@phdthesis{21651,
  abstract     = {Blockchains enable distributed consensus in permissionless settings, where participants
are unknown, dynamically changing, and do not trust each other. While Bitcoin,
based on Proof-of-Work (PoW), was the first protocol in this model, significant
research has focused on permissionless protocols using alternative physical resources,
specifically Proof-of-Space (PoSpace) and Verifiable Delay Functions (VDFs). This
thesis investigates the theoretical limits and design space of longest-chain protocols in
the fully permissionless and dynamically available settings using these three resources.
First, we address the feasibility of blockchains relying solely on storage as a resource.
We prove a fundamental impossibility result: there exists no secure longest-chain
protocol based exclusively on Proof-of-Space in the fully permissionless or dynamically
available settings. Further, we quantify the adversarial capabilities required to execute
a double-spend attack. Our result formally justifies the necessity of coupling PoSpace
with time-dependent primitives (such as VDFs) or to move to less permissive settings
(quasi-permissionless or permissioned) to ensure security.
Second, we generalize Nakamoto-like heaviest chain consensus to protocols utilizing
combinations of multiple physical resources. We analyze chain selection rules governed
by a weight function Γ(S, V,W), which assigns weight to blocks based on recorded
Space (S), VDF speed (V ), and Work (W). We provide a complete classification
of secure weight functions, proving that a weight function is secure against private
double-spend attacks if and only if it is homogeneous in the timed resources (V,W)
and sub-homogeneous in S. This framework unifies existing protocols like Bitcoin and
Chia under a single theoretical model and provides a powerful tool for designing new
longest-chain blockchains from a mix of physical resources.},
  author       = {Baig, Mirza Ahad},
  isbn         = {978-3-99078-078-7},
  issn         = {2663-337X},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{On secure chain selection rules from physical resources in a permissionless setting}},
  doi          = {10.15479/AT-ISTA-21651},
  year         = {2026},
}

@phdthesis{21854,
  abstract     = {As neural-network-based models grow both in size and popularity, interest has grown in making the models smaller and more efficient to train. To that end, many methods have been proposed to prune models by reducing their number of nonzero parameters. Additionally, parameter-efficient fine-tuning, in which a much smaller number of parameters than the total contained in the model is updated during training, has become very popular, especially in the space of Large Language Models. At the same time, the increasingly routine deployment of machine learning in real-world applications has spurred a drive to make them more trustworthy - in the sense of, among other things, being unbiased, interpretable, and editable. In this thesis, we examine the interplay between efficiency and trustworthiness.

First, we analyze the effects of model pruning on bias in computer vision models, demonstrating that increased sparsity leads to greater bias, largely as a function of increased model uncertainty in marginal cases. Based on this observation, we propose several bias mitigation techniques. Then, we demonstrate that example-specific model pruning can improve model interpretation methods while improving pruning efficiency to make example-specific model pruning feasible in real time. Then, we investigate the effectiveness of parameter-efficient and data-efficient model personalization via fine-tuning, demonstrating that it is highly feasible with very small computational and data resources. Finally, we consider efficiency in editing model knowledge using a custom synthetic data framework, demonstrating that parameter-efficient, low-rank fine-tuning frequently outperforms full-rank fine-tuning, and, additionally, that restricting which model blocks are fine-tuned frequently improves results. Together, the results in this thesis provide new insights and techniques for combining trustworthiness and efficiency during neural network inference and training.

-----------------“In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of [name of university or educational entity]’s products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to http://www.ieee.org/publications_standards/publications/rights/rights_link.html to learn how to obtain a License from RightsLink. If applicable, University Microfilms and/or ProQuest Library, or the Archives of Canada may supply single copies of the dissertation.”},
  author       = {Iofinova, Eugenia B},
  issn         = {2663-337X},
  pages        = {237},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{On the utility and effects of efficiency in artificial neural networks}},
  doi          = {10.15479/AT-ISTA-21854},
  year         = {2026},
}

@phdthesis{21863,
  abstract     = {Atoms and photons, two things so different but yet so alike. The former, the building block of matter, something we learn about in school and imagine it as some tiny marbles encircled by other tinier marbles. The latter, an electromagnetic wave, a light particle or an excitation of the electromagnetic field. Quantum mechanics tells us about the properties of these two entities. And even if it sounds, looks and writes counter-intuitive, it has proven right for over a century now.

