@phdthesis{20563, abstract = {The theory of optimal transport provides an elegant and powerful description of many evolution equations as gradient flows. The primary objective of this thesis is to adapt and extend the theory to deal with important equations that are not covered by the classical framework, specifically boundary value problems and kinetic equations. Additionally, we establish new results in periodic homogenization for discrete dynamical optimal transport and in quantization of measures. Section 1.1 serves as an invitation to the classical theory of optimal transport, including the main definitions and a selection of well-established theorems. Sections 1.2-1.5 introduce the main results of this thesis, outline the motivations, and review the current state of the art. In Chapter 2, we consider the Fokker–Planck equation on a bounded set with positive Dirichlet boundary conditions. We construct a time-discrete scheme involving a modification of the Wasserstein distance and, under weak assumptions, prove its convergence to a solution of this boundary value problem. In dimension 1, we show that this solution is a gradient flow in a suitable space of measures. Chapter 3 presents joint work with Giovanni Brigati and Jan Maas. We introduce a new theory of optimal transport to describe and study particle systems at the mesoscopic scale. We prove adapted versions of some fundamental theorems, including the Benamou–Brenier formula and the identification of absolutely continuous curves of measures. Chapter 4 presents joint work with Lorenzo Portinale. We prove convergence of dynamical transportation functionals on periodic graphs in the large-scale limit when the cost functional is asymptotically linear. Additionally, we show that discrete 1-Wasserstein distances converge to 1-Wasserstein distances constructed from crystalline norms on R d . Chapter 5 concerns optimal empirical quantization: the problem of approximating a measure by the sum of n equally weighted Dirac deltas, so as to minimize the error in the p-Wasserstein distance. Our main result is an analog of Zador’s theorem, providing asymptotic bounds for the minimal error as n tends to infinity. }, author = {Quattrocchi, Filippo}, issn = {2663-337X}, keywords = {optimal transport, kinetic equations, boundary value problems, quantization, gradient flows, homogenization}, pages = {240}, publisher = {Institute of Science and Technology Austria}, title = {{Optimal transport methods for kinetic equations, boundary value problems, and discretization of measures}}, doi = {10.15479/AT-ISTA-20563}, year = {2025}, } @phdthesis{19456, abstract = {Making decisions requires flexibly adapting to changing environments, a process that depends on accurately interpreting current contingencies and integrating them with past experience. Two brain regions are particularly critical for this process, the medial prefrontal cortex (mPFC) and the hippocampus. Using contextual information from the hippocampus, the mPFC selects relevant cognitive frameworks and suppresses irrelevant ones to guide appropriate actions. Several studies have shown that some mPFC pyramidal neurons become spatially tuned when spatial information is required to guide goal-directed behavior. However, the role of prefrontal spatial representations in learning and decision making is not well understood. This work aims to characterize the role of mPFC spatial tuning in supporting a contextual association task. Rats were trained to learn two cue–location associations on a radial arm maze over multiple days, while we simultaneously recorded from dorsal CA1 of the hippocampus and the prelimbic area of the mPFC. We describe a subset of spatially tuned hippocampal and prefrontal pyramidal neurons that “flicker” between multiple spatial representations on different trials, suggesting dynamic, context-dependent coding. This flickering may provide a substrate for how the network reorganizes in response to task demands, likely by enabling the flexible evaluation of competing representations. }, author = {Cumpelik, Andrea D}, isbn = {978-3-99078-056-5}, issn = {2663-337X}, keywords = {neuroscience, decision making, learning, cognitive flexibility, medial prefrontal cortex, hippocampus, electrophysiology}, pages = {96}, publisher = {Institute of Science and Technology Austria}, title = {{The role of prefrontal spatial coding in supporting a contextual association task}}, doi = {10.15479/AT-ISTA-19456}, year = {2025}, } @phdthesis{19993, abstract = {Ants are frequently challenged by different pathogens, which they counter with individual and collective responses. Usually, the pathogens like fungi or viruses are solitary and passive pathogens transmitted from host to host. Here, we use a nematobacterial pathogen complex to study worm-borne disease in black garden ants. These entomopathogenic nematodes are active parasites with an own behavior and chasing pray. In the first chapter, we investigated the basic biology of the host-pathogen relationship. We tested different ant life stages and found that adult ants display defense behaviors and are generally resistant to nematode infection, whereas brood is highly susceptible. In the case of worker pupae, we found a slight protective effect of the cocoon. When larvae are accompanied by adults, meaning a queen or a group of workers, survival is significantly enhanced. Moreover, we found that nematodes can transmit from infected cadavers to healthy worker larvae, confirming a transmissible disease in ants. Again, worker presence significantly reduces transmission risk. In the end, we were also able to disentangle the pathogen system and investigate the pathogenic effect of the bacterial and nematode components. In the second chapter, we studied the effect of multiple infections in adult queens and queen larvae. By multiple exposures in the mode of coinfection and superinfections, we wanted to assess the detrimental effect of combined fungal and nematode exposure to better understand how the pathogens interact with each other in an ant host. We found instances where combined exposure lead to higher mortality in a given time frame in both, adult queens and queen larvae. Overall entomopathogenic nematodes are a promising model to study worm infections in ants which extend our knowledge on collective disease defense.