@article{20591, abstract = {In this paper we derive estimates for the Hessian of the logarithm (log-Hessian) for solutions to the heat equation. For initial data in the form of log-Lipschitz perturbation of strongly log-concave measures, the log-Hessian admits an explicit, uniform (in space) lower bound. This yields a new estimate for the Lipschitz constant of a transport map pushing forward the standard Gaussian to a measure in this class. On the other hand, we show that assuming only fast decay of the tails of the initial datum does not suffice to guarantee uniform log-Hessian upper bounds.}, author = {Brigati, Giovanni and Pedrotti, Francesco}, issn = {1083-589X}, journal = {Electronic Communications in Probability}, publisher = {Institute of Mathematical Statistics}, title = {{Heat flow, log-concavity, and Lipschitz transport maps}}, doi = {10.1214/25-ECP717}, volume = {30}, year = {2025}, } @article{20050, abstract = {We prove upper bounds on the L∞-Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information inequality involving the L∞-Wasserstein metric and the relative L∞-Fisher information. We show that this inequality can be sharpened significantly in situations where the involved densities are anisotropic. Our proof is based on probabilistic techniques using Langevin dynamics. As an application of these results, we obtain sharp exponential rates of convergence in Fisher’s infinitesimal model from quantitative genetics, generalising recent results by Calvez, Poyato, and Santambrogio in dimension 1 to arbitrary dimensions.}, author = {Khudiakova, Kseniia and Maas, Jan and Pedrotti, Francesco}, issn = {1050-5164}, journal = {The Annals of Applied Probability}, number = {3}, pages = {1913--1940}, publisher = {Institute of Mathematical Statistics}, title = {{L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model}}, doi = {10.1214/25-aap2162}, volume = {35}, year = {2025}, } @unpublished{22807, abstract = {Cleavage - the series of rapid cell divisions that follow fertilization - marks the onset of metazoan development and represents a deeply conserved evolutionary process. Across animals, two principal modes exist: complete (holoblastic) and incomplete (meroblastic) cleavage. While holoblastic cleavage resembles conventional cytokinesis both in vitro and in vivo, the mechanisms underlying meroblastic cleavage have remained poorly understood. Using zebrafish embryos as a model, we show that meroblastic cleavage proceeds through a distinct two-step mechanism. The process begins with the assembly and contraction of a large, arc-shaped actomyosin cable. However, this contractile event alone is insufficient to complete division. A second phase, driven by cadherin-mediated membrane adhesion, is required to invaginate the furrow ridge. Strikingly, this transition depends on mechanical uncoupling of the contractile cable from the surrounding cortex. We demonstrate that such uncoupling arises from an active nematic instability, which both enhances contractility along the cable and generates actin depletion zones that relieve lateral connections. Together, these findings reveal that meroblastic cleavage is governed not by a single actomyosin-based event but by a sequential interplay between cytoskeletal contraction and cadherin-dependent adhesion, highlighting a mechanism fundamentally distinct from canonical cytokinesis.}, author = {Tong, Xin and Li, Yuting I and Schelle, Joséphine and Hannezo, Edouard B and Heisenberg, Carl-Philipp J}, booktitle = {bioRxiv}, title = {{Non-canonical cytokinesis driven by mechanical uncoupling via nematic flows and adhesion-based invagination}}, doi = {10.1101/2025.10.15.682552}, year = {2025}, } @article{20705, abstract = {Optical tweezers are widely used as a highly sensitive tool to measure forces on micron-scale particles. One such application is the measurement of the electric charge of a particle, which can be done with high precision in liquids, air, or vacuum. We experimentally investigate how the trapping laser itself can electrically charge such a particle, in our case a ∼1  μ⁢m SiO2 sphere in air. We model the charging mechanism as a two-photon process which reproduces the experimental data with high fidelity.