag increase. The ambiguity arises because, in addition to particle concentration, particle shape, size, and density also affect the net drag. Even similar particles might affect the flow dissimilarly in different Reynolds number and concentration ranges. In the present study, we explored a wide range of both Reynolds number and concentration, using spherical as well as cylindrical particles. We found that the spherical particles do not reduce drag while the cylindrical particles are drag-reducing within a specific Reynolds number interval. The interval strongly depends on the particle concentration and the relative size of the pipe and particles. Within this interval, the magnitude of drag reduction reaches a maximum. These drag reduction maxima appear to fall onto a distinct power-law curve irrespective of the pipe diameter and particle concentration, and this curve can be considered as the maximum drag reduction asymptote for a given fibre shape. Such an asymptote is well known for polymeric flows but had not been identified for particle-laden flows prior to this work.
AU - Agrawal, Nishchal
ID - 9728
KW - Drag Reduction
KW - Transition to Turbulence
KW - Multiphase Flows
KW - particle Laden Flows
KW - Complex Flows
KW - Experiments
KW - Fluid Dynamics
SN - 2663-337X
TI - Transition to turbulence and drag reduction in particle-laden pipe flows
ER -
TY - THES
AB - Cytoplasmic reorganizations are essential for morphogenesis. In large cells like oocytes, these reorganizations become crucial in patterning the oocyte for later stages of embryonic development. Ascidians oocytes reorganize their cytoplasm (ooplasm) in a spectacular manner. Ooplasmic reorganization is initiated at fertilization with the contraction of the actomyosin cortex along the animal-vegetal axis of the oocyte, driving the accumulation of cortical endoplasmic reticulum (cER), maternal mRNAs associated to it and a mitochondria-rich subcortical layer – the myoplasm – in a region of the vegetal pole termed contraction pole (CP). Here we have used the species Phallusia mammillata to investigate the changes in cell shape that accompany these reorganizations and the mechanochemical mechanisms underlining CP formation.
We report that the length of the animal-vegetal (AV) axis oscillates upon fertilization: it first undergoes a cycle of fast elongation-lengthening followed by a slow expansion of mainly the vegetal pole (VP) of the cell. We show that the fast oscillation corresponds to a dynamic polarization of the actin cortex as a result of a fertilization-induced increase in cortical tension in the oocyte that triggers a rupture of the cortex at the animal pole and the establishment of vegetal-directed cortical flows. These flows are responsible for the vegetal accumulation of actin causing the VP to flatten.
We find that the slow expansion of the VP, leading to CP formation, correlates with a relaxation of the vegetal cortex and that the myoplasm plays a role in the expansion. We show that the myoplasm is a solid-like layer that buckles under compression forces arising from the contracting actin cortex at the VP. Straightening of the myoplasm when actin flows stops, facilitates the expansion of the VP and the CP. Altogether, our results present a previously unrecognized role for the myoplasm in ascidian ooplasmic segregation.
AU - Caballero Mancebo, Silvia
ID - 9623
SN - 2663-337X
TI - Fertilization-induced deformations are controlled by the actin cortex and a mitochondria-rich subcortical layer in ascidian oocytes
ER -
TY - THES
AB - Left-right asymmetries can be considered a fundamental organizational principle of the vertebrate central nervous system. The hippocampal CA3-CA1 pyramidal cell synaptic connection shows an input-side dependent asymmetry where the hemispheric location of the presynaptic CA3 neuron determines the synaptic properties. Left-input synapses terminating on apical dendrites in stratum radiatum have a higher density of NMDA receptor subunit GluN2B, a lower density of AMPA receptor subunit GluA1 and smaller areas with less often perforated PSDs. On the other hand, left-input synapses terminating on basal dendrites in stratum oriens have lower GluN2B densities than right-input ones. Apical and basal synapses further employ different signaling pathways involved in LTP. SDS-digested freeze-fracture replica labeling can visualize synaptic membrane proteins with high sensitivity and resolution, and has been used to reveal the asymmetry at the electron microscopic level. However, it requires time-consuming manual demarcation of the synaptic surface for quantitative measurements. To facilitate the analysis of replica labeling, I first developed a software named Darea, which utilizes deep-learning to automatize this demarcation. With Darea I characterized the synaptic distribution of NMDA and AMPA receptors as well as the voltage-gated Ca2+ channels in CA1 stratum radiatum and oriens. Second, I explored the role of GluN2B and its carboxy-terminus in the establishment of input-side dependent hippocampal asymmetry. In conditional knock-out mice lacking GluN2B expression in CA1 and GluN2B-2A swap mice, where GluN2B carboxy-terminus was exchanged to that of GluN2A, no significant asymmetries of GluN2B, GluA1 and PSD area were detected. We further discovered a previously unknown functional asymmetry of GluN2A, which was also lost in the swap mouse. These results demonstrate that GluN2B carboxy-terminus plays a critical role in normal formation of input-side dependent asymmetry.
