@article{19003, abstract = {Super-resolution methods provide far better spatial resolution than the optical diffraction limit of about half the wavelength of light (∼200-300 nm). Nevertheless, they have yet to attain widespread use in plants, largely due to plants’ challenging optical properties. Expansion microscopy improves effective resolution by isotropically increasing the physical distances between sample structures while preserving relative spatial arrangements and clearing the sample. However, its application to plants has been hindered by the rigid, mechanically cohesive structure of plant tissues. Here, we report on whole-mount expansion microscopy of thale cress (Arabidopsis thaliana) root tissues (PlantEx), achieving a four-fold resolution increase over conventional microscopy. Our results highlight the microtubule cytoskeleton organization and interaction between molecularly defined cellular constituents. Combining PlantEx with stimulated emission depletion (STED) microscopy, we increase nanoscale resolution and visualize the complex organization of subcellular organelles from intact tissues by example of the densely packed COPI-coated vesicles associated with the Golgi apparatus and put these into a cellular structural context. Our results show that expansion microscopy can be applied to increase effective imaging resolution in Arabidopsis root specimens. }, author = {Gallei, Michelle C and Truckenbrodt, Sven M and Kreuzinger, Caroline and Inumella, Syamala and Vistunou, Vitali and Sommer, Christoph M and Tavakoli, Mojtaba and Agudelo Duenas, Nathalie and Vorlaufer, Jakob and Jahr, Wiebke and Randuch, Marek and Johnson, Alexander J and Benková, Eva and Friml, Jiří and Danzl, Johann G}, issn = {1532-298X}, journal = {The Plant Cell}, number = {4}, publisher = {Oxford University Press}, title = {{Super-resolution expansion microscopy in plant roots}}, doi = {10.1093/plcell/koaf006}, volume = {37}, year = {2025}, } @article{17884, abstract = {Human T cell leukemia virus type 1 (HTLV-1) immature particles differ in morphology from other retroviruses, suggesting a distinct way of assembly. Here we report the results of cryo-electron tomography studies of HTLV-1 virus-like particles assembled in vitro, as well as derived from cells. This work shows that HTLV-1 uses a distinct mechanism of Gag–Gag interactions to form the immature viral lattice. Analysis of high-resolution structural information from immature capsid (CA) tubular arrays reveals that the primary stabilizing component in HTLV-1 is the N-terminal domain of CA. Mutagenesis analysis supports this observation. This distinguishes HTLV-1 from other retroviruses, in which the stabilization is provided primarily by the C-terminal domain of CA. These results provide structural details of the quaternary arrangement of Gag for an immature deltaretrovirus and this helps explain why HTLV-1 particles are morphologically distinct.}, author = {Obr, Martin and Percipalle, Mathias and Chernikova, Darya and Yang, Huixin and Thader, Andreas and Pinke, Gergely and Porley, Dario J and Mansky, Louis M. and Dick, Robert A. and Schur, Florian KM}, issn = {1545-9985}, journal = {Nature Structural & Molecular Biology}, pages = {268--276}, publisher = {Springer Nature}, title = {{Distinct stabilization of the human T cell leukemia virus type 1 immature Gag lattice}}, doi = {10.1038/s41594-024-01390-8}, volume = {32}, year = {2025}, } @inproceedings{19010, abstract = {Causal representation learning aims at recovering latent causal variables from high-dimensional observations to solve causal downstream tasks, such as predicting the effect of new interventions or more robust classification. A plethora of methods have been developed, each tackling carefully crafted problem settings that lead to different types of identifiability. The folklore is that these different settings are important, as they are often linked to different rungs of Pearl's causal hierarchy, although not all neatly fit. Our main contribution is to show that many existing causal representation learning approaches methodologically align the representation to known data symmetries. Identification of the variables is guided by equivalence classes across different "data pockets" that are not necessarily causal. This result suggests important implications, allowing us to unify many existing approaches in a single method that can mix and match different assumptions, including non-causal ones, based on the invariances relevant to our application. It also significantly benefits applicability, which we demonstrate by improving treatment effect estimation on real-world high-dimensional ecological data. Overall, this paper clarifies the role of causality assumptions in the discovery of causal variables and shifts the focus to preserving data symmetries.