In this work, I elaborate on how we tested the laws of quantum mechanics and how we used them learn more about the tiny building blocks of nature and the fields they use to talk to each other. The atoms we use, are artificial. Superconducting qubits, small electrical circuits with quantized energy levels behave like electrons that transition between different orbitals in an atom. One of the qubits' advantages, is also a big disadvantage. We design the circuits' energy levels and fabricate them in a cleanroom. This allows for arbitrary spaced energy levels but in contrast to real atoms, prevents two superconducting qubits from being alike. Still, this qubit platform is one of the frontrunners for future quantum computing technology and testing fundamental physics due to their scalability.

We interface superconducting qubits, which operate in the GHz regime, with microwave photons. We use 3D aluminum cavities as mediators between qubits and photons. The cavities allow for non-destructive readout of the qubit state, they shield the qubits from noise at the qubit frequency and they give us an easy way to frequency-tune these joint systems.

We need to operate superconducting qubits and their cavities at millikelvin temperatures in dilution refrigerators. At higher temperatures, superconductivity suffers and even worse, the environment is filled with thermal noise photons. This poses a fundamental limitation on the scalability of superconducting qubit devices. Also connecting multiple devices in different fridges does not work over room temperature links because the microwave photons used for this purpose will be covered in noise and the quantum information they carry, will be unusable.

Infrared photons do not suffer from this noise problem since there are close to zero thermal noise photons at their frequencies at room temperature. We cannot simply interface superconducting devices with optical photons due their frequency mismatch and the destructive effect of optical photons on superconductors. Therefore, we use microwave-to-optics transducers that allow to convert microwave photons into optical ones and vice-versa. The transducers that we use are macroscopic electro-optic transducers using the Pockels effect in a disk-shaped Lithium Niobate whispering gallery mode resonator. By using a strong optical pump, photons from the two frequency domains experience a beam-splitter interaction and get converted from one to the other.

We measure the generated optical photons using elaborate optical setups, optical heterodyning and single photon detectors to gain knowledge about the qubit state or the converted microwave photons. Bridging the microwave and the optical world allows us to take advantage of both of their strengths but it also requires deep knowledge about both of their working principles.

In this work, we describe two experiments that our group conducted to showcase the opportunities that arise from interfacing superconducting qubits with optical photons but also the pitfalls, one may encounter on the way.

In the first experiment, we managed to all-optically read out a superconducting qubit. We show that the assignment fidelity, the probability that a measurement of the qubit state matches the prepared state, is close to equal for all-optical, microwave-to-optics and conventional microwave readout. We show T1 and T2 measurements for all three readout types and give an analysis of the noise caused by the optics. Finally, we show that the infrared light does not affect the qubit performance in a negative way but that the heating it causes does. This is an important insight that we used in the next experiment.

The second experiment is the upconversion of itinerant single microwave photons to the optical domain. We show that we can generate single microwave photons from a qubit-cavity system. We upconvert these single photons, measure them with a single photon detector and reconstruct their shape. By conducting a single photon Rabi measurement, we show correlations between the microwave and the optical domain. And by thorough signal-to-noise measurements and noise analysis, we find that we can generate single infrared photons with high signal-to-noise ratio 5.1 and low transducer added noise (<0.012 quanta). We show that this measurement creates a path towards entanglement of a superconducting qubit and an optical photon and what parameters need to be improved to achieve it. Additionally, this experiment is a proof of principle for an on-demand infrared single photon source. More generally, it allows to link microwave quantum technology in general to the optical domain.},
  author       = {Werner, Thomas},
  issn         = {2663-337X},
  keywords     = {Superconducting qubits, Quantum optics, Single photons and quantum effects, Nonlinear optics},
  pages        = {97},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Interfacing superconducting qubits with optical photons}},
  doi          = {10.15479/AT-ISTA-21863},
  year         = {2026},
}

@phdthesis{21918,
  author       = {Khudiakova, Kseniia},
  issn         = {2663-337X},
  pages        = {89},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{How epistasis and purifying selection shape genetic diversity}},
  doi          = {10.15479/AT-ISTA-21918},
  year         = {2026},
}

@phdthesis{21957,
  abstract     = {This thesis investigates algorithmic certification and approximation methods for degenerate semidefinite programs (SDPs) and the singular roots of polynomial systems. In the first part, we present a hybrid symbolic-numeric algorithm for certifying the feasibility of weakly feasible, degenerate SDPs. By reformulating linear matrix inequalities (LMIs) into a structured polynomial system via facial reduction and incidence varieties, we guarantee the existence of an isolated exact solution. This algebraic reduction enables the certification of maximum-rank numerical approximations using methods from algebraic geometry.