AU - Kleindienst, David
ID - 9562
SN - 2663-337X
TI - 2B or not 2B: Hippocampal asymmetries mediated by NMDA receptor subunit GluN2B C-terminus and high-throughput image analysis by Deep-Learning
ER -
TY - THES
AB - Accumulation of interstitial fluid (IF) between embryonic cells is a common phenomenon in vertebrate embryogenesis. Unlike other model systems, where these accumulations coalesce into a large central cavity – the blastocoel, in zebrafish, IF is more uniformly distributed between the deep cells (DC) before the onset of gastrulation. This is likely due to the presence of a large extraembryonic structure – the yolk cell (YC) at the position where the blastocoel typically forms in other model organisms. IF has long been speculated to play a role in tissue morphogenesis during embryogenesis, but direct evidence supporting such function is still sparse. Here we show that the relocalization of IF to the interface between the YC and DC/epiblast is critical for axial mesendoderm (ME) cell protrusion formation and migration along this interface, a key process in embryonic axis formation. We further demonstrate that axial ME cell migration and IF relocalization engage in a positive feedback loop, where axial ME migration triggers IF accumulation ahead of the advancing axial ME tissue by mechanically compressing the overlying epiblast cell layer. Upon compression, locally induced flow relocalizes the IF through the porous epiblast tissue resulting in an IF accumulation ahead of the leading axial ME. This IF accumulation, in turn, promotes cell protrusion formation and migration of the leading axial ME cells, thereby facilitating axial ME extension. Our findings reveal a central role of dynamic IF relocalization in orchestrating germ layer morphogenesis during gastrulation.
AU - Huljev, Karla
ID - 9397
SN - 2663-337X
TI - Coordinated spatiotemporal reorganization of interstitial fluid is required for axial mesendoderm migration in zebrafish gastrulation
ER -
TY - THES
AB - In this thesis, we consider several of the most classical and fundamental problems in static analysis and formal verification, including invariant generation, reachability analysis, termination analysis of probabilistic programs, data-flow analysis, quantitative analysis of Markov chains and Markov decision processes, and the problem of data packing in cache management.
We use techniques from parameterized complexity theory, polyhedral geometry, and real algebraic geometry to significantly improve the state-of-the-art, in terms of both scalability and completeness guarantees, for the mentioned problems. In some cases, our results are the first theoretical improvements for the respective problems in two or three decades.
AU - Goharshady, Amir Kafshdar
ID - 8934
SN - 2663-337X
TI - Parameterized and algebro-geometric advances in static program analysis
ER -
TY - THES
AB - The brain is one of the largest and most complex organs and it is composed of billions of neurons that communicate together enabling e.g. consciousness. The cerebral cortex is the largest site of neural integration in the central nervous system. Concerted radial migration of newly born cortical projection neurons, from their birthplace to their final position, is a key step in the assembly of the cerebral cortex. The cellular and molecular mechanisms regulating radial neuronal migration in vivo are however still unclear. Recent evidence suggests that distinct signaling cues act cell-autonomously but differentially at certain steps during the overall migration process. Moreover, functional analysis of genetic mosaics (mutant neurons present in wild-type/heterozygote environment) using the MADM (Mosaic Analysis with Double Markers) analyses in comparison to global knockout also indicate a significant degree of non-cell-autonomous and/or community effects in the control of cortical neuron migration. The interactions of cell-intrinsic (cell-autonomous) and cell-extrinsic (non-cell-autonomous) components are largely unknown. In part of this thesis work we established a MADM-based experimental strategy for the quantitative analysis of cell-autonomous gene function versus non-cell-autonomous and/or community effects. The direct comparison of mutant neurons from the genetic mosaic (cell-autonomous) to mutant neurons in the conditional and/or global knockout (cell-autonomous + non-cell-autonomous) allows to quantitatively analyze non-cell-autonomous effects. Such analysis enable the high-resolution analysis of projection neuron migration dynamics in distinct environments with concomitant isolation of genomic and proteomic profiles. Using these experimental paradigms and in combination with computational modeling we show and characterize the nature of non-cell-autonomous effects to coordinate radial neuron migration. Furthermore, this thesis discusses recent developments in neurodevelopment with focus on neuronal polarization and non-cell-autonomous mechanisms in neuronal migration.
