@article{19370, abstract = {Sex-linked and autosomal loci experience different selective pressures and evolutionary dynamics. X (or Z) chromosomes are often hemizygous in males (or females), as Y (or W) chromosomes often degenerate. Such hemizygous regions can be under greater efficacy of selection, as recessive mutations are immediately exposed to selection in the heterogametic sex leading to faster adaptation and faster divergence on the X chromosome (the so-called Faster-X or Faster-Z effect). However, in young nonrecombining regions, Y/W chromosomes often have many functional genes, and many X/Z-linked loci are therefore diploid. The sheltering of recessive mutations on the X/Z by the Y/W homolog is expected to drive slower adaptation for diploid X/Z loci, i.e. a reduction in the efficacy of selection. While the Faster-X effect has been studied extensively, much less is known empirically about the evolutionary dynamics of diploid X or Z chromosomes. Here, we took advantage of published population genomic data in the female-heterogametic human parasite Schistosoma japonicum to characterize the gene content and diversity levels of the diploid and hemizygous regions of the Z chromosome. We used different metrics of selective pressures acting on genes to test for differences in the efficacy of selection in hemizygous and diploid Z regions, relative to autosomes. We found consistent patterns suggesting reduced Ne, and reduced efficacy of purifying selection, on both hemizygous and diploid Z regions. Moreover, relaxed selection was particularly pronounced for female-biased genes on the diploid Z, as predicted by recent theoretical work.}, author = {Mrnjavac, Andrea and Vicoso, Beatriz}, issn = {1759-6653}, journal = {Genome Biology and Evolution}, number = {2}, publisher = {Oxford University Press}, title = {{Reduced efficacy of selection on a young Z chromosome region of schistosoma japonicum}}, doi = {10.1093/gbe/evaf021}, volume = {17}, year = {2025}, } @phdthesis{19393, abstract = {Rotations constitute one of the fundamental symmetries in physics, characterized by their intricate group structure and infinite dimensional representations. In contrast to classical rotations, quantum mechanics unveils the SO(3) symmetry group structure, manifesting in phenomena without classical counterparts, from angular momentum quantization to non-trivial addition of angular momenta. While most studies of topological physics have focused on two-band systems, the SO(3) symmetry group of quantum rotors offers an inherently more complex platform with unprecedented possibilities for exploring topological phenomena. Despite their ubiquity in nature– from molecules to nanorotors– their potential for hosting topological phases has remained largely unexamined. In this thesis, we mainly focus on periodically driven linear molecules as a prototype for studying topological phenomena in quantum rotors. Recent technological advances in coherent control of molecules, particularly through precisely shaped laser pulses, have made it possible to investigate linear rotors in the context of topology. While planar rotors have received some attention in recent years, threedimensional rotors–particularly linear molecules–harbor substantially richer topological phenomena due to their non-abelian nature and their additional angular degrees of freedom. We demonstrate that these systems can host novel edge states and topological features fundamentally impossible in planar systems. We begin by establishing a theoretical bridge between periodically kicked rotors and "crystalline" lattices in angular momentum space. Using non-interacting linear molecules as our primary example, we show how quantum interference and revival patterns lead to the possibility to simulate band models with arbitrary number of bands N. While our framework applies to various quantum rotors, including nanorotors and kicked Bose-Einstein condensates, linear molecules provide an ideal experimental platform due to their abovementioned precise controllability. The core of this work examines adiabatic dynamics of 3D quantum rotors, establishing a geometric framework based on the Euler class to characterize its non-abelian topology. The non-Hermitian nature of the system enables novel braiding behaviors and topological transitions impossible in static systems, leading to an anomalous Dirac string phase with edge states in each gap, even though the Berry phases are all zero. These features can be directly observed through molecular alignment and rotational level populations. These findings establish quantum rotors as an alternative platform for studying multi-band topological physics, while suggesting practical implementations for quantum computation where topological protection could offer natural resilience against decoherence. The rich structure of three-dimensional rotation groups, combined with the tunability of topological features through driving parameters, makes this platform particularly valuable for exploring fundamental physics and developing quantum technologies.