@misc{22704, abstract = {The medial habenula (MHb) is implicated in regulating emotional responses to aversive events. Studies in zebrafish have identified a remarkable morphological left–right asymmetry in the dorsal habenula (zebrafish equivalent of mammalian MHb)-interpeduncular nucleus (IPN) pathway and its asymmetrical roles in behavior. However, there is little evidence for structural or functional lateralization in the mammalian MHb-IPN pathway. Here, we investigated the synaptic properties of left- and right-MHb afferents to the IPN and their roles in the expression of conditioned fear in mice. We found that each IPN neuron receives inputs from both left and right MHb, but the left MHb-originating synapses exhibit lower release probability and higher γ-aminobutyric acid type B receptor (GABABR)-mediated potentiation compared to the right MHb-originating synapses. Interestingly, these asymmetrical properties persist in the inversus visceral mutant mice with normal internal organ laterality (situs solitus), but nearly disappear in those with reversed internal organ laterality (situs inversus). Behaviorally, chemogenetic inhibition of cholinergic neurons and conditional deletion of GABABR in the left, but not the right, MHb significantly attenuated cue-dependent fear recall. Our results demonstrate functional asymmetry of the MHb under partial influence of the nodal flow in mice, revealing a predominant role of GABABR-mediated signaling in the left MHb-IPN pathway in modulating fear memories. These findings suggest that lateralized MHb pathways could represent a fundamental principle in the neural regulation of emotion across species but that they develop differently in zebrafish and mice. }, author = {Le Monnier, Elodie and Önal, Cihan}, publisher = {Institute of Science and Technology Austria}, title = {{Asymmetrical modulation of fear expression via GABAB receptors in the mouse medial habenula}}, doi = {10.15479/AT-ISTA-22704}, year = {2026}, } @article{22923, abstract = {We study the sensitivity of the eigenvectors of random matrices, showing that even small perturbations make the eigenvectors almost orthogonal. More precisely, we consider two deformed Wigner matrices 𝑊 +𝐷1, 𝑊 +𝐷2 and show that their bulk eigenvectors become asymptotically orthogonal as soon as Tr⁡(𝐷1−𝐷2)2 ≫1, or their respective energies are separated on a scale much bigger than the local eigenvalue spacing. Furthermore, we show that quadratic forms of eigenvectors of 𝑊 +𝐷1, 𝑊 +𝐷2 with any deterministic matrix 𝐴 ∈𝐂𝑁×𝑁 in a specific subspace of codimension one are of size 𝑁−1/2. This proves a generalization of the eigenstate thermalization hypothesis to eigenvectors belonging to two different spectral families.}, author = {Cipolloni, Giorgio and Erdös, László and Henheik, Sven Joscha and Kolupaiev, Oleksii}, issn = {1050-5164}, journal = {Annals of Applied Probability}, keywords = {characteristic flow, Davis–Kahan theorem, Eigenstate thermalization, Eigenvector perturbation theory, Local law, zigzag strategy}, number = {4}, pages = {3707--3756}, publisher = {Institute of Mathematical Statistics}, title = {{Eigenvector decorrelation for random matrices}}, doi = {10.1214/26-AAP2318}, volume = {36}, year = {2026}, } @inbook{22926, abstract = {Adeno-associated viruses (AAVs) provide a versatile tool for labeling neurons in the Xenopus central nervous system across developmental stages. AAV-mediated transgene expression is long-lasting and stable, enabling robust labeling of neuronal populations without genomic integration and without the need to generate transgenic lines. The choice of AAV capsid and promoter can restrict expression to a population of interest, and depending on the route and timing of delivery, AAVs can selectively target either progenitor-derived neuronal cohorts or mature neuronal populations. Here, we have outlined two labeling strategies. First, intraventricular injections in tadpoles transduce neural progenitor cells lining the ventricular system, resulting in cohort-based labeling of neurons as they differentiate during development. Second, direct intraparenchymal injections in post-metamorphic frogs enable spatially restricted labeling and anterograde or retrograde tracing of connectivity within defined brain regions. Together, these approaches provide selective access to developing and mature neural circuits in X. laevis, supporting applications ranging from anatomical tracing to functional imaging and manipulation of neural circuits.