AU - Hansen, Andi H
ID - 9962
KW - Neuronal migration
KW - Non-cell-autonomous
KW - Cell-autonomous
KW - Neurodevelopmental disease
SN - 2663-337X
TI - Cell-autonomous gene function and non-cell-autonomous effects in radial projection neuron migration
ER -
TY - THES
AB - This work is concerned with two fascinating circuit quantum electrodynamics components, the Josephson junction and the geometric superinductor, and the interesting experiments that can be done by combining the two. The Josephson junction has revolutionized the field of superconducting circuits as a non-linear dissipation-less circuit element and is used in almost all superconducting qubit implementations since the 90s. On the other hand, the superinductor is a relatively new circuit element introduced as a key component of the fluxonium qubit in 2009. This is an inductor with characteristic impedance larger than the resistance quantum and self-resonance frequency in the GHz regime. The combination of these two elements can occur in two fundamental ways: in parallel and in series. When connected in parallel the two create the fluxonium qubit, a loop with large inductance and a rich energy spectrum reliant on quantum tunneling. On the other hand placing the two elements in series aids with the measurement of the IV curve of a single Josephson junction in a high impedance environment. In this limit theory predicts that the junction will behave as its dual element: the phase-slip junction. While the Josephson junction acts as a non-linear inductor the phase-slip junction has the behavior of a non-linear capacitance and can be used to measure new Josephson junction phenomena, namely Coulomb blockade of Cooper pairs and phase-locked Bloch oscillations. The latter experiment allows for a direct link between frequency and current which is an elusive connection in quantum metrology. This work introduces the geometric superinductor, a superconducting circuit element where the high inductance is due to the geometry rather than the material properties of the superconductor, realized from a highly miniaturized superconducting planar coil. These structures will be described and characterized as resonators and qubit inductors and progress towards the measurement of phase-locked Bloch oscillations will be presented.
AU - Peruzzo, Matilda
ID - 9920
KW - quantum computing
KW - superinductor
KW - quantum metrology
SN - 2663-337X
TI - Geometric superinductors and their applications in circuit quantum electrodynamics
ER -
TY - THES
AB - The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis.
AU - Hensel, Sebastian
ID - 10007
SN - 2663-337X
TI - Curvature driven interface evolution: Uniqueness properties of weak solution concepts
ER -
TY - THES
AB - This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author.
AU - Feliciangeli, Dario
ID - 9733
SN - 2663-337X
TI - The polaron at strong coupling
ER -
TY - THES
AB - Blood – this is what animals use to heal wounds fast and efficient. Plants do not have blood circulation and their cells cannot move. However, plants have evolved remarkable capacities to regenerate tissues and organs preventing further damage. In my PhD research, I studied the wound healing in the Arabidopsis root. I used a UV laser to ablate single cells in the root tip and observed the consequent wound healing. Interestingly, the inner adjacent cells induced a
division plane switch and subsequently adopted the cell type of the killed cell to replace it. We termed this form of wound healing “restorative divisions”. This initial observation triggered the questions of my PhD studies: How and why do cells orient their division planes, how do they feel the wound and why does this happen only in inner adjacent cells.
For answering these questions, I used a quite simple experimental setup: 5 day - old seedlings were stained with propidium iodide to visualize cell walls and dead cells; ablation was carried out using a special laser cutter and a confocal microscope. Adaptation of the novel vertical microscope system made it possible to observe wounds in real time. This revealed that restorative divisions occur at increased frequency compared to normal divisions. Additionally,
the major plant hormone auxin accumulates in wound adjacent cells and drives the expression of the wound-stress responsive transcription factor ERF115. Using this as a marker gene for wound responses, we found that an important part of wound signalling is the sensing of the collapse of the ablated cell. The collapse causes a radical pressure drop, which results in strong tissue deformations. These deformations manifest in an invasion of the now free spot specifically by the inner adjacent cells within seconds, probably because of higher pressure of the inner tissues. Long-term imaging revealed that those deformed cells continuously expand towards the wound hole and that this is crucial for the restorative division. These wound-expanding cells exhibit an abnormal, biphasic polarity of microtubule arrays
before the division. Experiments inhibiting cell expansion suggest that it is the biphasic stretching that induces those MT arrays. Adapting the micromanipulator aspiration system from animal scientists at our institute confirmed the hypothesis that stretching influences microtubule stability. In conclusion, this shows that microtubules react to tissue deformation
and this facilitates the observed division plane switch. This puts mechanical cues and tensions at the most prominent position for explaining the growth and wound healing properties of plants. Hence, it shines light onto the importance of understanding mechanical signal transduction.