}, author = {Karle, Volker}, issn = {2663-337X}, pages = {192}, publisher = {Institute of Science and Technology Austria}, title = {{Non-equilibrium topological phases with periodically driven molecules and quantum rotors}}, doi = {10.15479/AT-ISTA-19393}, year = {2025}, } @article{20603, abstract = {We study the growth of sumsets A+B⊂S⊂G, where S does not contain an arithmetic progression of length 2k+1, and where G is a commutative group, in which every nonzero element has an order of at least 2k+1. More specifically, we show the following: if A,B⊂G are sets such that A+B does not contain an arithmetic progression of length 2k+1, then |A+B|≥|A|2k−13k−2|B|k3k−2. As an application we derive upper bounds on the cardinality of the summands in sumsets A+B+C contained in the set of t-th powers, where t≥2 is an integer. In particular, we show that min(|A|,|B|,|C|)≪(logN)4/5 for t=2, and min(|A|,|B|,|C|)≪t(logN)1/2 for t≥3.}, author = {Elsholtz, Christian and Ruzsa, Imre Z. and Wurzinger, Lena}, issn = {1730-6264}, journal = {Acta Arithmetica}, pages = {289--303}, publisher = {Institute of Mathematics}, title = {{Sumset growth in progression-free sets}}, doi = {10.4064/aa250115-14-7}, volume = {220}, year = {2025}, } @unpublished{20465, abstract = {For tissues to spread, they must be deformable while maintaining their structural integrity. How these opposing requirements are balanced within spreading tissues is not yet well understood. Here, we show that keratin intermediate filaments function in epithelial spreading by adapting tissue mechanical resilience to the stresses arising in the tissue during the spreading process. By analysing the expansion of the enveloping cell layer (EVL) over the large yolk cell in early zebrafish embryos in vivo, we found that keratin network maturation in EVL cells is promoted by stresses building up within the spreading tissue. Through genetic interference and tissue rheology experiments, complemented by a vertex model with mechanochemical feedback, we demonstrate that stress-induced keratin network maturation in the EVL increases tissue viscosity, which is essential for preventing tissue rupture. Interestingly, keratins are also required in the yolk cell for mechanosensitive actomyosin network contraction and flow, the force-generating processes pulling the EVL. These dual mechanosensitive functions of keratins enable a balance between pulling force production in the yolk cell and the mechanical resilience of the EVL against stresses generated by these pulling forces, thereby ensuring uniform and robust tissue spreading.}, author = {Naik, Suyash and Keta, Yann-Edwin and Pranjic-Ferscha, Kornelija and Hannezo, Edouard B and Henkes, Silke and Heisenberg, Carl-Philipp J}, booktitle = {bioRxiv}, title = {{Keratins coordinate tissue spreading by balancing spreading forces with tissue material properties}}, doi = {10.1101/2025.02.14.638262}, year = {2025}, } @article{20662, abstract = {Task-based functional magnetic resonance imaging (fMRI) reveals individual differences in neural correlates of cognition but faces scalability challenges due to cognitive demands, protocol variability, and limited task coverage in large datasets. Here, we propose DeepTaskGen, a deep-learning approach that synthesizes non-acquired task-based contrast maps from resting-state (rs-) fMRI. We validate this approach using the Human Connectome Project lifespan data, then generate 47 contrast maps from 7 different cognitive tasks for over 20,000 individuals from UK Biobank. DeepTaskGen outperforms several benchmarks in generating synthetic task-contrast maps, achieving superior reconstruction performance while retaining inter-individual variation essential for biomarker development. We further show comparable or superior predictive performance of synthetic maps relative to actual maps and rs-connectomes across diverse demographic, cognitive, and clinical variables. This approach facilitates the study of individual differences and the generation of task-related biomarkers by enabling the generation of arbitrary functional cognitive tasks from readily available rs-fMRI data.