}, author = {Vijatovic, David and Sweeney, Lora Beatrice Jaeger}, booktitle = {Xenopus}, editor = {Beck, Caroline W.}, issn = {1940-6029}, pages = {219--229}, publisher = {Springer}, title = {{Adeno-Associated Virus (AAV) for tracking neural development and connectivity in Xenopus}}, doi = {10.1007/978-1-0716-5360-9_9}, volume = {3049}, year = {2026}, } @inbook{22925, abstract = {Hybridization Chain Reaction (HCR) enables highly sensitive and multiplexed detection of mRNA with subcellular spatial resolution. It employs fluorophore-tagged DNA hairpins that self-assemble on target-bound probe pairs, amplifying the signal without enzymatic reactions. Here, we describe a protocol for performing HCR fluorescence in situ hybridization (FISH) on Xenopus tissue sections. We also outline a semi-automated image analysis pipeline that enables per-cell quantification of probe expression and co-localization. This method provides a robust and quantitative approach for visualizing gene expression patterns in situ.}, author = {Vijatovic, David and Papadopoulos, Stavros and Dalla Vecchia, Marco and Sweeney, Lora Beatrice Jaeger}, booktitle = {Xenopus}, editor = {Beck, Caroline W.}, issn = {1940-6029}, keywords = {mRNA FISH, Hybridization chain reaction, In situ hybridization, Fluorescence microscopy}, pages = {245--259}, publisher = {Springer}, title = {{Fluorescent in situ mRNA hybridization (FISH) using Hybridization Chain Reaction (HCR) in Xenopus cryosections}}, doi = {10.1007/978-1-0716-5360-9_11}, volume = {3049}, year = {2026}, } @article{22927, abstract = {Auxin and calcium (Ca2+) are central plant signals that coordinate growth, development, and responses to environmental cues. Typically studied as largely parallel pathways, they are now increasingly recognized as interconnected networks whose activities converge at multiple regulatory levels. Recent advances in live imaging, biosensors, optogenetics, and structural approaches have revealed that auxin can rapidly trigger Ca2+ influx from the apoplast via TRANSPORT INHIBITOR RESPONSE1 (TIR1)/AUXIN-SIGNALING F-BOX (AFB)-dependent signaling mechanisms and Ca2+ channels, presumably involving cyclic nucleotides produced by TIR1/AFB auxin receptors. Conversely, Ca2+ signals arising from mechanosensing, wounding, and environmental stress can modulate auxin transport, signaling, and transcriptional outputs. Together, these discoveries highlight a dynamic, reciprocal signaling axis where Ca2+ acts both downstream and upstream of auxin to shape growth, development, tropisms, and regeneration.}, author = {Zupunski, Milan and Grossmann, Guido and Friml, Jiří}, issn = {1878-4372}, journal = {Trends in Plant Science}, keywords = {auxin, calcium, rapid signaling, crosstalk, growth regulation, cyclic nucleotides}, publisher = {Cell Press}, title = {{Decoding dialog: The auxin–calcium signaling crosstalk in plants}}, doi = {10.1016/j.tplants.2026.08.002}, year = {2026}, } @inproceedings{22914, abstract = {We present the first truly subquadratic time algorithm to compute diameter and eccentricities in real-weighted directed graphs with constant distance VC-dimension and strongly sublinear-sized balanced separators. For real-weighted K_h-minor-free digraphs, this runs in O(n^{2-1/(2h-2)} polylog(n)) time. Prior to this work, truly subquadratic time computation of diameter was only known for real-weighted planar graphs, while extensions to broader classes like minor-free graphs were restricted to unweighted settings. In particular, existing algorithms that use VC-dimension [Ducoffe, Habib, Viennot; SICOMP 2022] [Le, Wulff-Nilsen; SODA 2024] [Chan, Chang, Gao, Le, Kisfaludi-Bak, Zheng; FOCS 2025] work with small integer weights, but do not naturally generalize to real weights. We overcome this barrier by introducing a randomized search-to-decision reduction, demonstrating that VC-dimension is a sufficiently powerful tool in the real-weighted regime.