}, author = {Stöllner, Andrea and Lenton, Isaac C and Volosniev, Artem and Millen, James and Shibuya, Renjiro and Ishii, Hisao and Rak, Dmytro and Alpichshev, Zhanybek and David, Grégory and Signorell, Ruth and Muller, Caroline J and Waitukaitis, Scott R}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {21}, publisher = {American Physical Society}, title = {{Using optical tweezers to simultaneously trap, charge, and measure the charge of a microparticle in air}}, doi = {10.1103/5xd9-4tjj}, volume = {135}, 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}, } @inproceedings{21281, abstract = {A strategy profile in a multi-player game is a Nash equilibrium if no player can unilaterally deviate to achieve a strictly better payoff. A profile is an ε-Nash equilibrium if no player can gain more than ε by unilaterally deviating from their strategy. In this work, we use ε-Nash equilibria to approximate the computation of Nash equilibria. Specifically, we focus on turn-based, multiplayer stochastic games played on graphs, where players are restricted to stationary strategies - strategies that use randomness but not memory. The problem of deciding the constrained existence of stationary Nash equilibria - where each player’s payoff must lie within a given interval - is known to be ∃ℝ-complete in such a setting (Hansen and Sølvsten, 2020). We extend this line of work to stationary ε-Nash equilibria and present an algorithm that solves the following promise problem: given a game with a Nash equilibrium satisfying the constraints, compute an ε-Nash equilibrium that ε-satisfies those same constraints - satisfies the constraints up to an ε additive error. Our algorithm runs in FNP^NP time. To achieve this, we first show that if a constrained Nash equilibrium exists, then one exists where the non-zero probabilities are at least an inverse of a double-exponential in the input. We further prove that such a strategy can be encoded using floating-point representations, as in the work of Frederiksen and Miltersen (2013), which finally gives us our FNP^NP algorithm. We further show that the decision version of the promise problem is NP-hard. Finally, we show a partial tightness result by proving a lower bound for such techniques: if a constrained Nash equilibrium exists, then there must be one where the probabilities in the strategies are double-exponentially small.}, author = {Asadi, Ali and Brice, Leonard and Chatterjee, Krishnendu and Thejaswini, K. S.}, booktitle = {45th Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, isbn = {9783959774062}, location = {Pilani, India}, pages = {9:1--9:17}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{ε-stationary Nash equilibria in multi-player stochastic graph games}}, doi = {10.4230/lipics.fsttcs.2025.9}, volume = {360}, year = {2025}, } @article{23129, abstract = {Abstract The Arabidopsis root apical meristem is an excellent model for studying plant organ growth. This involves a coordinated process of cell division, elongation, and differentiation, with each tissue type developing according to its own schedule. Among these tissues, the protophloem is particularly important, differentiating early to supply nutrients and signalling molecules to the growing root tip. The OCTOPUS (OPS) protein and its homologue OPS-LIKE 2 (OPL2) are essential for proper root protophloem differentiation and, probably through this role, indirectly promote root growth. Here, we explored the roles of the other three OPS homologues in Arabidopsis, OPL1, OPL3, and OPL4. OPS/OPL genes exhibited overlapping expression patterns and functions, with a high degree of redundancy among them. Although higher order mutants did not display more severe phloem defects, they exhibited significantly reduced root growth compared with the ops opl2 mutant. These results indicate a direct contribution of the investigated OPL genes to meristematic activity. While our focus was on root growth, the OPS/OPL gene family also plays a positive role in regulating shoot growth, emphasizing its broader impact on plant development. Furthermore, our analyses reiterate the central role of OPS and the phloem domain in controlling overall plant growth.}, author = {Crivelli, Simona and Bartusch, Kai and Ruiz-Sola, M Aguila and Coiro, Mario and Schmidt Kjølner Hansen, Signe and Truernit, Elisabeth}, issn = {1460-2431}, journal = {Journal of Experimental Botany}, number = {6}, pages = {1752--1766}, publisher = {Oxford University Press}, title = {{Distinct and redundant roles of the Arabidopsis OCTOPUS gene family in plant growth beyond phloem development}}, doi = {10.1093/jxb/eraf010}, volume = {76}, year = {2025}, } @phdthesis{19395, abstract = {Plant growth and development rely significantly on phytohormones, with auxin serving as a master regulator, orchestrating processes from embryogenesis to organogenesis, vascular patterning, and environmental adaptation. Since its conceptual proposition by Charles Darwin in 1880 as an endogenous chemical signal influencing phototropism in grass, auxin has captivated scientists seeking to understand how such a small molecule exerts a profound influence on plant development. One particularly fascinating aspect of auxin function is its ability to self-organize its transport. Through a feedback mechanism between auxin perception and directional transport—primarily mediated by PIN auxin