AU - Hörmayer, Lukas
ID - 9992
SN - 2663-337X
TI - Wound healing in the Arabidopsis root meristem
ER -
TY - THES
AB - This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning
non-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces.
AU - Portinale, Lorenzo
ID - 10030
SN - 2663-337X
TI - Discrete-to-continuum limits of transport problems and gradient flows in the space of measures
ER -
TY - THES
AB - Algorithms in computational 3-manifold topology typically take a triangulation as an input and return topological information about the underlying 3-manifold. However, extracting the desired information from a triangulation (e.g., evaluating an invariant) is often computationally very expensive. In recent years this complexity barrier has been successfully tackled in some cases by importing ideas from the theory of parameterized algorithms into the realm of 3-manifolds. Various computationally hard problems were shown to be efficiently solvable for input triangulations that are sufficiently “tree-like.”
In this thesis we focus on the key combinatorial parameter in the above context: we consider the treewidth of a compact, orientable 3-manifold, i.e., the smallest treewidth of the dual graph of any triangulation thereof. By building on the work of Scharlemann–Thompson and Scharlemann–Schultens–Saito on generalized Heegaard splittings, and on the work of Jaco–Rubinstein on layered triangulations, we establish quantitative relations between the treewidth and classical topological invariants of a 3-manifold. In particular, among other results, we show that the treewidth of a closed, orientable, irreducible, non-Haken 3-manifold is always within a constant factor of its Heegaard genus.
AU - Huszár, Kristóf
ID - 8032
SN - 2663-337X
TI - Combinatorial width parameters for 3-dimensional manifolds
ER -
TY - THES
AB - In the thesis we focus on the interplay of the biophysics and evolution of gene regulation. We start by addressing how the type of prokaryotic gene regulation – activation and repression – affects spurious binding to DNA, also known as
transcriptional crosstalk. We propose that regulatory interference caused by excess regulatory proteins in the dense cellular medium – global crosstalk – could be a factor in determining which type of gene regulatory network is evolutionarily preferred. Next,we use a normative approach in eukaryotic gene regulation to describe minimal
non-equilibrium enhancer models that optimize so-called regulatory phenotypes. We find a class of models that differ from standard thermodynamic equilibrium models by a single parameter that notably increases the regulatory performance. Next chapter addresses the question of genotype-phenotype-fitness maps of higher dimensional phenotypes. We show that our biophysically realistic approach allows us to understand how the mechanisms of promoter function constrain genotypephenotype maps, and how they affect the evolutionary trajectories of promoters.
In the last chapter we ask whether the intrinsic instability of gene duplication and amplification provides a generic alternative to canonical gene regulation. Using mathematical modeling, we show that amplifications can tune gene expression in many environments, including those where transcription factor-based schemes are
hard to evolve or maintain.
AU - Grah, Rok
ID - 8155
SN - 2663-337X
TI - Gene regulation across scales – how biophysical constraints shape evolution
ER -
TY - THES
AB - Designing and verifying concurrent programs is a notoriously challenging, time consuming, and error prone task, even for experts. This is due to the sheer number of possible interleavings of a concurrent program, all of which have to be tracked and accounted for in a formal proof. Inventing an inductive invariant that captures all interleavings of a low-level implementation is theoretically possible, but practically intractable. We develop a refinement-based verification framework that provides mechanisms to simplify proof construction by decomposing the verification task into smaller subtasks.