}, author = {Zheng, Da Wei}, booktitle = {34th Annual European Symposium on Algorithms}, isbn = {9783959774451}, issn = {1868-8969}, keywords = {Diameter, eccentricities, minor-free graphs, real weights, VC-dimension}, location = {L’Aquila, Italy}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Real-weighted diameter and eccentricities of minor-free and bounded VC-dimension graphs in truly subquadratic time}}, doi = {10.4230/LIPIcs.ESA.2026.61}, volume = {388}, year = {2026}, } @article{22928, abstract = {We present deep ALMA Band 7 observations of the [O iii] 88 µm line and underlying dust continuum emission in four UV-bright, gravitationally lensed (magnification µ = 1.4 − 3.8), JWST-selected galaxies at z = 8.5 − 10.3, with observed magnitudes −22.5 ≲ MUV ≲ −20.5. [O iii] 88 µm is confidently detected in UNCOVER-10646 at z = 8.5080 ± 0.0011 (15σ) and DHZ1 at z = 9.3113 ± 0.0006 (6σ), with both being intrinsically luminous systems [L[O iii] = (1.1− 1.6) ×109 L⊙] that follow the local [O iii]-SFR relation. [O iii] 88 µm remains undetected in the two z > 10 targets, including in the z = 10.07 X-ray AGN UHZ1, where we obtain a deep limit of L[O iii] < 6 × 107 L⊙. Dust emission is not detected in any individual source nor in a stack (< 3σ). The high S/N [O iii] 88 µm detection in UNCOVER-10646 uniquely reveals an additional broad component (FWHM = 1366+473 −329 km/s; ∆BIC ≈ 20) indicative of an ionized outflow. We infer a high outflow rate of M˙ out = 128+80 −46 M⊙ yr−1 , corresponding to a mass loading factor η = M˙ out/SFR = 2.9 +1.8 −1.0 that matches or exceeds theoretical predictions and JWST-based studies of ionized outflows at high redshift. While high-resolution ALMA follow-up is required to confirm and spatially resolve the outflow, this first systematic study at z > 8 highlights the unique diagnostic power of [O iii] 88 µm in characterizing galaxies in the early Universe.}, author = {Algera, Hiddo S.B. and Weaver, John R. and Bakx, Tom J.L.C. and Aravena, Manuel and Bouwens, Rychard J. and Cescon, Karin and Chen, Chian Chou and Da Cunha, Elisabete and Dayal, Pratika and Faisst, Andreas and Ferrara, Andrea and Fujimoto, Seiji and Hashimoto, Takuya and Heintz, Kasper and Herrera-Camus, Rodrigo and Hodge, Jacqueline and Inami, Hanae and Inoue, Akio K. and Matthee, Jorryt J and Meyer, Romain and Mizukoshi, Shoichiro and Mondal, Chayan and Nanayakkara, Themiya and Oesch, Pascal A. and Pallottini, Andrea and Röttgering, Huub and Rowland, Lucie E. and Schouws, Sander and Smit, Renske and Sommovigo, Laura and Stark, Daniel P. and Sugahara, Yuma and Vallini, Livia and Vijarnwannaluk, Bovornpratch and Van Der Werf, Paul and Werner, Norbert and Witstok, Joris and Xiao, Mengyuan}, issn = {2565-6120}, journal = {The Open Journal of Astrophysics}, publisher = {Maynooth Academic Publishing}, title = {{A first systematic study of [OIII] 88μm at z>8: two luminous oxygen lines and a powerful ionized outflow in the first 600 million years}}, doi = {10.33232/001c.165333}, volume = {9}, year = {2026}, } @inproceedings{22920, abstract = {Two-player games on graphs are a classical framework for analyzing strategic decision making. In turn-based games, two players move a token along the edges of the graph, and the right to move the token is determined by the current vertex. In traditional bidding games - referred to as pure bidding games - the right to move the token is determined at each step through bidding; here we consider Richman bidding, where the winning player of a bid pays the losing player. The winner is decided based on a temporal or quantitative specification evaluated over the resulting infinite play. In this work, we combine turn-based games and pure bidding games into generalized bidding games, with player-1 vertices, player-2 vertices, and bidding vertices. This natural and simple generalization of bidding games has far-reaching consequences. First, we show that, as a model, generalized bidding games are more expressive than pure bidding games, and we provide several applications. Second, and most importantly, we show that generalized Richman bidding games are structurally equivalent to simple stochastic games, a well-studied model: they are linearly interreducible to each other. As was previously known, the special case of pure Richman bidding games corresponds to random-turn games. In other words, generalized bidding games extend pure bidding games in the same way that simple stochastic games extend random-turn games. We use this connection to solve generalized Richman bidding games for temporal (parity) and quantitative (mean-payoff and discounted-sum) specifications. From a computational perspective, we establish that generalized bidding games with parity and mean-payoff specifications retain the best known upper bounds for turn-based games and pure bidding games, namely NP∩coNP. Finally, we study a repair problem that asks whether bidding vertices can be assigned "owners" so as to bring the threshold budget required to win the game below a given target. This problem has direct applications in compositional policy synthesis for multi-objective settings, and we show it to be NP-complete.