transporters—auxin establishes narrow transport channels. This phenomenon, known as auxin canalization, is fundamental to vascular formation, regeneration, and other key developmental processes. Despite advances in our understanding, driven by experimental studies and computational models, auxin canalization remains an enigma, with many unanswered questions. Like other hormones, auxin functions through intricate signaling pathways. It operates through at least two distinct signaling mechanisms: the well-characterized canonical pathway and the less understood non-canonical pathway. While significant progress has been made in elucidating the canonical pathway, the non-canonical mechanisms remain less defined and require further investigation. In this study, we revisit the non-canonical auxin signaling pathway mediated by the cell-surface complex Auxin Binding Protein 1-Transmembrane Kinase 1 (ABP1-TMK1), with a particular focus on its downstream phosphorylation events. We reveal that this auxin-mediated phosphorylation is conserved across the green lineage, underscoring its fundamental role in plant development. We explore key phosphorylation targets, particularly PIN2, which is essential for root gravitropism. To further understand TMK1’s role in diverse developmental processes, we identified and investigated its interactors as potential co-receptors or regulatory components within its signaling network. Given the previously established role of ABP1-TMK1 in auxin canalization, we sought to further investigate this process and identified several TMK1 interactors also involved in this intricate mechanism. These findings provide new insights into the complex regulation of auxin canalization, highlighting a broader and more interconnected signaling framework than previously understood.}, author = {Monzer, Aline}, issn = {2663-337X}, pages = {160}, publisher = {Institute of Science and Technology Austria}, title = {{Cell-surface auxin signaling: Linking molecular pathways to plant development}}, doi = {10.15479/AT-ISTA-19395}, year = {2025}, } @inproceedings{21074, abstract = {Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different representations, even when learning the same task on the same data. However, it has recently been shown that when a latent structure is shared between distinct latent spaces, relative distances between representations can be preserved, up to distortions. Building on this idea, we demonstrate that exploiting the differential-geometric structure of latent spaces of neural models, it is possible to capture precisely the transformations between representational spaces trained on similar data distributions. Specifically, we assume that distinct neural models parametrize approximately the same underlying manifold, and introduce a representation based on the pullback metric that captures the intrinsic structure of the latent space, while scaling efficiently to large models. We validate experimentally our method on model stitching and retrieval tasks, covering autoencoders and vision foundation discriminative models, across diverse architectures, datasets, pretraining schemes and modalities. Code is available at the following link.}, author = {Yu, Hanlin and Inal, Befrin and Arvanitidis, Georgios and Hauberg, Soren and Locatello, Francesco and Fumero, Marco}, booktitle = {39th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {San Diego, CA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{Connecting neural models latent geometries with relative geodesic representations}}, doi = {10.52202/085713-3769}, volume = {38}, year = {2025}, } @inproceedings{21076, abstract = {In many scientific experiments, the data annotating cost constraints the pace for testing novel hypotheses. Yet, modern machine learning pipelines offer a promising solution—provided their predictions yield correct conclusions. We focus on Prediction-Powered Causal Inferences (PPCI), i.e., estimating the treatment effect in an unlabeled target experiment, relying on training data with the same outcome annotated but potentially different treatment or effect modifiers. We first show that conditional calibration guarantees valid PPCI at population level. Then, we introduce a sufficient representation constraint transferring validity across experiments, which we propose to enforce in practice in Deconfounded Empirical Risk Minimization, our new model-agnostic training objective. We validate our method on synthetic and real-world scientific data, solving impossible problem instances for Empirical Risk Minimization even with standard invariance constraints. In particular, for the first time, we achieve valid causal inference on a scientific experiment with complex recording and no human annotations, fine-tuning a foundational model on our similar annotated experiment.