In a first line of work, we present a foundation for refinement reasoning over structured concurrent programs. We introduce layered concurrent programs as a compact notation to represent multi-layer refinement proofs. A layered concurrent program specifies a sequence of connected concurrent programs, from most concrete to most abstract, such that common parts of different programs are written exactly once. Each program in this sequence is expressed as structured concurrent program, i.e., a program over (potentially recursive) procedures, imperative control flow, gated atomic actions, structured parallelism, and asynchronous concurrency. This is in contrast to existing refinement-based verifiers, which represent concurrent systems as flat transition relations. We present a powerful refinement proof rule that decomposes refinement checking over structured programs into modular verification conditions. Refinement checking is supported by a new form of modular, parameterized invariants, called yield invariants, and a linear permission system to enhance local reasoning.
In a second line of work, we present two new reduction-based program transformations that target asynchronous programs. These transformations reduce the number of interleavings that need to be considered, thus reducing the complexity of invariants. Synchronization simplifies the verification of asynchronous programs by introducing the fiction, for proof purposes, that asynchronous operations complete synchronously. Synchronization summarizes an asynchronous computation as immediate atomic effect. Inductive sequentialization establishes sequential reductions that captures every behavior of the original program up to reordering of coarse-grained commutative actions. A sequential reduction of a concurrent program is easy to reason about since it corresponds to a simple execution of the program in an idealized synchronous environment, where processes act in a fixed order and at the same speed.
Our approach is implemented the CIVL verifier, which has been successfully used for the verification of several complex concurrent programs. In our methodology, the overall correctness of a program is established piecemeal by focusing on the invariant required for each refinement step separately. While the programmer does the creative work of specifying the chain of programs and the inductive invariant justifying each link in the chain, the tool automatically constructs the verification conditions underlying each refinement step.
AU - Kragl, Bernhard
ID - 8332
SN - 2663-337X
TI - Verifying concurrent programs: Refinement, synchronization, sequentialization
ER -
TY - THES
AB - Fabrication of curved shells plays an important role in modern design, industry, and science. Among their remarkable properties are, for example, aesthetics of organic shapes, ability to evenly distribute loads, or efficient flow separation. They find applications across vast length scales ranging from sky-scraper architecture to microscopic devices. But, at
the same time, the design of curved shells and their manufacturing process pose a variety of challenges. In this thesis, they are addressed from several perspectives. In particular, this thesis presents approaches based on the transformation of initially flat sheets into the target curved surfaces. This involves problems of interactive design of shells with nontrivial mechanical constraints, inverse design of complex structural materials, and data-driven modeling of delicate and time-dependent physical properties. At the same time, two newly-developed self-morphing mechanisms targeting flat-to-curved transformation are presented.
In architecture, doubly curved surfaces can be realized as cold bent glass panelizations. Originally flat glass panels are bent into frames and remain stressed. This is a cost-efficient fabrication approach compared to hot bending, when glass panels are shaped plastically. However such constructions are prone to breaking during bending, and it is highly
nontrivial to navigate the design space, keeping the panels fabricable and aesthetically pleasing at the same time. We introduce an interactive design system for cold bent glass façades, while previously even offline optimization for such scenarios has not been sufficiently developed. Our method is based on a deep learning approach providing quick
and high precision estimation of glass panel shape and stress while handling the shape
multimodality.
Fabrication of smaller objects of scales below 1 m, can also greatly benefit from shaping originally flat sheets. In this respect, we designed new self-morphing shell mechanisms transforming from an initial flat state to a doubly curved state with high precision and detail. Our so-called CurveUps demonstrate the encodement of the geometric information
into the shell. Furthermore, we explored the frontiers of programmable materials and showed how temporal information can additionally be encoded into a flat shell. This allows prescribing deformation sequences for doubly curved surfaces and, thus, facilitates self-collision avoidance enabling complex shapes and functionalities otherwise impossible.
Both of these methods include inverse design tools keeping the user in the design loop.
AU - Guseinov, Ruslan
ID - 8366
KW - computer-aided design
KW - shape modeling
KW - self-morphing
KW - mechanical engineering
SN - 2663-337X
TI - Computational design of curved thin shells: From glass façades to programmable matter
ER -
TY - THES
AB - Form versus function is a long-standing debate in various design-related fields, such as architecture as well as graphic and industrial design. A good design that balances form and function often requires considerable human effort and collaboration among experts from different professional fields. Computational design tools provide a new paradigm for designing functional objects. In computational design, form and function are represented as mathematical
quantities, with the help of numerical and combinatorial algorithms, they can assist even novice users in designing versatile models that exhibit their desired functionality. This thesis presents three disparate research studies on the computational design of functional objects: The appearance of 3d print—we optimize the volumetric material distribution for faithfully replicating colored surface texture in 3d printing; the dynamic motion of mechanical structures—
our design system helps the novice user to retarget various mechanical templates with different functionality to complex 3d shapes; and a more abstract functionality, multistability—our algorithm automatically generates models that exhibit multiple stable target poses. For each of these cases, our computational design tools not only ensure the functionality of the results but also permit the user aesthetic freedom over the form. Moreover, fabrication constraints
were taken into account, which allow for the immediate creation of physical realization via 3D printing or laser cutting.