}, author = {Serin, Emin and Ritter, Kerstin and Schumann, Gunter and Banaschewski, Tobias and Marquand, Andre and Walter, Henrik and Ogoh, George and Stahl, Bernd Carsten and Brandlistuen, Ragnhild and Schikowski, Tamara and Young, Allan H. and Xinyang, Yu and Zhang, Zuo and Agunbiade, Kofoworola and Chen, Di and Desrivières, Sylvane and Clinton, Nicholas and Thompson, Paul and Köhler, Venessa and Schwalber, Ameli and Calhoun, Vince D. and Chang, Xiao and Zhang, Yanqing and Li, Yuzhu and Dai, Yuxiang and Yuan, Jiacan and Xia, Yunman and Jia, Tianye and Renner, Paul and Hese, Sören and Spanlang, Bernhard and Pearmund, Charlie and Athanasiadis, Anastasios Polykarpos and Petkoski, Spase and Jirsa, Viktor and Schmitt, Karen and Wilbertz, Johannes H. and Patraskaki, Myrto and Sommer, Peter and Heilmann-Heimbach, Stefanie and Mathey, Carina M. and Miller, Abigail J. and Claus, Isabelle and Nöthen, Markus M. and Hoffmann, Per and Forstner, Andreas J. and Pastor, Alvaro and Gallego, Jaime and Itatani, Reiya and Eiroa-Orosa, Francisco and Feixas, Guillem and Slater, Mel and Novarino, Gaia and Böttger, Sarah Jane and Tschorn, Mira and Rapp, Michael and Ask, Helga and Kjelkenes, Rikka and Fernandez, Sara and Van Der Meer, Dennis and Westlye, Lars T. and Andreassen, Ole A. and Aden, Rieke and Seefried, Beke and Nees, Frauke and Neidhart, Maja and Stringaris, Argyris and Schwarz, Emanuel and Holz, Nathalie and Tost, Heike and Meyer-Lindenberg, Andreas and Christmann, Nina and Janson, Karina and Schepanski, Kerstin and Schütz, Tatjana and Taron, Ulrike Helene and Eils, Roland and Roy, Jean Charles and Lett, Tristram A. and Kebir, Hedi and Polemiti, Elli and Hitchen, Esther and Jentsch, Marcel and Serin, Emin and Bernas, Antoine and Vaidya, Nilakshi and Twardziok, Sven and Ralser, Markus and Heinz, Andreas and Schumann, Gunter}, issn = {2399-3642}, journal = {Communications Biology}, publisher = {Springer Nature}, title = {{Generating synthetic task-based brain fingerprints for population neuroscience using deep learning}}, doi = {10.1038/s42003-025-09158-6}, volume = {8}, year = {2025}, } @phdthesis{20735, abstract = {Left–right alternation is a defining feature of spinal locomotor circuits, yet the level of neuronal detail required to generate and maintain this pattern remains unclear. This thesis investigates how models spanning multiple levels of abstraction—from biophysically detailed Hodgkin–Huxley (HH) neurons to adaptive integrate–and–fire (I&F) formulations and synfire-chain modules—can account for the generation of fictive swimming in the spinal cord of the Xenopus laevis tadpole. The guiding hypothesis is that a small set of neuronal mechanisms is sufficient to reproduce the essential features of rhythmic alternation, and that moving between modeling scales helps distinguish core principles from biological detail. A minimal bilateral HH network comprising only four canonical neuron classes—excitatory descending interneurons (dINs), inhibitory commissural interneurons (cINs), ipsilateral inhibitory interneurons (aINs) and motoneurons—served as a biophysical proof of concept. Tuned to reproduce experimentally observed firing modes, the model demonstrated that rebound-prone dIN excitability, contralateral inhibition and modest electrical coupling are sufficient to generate stable alternating activity, even in very small networks. These results motivated the transition to simpler models capable of efficient analysis and scaling. Adaptive exponential I&F (AdEx) neurons were calibrated to physiological recordings using simulation-based inference, yielding tonic and phasic/rebound templates that preserved the key dynamical signatures of the HH model. Phase-plane analysis clarified the mechanisms underlying single-spike responses and rebound firing in dINs. At network level, the I&F models robustly reproduced left–right alternation, while highlighting constraints on synaptic kinetics and adaptation needed to avoid multi-spike responses. Finally, a synfire-chain framework provided a complementary, timing-centric perspective, demonstrating how precise spike synchrony, synaptic delays and minimal inhibitory coupling can generate alternating left–right sequences in a feedforward setting. Together, these approaches converge on a common conclusion: rebound-prone ipsilateral excitation combined with precisely timed contralateral inhibition constitutes a sufficient substrate for alternating spinal rhythms. By integrating bottom-up and top-down modeling strategies, this thesis provides a unified, extensible framework for studying spinal pattern generation. The results show that essential locomotor dynamics can be captured across multiple abstraction levels, offering both mechanistic insight and practical tools for future data-driven investigations of spinal circuit development, robustness and modulation.