}, author = {Strahodinsky, Florian}, issn = {2663-337X}, pages = {138}, publisher = {Institute of Science and Technology Austria}, title = {{Social immunity in a tri-partite host-pathogen relationship}}, doi = {10.15479/AT-ISTA-19993}, year = {2025}, } @phdthesis{19906, abstract = {Flows of ordinary fluids such as water or air transition from laminar to turbulent motion as the velocity increases. This simple dependence of the flow state solely on inertia, does not apply to more complex substances such as polymericand biofluids which commonly have elastic as well as viscous properties. Here various different instabilities and turbulent states can arise at low and even vanishing inertia, while high inertia turbulence counterintuitively is suppressed and its drag strongly reduced. We here show in experiments of a viscoelastic model fluid that the phenomena observed at low and high inertia have a common origin and that the same dynamical state, elasto-inertial turbulence, persists across four orders of magnitude in Reynolds number, ranging from very low inertia, all the way to high inertia Maximum drag reduction (MDR) asymptote. We also explore the transitions from Newtonian turbulence to MDR, and specific cases of flow at high polymer concentrations, exploring the relationship between flow at these wide range of control parameters. }, author = {Suresh, Sarath S}, issn = {2663-337X}, pages = {82}, publisher = {Institute of Science and Technology Austria}, title = {{Turbulence in polymeric flows : A characterisation of elasto-inertial turbulence and the maximum drag reduction asymptote}}, doi = {10.15479/AT-ISTA-19906}, year = {2025}, } @phdthesis{19763, abstract = {Pattern formation in developing organs is controlled by morphogens. These signalling molecules form concentration gradients across tissues, thereby providing positional information that instructs the pattern of cell differentiation. Morphogen gradients are highly dynamic in space and time. Many factors such as morphogen production, spreading, degradation, cellular rearrangements and others could contribute to changes in the gradient shape, yet how the spatiotemporal signalling dynamics arise in many systems is still unclear. We studied the dynamics of morphogen signalling and tissue patterning in the developing vertebrate neural tube. In this system, neural crest, roof plate and distinct dorsal progenitor subtypes are specified in a spatially and temporally ordered manner in response to dorsal-toventral gradients of BMP and WNT signalling activity. How the BMP and WNT gradients are established and interpreted to ensure ordered cell specification is poorly understood. To address this question, we developed a 2D embryonic stem cell differentiation system that captures key features of dorsal neural tube development. In this system, differentiated colonies display remarkable self-organised pattern formation in response to uniformly applied BMP ligand. We established a method of differentiating the colonies using microfabricated stencils, which allowed us to control the initial size and shape of colonies without confining cell migration and colony growth. This led to highly reproducible pattern formation that facilitates quantification. Using this approach, we observed striking two-phase temporal dynamics of BMP signalling in our colonies: a BMP gradient rapidly forms from the periphery to the centre of colonies, subsequently disappears and is re-established again in the second phase. By combining our quantitative data with a data-driven theoretical model, we uncovered a temporal relay mechanism that underlies this biphasic BMP signalling dynamics. The first signalling phase is controlled by fast tissue-autonomous negative feedback that restricts the duration of the initial response to BMP. The early BMP activity gradient moreover controls the spatial organisation of the cell type pattern: the absence of a first phase results in disordered cell type pattern. The second phase is controlled by slow positive regulation of BMP signalling by the transcription factor LMX1A, a key regulator of roof plate identity. WNT promotes the second phase of BMP signalling via positive feedback on LMX1A. Altogether, the mechanism that we uncovered ensures the coupling of sequential developmental events, making pattern formation spatially and temporally organised. Furthermore, this mechanism allows the BMP signalling pathway to be reused in different contexts – first for the establishment of the neural plate border, and subsequently for dorsal neural progenitor patterning. Our study supports a general developmental principle in which multiple morphogens interact with transcriptional networks resulting in complex spatiotemporal signalling dynamics that ultimately drive organised pattern formation.}, author = {Rus, Stefanie}, issn = {2663-337X}, pages = {129}, publisher = {Institute of Science and Technology Austria}, title = {{Dynamics of morphogen signalling and cell fate decisions in the dorsal neural tube}}, doi = {10.15479/AT-ISTA-19763}, year = {2025}, } @phdthesis{18871, abstract = {"Can we do this with a new type of computer - a quantum computer?". This famous quotation of the brilliant Richard Feynman within a conference talk on "Simulating physics with computers.” is often reverently praised as the origin of the field of quantum computing. The idea was to use quantum mechanical systems itself to simulate "Nature", which is inherently quantum mechanical. Now, 43 years later, the theoretical framework of how such a computer can operate has been developed. Two main important concepts for a potential quantum supremacy, superposition and entanglement, have been exploited to design quantum algorithms to significantly speed up certain tasks. Yet, the specific hardware implementation is still far from being certain, in fact the race between the most promising platforms such as superconducting qubits, bosonic codes, cold atoms, trapped ions, optical computing as well as spin qubits has recently intensified. If one also includes the most mature applications of quantum communication technologies, secure quantum key distribution and quantum random number generators, as part of a quantum information technology ecosystem, we are confronted with a plethora of different materials, concepts, and also operation frequencies. While superconducting qubits, bosonic codes and spin qubits work in the regime of approximately 5 GHz and are controlled by electrical fields, trapped ions, cold atoms, and optical quantum computing operate with light in the infrared or visible range. Consequently, a quantum frequency converter or microwave-optic transducer is required to interface the different frequency domains or establish a long-range network connection with suitable telecom fibers. In fact, the combination of different frequency regimes is also an essential part in our classical modern communication network, where computations are performed in electrical circuits and the information exchange over longer distances happens via optical fibers. However, the specific challenges specific to building a quantum computer, also apply to the development of such a quantum frequency transducer: 1) As we deal with single excitations as the carrier of information, i.e. the smallest possible quantity, the signal can easily be corrupted by other noise sources which needs to be avoided by all means. This is also the reason why microwave quantum computers operate at temperature environments close to zero temperature (< 0.1 Kelvin) to avoid corruption by thermal noise. 