}, author = {Cadei, Riccardo and Demirel, Ilker and De Bartolomeis, Piersilvio and Lindorfer, Lukas and Cremer, Sylvia and Schmid, Cordelia and Locatello, Francesco}, booktitle = {39th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {San Diego, CA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{Prediction-powered causal inferences}}, doi = {10.52202/085713-2479}, volume = {38}, year = {2025}, } @inproceedings{21072, abstract = {Language and vision-language models have shown impressive performance across a wide range of tasks, but their internal mechanisms remain only partly understood. In this work, we study how individual attention heads in text-generative models specialize in specific semantic or visual attributes. Building on an established interpretability method, we reinterpret the practice of probing intermediate activations with the final decoding layer through the lens of signal processing. This lets us analyze multiple samples in a principled way and rank attention heads based on their relevance to target concepts. Our results show consistent patterns of specialization at the head level across both unimodal and multimodal transformers. Remarkably, we find that editing as few as 1% of the heads, selected using our method, can reliably suppress or enhance targeted concepts in the model output. We validate our approach on language tasks such as question answering and toxicity mitigation, as well as vision-language tasks including image classification and captioning. Our findings highlight an interpretable and controllable structure within attention layers, offering simple tools for understanding and editing large-scale generative models.}, author = {Basile, Lorenzo and Maiorca, Valentino and Doimo, Diego and Locatello, Francesco and Cazzaniga, Alberto}, booktitle = {39th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {San Diego, CA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{Head pursuit: Probing attention specialization in multimodal transformers}}, doi = {10.52202/085713-3752}, volume = {38}, year = {2025}, } @inproceedings{21068, abstract = {Causal reasoning and discovery, two fundamental tasks of causal analysis, often face challenges in applications due to the complexity, noisiness, and highdimensionality of real-world data. Despite recent progress in identifying latent causal structures using causal representation learning (CRL), what makes learned representations useful for causal downstream tasks and how to evaluate them are still not well understood. In this paper, we reinterpret CRL using a measurement model framework, where the learned representations are viewed as proxy measurements of the latent causal variables. Our approach clarifies the conditions under which learned representations support downstream causal reasoning and provides a principled basis for quantitatively assessing the quality of representations using a new Test-based Measurement EXclusivity (T-MEX) score. We validate T-MEX across diverse causal inference scenarios, including numerical simulations and real-world ecological video analysis, demonstrating that the proposed framework and corresponding score effectively assess the identification of learned representations and their usefulness for causal downstream tasks. Reproducible code can be found at https://github.com/shimenghuang/a-measurement-perspective-of-crl.}, author = {Yao, Dingling and Huang, Shimeng and Cadei, Riccardo and Zhang, Kun and Locatello, Francesco}, booktitle = {39th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {San Diego, CA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{The third pillar of causal analysis? A measurement perspective on causal representations}}, doi = {10.52202/085713-1444}, volume = {38}, year = {2025}, } @article{18631, abstract = {Within the established framework of structure formation, galaxies start as systems of low stellar mass and gradually grow into far more massive galaxies. The existence of massive galaxies in the first billion years of the Universe, as suggested by recent observations, seems to challenge this model, as such galaxies would require highly efficient conversion of baryons into stars. An even greater challenge in this epoch is the existence of massive galaxies that have already ceased forming stars. However, robust detections of early massive quiescent galaxies have been challenging due to the coarse wavelength sampling of photometric surveys. Here we report the spectroscopic confirmation with the James Webb Space Telescope of the quiescent galaxy RUBIES-EGS-QG-1 at redshift z = 4.90, 1.2 billion years after the Big Bang. Deep stellar absorption features in the spectrum reveal that the stellar mass of the galaxy of 1011 M⊙ formed in a short 200 Myr burst of star formation, after which star formation activity dropped rapidly and persistently. According to current galaxy formation models, systems with such rapid stellar mass growth and early quenching are too rare to plausibly occur in the small area probed spectroscopically with JWST. Instead, the discovery of RUBIES-EGS-QG-1 implies that early massive quiescent galaxies can be quenched earlier or exhaust gas available for star formation more efficiently than assumed at present.