}, author = {Wilson, Alexia C}, issn = {2791-4585}, pages = {110}, publisher = {Institute of Science and Technology Austria}, title = {{Modelling the spinal cord of a tadpole: Exploring different ways to model the spinal cord in the Xenopus frog}}, doi = {10.15479/AT-ISTA-20735}, year = {2025}, } @phdthesis{20607, author = {Mondal, Soumyadip}, isbn = {978-3-99078-071-8}, issn = {2663-337X}, pages = {71}, publisher = {Institute of Science and Technology Austria}, title = {{Oxygen and sulfur redox: Conversion kinetics and phase equilibria}}, doi = {10.15479/AT-ISTA-20607}, year = {2025}, } @unpublished{21398, abstract = {Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory faces many challenges, most importantly that only a limited number of notions and results have been implemented so far. In this work, we formalize the proof of the forward (composition) direction of Seymour's theorem for regular matroids. To this end, we develop a library in Lean 4 that implements definitions and results about totally unimodular matrices, vector matroids, their standard representations, regular matroids, and 1-, 2-, and 3-sums of matrices and binary matroids given by their standard representations. Using this framework, we formally state Seymour's decomposition theorem and implement a formally verified proof of the composition direction in the setting where the matroids have finite rank and may have infinite ground sets.}, author = {Dvorak, Martin and Figueroa-Reid, Tristan and Hamadani, Rida and Hwang, Byung-Hak and Karunus, Evgenia and Kolmogorov, Vladimir and Meiburg, Alexander and Nelson, Alexander and Nelson, Peter and Sandey, Mark and Sergeev, Ivan}, booktitle = {arXiv}, title = {{Composition direction of Seymour's theorem for regular matroids — Formally verified}}, doi = {10.48550/arXiv.2509.20539}, year = {2025}, } @phdthesis{20811, abstract = { This thesis is organized into two parts, each comprising two chapters: Chapter 1 and 2 offer models for the evolution of vaccine resistance in response to diverse vaccination strategies. Chapter 3 and 4 review the statistics of records, their connection to models of innovation and an application to the cultural evolution of sports. In chapter 1 we present a modelling study from 2021 on the evolution of SARS-CoV-2. At that time the vaccine-resistant Omicron variant had not yet evolved. In our model we consider a population that is becoming vaccinated over time, while a pathogen is spreading in the population and eventually becoming resistant to the vaccine. We explore effective pharmaceutical and non-pharmaceutical interventions to prevent the emergence of vaccine resistance. In chapter 2 we model a particular set of complex vaccination strategies, mosaic and pyramid vaccination, where an immunologically diverse portfolio of vaccines is considered. We find that a bet-hatching strategy, in which vaccine types are distributed in the population, is effective at hindering the evolution of vaccine resistance if mutation rates are high. In chapter 3 we switch gears and present a review on the statistics of records. We highlight similarities and analogies to other models in the fields of statistical physics, evolution and innovation. This offers interesting complimentary perspectives on well-known models. In chapter 4 we apply models of record statistics and innovation to study cultural evolution in sport. We propose a model of sport evolution that combines deterministic improvements in performance and stochastic bursts of improvements due to innovation. }, author = {Rella, Simon}, issn = {2663-337X}, pages = {95}, publisher = {Institute of Science and Technology Austria}, title = {{Adaptive processes in biology and culture: Models of evolving vaccine resistance and the record statistics of innovation}}, doi = {10.15479/AT-ISTA-20811}, year = {2025}, } @phdthesis{20276, abstract = {Complex 3D shapes can be created by morphing flat 2D configurations. Such deformations either preserve the intrinsic material geometry (e.g., folding paper) or modify it through localized contraction. Once transformed, the 3D shape can be further controlled to achieve a target functionality. A key challenge is to take the material specifications and the actuation process as input to automatically design the target 3D shape and its functionality. This thesis presents two novel computational pipelines for the design and control of shape-morphing structures used to create functional prototypes. The first pipeline borrows from the art of origami to fold paper into intricate shapes and applies this principle to make 3D lighting displays. We introduce, PCBend a computational design approach that covers a surface with individually addressable RGB LEDs, effectively forming a low-resolution surface by folding rigid printed circuit boards (PCBs). We optimize cut patterns on PCBs to act as hinges and co-design LED placement, circuit routing, and fabrication constraints to produce PCB blueprints. The PCBs are fabricated using automated standard manufacturing services with LEDs embedded on them. Finally, the fabricated PCBs are cut along the contour and folded onto a 3D-printed support. The 3D lighting display is then controlled to display complex surface light patterns. Creating 3D shapes through folding is only possible if their planar configuration, called ”unfolding” exists without any distortion or overlap. Existing methods often permit distortion