}, author = {Asadi, Ali and Henzinger, Thomas A and Kafshdar Goharshadi, Ehsan and Kebis, Pavol and Mallik, Kaushik}, booktitle = {37th International Conference on Concurrency Theory}, isbn = {9783959774475}, issn = {1868-8969}, keywords = {Bidding Games, Stochastic Games}, location = {Liverpool, United Kingdom}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Generalized bidding games: Where bidding and stochastic games meet}}, doi = {10.4230/LIPIcs.CONCUR.2026.13}, volume = {391}, year = {2026}, } @inproceedings{22919, abstract = {Reachability is the most fundamental logical objective, yet it is notoriously difficult to learn in reinforcement learning settings: even for Markov decision processes, PAC learning of reachability is impossible without additional assumptions. This difficulty also holds in turn-based stochastic games (TBSGs), where two adversarial players interact on a finite state space. In this work, we consider turn-based stochastic games with reachability objectives. For such settings, adversarial learning, in which players are adversarial even in the learning phase, is impossible. Therefore, the goal is to consider learning, in which both players learn the unknown model together. In this spirit, previous literature on PAC learning in TBSGs considers (a) public information shared by both players; and (b) centralized learning, which means that players share the same learning algorithm. In this work, our contribution is two-fold. First, we relax these strong assumptions and ensure learning: (i) with private information not shared with the other player; and (ii) decentralized learning where the players do not share the same learning algorithm. To the best of our knowledge, this work is the first positive result for decentralized and private information learning of TBSGs with reachability objectives. Second, we introduce a game-theoretic generalization of the Expected Conditional Distance (ECD) parameter, which measures the expected length of reaching the target set. We establish a polynomial-sample complexity bound with respect to the number of states, actions, ECD parameter, and inverses of error tolerance and failure probability.}, author = {Asadi, Ali and Chatterjee, Krishnendu and Kebis, Pavol}, booktitle = {37th International Conference on Concurrency Theory}, isbn = {9783959774475}, issn = {1868-8969}, keywords = {formal methods, games and logic, logical aspects of AI, model checking}, location = {Liverpool, United Kingdom}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{PAC learning in turn-based stochastic games with reachability objectives: A decentralized private approach via expected conditional distance}}, doi = {10.4230/LIPIcs.CONCUR.2026.12}, volume = {391}, year = {2026}, } @inproceedings{22918, abstract = {Given a weighted digraph G, a (t,g,μ)-DAG cover is a collection of g dominating DAGs D_1,… ,D_g such that all distances are approximately preserved: for every pair (u,v) of vertices, min_id_{D_i}(u,v) ≤ t⋅ d_G(u,v), and the total number of non-G edges is bounded by |(∪_i D_i)⧵ G| ≤ μ. Assadi, Hoppenworth, and Wein [STOC 25] and Filtser [SODA 26] studied DAG covers for general digraphs. This paper initiates the study of Steiner DAG cover, where the DAGs are allowed to contain Steiner points. We obtain Steiner DAG covers on the important classes of planar digraphs and low-treewidth digraphs. Specifically, we show that any digraph with treewidth tw admits a (1,2,Õ(n⋅tw))-Steiner DAG cover. For planar digraphs we provide a (1+ε,2,Õ_ε(n))-Steiner DAG cover. We also demonstrate a stark difference between Steiner and non-Steiner DAG covers. As a lower bound, we show that any non-Steiner DAG cover for graphs with treewidth 1 with stretch t < 2 and sub-quadratic number of extra edges requires Ω(log n) DAGs.