}, author = {De Graaff, Anna and Setton, David J. and Brammer, Gabriel and Cutler, Sam and Suess, Katherine A. and Labbé, Ivo and Leja, Joel and Weibel, Andrea and Maseda, Michael V. and Whitaker, Katherine E. and Bezanson, Rachel and Boogaard, Leindert A. and Cleri, Nikko J. and De Lucia, Gabriella and Franx, Marijn and Greene, Jenny E. and Hirschmann, Michaela and Matthee, Jorryt J and Mcconachie, Ian and Naidu, Rohan P. and Oesch, Pascal A. and Price, Sedona H. and Rix, Hans Walter and Valentino, Francesco and Wang, Bingjie and Williams, Christina C.}, issn = {2397-3366}, journal = {Nature Astronomy}, pages = {280--292}, publisher = {Springer Nature}, title = {{Efficient formation of a massive quiescent galaxy at redshift 4.9}}, doi = {10.1038/s41550-024-02424-3}, volume = {9}, year = {2025}, } @inproceedings{21070, abstract = {Deep learning systems deployed in real-world applications often encounter data that is different from their in-distribution (ID). A reliable model should ideally abstain from making decisions in this out-of-distribution (OOD) setting. Existing state-of-the-art methods primarily focus on feature distances, such as k-th nearest neighbors and distances to decision boundaries, either overlooking or ineffectively using in-distribution statistics. In this work, we propose a novel angle-based metric for OOD detection that is computed relative to the in-distribution structure. We demonstrate that the angles between feature representations and decision boundaries, viewed from the mean of in-distribution features, serve as an effective discriminative factor between ID and OOD data. We evaluate our method on nine ImageNet-pretrained models. Our approach achieves the lowest FPR in 5 out of 9 ImageNet models, obtains the best average FPR overall, and consistently ranking among the top 3 across all evaluated models. Furthermore, we highlight the benefits of contrastive representations by showing strong performance with ResNet SCL and CLIP architectures. Finally, we demonstrate that the scale-invariant nature of our score enables an ensemble strategy via simple score summation. }, author = {Demirel, Berker and Fumero, Marco and Locatello, Francesco}, booktitle = {39th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {San Diego, CA, United States}, publisher = {Neural Information Processing Systems Foundation}, title = {{Out-of-Distribution detection with relative angles}}, doi = {10.52202/085713-3125}, volume = {38}, year = {2025}, } @inproceedings{22823, abstract = {This position paper argues that setting the privacy budget in differential privacy should not be viewed as an important limitation of differential privacy compared to alternative methods for privacy-preserving machine learning. The so-called problem of interpreting the privacy budget is often presented as a major hindrance to the wider adoption of differential privacy in real-world deployments and is sometimes used to promote alternative mitigation techniques for data protection. We believe this misleads decision-makers into choosing unsafe methods. We argue that the difficulty in interpreting privacy budgets does not stem from the definition of differential privacy itself, but from the intrinsic difficulty of estimating privacy risks in context, a challenge that any rigorous method for privacy risk assessment face. Moreover, we claim that any sound method for estimating privacy risks should, given the current state of research, be expressible within the differential privacy framework or justify why it cannot.}, author = {Cyffers, Edwige Audrey Lucienne}, booktitle = {39th Conference on Neural Information Processing Systems}, isbn = {9798331338275}, issn = {1049-5258}, location = {San Diego, CA, United States}, pages = {159016--159028}, publisher = {Neural Information Processing Systems Foundation}, title = {{Setting ε is not the issue in differential privacy}}, doi = {10.52202/085713-4798}, volume = {38}, year = {2025}, } @phdthesis{19903, abstract = {Cooperation, that is, one person paying a cost for another's benefit, is a fundamental principle without which no form of society could exist. The extent to which humans cooperate with each other is also an essential feature that differentiates them from other animals. Cooperation occurs even in the absence of altruistic motivations, when it is selfishly incentivised