or require multiple patches, which are unsuitable for fabrication pipelines that rely on folding non-stretchable materials. We reinforce such fabrication pipelines by providing a geometric relaxation to the problem, where the input shape is modified to admit overlap-free unfolding. The second fabrication pipeline extends shape morphing to soft robotics by emulating nature’s blueprint of distributed actuation. Inspired by vertebrates, we build musculoskeletal robots using modular active actuators, employing Liquid Crystal Elastomers (LCEs) as shrinkable artificial muscles integrated with 3D-printed bones. The chemical composition of LCEs is altered to enable untethered actuation through infrared radiation, allowing active control of individual muscles and their corresponding bones. The combined motion of individual bones defines the robot’s overall shape and functionality. Our proposed system significantly expands both the design and control spaces of soft robots, which we harness using our computational design tools. We build several physical robots that exhibit complex shape morphing and varied terrain navigation, showcasing the versatility of our pipeline. This thesis explores applications ranging from intricate light patterns displayed on 3D shapes formed by folding rigid PCBs to untethered robots that use contractile muscles to exhibit shape morphing and locomotion. Through these examples, the thesis highlights how computational design and distributed actuation, integrated with novel materials, can transform passive structures into functional prototypes.}, author = {Bhargava, Manas}, isbn = {978-3-99078-065-7}, issn = {2663-337X}, pages = {96}, publisher = {Institute of Science and Technology Austria}, title = {{Design and control of deformable structures: From PCB lighting displays to elastomer robots}}, doi = {10.15479/AT-ISTA-20276}, year = {2025}, } @phdthesis{20203, abstract = {Tribocharging, or contact electrification, is the phenomenon in which two initially neutral materials exchange electric charge through contact and subsequent separation. While it is widely observed in everyday life and crucial to numerous natural processes, even the most basic aspects of tribocharging are still a mystery—what are the charge carriers involved and what drives their exchange? This work spans three separate projects that address different aspects of tribocharging. First, we introduce a novel strategy combining Finite Element Method (FEM) simulations with Kelvin Probe Force Microscopy (KPFM) to quantitatively extract surface charge density from surface voltage maps. Second, we present a simple theoretical model that allows for the existence of triboelectric cycles, under the assumption that multiple charge carrying species are involved. Third, we present experimental evidence that identical materials can spontaneously evolve into a triboelectric series, driven by contact history. Modeling this behavior enables the replication of experimental results with simulations, and even experimentally forcing the appearance of a pre-designed series by manipulating contact history. Together, the findings from these projects challenge traditional views on tribocharging, provide new tools for probing it, and open up new avenues of research—all with the hopes of bringing us closer to understanding this puzzling phenomenon.}, author = {Sobarzo Ponce, Juan Carlos A}, isbn = {978-3-99078-062-6}, issn = {2663-337X}, pages = {96}, publisher = {Institute of Science and Technology Austria}, title = {{Tribocharging of identical insulators: Triboelectric series, triboelectric cycles and surface charges}}, doi = {10.15479/AT-ISTA-20203}, year = {2025}, } @article{18565, abstract = {We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing for map distortions or multiple patches. Instead, we propose a geometric relaxation of the problem: We modify the input shape until it admits an overlap‐free unfolding. We achieve this by locally displacing vertices and collapsing edges, guided by the unfolding process. We validate our algorithm quantitatively and qualitatively on a large dataset of complex shapes and show its proficiency by fabricating real shapes from paper.