}, author = {Yao, Dingling and Rancati, Dario and Cadei, Riccardo and Fumero, Marco and Locatello, Francesco}, booktitle = {13th International Conference on Learning Representations}, location = {Singapore}, publisher = {ICLR}, title = {{Unifying causal representation learning with the invariance principle}}, year = {2025}, } @article{19704, abstract = {The information-processing capability of the brain’s cellular network depends on the physical wiring pattern between neurons and their molecular and functional characteristics. Mapping neurons and resolving their individual synaptic connections can be achieved by volumetric imaging at nanoscale resolution1,2 with dense cellular labelling. Light microscopy is uniquely positioned to visualize specific molecules, but dense, synapse-level circuit reconstruction by light microscopy has been out of reach, owing to limitations in resolution, contrast and volumetric imaging capability. Here we describe light-microscopy-based connectomics (LICONN). We integrated specifically engineered hydrogel embedding and expansion with comprehensive deep-learning-based segmentation and analysis of connectivity, thereby directly incorporating molecular information into synapse-level reconstructions of brain tissue. LICONN will allow synapse-level phenotyping of brain tissue in biological experiments in a readily adoptable manner.}, author = {Tavakoli, Mojtaba and Lyudchik, Julia and Januszewski, Michał and Vistunou, Vitali and Agudelo Duenas, Nathalie and Vorlaufer, Jakob and Sommer, Christoph M and Kreuzinger, Caroline and Oliveira, Bárbara and Cenameri, Alban and Novarino, Gaia and Jain, Viren and Danzl, Johann G}, issn = {1476-4687}, journal = {Nature}, pages = {398--410}, publisher = {Springer Nature}, title = {{Light-microscopy-based connectomic reconstruction of mammalian brain tissue}}, doi = {10.1038/s41586-025-08985-1}, volume = {642}, 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}, } @article{19401, abstract = {High kinetic inductance superconductors are gaining increasing interest for the realisation of qubits, amplifiers and detectors. Moreover, thanks to their high impedance, quantum buses made of such materials enable large zero-point fluctuations of the voltage, boosting the coupling rates to spin and charge qubits. However, fully exploiting the potential of disordered or granular superconductors is challenging, as their inductance and, therefore, impedance at high values are difficult to control. Here, we report a reproducible fabrication of granular aluminium resonators by developing a wireless ohmmeter, which allows in situ measurements during film deposition and, therefore, control of the kinetic inductance of granular aluminium films. Reproducible fabrication of circuits with impedances (inductances) exceeding 13 kΩ (1 nH per square) is now possible. By integrating a 7.9 kΩ resonator with a germanium double quantum dot, we demonstrate strong charge-photon coupling with a rate of gc/2π = 566 ± 2 MHz. This broadly applicable method opens the path for novel qubits and high-fidelity, long-distance two-qubit gates.}, author = {Janik, Marian and Roux, Kevin Etienne Robert and Borja Espinosa, Carla N and Sagi, Oliver and Baghdadi, Abdulhamid and Adletzberger, Thomas and Calcaterra, Stefano and Botifoll, Marc and Garzón Manjón, Alba and Arbiol, Jordi and Chrastina, Daniel and Isella, Giovanni and Pop, Ioan M. and Katsaros, Georgios}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Strong charge-photon coupling in planar germanium enabled by granular aluminium superinductors}}, doi = {10.1038/s41467-025-57252-4}, volume = {16}, year = {2025}, } @misc{18886, abstract = {Research Data for publication 'Strong charge-photon coupling in planar germanium enabled by granular aluminium superinductors'}, author = {Janik, Marian}, publisher = {Institute of Science and Technology Austria}, title = {{Research data for publication 'Strong charge-photon coupling in planar germanium enabled by granular aluminium superinductors'}}, doi = {10.15479/AT:ISTA:18886}, 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}, } @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}, } @phdthesis{19759, abstract = {Despite generating remarkable results in various computer vision tasks, deep learning comes with some surprising shortcomings. For example, tiny perturbations, often imperceptible to the human eye, can completely change the predictions of image classifiers. Despite a decade of research, the field has made limited progress in developing image classifiers that are both accurate and robust. This thesis aims to address this gap. As our first contribution, we aim to simplify the process of training certifiably robust image classifiers. We do this by designing a convolutional layer that does not require executing an iterative procedure in every forward pass, but relies on an explicit bound instead. We also propose a loss function that allows optimizing for a particular margin more precisely. Next, we provide an overview and comparison of various methods that create robust image classifiers by constraining the Lipschitz constant. This is important since generally longer training times and more parameters improve the performance of robust classifiers, making it challenging to determine the most practical and effective methods from existing literature. In 1-Lipschitz classification, the performance of current methods is still much worse than what we expect on the simple tasks we consider. Therefore, we next investigate potential causes of this shortcoming. We first consider the role of the activation function. We prove a theoretical shortcoming of the commonly used activation function, and provide an alternative without it. However this theoretical improvement does barely translate to the empirical performance of robust classifiers, suggesting a different bottleneck. Therefore, in the final