In the second part, we address the severe ill-conditioning and loss of quadratic convergence that plague standard path-tracking methods near isolated singular roots. To overcome this, we propose tracking algorithms that achieve superlinear convergence without the computational bloat characteristic of classical deflation techniques. By modeling the solution path as a generalized fractional Puiseux series, our approach combines an explicitly derived algebraic predictor with a localized hyperplane desingularization phase during the corrector step. Furthermore, we introduce a continuous path-limit method and an extension of the geometric sequence rule to directly extract exact fractional exponents. This bypasses traditional heuristic trial-and-error methods and explicitly accommodates sparse series expansions. Numerical experiments confirm that our method significantly reduces the cumulative number of matrix inversions while achieving high-accuracy root approximations, even for heavily degenerate systems exhibiting higher coranks.},
  author       = {Zapata, Jeferson},
  isbn         = {978-3-99078-079-4},
  issn         = {2663-337X},
  pages        = {89},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Overcoming degeneracy and singularity : Techniques for semidefinite programs and homotopy continuation endgames}},
  doi          = {10.15479/AT-ISTA-21957},
  year         = {2026},
}

@phdthesis{20991,
  abstract     = {Rapid local adaptation to new environments is critical for species persistence, especially in introduced populations. The evolutionary success of these populations is fundamentally dictated by the organization of genetic variation—the genomic architecture—in the face of severe demographic constraints, such as the founder effects and genetic bottlenecks that frequently accompany colonization. A central question in evolutionary biology is whether rapid adaptation relies on major-effect loci, such as chromosomal inversions, or on many small-effect loci dispersed across the genome. Furthermore, the genomic architecture strongly influences the extent to which evolutionary outcomes are predictable. Using introduced populations of the marine snail, Littorina saxatilis, as a model, this thesis investigates how genetic variation and genomic structure drive adaptation following introduction. We employed a population genomics approach on experimentally and accidentally introduced populations to dissect the specific genomic features that underpin divergence in newly colonized environments.

In Chapter 2, we tested the predictability of local adaptation through an uncommon 30-year transplant experiment in nature. By distinguishing allele and chromosomal inversion frequency changes from neutral expectations, we found that evolutionary change was highly predictable at the macro-scale (phenotypes and chromosomal inversions), but less robust at the level of individual collinear loci. This result demonstrates that evolution can be predictable when a population possesses sufficient standing genetic variation (SGV), with chromosomal inversions acting as key integrated units that facilitate a rapid response to selection. Building on this, Chapter 3 applied whole-genome sequencing to three accidentally introduced populations (Venice, San Francisco, and Redwood City) to investigate their likely source and genomic patterns of divergence. We identified genomic regions of remarkable divergence potentially associated with local adaptation, and likely fuelled by SGV, while explicitly acknowledging the difficulty in disentangling selection signals from the genome-wide effects of demographic processes. Furthermore, we found that the divergence patterns relied extensively on the collinear genome in these introduced populations, and less clearly on the chromosomal inversions. This observation contrasts with local adaptation observed in the experimental system that relied on both collinear loci and highly selected chromosomal inversions, highlighting how demographic history and genomic architecture influence the detectable signature of local adaptation.

A major limitation to conducting large-scale comparative evolutionary studies is the lack of data standardization, which prevents the integration of community knowledge and high-resolution environmental and genetic data. Chapter 4 addresses this by developing a community database for the Littorina system. This platform implements standardized protocols for the integration of diverse phenotypic and environmental data from multiple Littorina species. Likewise, the platform also centralizes the availability of associated genomic data through links to external repositories. This database represents a crucial tool to test complex, large-scale evolutionary hypotheses.

Collectively, this thesis strongly reinforces the fundamental importance of SGV as the raw material for successful local adaptation, a conclusion supported by evidence in both experimental and accidental introductions. Furthermore, this work highlights the critical role of the genomic architecture—specifically chromosomal inversions—in driving the predictability and effectiveness of adaptive responses. Our findings underscore how the interplay between SGV and genomic architecture dictates the trajectory and detectability of evolution in colonizing populations, while simultaneously providing a necessary tool to advance comparative evolutionary genomics in emerging model organisms.},
  author       = {Garcia Castillo, Diego Fernando},
  isbn         = {978-3-99078-077-0},
  issn         = {2663-337X},
  pages        = {199},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{The genomic architecture of local adaptation in introduced populations}},
  doi          = {10.15479/AT-ISTA-20991},
  year         = {2026},
}