}, author = {Bhargava, Manas and Schreck, Camille and Freire, M. and Hugron, P. A. and Lefebvre, S. and Sellán, S. and Bickel, Bernd}, issn = {1467-8659}, journal = {Computer Graphics Forum}, keywords = {fabrication, single patch unfolding, mesh simplification}, number = {1}, publisher = {Wiley}, title = {{Mesh simplification for unfolding}}, doi = {10.1111/cgf.15269}, volume = {44}, year = {2025}, } @unpublished{20286, abstract = {Natural organisms utilize distributed actuation through their musculoskeletal systems to adapt their gait for traversing diverse terrains or to morph their bodies for varied tasks. A longstanding challenge in robotics is to emulate this capability of natural organisms, which has motivated the development of numerous soft robotic systems. However, such systems are generally optimized for a single functionality, lack the ability to change form or function on demand, or remain tethered to bulky control systems. To address these limitations, we present a framework for designing and controlling robots that utilize distributed actuation. We propose a novel building block that integrates 3D-printed bones with liquid crystal elastomer (LCE) muscles as lightweight actuators, enabling the modular assembly of musculoskeletal robots. We developed LCE rods that contract in response to infrared radiation, thereby providing localized, untethered control over the distributed skeletal network and producing global deformations of the robot. To fully capitalize on the extensive design space, we introduce two computational tools: one for optimizing the robot's skeletal graph to achieve multiple target deformations, and another for co-optimizing skeletal designs and control gaits to realize desired locomotion. We validate our framework by constructing several robots that demonstrate complex shape morphing, diverse control schemes, and environmental adaptability. Our system integrates advances in modular material building, untethered and distributed control, and computational design to introduce a new generation of robots that brings us closer to the capabilities of living organisms.}, author = {Bhargava, Manas and Hiraki, Takefumi and Strugaru, Irina-Malina and Zhang, Yuhan and Piovarci, Michael and Daraio, Chiara and Iwai, Daisuke and Bickel, Bernd}, booktitle = {arXiv}, title = {{Computational design and fabrication of modular robots with untethered control}}, doi = {10.48550/arXiv.2508.05410}, year = {2025}, } @phdthesis{20371, abstract = {Quantum mechanics reveals a world that defies classical determinism, where uncertainty, superposition, and fluctuations are fundamental aspects. Engineering devices that harness these quantum features requires not only precision, but also a deep understanding of how they interact with their surrounding environment. Superconducting circuits, which exploit macroscopic quantum coherence in low-loss superconducting materials, provide a scalable platform for implementing such systems. Among the critical elements in these circuits, superinductors—high-impedance, dissipation-free inductive components—play a central role by suppressing charge fluctuations. They allow quantum states to be delocalized in phase space, protect qubits from environmental noise, and facilitate access to phenomena such as dual Josephson physics and ultra-strong coupling regimes. This thesis explores two complementary implementations of high-impedance circuits: geometric superinductors, demonstrating that high impedance can be achieved beyond kinetic inductance, and Josephson junction chains, used to investigate both microwave mode properties and DC transport across the superconductor-to-insulator transition. Part I addresses geometric superinductors. Contrary to the common belief that high-impedance superconducting circuits require kinetic inductance, we demonstrate that purely geometric designs can achieve characteristic impedance exceeding the resistance quantum. By exploiting mutual coupling between adjacent turns, coil-based inductors achieve enhanced self-inductance, creating a reliable platform for qubits and resonators. Modeling, simulation, fabrication, and characterization confirm that these elements behave as superinductor. With low loss, high linearity, and minimal stray capacitance, these elements are reproducible, free of uncontrolled tunneling events, and capable of strong magnetic coupling. This establishes geometric superinductors as robust, single-wave-function superconducting devices suitable for hardware protected qubits and hybrid systems. Part II presents classical numerical simulations of a Quantum Phase Slip circuit to study dual Shapiro steps. The circuit consists of an ideal Quantum Phase Slip element embedded in a resistive-inductive environment with a parasitic capacitance. Part III extends the investigation of high characteristic-impedance circuit elements to one-dimensional Josephson junction chains, which act as a quantum simulator for many-body physics and the superconductor–insulator transition. Different devices are realized on both sides of the DC phase transition, showing either a supercurrent branch or Coulomb blockade at zero bias. The effect of the crossover on microwave modes, however, remains insufficiently investigated. Studying these modes provides insight into the interplay between disorder and phase-slip events. Small differences in circuit component sizes determine which side of the transition a device falls on, making these results relevant not only for fundamental understanding but also for the design of