@article{19074, abstract = {The public goods game is among the most studied metaphors of cooperation in groups. In this game, individuals can use their endowments to make contributions towards a good that benefits everyone. Each individual, however, is tempted to free-ride on the contributions of others. Herein, we study repeated public goods games among asymmetric players. Previous work has explored to which extent asymmetry allows for full cooperation, such that players contribute their full endowment each round. However, by design that work focusses on equilibria where individuals make the same contribution each round. Instead, here we consider players whose contributions along the equilibrium path can change from one round to the next. We do so for three different models – one without any budget constraints, one with endowment constraints, and one in which individuals can save their current endowment to be used in subsequent rounds. In each case, we explore two key quantities: the welfare and the resource efficiency that can be achieved in equilibrium. Welfare corresponds to the sum of all players’ payoffs. Resource efficiency relates this welfare to the total contributions made by the players. Compared to constant contribution sequences, we find that time-dependent contributions can improve resource efficiency across all three models. Moreover, they can improve the players’ welfare in the model with savings.}, author = {Hübner, Valentin and Hilbe, Christian and Staab, Manuel and Kleshnina, Maria and Chatterjee, Krishnendu}, issn = {2153-0793}, journal = {Dynamic Games and Applications}, pages = {1617--1645}, publisher = {Springer Nature}, title = {{Time-dependent strategies in repeated asymmetric public goods games}}, doi = {10.1007/s13235-025-00627-5}, volume = {15}, 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}, } @phdthesis{20449, author = {Bett, Vincent K}, issn = {2663-337X}, pages = {114}, publisher = {Institute of Science and Technology Austria}, title = {{Evolution and regulation of the Z chromosome}}, doi = {10.15479/AT-ISTA-20449}, year = {2025}, } @phdthesis{20777, author = {Zivadinovic, Predrag}, issn = {2663-337X}, pages = {104}, publisher = {Institute of Science and Technology Austria}, title = {{Scale-free activity as a basis for spatial learning and memory in the brain}}, doi = {10.15479/AT-ISTA-20777}, 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{20322, abstract = {For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states typically exhibits only square root edge or cubic root cusp singularities, our result completes the proof of the Wigner–Dyson–Mehta universality conjecture in all spectral regimes for a very general class of random matrices. Previously only the bulk and the edge universality were established in this generality (Alt et al. in Ann Probab 48(2):963–1001, 2020), while cusp universality was proven only for Wigner-type matrices with independent entries (Cipolloni et al. in Pure Appl Anal 1:615–707, 2019; Erdős et al. in Commun. Math. Phys. 378:1203–1278, 2018). As our main technical input, we prove an optimal local law at the cusp using the Zigzag strategy, a recursive tandem of the characteristic flow method and a Green function comparison argument. Moreover, our proof of the optimal local law holds uniformly in the spectrum, thus we also provide a significantly simplified alternative proof of the local eigenvalue universality in the previously studied bulk (Erdős et al. in Forum Math. Sigma 7:E8, 2019) and edge (Alt et al. in Ann Probab 48(2):963–1001, 2020) regimes.}, author = {Erdös, László and Henheik, Sven Joscha and Riabov, Volodymyr}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, number = {10}, publisher = {Springer Nature}, title = {{Cusp universality for correlated random matrices}}, doi = {10.1007/s00220-025-05417-z}, volume = {406}, year = {2025}, } @unpublished{20576, abstract = {We prove that a very general class of $N\times N$ Hermitian random band matrices is in the delocalized phase when the band width $W$ exceeds the critical threshold, $W\gg \sqrt{N}$. In this regime, we show that, in the bulk spectrum, the eigenfunctions are fully delocalized, the eigenvalues follow the universal Wigner-Dyson statistics, and quantum unique ergodicity holds for general diagonal observables with an optimal convergence rate. Our results are valid for general variance profiles, arbitrary single entry distributions, in both real-symmetric and complex-Hermitian symmetry classes. In particular, our work substantially generalizes the recent breakthrough result of Yau and Yin [arXiv:2501.01718], obtained for a specific complex Hermitian Gaussian block band matrix. The main technical input is the optimal multi-resolvent local laws -- both in the averaged and fully isotropic form. We also generalize the $\sqrtη$-rule from [arXiv:2012.13215] to exploit the additional effect of traceless observables. Our analysis is based on the zigzag strategy, complemented with a new global-scale estimate derived using the static version of the master inequalities, while the zig-step and the a priori estimates on the deterministic approximations are proven dynamically.