2) The frequency interface generally needs to preserve the phase of the signal as an essential part of the quantum state. And 3) Quantum signals cannot be copied which would be a typical strategy to account for errors in classical computers. And finally, there is a challenge specific to microwave-optic transducers: While quantum computers are operating in one specific frequency domain, microwave-optic transducers combine microwave and optical fields in one device. This results in the particular challenge that high-energy optical radiation, which is usually well-shielded from superconducting microwave quantum processors, are now an essential part of the device. The concomitant optical radiation in the operating transducer will inevitably have a detrimental effect on the superconducting microwave components. Together with the requirement of minimal background noise for quantum-limited operation as described above, v heating from the absorption of optical photons within the same device where single microwave excitations are processed forms a formidable challenge. This thesis aims to address this challenge by developing microwave-optic transducers where the impact of optical absorption on superconducting circuits in general and superconducting qubits specifically can be mitigated. In our first approach, we developed a compact device with optimized interaction strengths between the different frequency domains. This minimizes the optical powers used for transducer operation and thus the optical absorption heating. This work was - to the best of our knowledge - the first comprehensive noise study, in an integrated microwave-optic transducer. Unfortunately, we saw that the optical absorption heating added noise way above a single excitation. Consequently, a potential quantum signal would have been buried in the noise, added by the transduction. Building on this insight, we utilized a three-dimensional microwave-optic transducer instead of an integrated device. The larger heat capacity of the macroscopic device with a size of a few millimeters can absorb a larger fraction of the optical heating before it increases the temperature of the device. This allowed us to interface the transducer directly with a superconducting qubit to readout the qubit state in a novel all-optical manner. We showed that the microwave-optic transducer can be operated in a regime in which optical fields don’t harm the sensitive qubit. This is an important prerequisite for the operation of microwave-optic transducers in conjunction with microwave quantum processors and brings the integration and seamless orchestration of different frequency components in a quantum network a step closer. }, author = {Arnold, Georg M}, issn = {2663-337X}, pages = {135}, publisher = {Institute of Science and Technology Austria}, title = {{Microwave-optic interconnects for superconducting circuits}}, doi = {10.15479/at:ista:18871}, year = {2025}, } @phdthesis{20694, abstract = {Understanding the mechanisms underlying speciation is a central aim of evolutionary biology. A persistent challenge in the field is to identify loci that contribute to reproductive isolation, while disentangling signals of selection from demography, linkage and intrinsic genomic features. Traditional population genomic approaches that rely on site-based statistics in arbitrary fixed windows face inherent limitations, as they conflate historical and contemporary processes of divergence and overlook haplotype structure. Recent advances in whole-genome sequencing and methods to infer ancestral recombination graphs (ARGs) now offer the opportunity to study genealogical relationships explicitly, revealing how lineages coalesce and recombine through time. By directly analysing haplotype clustering by species or phenotype and their patterns of coalescence, ARG-based methods show promise for diagnosing sweeps, identifying barrier loci maintained under divergent selection amid gene flow, and tracing their evolutionary history. In this thesis, I explore the utility of genealogical approaches for studying species divergence. In chapter 2, I propose a conceptual framework for defining haplotype blocks through the structure of the ARG, using simulations and empirical data to highlight how genealogical processes generate rich and often overlooked haplotypic patterns. In chapter 3, I examine the genomic basis of a key evolutionary innovation in marine snails Littorina. These snails offer a unique opportunity to study an innovation because they include a very recent transition from egg-laying to live bearing, yet snails with the different reproductive modes are not reciprocally monophyletic. I exploited this by using topology clustering in ARG-derived local genealogical trees to pinpoint narrow genomic regions or haplotype blocks that carry swept alleles, thus revealing that the transition from egg-laying to live-bearing involves multiple, live-bearer-specific sweeps. Chapter 4 establishes a population-scale, phased genomic resource for Antirrhinum majus, using cost-effective haplotagging, then optimizes imputation from low-coverage data against high-accuracy KASP sequencing to maximize sequence completeness with modest accuracy trade-offs against a traditional short-read sequence pipeline. A hybrid phasing strategy combines molecular phasing with statistical phasing to generate phased whole genome sequences of 1084 Antirrhinum individuals at a fraction of long-read sequencing costs. In chapter 5, I analyse hybridising populations from two replicate hybrid zones to find a parallel genetic basis of flower colour, amidst the noise in genomic differentiation landscape driven by variation in demographic history. While outlier genome scans of FST failed to dissect the causes of differentiation, ARG-based topology clustering revealed a reuse of colour associated haplotypes across hybrid zones. In addition to the biological insight, this chapter also presents a comparison of the latest ARG inference tools, showing that signals of Abstract viii topological clustering qualitatively agree between methods, despite differences in the tree sequences. Next, in chapter 6, by leveraging ~1000 individuals in one of the hybrid zones, I integrated genome-wide association studies of floral pigmentation with genealogical inference, to test for additional colour loci, and confirm the effect of previously described loci. This work demonstrates that flower colour variation is driven by a small number of large effect loci, while also hinting at the presence of a new candidate regulatory factor. Finally in chapter 7, in a preliminary analysis, I begin to dissect the genomic island of speciation around Rosea/Eluta to understand its evolutionary origins. My results show that it consists of 5 highly divergent loci, each of which is associated with flower colour. Using patterns of coalescence in genealogical trees, I find evidence of staggered selective sweeps and a persistent localized barrier to gene flow within an otherwise permeable genome. Together, these chapters add to the increasing pool of studies using genealogical approaches to complement and extend site-based statistics to use haplotype structures in speciation research. By tracking haplotypes directly and connecting genealogical clustering to population processes, ARG-based inference promises to provide new insights into how local selective pressures, demographic history, and long-term barriers interact to shape the genomic architecture of divergence. By underscoring the value of ARGs in revealing the finescale origins and maintenance of biodiversity, this thesis presents cautious optimism about the benefits of using genealogical inference to learn more than what site-based statistics could tell us.