@phdthesis{21021,
  abstract     = {This thesis examines how geometry and topology intersect in the representation, transformation, and analysis of complex shapes. It considers how continuous manifolds relate to their discrete analogues, how topological structures evolve in persistence vineyards, and how tools from topological data analysis can illuminate problems in mathematical physics. Central to this exploration is the question of how structure, both geometric and topological, persists or changes under approximation, sampling, or deformation. The work develops new approaches to skeletal and grid-based representations of surfaces, reveals the full expressive capacity of persistence vineyards, and applies topological methods to the longstanding problem of equilibria in electrostatic fields. These threads braid together into a broader understanding of how topology and geometry inform one another across theory, computation, and application.},
  author       = {Fillmore, Christopher D},
  issn         = {2663-337X},
  pages        = {122},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Braiding geometry and topology to study shapes and data}},
  doi          = {10.15479/AT-ISTA-21021},
  year         = {2026},
}

@phdthesis{21198,
  abstract     = {In recent years there has been a massive increase in the amount of data generated in a
decentralized manner. Ever more powerful edge devices, such as smartphones, have become
ubiquitous in most societies on earth. Through text typed, photos taken and apps used,
these devices, which we refer to as clients, generate enormous amounts of high quality and
complex data. Moreover, the nature of these devices means the data they generate is often
sensitive and privacy concerns prevent it being gathered and stored in a central location. This
presents a challenge to the modern machine learning paradigm that requires central access
to large amounts of data. Federated learning (FL) has emerged as one of the answers to
this problem. Rather than bringing the data to the model, FL sends the model to the data.
Model training takes place on device, with periodically synchronized updates, allowing data to
remain locally stored. While this approach offers significant privacy advantages it comes with
its own set of unique challenges. These include: data heterogeneity, the notion that different
devices generate data in distinct ways which can negatively impact training dynamics; systems
heterogeneity, meaning that different devices may have differing hardware specifications; high
communication costs, which are induced by the repeated transferring of models over the
network and low device computational power, which limits the use of larger models on device.
In this thesis we present a range of methods for federated learning. We focus primarily on
the challenge of data heterogeneity, though the methods presented are designed to be well
adapted to the other challenges of a federated setting, such as the constraints of limited
compute and communication overhead. We first present a method for explicitly modeling client
data heterogeneity. The approach formulates clients as samples from a certain probability
distribution and infers the parameters of this distribution from the available training clients.
This learned distribution then represents the heterogeneity present among the clients and can
be sampled from in order to create new simulated clients that are similar to the real clients we
have observed so far. Following this we present two methods for directly dealing with data
heterogeneity through personalization. Highly heterogeneous client data distributions can mean
that learning a single global model becomes suboptimal, and some form of personalization of
models to each individual client is required. Our approaches are based around hypernetworks,
which we use to generate personalized model parameters without the need for additional
training or finetuning. In the first approach we focus on generating full parameterizations of
client models using learned embeddings of client data and labels, with a hypernetwork located
on the central server. In the second approach we address the more challenging scenario where
we want to generate a personalized model for a client without any label information. The
hypernetwork is trained to generate a low dimensional representation of a client’s personalized
model parameters, allowing it to be transferred to and run on the client devices. In our final
presented method, we change our focus and rather than aim to directly address the challenge
of data heterogeneity, we instead ensure we are unaffected by it. This is done in the context
of k-means clustering and we present a method for federated clustering with a focus on added
privacy guarantees.},
  author       = {Scott, Jonathan A},
  issn         = {2663-337X},
  pages        = {158},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Data heterogeneity and personalization in federated learning}},
  doi          = {10.15479/AT-ISTA-21198},
  year         = {2026},
}

@phdthesis{21360,
  author       = {Riegler, Stefan},
  issn         = {2663-337X},
  pages        = {185},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Root system plasticity under nutrient limitation : Investigating hormonal and molecular drivers in Arabidopsis thaliana and Coffea  species}},
  doi          = {10.15479/AT-ISTA-21360},
  year         = {2026},
}

@phdthesis{21393,
  abstract     = {This thesis documents a voyage towards truth and beauty via formal verification of theorems. To this end, we develop libraries in Lean 4 that present definitions and results from diverse areas of MathematiCS (i.e., Mathematics and Computer Science). The aim is to create code that is understandable, believable, useful, and elegant. The code should stand for itself as much as possible without a need for documentation; however, this text redundantly documents our code artifacts and provides additional context that isn’t present in the code. This thesis is written for readers who know Lean 4 but are not familiar with any of the topics presented. We manifest truth and beauty in three formalized areas of MathematiCS.

We formalize general grammars in Lean 4 and use grammars to show closure of the class of type-0 languages under four operations; union, reversal, concatenation, and the Kleene star.

Our second stop is the theory of optimization. Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the case when some coefficients are allowed to take “infinite values”. Additionally, we develop the basics of the theory of optimization in terms of the framework called General-Valued Constraint Satisfaction Problems, and we prove that, if a Rational-Valued Constraint Satisfaction Problem template has symmetric fractional polymorphisms of all arities, then its basic LP relaxation is tight.