chapter, we study how the performance depends on the amount of training data. We prove that in the worst case, we might require far more data to train a robust classifier compared to a normal one. We furthermore find that the amount of training data is a key determinant of the performance current methods achieve on popular datasets. Additionally, we show that linear subspaces exist with tiny data variance, and yet we can still train very accurate classifiers after projecting into those subspaces. This shows that on the datasets considered, enforcing robustness in classification makes the task strictly more challenging. }, author = {Prach, Bernd}, issn = {2663-337X}, pages = {84}, publisher = {Institute of Science and Technology Austria}, title = {{Robust image classification with 1-Lipschitz networks}}, doi = {10.15479/10.15479/at-ista-19759}, year = {2025}, } @inproceedings{20455, abstract = {Despite extensive research since the community learned about adversarial examples 10 years ago, we still do not know how to train high-accuracy classifiers that are guaranteed to be robust to small perturbations of their inputs. Previous works often argued that this might be because no classifier exists that is robust and accurate at the same time. However, in computer vision this assumption does not match reality where humans are usually accurate and robust on most tasks of interest. We offer an alternative explanation and show that in certain settings robust generalization is only possible with unrealistically large amounts of data. Specifically, we find a setting where a robust classifier exists, it is easy to learn an accurate classifier, yet it requires an exponential amount of data to learn a robust classifier. Based on this theoretical result, we evaluate the influence of the amount of training data on datasets such as CIFAR10. Our findings indicate that the the amount of training data is the main factor determining the robust performance. Furthermore we show that that there are low magnitude directions in the data which are useful for non-robust generalization but are not available for robust classifiers. This implies that robust classification is a strictly harder tasks than normal classification, thereby providing an explanation why robust classification requires more data.}, author = {Prach, Bernd and Lampert, Christoph}, booktitle = {2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops}, isbn = {9798331599942}, issn = {2160-7516}, location = {Nashville, TN, United States}, pages = {660--669}, publisher = {IEEE}, title = {{Intriguing properties of robust classification}}, doi = {10.1109/CVPRW67362.2025.00071}, year = {2025}, } @phdthesis{19630, abstract = {This thesis consists of three chapters, each corresponding to one publication. While each of these projects tackles a topic in a different area of research, they all share a common thread in the type of topological structure they handle - a partition of space into volumes separated by interfaces that meet in non-manifold junctions. In Chapter 2, we study clusters of soap bubbles from a simulation perspective. In particular, we develop a surface-only algorithm that couples large scale motion and shape deformation of soap bubble clusters with the small scale evolution of the thin film's thickness, which is responsible for visual phenomena like surface vortices, Newton's interference patterns, capillary waves, and deformation-dependent rupturing of films in a foam. We model film thickness as a reduced degree of freedom in the Navier-Stokes equations and from them derive three sets of equations governing normal and tangential motion of the soap film surface, as well as the evolution of the thin film thickness. We discretize these equations on a non-manifold triangle mesh, extending and adapting operators to handle complex topology. We also present an incompressible fluid solver for 2.5D films and an advection algorithm for convecting fields across non-manifold surface junctions. Our simulations enhance bubble solvers with additional effects caused by convection, rippling, draining, and evaporation of the thin film. In Chapter 3, we introduce a multi-material non-manifold mesh-based surface tracking algorithm that converts mesh defects, such as overlaps, self-intersections, and inversions into topological changes. Our algorithm generalizes prior work on manifold surface tracking with topological changes: it preserves surface features like mesh-based methods, and it robustly handles topological changes like level set methods. Our method also offers improved efficiency and robustness over the state of the art. We demonstrate the effectiveness of the approach on a range of examples, including complex soap film simulations, such as those presented in Chapter 2, but with an order of magnitude more interacting bubbles than what we could achieve before, and Boolean unions of non-manifold meshes consisting of millions of triangles. Lastly, in Chapter 4, we utilize developments in the theory of random geometric complexes facilitated by observations from Discrete Morse theory. We survey the methods and results obtained with this new approach, and discuss some of its shortcomings. We use simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics.}, author = {Synak, Peter}, issn = {2663-337X}, pages = {106}, publisher = {Institute of Science and Technology Austria}, title = {{Methods for fluid simulation, surface tracking, and statistics of non-manifold structures}}, doi = {10.15479/AT-ISTA-19630}, year = {2025}, } @phdthesis{20551, abstract = {The space of codimension-2 shapes, such as curves in 3D and surfaces in 4D, is an infinite-dimensional manifold. This thesis explores geometric structures and dynamics on this space, with emphasis on their implications for physics, particularly hydrodynamics. Our investigation ranges from theoretical studies of infinite-dimensional symplectic and prequantum geometry to numerical computation of the time evolution of shapes. The thesis presents four main contributions. In the first part, we introduce implicit representations of codimension-2 shapes using a class of complex-valued functions, and prove that the space of these implicit representations forms a prequantum bundle over the codimension-2 shape space. This reveals a new geometric interpretation of the canonical symplectic structure on the codimension-2 shape space. In the second part, we use implicit representations to develop a simulation method for the dynamics of space curves. To handle chaotic systems such as vortex filaments in hydrodynamics, we exploit the infinite degrees of freedom, hidden in both the configuration and dynamics of implicit representations. In the third part, we introduce new symplectic structures on the space of space curves, which generalize the only previously known symplectic structure on this space, allowing for new Hamiltonian dynamics of space curves. In the fourth part, we apply a symplectic viewpoint to a differential geometric problem with practical applications. We derive a new area formula for spherical polygons via prequantization. }, author = {Ishida, Sadashige}, isbn = {978-3-99078-070-1}, issn = {2663-337X}, pages = {141}, publisher = {Institute of Science and Technology Austria}, title = {{Symplectic-prequantum structures and dynamics on the codimension-2 shape space}}, doi = {10.15479/AT-ISTA-20551}, 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{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}, } @phdthesis{19540, abstract = {This thesis deals with several different models for complex quantum mechanical systems and is structured in three main parts. In Part I, we study mean field random matrices as models for quantum Hamiltonians. Our focus lies on proving concentration estimates for resolvents of random matrices, so-called local laws, mostly in the setting of multiple resolvents. These estimates have profound consequences for eigenvector overlaps and thermalization problems. More concretely, we obtain, e.g., the optimal eigenstate thermalization hypothesis (ETH) uniformly in the spectrum for Wigner matrices, an optimal lower bound on non-Hermitian eigenvector overlaps, and prethermalization for deformed Wigner matrices. In order to prove our novel multi-resolvent local laws, we develop and devise two main methods, the static Psi-method and the dynamical Zigzag strategy. In Part II, we study Bardeen-Cooper-Schrieffer (BCS) theory, the standard mean field microscopic theory of superconductivity. We focus on asymptotic formulas for the characteristic critical temperature and energy gap of a superconductor and prove universality of their ratio in various physical regimes. Additionally, we investigate multi-band superconductors and show that inter-band coupling effects can only enhance the critical temperature. In Part III, we study quantum lattice systems. On the one hand, we show a strong version of the local-perturbations-perturb-locally (LPPL) principle for the ground state of weakly interacting quantum spin systems with a uniform on-site gap. On the other hand, we introduce a notion of a local gap and rigorously justify response theory and the Kubo formula under the weakened assumption of a local gap. Additionally, we discuss two classes of problems which do not fit into the three main parts of the thesis. These are deformational rigidity of Liouville metrics on the torus and relativistic toy models of particle creation via interior-boundary-conditions (IBCs). }, author = {Henheik, Sven Joscha}, isbn = {978-3-99078-057-2}, issn = {2663-337X}, pages = {720}, publisher = {Institute of Science and Technology Austria}, title = {{Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems}}, doi = {10.15479/AT-ISTA-19540}, year = {2025}, } @phdthesis{19048, abstract = {Rotations are found in physics problems at all scales: from spatial motion of celestial bodies, to transitions between quantum states of atoms and molecules. Mathematically, they represent a fundamental class of transformations and symmetries. Unlike spatial displacements, rotational transformations in three-dimensional space are non-commutative: the result of applying a sequence of rotations depends on the order of these operations. This feature makes the emergent physics that involves rotations rather intricate, but instrumental for studies of highly-interconnected many-body systems. In the presence of an environment, rotational properties of an object change, due to the interaction with particles of the environment. Owing to the complexity of this interaction, it can be engineered to exhibit certain properties of interest. In this Thesis, we examine several scenarios of how the rotational behavior of an impurity can be modified by interactions with its environment.