AU - Zhang, Ran
ID - 8386
SN - 2663-337X
TI - Structure-aware computational design and its application to 3D printable volume scattering, mechanism, and multistability
ER -
TY - THES
AB - Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications.
For the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries.
AU - Ölsböck, Katharina
ID - 7460
KW - shape reconstruction
KW - hole manipulation
KW - ordered complexes
KW - Alpha complex
KW - Wrap complex
KW - computational topology
KW - Bregman geometry
SN - 2663-337X
TI - The hole system of triangulated shapes
ER -
TY - THES
AB - We study the interacting homogeneous Bose gas in two spatial dimensions in the thermodynamic limit at fixed density. We shall be concerned with some mathematical aspects of this complicated problem in many-body quantum mechanics. More specifically, we consider the dilute limit where the scattering length of the interaction potential, which is a measure for the effective range of the potential, is small compared to the average distance between the particles. We are interested in a setting with positive (i.e., non-zero) temperature. After giving a survey of the relevant literature in the field, we provide some facts and examples to set expectations for the two-dimensional system. The crucial difference to the three-dimensional system is that there is no Bose–Einstein condensate at positive temperature due to the Hohenberg–Mermin–Wagner theorem. However, it turns out that an asymptotic formula for the free energy holds similarly to the three-dimensional case.
We motivate this formula by considering a toy model with δ interaction potential. By restricting this model Hamiltonian to certain trial states with a quasi-condensate we obtain an upper bound for the free energy that still has the quasi-condensate fraction as a free parameter. When minimizing over the quasi-condensate fraction, we obtain the Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity, which plays an important role in our rigorous contribution. The mathematically rigorous result that we prove concerns the specific free energy in the dilute limit. We give upper and lower bounds on the free energy in terms of the free energy of the non-interacting system and a correction term coming from the interaction. Both bounds match and thus we obtain the leading term of an asymptotic approximation in the dilute limit, provided the thermal wavelength of the particles is of the same order (or larger) than the average distance between the particles. The remarkable feature of this result is its generality: the correction term depends on the interaction potential only through its scattering length and it holds for all nonnegative interaction potentials with finite scattering length that are measurable. In particular, this allows to model an interaction of hard disks.
AU - Mayer, Simon
ID - 7514
SN - 2663-337X
TI - The free energy of a dilute two-dimensional Bose gas
ER -
TY - THES
AB - This thesis is based on three main topics: In the first part, we study convergence of discrete gradient flow structures associated with regular finite-volume discretisations of Fokker-Planck equations. We show evolutionary I convergence of the discrete gradient flows to the L2-Wasserstein gradient flow corresponding to the solution of a Fokker-Planck
equation in arbitrary dimension d >= 1. Along the argument, we prove Mosco- and I-convergence results for discrete energy functionals, which are of independent interest for convergence of equivalent gradient flow structures in Hilbert spaces.
The second part investigates L2-Wasserstein flows on metric graph. The starting point is a Benamou-Brenier formula for the L2-Wasserstein distance, which is proved via a regularisation scheme for solutions of the continuity equation, adapted to the peculiar geometric structure of metric graphs. Based on those results, we show that the L2-Wasserstein space over a metric graph admits a gradient flow which may be identified as a solution of a Fokker-Planck equation.
In the third part, we focus again on the discrete gradient flows, already encountered in the first part. We propose a variational structure which extends the gradient flow structure to Markov chains violating the detailed-balance conditions. Using this structure, we characterise contraction estimates for the discrete heat flow in terms of convexity of
corresponding path-dependent energy functionals. In addition, we use this approach to derive several functional inequalities for said functionals.
AU - Forkert, Dominik L
ID - 7629
SN - 2663-337X
TI - Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains
ER -