Our third stop is matroid theory. Seymour’s decomposition theorem is a hallmark result in matroid theory, presenting a structural characterization of the class of regular matroids. We aim to formally verify Seymour’s theorem in Lean 4. First, we build a library for working with totally unimodular matrices. We define binary matroids and their standard representations, and we prove that they form a matroid in the sense how Mathlib defines matroids. We define regular matroids to be matroids for which there exists a full representation rational matrix that is totally unimodular, and we prove that all regular matroids are binary. We define 1-sum, 2-sum, and 3 sum of binary matroids as specific ways to compose their standard representation matrices. We prove that the 1-sum, the 2-sum, and the 3-sum of regular matroids are a regular matroid, which concludes the composition direction of the Seymour’s theorem. The (more difficult) decomposition direction remains unproved.

In the pursuit of truth, we focus on identifying the trusted code in each project and presenting it faithfully. We emphasize the readability and believability of definitions rather than choosing definitions that are easier to work with. In search for beauty, we focus on the philosophical framework of Roger Scruton, who emphasizes that beauty is not a mere decoration but, most importantly, beauty is the means for shaping our place in the world and a source of redemption, where it can be viewed as a substitute for religion.},
  author       = {Dvorak, Martin},
  isbn         = {978-3-99078-074-9},
  issn         = {2663-337X},
  pages        = {160},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Pursuit of truth and beauty in Lean 4 : Formally verified theory of grammars, optimization, matroids}},
  doi          = {10.15479/AT-ISTA-21393},
  year         = {2026},
}

@phdthesis{21423,
  author       = {Dunajova, Zuzana},
  isbn         = {978-3-99078-076-3},
  issn         = {2663-337X},
  pages        = {110},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Geometry-driven self-organization of migrating cells and chiral filaments}},
  doi          = {10.15479/AT-ISTA-21423},
  year         = {2026},
}

@phdthesis{19478,
  author       = {Chen, Huihuang},
  issn         = {2663-337X},
  pages        = {118},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{The cAMP second messenger in auxin signalling}},
  doi          = {10.15479/AT-ISTA-19478},
  year         = {2025},
}

@phdthesis{19540,
  abstract     = {This thesis deals with several different models for complex quantum mechanical systems and is structured in three main parts. 
	
In Part I, we study mean field random matrices as models for quantum Hamiltonians. Our focus lies on proving concentration estimates for resolvents of random matrices, so-called local laws, mostly in the setting of multiple resolvents. These estimates have profound consequences for eigenvector overlaps and thermalization problems. More concretely, we obtain, e.g., the optimal eigenstate thermalization hypothesis (ETH) uniformly in the spectrum for Wigner matrices, an optimal lower bound on non-Hermitian eigenvector overlaps, and prethermalization for deformed Wigner matrices.	In order to prove our novel multi-resolvent local laws, we develop and devise two main methods, the static Psi-method and the dynamical Zigzag strategy. 
	
In Part II, we study Bardeen-Cooper-Schrieffer (BCS) theory, the standard mean field microscopic theory of superconductivity. We focus on asymptotic formulas for the characteristic critical temperature and energy gap of a superconductor and prove universality of their ratio in various physical regimes. Additionally, we investigate multi-band superconductors and show that inter-band coupling effects can only enhance the critical temperature. 
	
In Part III, we study quantum lattice systems. On the one hand, we show a strong version of the local-perturbations-perturb-locally (LPPL) principle for the ground state of weakly interacting quantum spin systems with a uniform on-site gap. On the other hand, we introduce a notion of a local gap and rigorously justify response theory and the Kubo formula under the weakened assumption of a local gap. 
	
Additionally, we discuss two classes of problems which do not fit into the three main parts of the thesis. These are deformational rigidity of Liouville metrics on the torus and relativistic toy models of particle creation via interior-boundary-conditions (IBCs).  },
  author       = {Henheik, Sven Joscha},
  isbn         = {978-3-99078-057-2},
  issn         = {2663-337X},
  pages        = {720},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems}},
  doi          = {10.15479/AT-ISTA-19540},
  year         = {2025},
}

@phdthesis{19557,
  author       = {Schwarz, Lena A},
  issn         = {2663-337X},
  pages        = {124},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Mapping developmental dynamics of autism spectrum disorder mouse models at single-cell resolution}},
  doi          = {10.15479/AT-ISTA-19557},
  year         = {2025},
}

@phdthesis{19630,
  abstract     = {This thesis consists of three chapters, each corresponding to one publication. While each of these projects tackles a topic in a different area of research, they all share a common thread in the type of topological structure they handle - a partition of space into volumes separated by interfaces that meet in non-manifold junctions.