}, author = {Pal, Arka}, issn = {2663-337X}, pages = {268}, publisher = {Institute of Science and Technology Austria}, title = {{Using genealogies to study the genomic basis of species divergence}}, doi = {10.15479/AT-ISTA-20694}, year = {2025}, } @phdthesis{19533, abstract = {This thesis explores advancements in quantum remote sensing and non-equilibrium phase transitions in the microwave regime, with a focus on dissipative phase transitions and quantumenhanced sensing. In the first project, I experimentally studied photon blockade breakdown as a dissipative phase transition in a zero-dimensional cavity-qubit system. By defining an appropriate thermodynamic limit, we demonstrated that the observed bistability is a genuine signature of a first-order phase transition in this system. This work provides insight into non-equilibrium quantum dynamics and phase transitions in driven-dissipative open quantum systems. The second project focuses on the experimental realization of a phase-conjugate receiver for quantum illumination (QI), a quantum sensing protocol that enhances target detection in noisy environments using entangled light. While an ideal spontaneous parametric down-conversion (SPDC) source and receiver could, in theory, provide up to a 6 dB advantage over classical illumination, no such ideal receiver exists. Instead, we explore an experimental realization of a phase-conjugate receiver for QI in the microwave regime at millikelvin temperatures using a Josephson parametric converter (JPC) as a source of continuous-variable Gaussian entangled signal-idler pairs, where a maximum 3 dB advantage is theoretically achievable. We investigate key experimental limitations that constrain practical QI performance, contributing to the development of quantum-enhanced sensing. Additionally, this thesis presents efficient digital signal processing (DSP) techniques implemented in C++ and Python in collaboration with Przemysław Zieliński and Luka Drmić. These methods, optimized using the Intel Integrated Performance Primitives (IPP) library, have been essential in data acquisition, noise filtering, and correlation analysis across multiple research projects. Although not real-time, these DSP techniques significantly enhance the accuracy of quantum measurements. Overall, this thesis advances quantum-enhanced sensing by establishing the thermodynamic limit in a single transmon-cavity system and experimentally exploring a phase-conjugate receiver for QI. These findings contribute to quantum metrology, particularly for weak signal detection and remote sensing in noisy environments. }, author = {Sett, Riya}, issn = {2663-337X}, keywords = {phase transition, open quantum system, phase diagram, cavity quantum electrodynamics, superconducting qubits, semiclassical physics, quantum optics, josephson junction, parametric converter, phase conjugation, quantum radar, quantum entanglement, correlation, quantum sensing}, pages = {109}, publisher = {Institute of Science and Technology Austria}, title = {{ Quantum remote sensing and non-equilibrium phase transitions in the microwave regime}}, doi = {10.15479/AT-ISTA-19533}, year = {2025}, } @phdthesis{19836, abstract = {Over the past century, researchers have been fascinated by the quantum nature of the physical world, initially striving to understand its fundamental principles and consequences, and eventually progressing toward engineering systems that can control and manipulate quantum properties. Today, we stand at the dawn of the quantum technology era. While some quantum technologies follow well-defined roadmaps, others are still in the exciting and uncertain early stages of development. In the fields of quantum computing and quantum simulation, research is being conducted across a wide variety of platforms. Each of these demonstrates control over quantum properties but also faces challenges in scaling up to the level of a mature technology. This thesis explores some of the fundamental properties of hole spin qubits in planar germanium. Semiconductor spin qubits are considered strong candidates for the realization of quantum processors, owing to their long relaxation and coherence times, as well as their compatibility with existing semiconductor industry infrastructure. Among these, hole spin qubits in planar germanium are particularly promising. Their advantages include a large effective mass, which eases fabrication constraints; inherent protection from hyperfine noise; and strong spin-orbit interaction, which enables fast and purely electrical control. However, spin-orbit coupling also introduces site-dependent variability across qubits, particularly in the g-tensors and spin-flip tunneling, which might cause that the quantization axes are not aligned. In this thesis, we investigate the tilt between the quantization axes of two hole spins hosted in a double quantum dot as a function of both the magnetic field direction and various electrostatic configurations, demonstrating that both parameters influence this tilt. We conclude by introducing a machine-learning-assisted routine to automatically tune baseband spin qubits. This approach may prove to be a powerful tool for characterizing spin-orbit effects and gaining deeper insight into the physics governing spin qubit behavior. }, author = {Saez Mollejo, Jaime}, issn = {2663-337X}, pages = {175}, publisher = {Institute of Science and Technology Austria}, title = {{Singlet-triplet qubits in planar Germanium : From exchange anisotropies to autonomous tuning }}, doi = {10.15479/AT-ISTA-19836}, year = {2025}, } @phdthesis{20470, abstract = {Systems design has classically relied on composable systems, in which individual subsystems have defined inputs, outputs, and interactions with each other; however, attempts at designing complex systems in synthetic biology has often run in to issues of crosstalk and interference, given that these systems must function within the context of the host. In nature, mobile genetic elements are systems that have evolved to travel between hosts, and thus appear to be a good candidate with which to evaluate composability. Selecting temperate phages as a model system, I used mathematical modelling to identify sources of information that temperate phages should respond to. I found that essential proteins of temperate phages can interfere with potential hosts, indicating limitations to composability. I also designed a lysogeny reporter construct and characterize its behavior across various laboratory and environmental strains, finding differences in phage lambda lysogens, and potential interference from prophages that already exist within the environmental strains. Although the information gathered is not conclusive, it suggests that composability is not a key property of temperate phages, implying that biological systems may not be composable, and that other system design principles should be considered when designing synthetic systems.