by the expectation of a future reward. For example, many economic interactions are well described that way. This kind of cooperation requires that people exhibit reciprocal behaviour that acts as a mechanism that rewards cooperation. With game-theoretic models, it is possible to formally study potential such mechanisms and under what conditions they can exist. This thesis contributes to this effort by analysing recently introduced models of cooperation that advance on previous work by taking into account the potential for pre-existing inequality among cooperating individuals as well as the different forms that reciprocity can take. Individuals may differ both intrinsically, in their abilities, as well as extrinsically, in the amount of resources they have available. Allowing for such differences in a model of cooperation helps to understand how inequality affects the potential for, and outcomes of, cooperation among unequals. In this thesis, it is shown that in the presence of intrinsic inequality, a similar unequal distribution of resources can increase the potential for cooperation. This effect is stronger the smaller the group is in which cooperation takes place. It is also shown that under particular assumptions, if the unequal members of a group vary the size of their contributions to a cooperative effort over time, they can thereby increase their efficiency and improve the collective outcome. Cooperative behaviour in a two-person interaction can be rewarded either by direct reciprocation whenever the same two people interact again, or indirectly by a third party who observed the interaction. In the latter case of indirect reciprocity, individuals are proximally rewarded by a good reputation, which ultimately translates to being rewarded with cooperative behaviour by others. This mechanism can enable selfishly motivated cooperation even in circumstances where individuals are unlikely to meet again, akin to how money facilitates trade. While these two forms of reciprocity have mostly been studied in isolation, this thesis analyses both direct and indirect reciprocity in a general model in order to compare their relative effectiveness under different circumstances. The contribution of this thesis is an extension of previous work regarding a specific kind of interaction, whose parameters allow for convenient mathematical analysis, to the most general set of possible interactions.}, author = {Hübner, Valentin}, issn = {2663-337X}, pages = {157}, publisher = {Institute of Science and Technology Austria}, title = {{Reciprocity and inequality in social dilemmas}}, doi = {10.15479/AT-ISTA-19903}, year = {2025}, } @phdthesis{20138, abstract = {The evolution shapes the world around us. Not only in biology, where the fittest individuals spread their genes but also in physics and social dynamics, the evolutionary forces determine the development of a state of matter or public opinions. Many models describe these dynamics. This thesis examines the role of the structure in the models of selection. The population structure is represented as a graph or a network, and each vertex is occupied by one individual. Every individual has a type and fitness that represents the reproductive potential and depends on the type, occupied vertex, and the arrangement of the neighbors. The evolution is modeled in discrete steps; in one step, one individual is replaced by a neighbor selected randomly with the influence of fitness. The role of the networks is widely examined in the literature. The structures that promote the spread of the desired type compared to the structureless case are called amplifiers. The existence of amplifiers in various settings is an intensively studied topic, and in some settings, the amplifiers have been identified. Moreover, there are other important questions about the number of steps until one type spreads over the whole network (fixation time), the computational complexity, and the questions about the robustness of these processes. This thesis explores the role of structure in evolution from many perspectives. First, it introduces different models and various choices that can be made in the models of evolution. It highlights the role of the structure in the real world and how this is reflected in these models. Then, it describes the previous results and open problems. Second, the thesis describes an amplifier for two variants of the Moran process: one with a constant birth rate and the other with a constant death rate. This is an important contribution to the robustness of the amplification. Third, the thesis determines the complexity of spatial games. These are processes where the fitness comes from a game, and the strength of selection is high. It shows that determining the fate of cooperation in these games is a PSPACE-complete