}, author = {Maslov, Mikhail}, issn = {2663-337X}, pages = {86}, publisher = {Institute of Science and Technology Austria}, title = {{Emergent physics of rotating quantum impurities in many-body environments}}, doi = {10.15479/at:ista:19048}, year = {2025}, } @article{17240, abstract = {We prove an upper bound on the energy density of the dilute spin-\(\frac {1}{2}\) Fermi gas capturing the leading correction to the kinetic energy\(8\pi a\rho _\uparrow\rho _\downarrow\) with an error of size smaller than\(a\rho^{2}(a^ 3\rho)^{1/3-\varepsilon}\) for any\(\varepsilon> 0\), where a denotes the scattering length of the interaction. The result is valid for a large class of interactions including interactions with a hard core. A central ingredient in the proof is a rigorous version of a fermionic cluster expansion adapted from the formal expansion of Gaudin et al. (Nucl Phys A 176(2):237–260, 1971. https://doi.org/10.1016/0375-9474(71)90267-3).}, author = {Lauritsen, Asbjørn Bækgaard}, issn = {1424-0637}, journal = {Annales Henri Poincare}, pages = {203--243}, publisher = {Springer Nature}, title = {{Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion}}, doi = {10.1007/s00023-024-01450-1}, volume = {26}, year = {2025}, } @phdthesis{20147, abstract = {Quantitative properties offer a framework for specifying and verifying system behaviors beyond the traditional boolean perspective. For example, while a boolean property may specify whether a server eventually grants every request it receives, a quantitative one may map each server execution to its average response time. This quantitative view is relatively well-studied in the context of static verification. However, although such properties often appear in practice as performance or robustness measures in a dynamic verification context, a general theoretical framework for their analysis and classification from a monitoring perspective is still missing. In this thesis, we aim to develop such a framework that takes resource-precision tradeoffs of monitors as a central consideration. We present the first theory of monitorability for quantitative properties where monitors can be naturally approximate and compared regarding their precision and resource use. In particular, we show that additional monitor resources such as registers or states lead to strictly better approximations for some properties. To enable such analyses in a machine-model independent way, we describe an abstract notion of monitors that can be instantiated with concrete models of monitors. Within this framework, we study how abstract monitors behave and identify classes of properties amenable to approximate monitoring with resource-precision considerations. We then extend the boolean safety-liveness dichotomy and safety-progress hierarchy to the quantitative setting with a monitoring perspective. In particular, we prove that every property is the pointwise minimum of a safety property and a liveness property, and properties that are both safe and co-safe can be approximately monitored arbitrarily precisely using only finitely many states. We also study the classes of quantitative properties definable by finite-state quantitative automata and provide algorithms for deciding their safety or liveness as well as their safety-liveness decompositions. Finally, we present the first general-purpose tool for automating the analysis, verification, and monitoring of quantitative automata. }, author = {Sarac, Naci E}, issn = {2663-337X}, pages = {149}, publisher = {Institute of Science and Technology Austria}, title = {{A monitoring-oriented theory and classification of quantitative specifications}}, doi = {10.15479/AT-ISTA-20147}, year = {2025}, } @article{10045, abstract = {Given a fixed finite metric space (V,μ), the {\em minimum 0-extension problem}, denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai: if metric μ is {\em orientable modular} then 0-Ext[μ] can be solved in polynomial time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed a theory of discrete convex functions on orientable modular graphs generalizing several known classes of functions in discrete convex analysis, such as L♮-convex functions. We consider a more general version of the problem in which unary functions fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where set F⊆(V2) is fixed. We extend the complexity classification above by providing an explicit condition on (μ,F) for the problem to be tractable. In order to prove the tractability part, we generalize Hirai's theory and define a larger class of discrete convex functions. It covers, in particular, another well-known class of functions, namely submodular functions on an integer lattice. Finally, we improve the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs. }, author = {Dvorak, Martin and Kolmogorov, Vladimir}, issn = {1436-4646}, journal = {Mathematical Programming}, keywords = {minimum 0-extension problem, metric labeling problem, discrete metric spaces, metric extensions, computational complexity, valued constraint satisfaction problems, discrete convex analysis, L-convex functions}, pages = {279--322}, publisher = {Springer Nature}, title = {{Generalized minimum 0-extension problem and discrete convexity}}, doi = {10.1007/s10107-024-02064-5}, volume = {209}, year = {2025}, }