}, author = {Wu, Bryan}, issn = {2663-337X}, pages = {102}, publisher = {Institute of Science and Technology Austria}, title = {{An examination on phages as a naturally composable system}}, doi = {10.15479/AT-ISTA-20470}, year = {2025}, } @phdthesis{17225, abstract = {This thesis describes the development of an atom interferometer designed to exploit the advantages of utilizing quantum entanglement for enhanced precision measurements beyond the standard quantum limit. While the project remains ongoing, significant progress has been made. A key contribution of this work is the development of Quantrol, an experimental control system leveraging the ARTIQ framework. This software enables precise timing and control without requiring prior knowledge of ARTIQ’s implementation details or coding experience. The interface offers user friendly visual comprehension of the experimental sequence and extended capabilities, allowing researchers to scan variables with a simple click of a mouse. The main proposed project is to implement atom interferometric sequence with squeezed input states inside of a dipole trap generated by a high finesse cavity. The presence of the dipole trap allows one dimensional atomic cloud split while maintaining relatively strong confinement in other directions. We are currently able to trap and cool 87Rb atoms to few micro kelvin temperatures, load them into the dipole trap and state prepare them to be used for squeezing and interferometric sequence.}, author = {Li, Vyacheslav}, issn = {2663-337X}, pages = {79}, publisher = {Institute of Science and Technology Austria}, title = {{Towards a quantum entanglement enhanced atom interferomter}}, doi = {10.15479/at:ista:17225}, year = {2024}, } @phdthesis{18443, abstract = {In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between the hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they conjecture an equivalence between categories of BBB and BAA-branes. At the classical level, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on algebraic integrable systems. In this thesis, we investigate the T-duality relation between hyperkähler structures and the corresponding branes on affine torus bundles. We use the techniques of generalized geometry to show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems. We also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform we upgrade the T-duality between generalized branes to T-duality of submanifolds endowed with U(1)-bundles and connections. This T-duality in the appropriate context specializes to T-duality between BBB and BAA-branes. }, author = {Sisak, Maria A}, issn = {2663-337X}, keywords = {hyperkaehler geometry, branes, mirror symmetry, T-duality}, pages = {178}, publisher = {Institute of Science and Technology Austria}, title = {{T-dual branes on hyperkähler manifolds}}, doi = {10.15479/at:ista:18443}, year = {2024}, } @phdthesis{17485, abstract = {Large language models (LLMs) have made tremendous progress in the past few years, from being able to generate coherent text to matching or surpassing humans in a wide variety of creative, knowledge or reasoning tasks. Much of this can be attributed to massively increased scale, both in the size of the model as well as the amount of training data, from 100s of millions to 100s of billions, or even trillions. This trend is expected to continue, which, although exciting, also raises major practical concerns. Already today's 100+ billion parameter LLMs require top-of-the-line hardware just to run. Hence, it is clear that sustaining these developments will require significant efficiency advances. Historically, one of the most practical ways of improving model efficiency has been compression, especially in the form of sparsity or quantization. While this has been studied extensively in the past, existing accurate methods are all designed for models around 100 million parameters; scaling them up to ones literally 1000x larger is highly challenging. In this thesis, we introduce a new unified sparsification and quantization approach OBC, which through additional algorithmic enhancements leads to GPTQ and SparseGPT, the first techniques fast and accurate enough to compress 100+ billion parameter models to 4- or even 3-bit precision and 50% weight-sparsity, respectively. Additionally, we show how weight-only quantizion does not just bring space savings but also up to 4.5x faster generation speed, via custom GPU kernels. In fact, we show for the first time that it is possible to develop an FP16 times INT4 mixed-precision matrix multiplication kernel, called Marlin, which comes close to simultaneously maximizing both memory and compute utilization, making weight-only quantization highly practical even for multi-user serving. Further, we demonstrate that GPTQ can be scaled to widely overparametrized trillion-parameter models, where extreme sub-1-bit compression rates can be achieved without any inference slow-down, by co-designing a bespoke entropy coding scheme together with an efficient kernel. Finally, we also study compression from the perspective of someone with access to massive amounts of compute resources for training large models completely from scratch. Here the key questions evolve around the joint scaling behavior between compression, model size, and amount of training data used. Based on extensive experimental results for both vision and text models, we introduce the first scaling law which accurately captures the relationship between weight-sparsity, number of non-zero weights and data. This further allows us to characterize the optimal sparsity, which we find to increase the longer a fixed cost model is being trained. Overall, this thesis presents contributions to three different angles of large model efficiency: affordable but accurate algorithms, highly efficient systems implementations, and fundamental scaling laws for compressed training.