problem. Fourth, the thesis describes the amplifier of cooperation for spatial games. This is the first amplifier in this setting. Fifth, the thesis examines the coexistence in the Moran process with environmental heterogeneity. In this setting, the fitness depends not only on the type of the individual but also on the occupied vertex. The chapter determines the relationship between the interactions of vertices of different types and the coexistence time. Sixth, the thesis examines the social balance on networks and proposes a stochastic dynamic partially aware of the state of the graph, which reaches a balanced position quickly. Finally, the thesis presents conclusions and outlines the directions for future work. }, author = {Svoboda, Jakub}, issn = {2663-337X}, pages = {167}, publisher = {Institute of Science and Technology Austria}, title = {{Structural properties of games on graphs}}, doi = {10.15479/AT-ISTA-20138}, year = {2025}, } @phdthesis{20575, abstract = {This thesis deals with eigenvalue and eigenvector universality results for random matrix ensembles equipped with non-trivial spatial structure. We consider both mean-field models with a general variance profile (Wigner-type matrices) and correlation structure (correlated matrices) among the entries, as well as non-mean-field random band matrices with bandwidth W >> N^(1/2). To extract the universal properties of random matrix spectra and eigenvectors, we obtain concentration estimates for their resolvent, the local laws, which generalize the celebrated Wigner semicircle law for a broad class of random matrices to much finer spectral scales. The local laws hold for both a single resolvent as well as for products of multiple resolvents, known as resolvent chains, and express the remarkable approximately-deterministic behavior of these objects down to the microscopic scale. Our primary tool for establishing the local laws is the dynamical Zigzag strategy, which we develop in the setting of spatially-inhomogeneous random matrices. Our proof method systematically addresses the challenges arising from non-trivial spatial structures and is robust to all types of singularities in the spectrum, as we demonstrate in the correlated setting. Furthermore, we incorporate the analysis of the deterministic resolvent chain approximations into the dynamical framework of the Zigzag strategy, synthesizing a unified toolkit for establishing multi-resolvent local laws. Using these methods, we prove complete eigenvector delocalization, the Eigenstate Thermalization Hypothesis, and Wigner-Dyson universality in the bulk for random band matrices down to the optimal bandwidth W >> N^(1/2). For mean-field ensembles, we establish universality of local eigenvalue statistics at the cups for random matrices with correlated entries, and the Eigenstate Thermalization Hypothesis for Wigner-type matrices in the bulk of the spectrum. Finally, this thesis also contains other applications of the multi-resolvent local laws to spatially-inhomogeneous random matrices, obtained prior to the development of the Zigzag strategy. In particular, we provide a complete analysis of mesoscopic linear-eigenvalue statistics of Wigner-type matrices in all spectral regimes, including the novel cusps, and rigorously establish the prethermalization phenomenon for deformed Wigner matrices. The main body of this thesis consists of seven research papers (listed on page xi), each presented in a separate chapter with its own introduction and all relevant context, suitable to be read independently. We ask the reader’s indulgence for the repetitions in the historical overviews and other minor redundancies that remain among the chapters as a result. The overall Introduction, preceding the chapters, provides a condensed, informal summary of the main ideas and concepts at the core of these works. }, author = {Riabov, Volodymyr}, isbn = {978-3-99078-064-0}, issn = {2663-337X}, pages = {436}, publisher = {Institute of Science and Technology Austria}, title = {{Universality in random matrices with spatial structure}}, doi = {10.15479/AT-ISTA-20575}, 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}, } @article{18764, abstract = {We prove that a class of weakly perturbed Hamiltonians of the form H_λ= H_0 + λW, with W being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by H_λ relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order λ^{-2}. Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix H_λ.}, author = {Erdös, László and Henheik, Sven Joscha and Reker, Jana and Riabov, Volodymyr}, issn = {1424-0637}, journal = {Annales Henri Poincare}, pages = {1991--2033}, publisher = {Springer Nature}, title = {{Prethermalization for deformed Wigner matrices}}, doi = {10.1007/s00023-024-01518-y}, volume = {26}, year = {2025}, }