In Chapter 2, we study clusters of soap bubbles from a simulation perspective. In particular, we develop a surface-only algorithm that couples large scale motion and shape deformation of soap bubble clusters with the small scale evolution of the thin film's thickness, which is responsible for visual phenomena like surface vortices, Newton's interference patterns, capillary waves, and deformation-dependent rupturing of films in a foam. We model film thickness as a reduced degree of freedom in the Navier-Stokes equations and from them derive three sets of equations governing normal and tangential motion of the soap film surface, as well as the evolution of the thin film thickness. We discretize these equations on a non-manifold triangle mesh, extending and adapting operators to handle complex topology. We also present an incompressible fluid solver for 2.5D films and an advection algorithm for convecting fields across non-manifold surface junctions. Our simulations enhance bubble solvers with additional effects caused by convection, rippling, draining, and evaporation of the thin film.

In Chapter 3, we introduce a multi-material non-manifold mesh-based surface tracking algorithm that converts mesh defects, such as overlaps, self-intersections, and inversions into topological changes. Our algorithm generalizes prior work on manifold surface tracking with topological changes: it preserves surface features like mesh-based methods, and it robustly handles topological changes like level set methods. Our method also offers improved efficiency and robustness over the state of the art. We demonstrate the effectiveness of the approach on a range of examples, including complex soap film simulations, such as those presented in Chapter 2, but with an order of magnitude more interacting bubbles than what we could achieve before, and Boolean unions of non-manifold meshes consisting of millions of triangles.

Lastly, in Chapter 4, we utilize developments in the theory of random geometric complexes facilitated by observations from Discrete Morse theory. We survey the methods and results obtained with this new approach, and discuss some of its shortcomings. We use simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics.},
  author       = {Synak, Peter},
  issn         = {2663-337X},
  pages        = {106},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Methods for fluid simulation, surface tracking, and statistics of non-manifold structures}},
  doi          = {10.15479/AT-ISTA-19630},
  year         = {2025},
}

@phdthesis{19684,
  abstract     = {The overarching goal of this thesis is to break down the complexity of turbulent flows in terms of enumerable, coherent structures and patterns. In a five-paper series, we adopt a variety of perspectives and techniques to relate the properties of systems of increasing complexity to their underlying coherent structures. 

Initially, we take a dynamical systems point of view, seeing turbulent flow as a chaotic trajectory bouncing between exact unstable solutions of the underlying equations of motion. Using persistent homology, the main tool of topological data analysis capturing the persistence across scales of topological features in a point cloud, we introduce a method that quantifies visits of turbulent trajectories to unstable time-periodic solutions, also called periodic orbits. We demonstrate this method first in the Rössler and Kuramoto–Sivashinsky systems. Using this method in 3D Kolmogorov flow, we extract a Markov chain from turbulent data, where each node corresponds to the neighbourhood of a periodic orbit. The invariant distribution of this Markov chain reproduces expectation values on turbulent data when it is used to weight averages on the respective periodic orbits.

In more realistic, wall-bounded settings, such as plane-Couette flow (pcf) driven by the relative motion of the walls, or plane-Poiseuille flow (ppf) driven by a pressure gradient, finding exact solutions is difficult. We use dynamic mode decomposition (DMD), a dimensionality reduction method for sequential data, to identify and approximate low-dimensional dynamics without knowing any exact solutions. Most spatially-extended systems are equivariant under translations, and in such cases spatial drifts dominate DMD, hindering its use in the search for and modelling of low-dimensional dynamics. We augment DMD with a symmetry reduction method trained on turbulent data to stop it from seeing translations as a feature, improving its ability to extract dynamical information in translation-equivariant systems. We find segments of turbulent trajectories that linearize well with their symmetry-reduced DMD spectra, akin to dynamics near exact solutions. Searching for harmonics in the spectra gives leads for periodic orbits with spatial drifts, one of which converges to a new solution.

In larger domains, turbulence can localize and coexist with surrounding laminar flow. Our preceding approaches are global, taking all of a domain into account at once, and cannot readily treat each localized patch individually. Working first in a minimal oblique domain that can host a single 1D-localized turbulent patch, we find that turbulence in ppf is connected to a stable periodic orbit at a flow velocity much lower than when turbulence is first onset. We show that, well in advance of sustained turbulence, chaos sets in explosively, and for long time horizons, time series are consistent with that of a random process.