}, author = {Frantar, Elias}, issn = {2663-337X}, pages = {129}, publisher = {Institute of Science and Technology Austria}, title = {{Compressing large neural networks : Algorithms, systems and scaling laws}}, doi = {10.15479/at:ista:17485}, year = {2024}, } @phdthesis{17208, abstract = {Can current quantum computers provide a speedup over their classical counterparts for some kinds of problems? In this thesis, with a focus on ground state search/preparation, we address some of the challenges that both quantum annealing and variational quantum algorithms suffer from, hindering any possible practical speedup in comparison to the best classical counterparts. In the first part of the thesis, we study the performance of quantum annealing for solving a particular combinatorial optimization problem called 3-XOR satisfability (3-XORSAT). The classical problem is mapped into a ground state search of a 3-local classical Hamiltonian $H_C$. We consider how modifying the initial problem, by adding more interaction terms to the corresponding Hamiltonian, leads to the emergence of a first-order phase transition during the annealing process. This phenomenon causes the total annealing duration, $T$, required to prepare the ground state of $H_C$ with a high probability to increase exponentially with the size of the problem. Our findings indicate that with the growing complexity of problem instances, the likelihood of encountering first-order phase transitions also increases, making quantum annealing an impractical solution for these types of combinatorial optimization problems. In the second part, we focus on the problem of barren plateaus in generic variational quantum algorithms. Barren plateaus correspond to flat regions in the parameter space where the gradient of the cost function is zero in expectation, and with the variance decaying exponentially with the system size, thus obstructing an efficient parameter optimization. We propose an algorithm to circumvent Barren Plateaus by monitoring the entanglement entropy of k-local reduced density matrices, alongside a method for estimating entanglement entropy via classical shadow tomography. We illustrate the approach with the paradigmatic example of the variational quantum eigensolver, and show that our algorithm effectively avoids barren plateaus in the initialization as well as during the optimization stage. Lastly, in the last two Chapters of this thesis, we focus on the quantum approximate optimization algorithm (QAOA), originally introduced as an algorithm for solving generic combinatorial optimization problems in near-term quantum devices. Specifically, we focus on how to develop rigorous initialization strategies with guarantee improvement. Our motivation for this study lies in that for random initialization, the optimization typically leads to local minima with poor performance. Our main result corresponds to the analytical construction of index-1 saddle points or transition states, stationary points with a single direction of descent, as a tool for systematically exploring the QAOA optimization landscape. This leads us to propose a novel greedy parameter initialization strategy that guarantees for the energy to decrease with an increasing number of circuit layers. Furthermore, with precise estimates for the negative Hessian eigenvalue and its eigenvector, we establish a lower bound for energy improvement following a QAOA iteration.}, author = {Medina Ramos, Raimel A}, issn = {2663-337X}, keywords = {Quantum computing, Variational Quantum Algorithms, Optimization}, pages = {133}, publisher = {Institute of Science and Technology Austria}, title = {{Exploring the optimization landscape of variational quantum algorithms}}, doi = {10.15479/at:ista:17208}, year = {2024}, } @phdthesis{18132, abstract = {In this thesis, we are dealing with both arithmetic and geometric problems coming from the study of rational points with a particular focus on function fields over finite fields: (1) Using the circle method we produce upper bounds for the number of rational points of bounded height on diagonal cubic surfaces and fourfolds over Fq(t). This is based on joint work with Leonhard Hochfilzer. (2) We study rational points on smooth complete intersections X defined by cubic and quadratic hypersurfaces over Fq(t). We refine the Farey dissection of the “unit square” developed by Vishe [202] and use the circle method with a Kloosterman refinement to establish an asymptotic formula for the number of rational points of bounded height on X when dim(X) ≥ 23. Under the same hypotheses, we also verify weak approximation. (3) In joint work with Hochfilzer, we obtain upper bounds for the number of rational points of bounded height on del Pezzo surfaces of low degree over any global field. Our approach is to take hyperplane sections, which reduces the problem to uniform estimates for the number of rational points on curves. (4) We develop a version of the circle method capable of counting Fq-points on jet schemes of moduli spaces of rational curves on hypersurfaces. Combining this with a spreading out argument and a result of Mustaţă [150], this allows us to show that these moduli spaces only have canonical singularities under suitable assumptions on the degree and the dimension. In addition, we give an overview of guiding questions and conjectures in the field of rational points and explain the basic mechanism underlying the circle method. }, author = {Glas, Jakob}, issn = {2663-337X}, pages = {195}, publisher = {Institute of Science and Technology Austria}, title = {{Counting rational points over function fields}}, doi = {10.15479/at:ista:18132}, year = {2024}, } @phdthesis{18667, abstract = {Many chemical and physical properties of materials are determined by the material’s shape, for example the size of its pores and the width of its tunnels. This makes materials science a prime application area for geometrical and topological methods. Nevertheless many methods in topological data analysis have not been satisfyingly extended to the needs of materials science. This thesis provides new methods and new mathematical theorems targeted at those specific needs by answering four different research questions. While the motivation for each of the research questions arises from materials science, the methods are versatile and can be applied in different areas as well. The first research question is concerned with image data, for example a three-dimensional computed tomography (CT) scan of a material, like sand or stone. There are two commonly used topologies for digital images and depending on the application either of them might be required. However, software for computing the topological data analysis method persistence homology, usually supports only one of the two topologies. We answer the question how to compute persistent homology of an image with respect to one of the two topologies using software that is intended for the other topology. The second research question is concerned with image data as well, and asks how much of the topological information of an image is lost when the resolution is coarsened. As computer tomography scanners are more expensive the higher the resolution, it is an important question in materials science to know which resolution is enough to get satisfying persistent homology. We give theoretical bounds on the information loss based on different geometrical properties of the object to be scanned. In addition, we conduct experiments on sand and stone CT image data. The third research question is motivated by comparing crystalline materials efficiently. As the atoms within a crystal repeat periodically, crystalline materials are either modeled by unmanageable infinite periodic point sets, or by one of their fundamental domains, which is unstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with appropriate properties such that comparing the crystals can be eased by comparing the fingerprints instead. We define the density fingerprint and prove the necessary properties. The fourth research question is motivated by studying the hole-structure or connectedness, i.e. persistent homology or merge trees, of crystalline materials. A common way to deal with periodicity is to take a fundamental domain and identify opposite boundaries to form a torus. However, computing persistent homology or merge trees on that torus loses some of the information materials scientists are interested in and is additionally not stable under certain noise. We therefore decorate the merge tree stemming from the torus with additional information describing the density and growth rate of the periodic copies of a component within a growing spherical window. We prove all desired properties, like stability and efficient computability.