}, author = {Erdös, László and Riabov, Volodymyr}, booktitle = {arXiv}, title = {{The zigzag strategy for random band matrices}}, doi = {10.48550/ARXIV.2506.06441}, 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}, } @article{19598, abstract = {We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear eigenvalue statistics at the cusp-like singularities were not studied in any ensemble. Our analysis covers not only the exact cusps but the entire transitionary regime from the square-root singularity at a regular edge through the sharp cusp to the bulk. We identify a new one-parameter family of functionals that govern the limiting bias and variance, continuously interpolating between the previously known formulas in the bulk and at a regular edge. Since cusps are the only possible singularities besides the regular edges, our result gives a complete description of the linear eigenvalue statistics in all regimes.}, author = {Riabov, Volodymyr}, issn = {1432-2064}, journal = {Probability Theory and Related Fields}, pages = {1183--1237}, publisher = {Springer Nature}, title = {{Linear Eigenvalue statistics at the cusp}}, doi = {10.1007/s00440-025-01373-w}, volume = {193}, 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{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{20798, author = {Wald, Sebastian}, isbn = {978-3-99078-075-6}, issn = {2663-337X}, keywords = {entanglement-enhanced atom interferometry, cavity QED, spin-squeezing, dipole trap, quantum optics}, pages = {152}, publisher = {Institute of Science and Technology Austria}, title = {{Atoms in a propagating-wave cavity for squeezed Mach-Zehnder atom interferometry}}, doi = {10.15479/AT-ISTA-20798}, 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}, } @article{19860, abstract = {An eight-partition of a finite set of points (respectively, of a continuous mass distribution) in R^3 consists of three planes that divide the space into 8 octants, such that each open octant contains at most 1/8 of the points (respectively, of the mass). In 1966, Hadwiger showed that any mass distribution in R^3 admits an eight-partition; moreover, one can prescribe the normal direction of one of the three planes. The analogous result for finite point sets follows by a standard limit argument. We prove the following variant of this result: any mass distribution (or point set) in R^3 admits an eight-partition for which the intersection of two of the planes is a line with a prescribed direction. Moreover, we present an efficient algorithm for calculating an eight-partition of a set of n points in R^3 (with prescribed normal direction of one of the planes) in time O(n^7/3). A preliminary version of this work appeared in SoCG’24 (Aronov et al., 40th International Symposium on Computational Geometry, 2024).}, author = {Aronov, Boris and Basit, Abdul and Ramesh, Indu and Tasinato, Gianluca and Wagner, Uli}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, publisher = {Springer Nature}, title = {{Eight-partitioning points in 3D, and efficiently too}}, doi = {10.1007/s00454-025-00739-0}, 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}, } @article{19001, abstract = {We consider two Hamiltonians that are close to each other, H1≈H2, and analyze the time-decay of the corresponding Loschmidt echo M(t):=|⟨ψ0,eitH2e−itH1ψ0⟩|2 that expresses the effect of an imperfect time reversal on the initial state ψ0. Our model Hamiltonians are deformed Wigner matrices that do not share a common eigenbasis. The main tools for our results are two-resolvent laws for such H1 and H2.}, author = {Erdös, László and Henheik, Sven Joscha and Kolupaiev, Oleksii}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, publisher = {Springer Nature}, title = {{Loschmidt echo for deformed Wigner matrices}}, doi = {10.1007/s11005-025-01904-5}, volume = {115}, 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}, }