quantum devices, emphasizing the crucial role of the electromagnetic environment in stabilizing and controlling fragile quantum states. Together, these results illustrate how carefully engineered high characteristic-impedance elements provide a link between macroscopic circuits and the inherently uncertain quantum world, enabling experiments that probe, control, and ultimately exploit quantum fluctuations for applications in quantum information, metrology, solid state physics and beyond. }, author = {Trioni, Andrea}, isbn = {978-3-99078-067-1}, issn = {2663-337X}, pages = {202}, publisher = {Institute of Science and Technology Austria}, title = {{High-impedance quantum circuits for mesoscopic physics: Geometric superinductors and insulating Josephson Chains}}, doi = {10.15479/AT-ISTA-20371}, year = {2025}, } @inproceedings{20008, abstract = {We study the complexity of a class of promise graph homomorphism problems. For a fixed graph H, the H-colouring problem is to decide whether a given graph has a homomorphism to H. By a result of Hell and Nešetřil, this problem is NP-hard for any non-bipartite loop-less graph H. Brakensiek and Guruswami [SODA 2018] conjectured the hardness extends to promise graph homomorphism problems as follows: fix a pair of non-bipartite loop-less graphs G, H such that there is a homomorphism from G to H, it is NP-hard to distinguish between graphs that are G-colourable and those that are not H-colourable. We confirm this conjecture in the cases when both G and H are 4-colourable. This is a common generalisation of previous results of Khanna, Linial, and Safra [Comb. 20(3): 393-415 (2000)] and of Krokhin and Opršal [FOCS 2019]. The result is obtained by combining the algebraic approach to promise constraint satisfaction with methods of topological combinatorics and equivariant obstruction theory.}, author = {Avvakumov, Sergey and Filakovský, Marek and Opršal, Jakub and Tasinato, Gianluca and Wagner, Uli}, booktitle = {Proceedings of the 57th Annual ACM Symposium on Theory of Computing}, isbn = {9798400715105}, issn = {0737-8017}, location = {Prague, Czechia}, pages = {72--83}, publisher = {Association for Computing Machinery}, title = {{Hardness of 4-colouring G-colourable graphs}}, doi = {10.1145/3717823.3718154}, year = {2025}, } @phdthesis{20339, abstract = {This thesis investigates the interplay between algebraic and topological methods and combinatorial problems, focusing on approximate graph colourings and mass partitioning. The unifying theme throughout the dissertation is the use of continuous maps and symmetry constraints to extract combinatorial insights. We first explore approximate graph colouring problems and more generally promise constraint satisfaction problems. Using tools from equivariant topology in combination with the general theory of polymorphism of a promise constraint satisfaction problem, we establish hardness for specific types of approximations. In the second part, we address mass partitioning problems, where one seeks to divide geometric objects or measures in Euclidean space into parts of equal size using hyperplanes. Employing techniques from topological combinatorics (configuration space/test map setup and Borsuk–Ulam type theorems), we both obtain a new equipartitioning result in the and provide a fast algorithm for computing equipartitioning of point sets in 3D. }, author = {Tasinato, Gianluca}, issn = {2663-337X}, pages = {106}, publisher = {Institute of Science and Technology Austria}, title = {{Topological methods in discrete geometry and theoretical computer science: Measure partitioning and constraint satisfaction problems}}, doi = {10.15479/AT-ISTA-20339}, year = {2025}, } @phdthesis{20234, abstract = {Game Theory is the mathematical formalization of social dynamics - systems where agents interact over time and the evolution of the state of the system depends on the decisions of every player. This thesis takes the perspective of a single player and focuses on what they can guarantee in the worst case over the behavior of other players. In other words, we consider that the objective of every other player in the game is exactly the opposite to the player. We focus on sustained interactions over time, where the players repeatedly obtain quantitative rewards over time, and they are interested in maximizing their long-term performance. Formally, this thesis focuses on zero-sum games with the liminf average objective. Two fundamental questions that Game Theory aims to answer are the following. 1. How much can a player guarantee to obtain after the interaction? 2. How to act in order to obtain the previously mentioned guarantee? These questions are formalized by the concepts of "value" and "optimal strategies". We study their properties on games that exhibit one or more of the following properties. 