}, author = {Heiss, Teresa}, isbn = {978-3-99078-052-7}, issn = {2663-337X}, keywords = {persistent homology, topological data analysis, periodic, crystalline materials, images, fingerprint}, pages = {111}, publisher = {Institute of Science and Technology Austria}, title = {{New methods for applying topological data analysis to materials science}}, doi = {10.15479/at:ista:18667}, year = {2024}, } @phdthesis{14711, abstract = {In nature, different species find their niche in a range of environments, each with its unique characteristics. While some thrive in uniform (homogeneous) landscapes where environmental conditions stay relatively consistent across space, others traverse the complexities of spatially heterogeneous terrains. Comprehending how species are distributed and how they interact within these landscapes holds the key to gaining insights into their evolutionary dynamics while also informing conservation and management strategies. For species inhabiting heterogeneous landscapes, when the rate of dispersal is low compared to spatial fluctuations in selection pressure, localized adaptations may emerge. Such adaptation in response to varying selection strengths plays an important role in the persistence of populations in our rapidly changing world. Hence, species in nature are continuously in a struggle to adapt to local environmental conditions, to ensure their continued survival. Natural populations can often adapt in time scales short enough for evolutionary changes to influence ecological dynamics and vice versa, thereby creating a feedback between evolution and demography. The analysis of this feedback and the relative contributions of gene flow, demography, drift, and natural selection to genetic variation and differentiation has remained a recurring theme in evolutionary biology. Nevertheless, the effective role of these forces in maintaining variation and shaping patterns of diversity is not fully understood. Even in homogeneous environments devoid of local adaptations, such understanding remains elusive. Understanding this feedback is crucial, for example in determining the conditions under which extinction risk can be mitigated in peripheral populations subject to deleterious mutation accumulation at the edges of species’ ranges as well as in highly fragmented populations. In this thesis we explore both uniform and spatially heterogeneous metapopulations, investigating and providing theoretical insights into the dynamics of local adaptation in the latter and examining the dynamics of load and extinction as well as the impact of joint ecological and evolutionary (eco-evolutionary) dynamics in the former. The thesis is divided into 5 chapters. Chapter 1 provides a general introduction into the subject matter, clarifying concepts and ideas used throughout the thesis. In chapter 2, we explore how fast a species distributed across a heterogeneous landscape adapts to changing conditions marked by alterations in carrying capacity, selection pressure, and migration rate. In chapter 3, we investigate how migration selection and drift influences adaptation and the maintenance of variation in a metapopulation with three habitats, an extension of previous models of adaptation in two habitats. We further develop analytical approximations for the critical threshold required for polymorphism to persist. The focus of chapter 4 of the thesis is on understanding the interplay between ecology and evolution as coupled processes. We investigate how eco-evolutionary feedback between migration, selection, drift, and demography influences eco-evolutionary outcomes in marginal populations subject to deleterious mutation accumulation. Using simulations as well as theoretical approximations of the coupled dynamics of population size and allele frequency, we analyze how gene flow from a large mainland source influences genetic load and population size on an island (i.e., in a marginal population) under genetically realistic assumptions. Analyses of this sort are important because small isolated populations, are repeatedly affected by complex interactions between ecological and evolutionary processes, which can lead to their death. Understanding these interactions can therefore provide an insight into the conditions under which extinction risk can be mitigated in peripheral populations thus, contributing to conservation and restoration efforts. Chapter 5 extends the analysis in chapter 4 to consider the dynamics of load (due to deleterious mutation accumulation) and extinction risk in a metapopulation. We explore the role of gene flow, selection, and dominance on load and extinction risk and further pinpoint critical thresholds required for metapopulation persistence. Overall this research contributes to our understanding of ecological and evolutionary mechanisms that shape species’ persistence in fragmented landscapes, a crucial foundation for successful conservation efforts and biodiversity management.}, author = {Olusanya, Oluwafunmilola O}, issn = {2663-337X}, pages = {183}, publisher = {Institute of Science and Technology Austria}, title = {{Local adaptation, genetic load and extinction in metapopulations}}, doi = {10.15479/at:ista:14711}, year = {2024}, } @phdthesis{17156, abstract = {This dissertation is the summary of the author’s work, concerning the relations between cohomology rings of algebraic varieties and rings of functions on zero schemes and fixed point schemes. For most of the thesis, the focus is on smooth complex varieties with an action of a principally paired group, e.g. a parabolic subgroup of a reductive group. The fundamental theorem 5.2.11 from co-authored article [66] says that if the principal nilpotent has a unique zero, then the zero scheme over the Kostant section is isomorphic to the spectrum of the equivariant cohomology ring, remembering the grading in terms of a C^* action. A similar statement is proved also for the G-invariant functions on the total zero scheme over the whole Lie algebra. Additionally, we are able to prove an analogous result for the GKM spaces, which poses the question on a joint generalisation. We also tackle the situation of a singular variety. As long as it is embedded in a smooth variety with regular action, we are able to study