Finally, in much larger domains, we study and compare 2D-localized turbulence that appears as large-scale inclined structures, called stripes, in ppf and pcf. While appearing similar, we find that stripes in these two settings differ significantly in terms of how they sustain themselves, and in higher velocities, how they proliferate.},
  author       = {Yalniz, Gökhan},
  issn         = {2663-337X},
  pages        = {155},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Transition to turbulence : Data-, solution-, and pattern-driven approaches}},
  doi          = {10.15479/AT-ISTA-19684},
  year         = {2025},
}

@phdthesis{19759,
  abstract     = {Despite generating remarkable results in various computer vision tasks, deep learning comes
with some surprising shortcomings. For example, tiny perturbations, often imperceptible to
the human eye, can completely change the predictions of image classifiers. Despite a decade
of research, the field has made limited progress in developing image classifiers that are both
accurate and robust. This thesis aims to address this gap.
As our first contribution, we aim to simplify the process of training certifiably robust image
classifiers. We do this by designing a convolutional layer that does not require executing an
iterative procedure in every forward pass, but relies on an explicit bound instead. We also
propose a loss function that allows optimizing for a particular margin more precisely.
Next, we provide an overview and comparison of various methods that create robust image
classifiers by constraining the Lipschitz constant. This is important since generally longer
training times and more parameters improve the performance of robust classifiers, making it
challenging to determine the most practical and effective methods from existing literature.
In 1-Lipschitz classification, the performance of current methods is still much worse than what
we expect on the simple tasks we consider. Therefore, we next investigate potential causes of
this shortcoming. We first consider the role of the activation function. We prove a theoretical
shortcoming of the commonly used activation function, and provide an alternative without it.
However this theoretical improvement does barely translate to the empirical performance of
robust classifiers, suggesting a different bottleneck.
Therefore, in the final chapter, we study how the performance depends on the amount of
training data. We prove that in the worst case, we might require far more data to train a
robust classifier compared to a normal one. We furthermore find that the amount of training
data is a key determinant of the performance current methods achieve on popular datasets.
Additionally, we show that linear subspaces exist with tiny data variance, and yet we can
still train very accurate classifiers after projecting into those subspaces. This shows that on
the datasets considered, enforcing robustness in classification makes the task strictly more
challenging.

-----------------“In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of [name of university or educational entity]’s products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to http://www.ieee.org/publications_standards/publications/rights/rights_link.html to learn how to obtain a License from RightsLink. If applicable, University Microfilms and/or ProQuest Library, or the Archives of Canada may supply single copies of the dissertation.”
},
  author       = {Prach, Bernd},
  issn         = {2663-337X},
  pages        = {84},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Robust image classification with 1-Lipschitz networks}},
  doi          = {10.15479/10.15479/at-ista-19759},
  year         = {2025},
}

@phdthesis{19903,
  abstract     = {Cooperation, that is, one person paying a cost for another's benefit, is a fundamental principle without which no form of society could exist. The extent to which humans cooperate with each other is also an essential feature that differentiates them from other animals. Cooperation occurs even in the absence of altruistic motivations, when it is selfishly incentivised by the expectation of a future reward. For example, many economic interactions are well described that way. This kind of cooperation requires that people exhibit reciprocal behaviour that acts as a mechanism that rewards cooperation.
With game-theoretic models, it is possible to formally study potential such mechanisms and under what conditions they can exist. This thesis contributes to this effort by analysing recently introduced models of cooperation that advance on previous work by taking into account the potential for pre-existing inequality among cooperating individuals as well as the different forms that reciprocity can take.
Individuals may differ both intrinsically, in their abilities, as well as extrinsically, in the amount of resources they have available. Allowing for such differences in a model of cooperation helps to understand how inequality affects the potential for, and outcomes of, cooperation among unequals. In this thesis, it is shown that in the presence of intrinsic inequality, a similar unequal distribution of resources can increase the potential for cooperation. This effect is stronger the smaller the group is in which cooperation takes place. It is also shown that under particular assumptions, if the unequal members of a group vary the size of their contributions to a cooperative effort over time, they can thereby increase their efficiency and improve the collective outcome.
Cooperative behaviour in a two-person interaction can be rewarded either by direct reciprocation whenever the same two people interact again, or indirectly by a third party who observed the interaction. In the latter case of indirect reciprocity, individuals are proximally rewarded by a good reputation, which ultimately translates to being rewarded with cooperative behaviour by others. This mechanism can enable selfishly motivated cooperation even in circumstances where individuals are unlikely to meet again, akin to how money facilitates trade. While these two forms of reciprocity have mostly been studied in isolation, this thesis analyses both direct and indirect reciprocity in a general model in order to compare their relative effectiveness under different circumstances. The contribution of this thesis is an extension of previous work regarding a specific kind of interaction, whose parameters allow for convenient mathematical analysis, to the most general set of possible interactions.},
  author       = {Hübner, Valentin},
  issn         = {2663-337X},
  pages        = {157},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Reciprocity and inequality in social dilemmas}},
  doi          = {10.15479/AT-ISTA-19903},
  year         = {2025},
}