1. Partial Observation: the players can not perfectly observe the current state of the system during the game. We consider the model of (finite) Partially Observable Markov Decision Processes and prove that finite-memory strategies are sufficient to approximately guarantee the value. 2. Perturbed Description: the formal description of the game is perturbed by a small parameter. We consider the model of (finite) Perturbed Matrix Games, and provide algorithms to check various robustness properties and to compute the parameterized value and optimal strategies. 3. Stochastic Transitions: the actions of the players determine the behavior of the evolution of the system, described as a probability distribution over the next state. We consider the model of (finite) Perturbed Stochastic Games and provide formulas for the marginal value. 4. Infinite States: the system can be in infinitely many states. We consider the model of Random Dynamic Games on a class of infinite graphs, prove the existence of the value, and quantify the concentration of finite-horizon values.}, author = {Saona Urmeneta, Raimundo J}, issn = {2663-337X}, pages = {125}, publisher = {Institute of Science and Technology Austria}, title = {{Robustness of solutions in game theory: Values and strategies in partially observable, perturbed, stochastic, and infinite games}}, doi = {10.15479/AT-ISTA-20234}, year = {2025}, } @article{19508, abstract = {We consider random two-player zero-sum dynamic games with perfect information on a class of infinite directed graphs. Starting from a fixed vertex, the players take turns to move a token along the edges of the graph. Every vertex is assigned a payoff known in advance by both players. Every time the token visits a vertex, Player 2 pays Player 1 the corresponding payoff. We consider a distribution over such games by assigning i.i.d. payoffs to the vertices. On the one hand, for acyclic directed graphs of bounded degree and sub-exponential expansion, we show that, when the duration of the game tends to infinity, the value converges almost surely to a constant at an exponential rate dominated in terms of the expansion. On the other hand, for the infinite d-ary tree (that does not fall into the previous class of graphs), we show convergence at a double-exponential rate.}, author = {Attia, Luc and Lichev, Lyuben and Mitsche, Dieter and Saona Urmeneta, Raimundo J and Ziliotto, Bruno}, issn = {2153-0793}, journal = {Dynamic Games and Applications}, pages = {1517--1535}, publisher = {Springer Nature}, title = {{Random zero-sum dynamic games on infinite directed graphs}}, doi = {10.1007/s13235-025-00636-4}, volume = {15}, year = {2025}, } @article{17037, abstract = {Zero-sum stochastic games are parameterized by payoffs, transitions, and possibly a discount rate. In this article, we study how the main solution concepts, the discounted and undiscounted values, vary when these parameters are perturbed. We focus on the marginal values, introduced by Mills in 1956 in the context of matrix games—that is, the directional derivatives of the value along any fixed perturbation. We provide a formula for the marginal values of a discounted stochastic game. Further, under mild assumptions on the perturbation, we provide a formula for their limit as the discount rate vanishes and for the marginal values of an undiscounted stochastic game. We also show, via an example, that the two latter differ in general.}, author = {Attia, Luc and Oliu-Barton, Miquel and Saona Urmeneta, Raimundo J}, issn = {1526-5471}, journal = {Mathematics of Operations Research}, number = {1}, pages = {482--505}, publisher = {Institute for Operations Research and the Management Sciences}, title = {{Marginal values of a stochastic game}}, doi = {10.1287/moor.2023.0297}, volume = {50}, year = {2025}, } @article{18112, abstract = {It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: we consider integrable deformations of a non-flat Liouville metric in a conformal class and show that for a fairly large class of such deformations, the deformed metric is again Liouville. The principal idea of the argument is that the preservation of rational invariant tori in the foliation of the phase space forces a linear combination on the Fourier coefficients of the deformation to vanish. Showing that the resulting linear system is non-degenerate will then yield the claim. Since our method of proof immediately carries over to higher dimensional tori, we obtain analogous statements in this more general case. To put our results in perspective, we review existing results about integrable metrics on the torus.}, author = {Henheik, Sven Joscha}, issn = {1469-4417}, journal = {Ergodic Theory and Dynamical Systems}, number = {2}, pages = {467--503}, publisher = {Cambridge University Press}, title = {{Deformational rigidity of integrable metrics on the torus}}, doi = {10.1017/etds.2024.48}, volume = {45}, year = {2025}, }