its cohomology as well by means of the zero scheme. In case of e.g. Schubert varieties this determines the cohomology ring completely. In largest generality, this allows us to see a significant part of the cohomology ring. We also show (Theorem 6.2.1) that the cohomology ring of spherical varieties appears as the ring of functions on the zero scheme. The computational aspect is not easy, but one can hope that this can bring some concrete information about such cohomology rings. Lastly, the K-theory conjecture 6.3.1 is studied, with some results attained for GKM spaces. The thesis includes also an introduction to group actions on algebraic varieties. In particular, the vector fields associated to the actions are extensively studied. We also provide a version of the Kostant section for arbitrary principally paired group, which parametrises the regular orbits in the Lie algebra of an algebraic group. Before proving the main theorem, we also include a historical overview of the field. In particular we bring together the results of Akyildiz, Carrell and Lieberman on non-equivariant cohomology rings.}, author = {Rychlewicz, Kamil P}, issn = {2663-337X}, keywords = {equivariant cohomology, zero schemes, algebraic groups, Lie algebras}, pages = {117}, publisher = {Institute of Science and Technology Austria}, title = {{Equivariant cohomology and rings of functions}}, doi = {10.15479/at:ista:17156}, year = {2024}, } @phdthesis{18515, abstract = {Understanding the role of evolutionary processes in shaping genetic variation has been a primary goal in evolutionary genetics. In this regard, a key question is how genetically distinct populations evolve in the face of gene flow, thereby generating genetic and phenotypic divergence and reproductive isolation (RI). This requires quantifying the role and relative contributions of prezygotic and postzygotic isolating mechanisms on the reduction of gene exchange between populations, and identifying regions in the genome that mediate RI, which is often polygenic. Further, this needs distinguishing neutral and selected regions in the genome, and discerning how selection influences patterns of neutral divergence. Population structure, defined as any deviation from panmixia, such as geographic distribution, movement and mating patterns of individuals, influences how genetic variation is structured in space and shapes the neutral null model. Availability of large scale spatial genomic datasets now enables us to detect signatures of population structure in genetic data and infer population genetic parameters. Such inferences are crucial and have wide applications in biodiversity, conservation genetics, population management and medical genetics. However, inferences are based on assumptions that do not always match the complex reality, thus leading to erroneous conclusions. Moreover, the role and interaction of heterogeneous population density and dispersal, which are ubiquitous in nature, has been challenging to study owing to their mathematical complexity. In such scenarios, feedback between theory, data and simulations can prove to be useful. In this thesis, I examine the effect of population structure on neutral genetic variation and barriers to gene exchange in hybridising populations, thereby bridging together the fields of spatial population genetics and speciation. Despite being a key concept in speciation, reproductive isolation (RI) lacks a quantitative definition and has been used and measured differently across different fields. Chapter 2 gives a quantitative definition of RI, in terms of the effect of genetic differences on gene flow. We give analytical predictions for RI in a range of scenarios, in terms of effective migration rates for discrete populations and barrier strength for continuous populations. In addition to this, we discuss current measures of RI and their limitations, and propose the need for new measures that combine organismal and genetic perspectives of RI. In chapter 3, I examine the combined effect of assortative mating, sexual selection and viability selection on RI. For this, we consider a polygenic ‘magic’ trait under a mainland-island model. We obtain novel theoretical predictions for molecular divergence in terms of effective migration rates, which bears a simple relationship to measurable fitness components of migrants and various early generation hybrids. We explore the conditions under which local adaptation can be maintained despite maladaptive gene flow and quantify the relative contributions of viability and sexual selection to genome-wide barriers to gene flow. The next two chapters of the thesis focus on a hybrid zone of Antirrhinum majus that consist of two subspecies- the magenta flowered A. m. pseudomajus and the yellow flowered A.m. striatum. Previous studies have suggested that flower colour is target of pollinator mediated selection and is influenced only by few genes. While these regions show high genetic differentiation between the subspecies, the rest of the genome is seen to be well mixed. Chapter 4 examines the effects of heterogeneous population density and leptokurtic dispersal on isolation by distance and the distribution of heterozygosity by focusing on non-flower colour markers. Chapter 5 analyses cline shapes and associations among 6 focal flower colour markers to understand how selection and dispersal maintain this hybrid zone. We see sharp coincident stepped clines at all loci and positive associations throughout the hybrid zone, contrary to the expected patterns from diffusive gene flow. With a novel scheme of inferring dispersal combined with multilocus simulations, we show that stepped clines do not reflect genetic barriers to gene flow, but are rather a result of long-distance migration. This framework allows us to get realistic estimates gene flow and selection and shows how traditional cline analysis may lead to inaccurate conclusions when assumptions of the theory are not met. Overall, this thesis investigates how different features of population structure leave detectable signatures in genetic variation, namely in patterns of isolation by distance, linkage disequilibrium and genetic divergence. It also highlights how effective migration rates provide useful way of analysing polygenic architectures and shed new light into hybrid zones. In doing so, I identify scenarios when simple models become insufficient and suggest possibe directions by combining genetic data with simulations.}, author = {Surendranadh, Parvathy}, issn = {2663-337X}, pages = {219}, publisher = {Institute of Science and Technology Austria}, title = {{Effect of population structure on neutral genetic variation and barriers to gene exchange}}, doi = {10.15479/at:ista:18515}, year = {2024}, } @phdthesis{18681, author = {Tavakoli, Mojtaba}, isbn = {978-3-99078-048-0}, issn = {2663-337X}, pages = {230}, publisher = {Institute of Science and Technology Austria}, title = {{Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics reconstruction with light microscopy}}, doi = {10.15479/at:ista:18681}, year = {2024}, }