@phdthesis{20074,
  abstract     = {Prenatal immune challenges pose significant risks to human embryonic brain and eye development. However, we still lack knowledge about the safe usage of anti-inflammatory drugs during pregnancy. Human induced pluripotent stem cell (hIPSC)-derived brain organoid models provide a unique opportunity to investigate neuronal development and have started to explore functional consequences upon viral infection. However, brain organoids usually lack microglia, the brain-resident immune cells. They are present in the early human embryonic brain and actively participate in neuronal circuit development. At the same time, microglia are known for their immune-sensing properties and will influence viral-mediated effects. In my thesis, I was interested to study the multifunctional role of human microglia during retinal development. 
In chapter 1, I characterize the innate occurrence of IBA1+-microglia-like cells within the retinal organoid differentiation (Bartalska et al., 2022). Therefore, we differentiate hIPSC using an unguided retinal organoid differentiation protocol and observe the presence of IBA1+-microglia-like cells alongside retinal cups between week 3 and 4 in 2.5D culture. However, instead of infiltrating the neuroectodermal sides, they enrich within non-pigmented, 3D-cystic compartments that develop in low numbers parallel to 3D-retinal organoids. To enrich for IBA1+-microglia precursors (preMG), we guided the differentiation with a low-dosed BMP4 application, which prevents retinal cup development and enhances microglia and 3D-cysts formation. We characterize the differentiated preMG for their microglia-like identity and validated their functionality. In parallel, mass spectrometry identifies the 3D-cysts to express mesenchymal and epithelial markers. We confirm that comparable 3D-cysts are also the preferential environment for IBA1+-microglia-like cells within the unguided retinal organoid differentiation. 
In chapter 2, I investigate how microglia influence retinal development and whether they contribute to viral-mediated consequences (Schmied et al., 2025). Here, we assemble preMG, which we have characterized in chapter 1, into 3D-retinal organoids. Once the outer plexiform layer forms, microglia-like cells (iMG) populate them and interact with retinal cell types. However, at this developmental stage, the ganglion cell number decreases in 3D-retinal organoids. Thus, we adapted the model into 2D which promotes their survival. Integrated iMG engulf ganglion cells and control their cell number. In parallel, we apply the immunostimulant POLY(I:C) to mimic a fetal viral infection. Although POLY(I:C) stimulation affects iMG phenotype, it does not influence their interaction with ganglion cells. Furthermore, iMG presence significantly contributes to the supernatant’s inflammatory secretome and increases retinal cell proliferation. Simultaneous exposure to the non-steroidal anti-inflammatory drug (NSAID) ibuprofen dampens POLY(I:C)-mediated consequences of the iMG phenotype and ameliorates cell proliferation. Remarkably, while POLY(I:C) disrupts neuronal calcium dynamics independent of iMG presence, ibuprofen rescues this effect only in the presence of iMG. Mechanistically, ibuprofen blocks the enzymes cyclooxygenase 1 and 2 (COX1/ PTGS1 and COX2/ PTGS2) simultaneously, from which iMG predominantly express COX1. Selective inhibition of COX1 does not restore the calcium peak amplitude upon POLY(I:C) stimulation, indicating ibuprofen’s effect depends on the presence and interplay of both, COX1 and COX2. 
In summary, we characterized the 3D-retinal organoid model for the occurrence of IBA1+-microglia like cells. As the innately developing IBA1+-cells enrich in mesenchymal over retinal structures, we optimized a protocol to differentiate IBA1+-microglia precursors. By combining these two models we generate microglia-assembled retinal organoids. Our results underscore the importance of microglia during neurodevelopment, in the context of prenatal immune challenges and provide insight into the mechanisms by which ibuprofen exerts its protective effects during embryonic development.},
  author       = {Hübschmann, Verena},
  isbn         = {978-3-99078-060-2},
  issn         = {2663-337X},
  pages        = {151},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{ Human microglia impact neuronal development in retinal organoids}},
  doi          = {10.15479/AT-ISTA-20074},
  year         = {2025},
}

@phdthesis{20117,
  author       = {Wang, Yiqun},
  issn         = {2663-337X},
  pages        = {108},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{The role of dynamin related protein 2A in cytokinin regulated plant growth and development}},
  doi          = {10.15479/AT-ISTA-20117},
  year         = {2025},
}