}, author = {Bhore, Sujoy and Chang, Hsien Chih and Conroy, Jonathan and Filtser, Arnold and Oh, Eunjin and Wein, Nicole and Zheng, Da Wei}, booktitle = {34th Annual European Symposium on Algorithms}, isbn = {9783959774451}, issn = {1868-8969}, keywords = {Directed graphs, DAG (directed acyclic graphs), distortion, metric embeddings, planar graph, treewidth}, location = {L’Aquila, Italy}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{DAG covers for structured graphs: The Steiner point effect}}, doi = {10.4230/LIPIcs.ESA.2026.94}, volume = {388}, year = {2026}, } @inproceedings{22917, abstract = {A heap is a dynamic data structure that stores a set of labeled values under the following operations: pop returns the minimum value of the heap, Push(x_i) pushes a new value x_i onto the heap, and DecreaseKey(i, v) decreases the value x_i to v. A working-set heap is a heap that supports the x_i ← pop() operation in O(log Γ(x_i)) time where Γ(x_i) is the size of the working set: the number of elements that were pushed onto the heap while x_i was in the heap. The goal of working set heap design is to maintain the working set property while minimizing the overhead of the Push and DecreaseKey operations. On a word RAM, there exist working set heaps that support Push and DecreaseKey in amortized constant time. In this paper, we show via a simple construction that pointer machines, one of the most general and least-assuming computational models, support working set heaps that support Push in amortized constant time and DecreaseKey in inverse-Ackermann time. A by-product of this analysis is that Dijkstra’s shortest path algorithm can be near-universally optimal on a pointer machine - incurring only an additive O(m α(m)) overhead compared to the optimal running time for distance ordering, where m denotes the number of edges in the graph.}, author = {Van Der Hoog, Ivor and Iacono, John and Rotenberg, Eva and Rutschmann, Daniel P}, booktitle = {34th Annual European Symposium on Algorithms}, isbn = {9783959774451}, issn = {1868-8969}, keywords = {Data structures, graph algorithms, amortized analysis}, location = {L’Aquila, Italy}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Near-optimal working-set heaps and dijkstra on pointer machines}}, doi = {10.4230/LIPIcs.ESA.2026.45}, volume = {388}, year = {2026}, } @article{22408, abstract = {Solitons—localized wave packets that travel without spreading—play a central role in understanding transport and properties of nonlinear systems. In quantum many-body systems, however, such robust excitations are typically destroyed by thermalization. Here, we theoretically demonstrate the existence of solitonic excitations in high-energy states of Rydberg atom chains in the regime of strong nearest-neighbor Rydberg blockade. These localized wave packets propagate directionally atop a special class of reviving initial states related to quantum many-body scars and are capable of carrying energy. Exhibiting long coherence times, these states constitute a form of non-ergodic quantum dynamics and can be efficiently implemented on Rydberg atom simulators. In this work, in addition to a phenomenological description of solitons, we identify their counterpart in a classical nonlinear dynamical system, demonstrate their potential use in quantum information transfer, and conjecture their relevance for anomalous energy transport reported in numerical studies of Rydberg atom arrays.}, author = {Kerschbaumer, Aron and Desaules, Jean-Yves Marc and Ljubotina, Marko and Serbyn, Maksym}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Quasi-solitons in Rydberg atom chains}}, doi = {10.1038/s41467-026-75598-1}, volume = {17}, year = {2026}, } @misc{21960, abstract = {Solitons - localized wave packets that travel without spreading - play a central role in understanding transport and properties of nonlinear systems. In quantum many-body systems, however, such robust excitations are typically destroyed by thermalization. Here, we theoretically demonstrate the existence of solitonic excitations in high-energy states of Rydberg atom chains in the regime of strong nearest-neighbor Rydberg blockade. These localized wave packets propagate directionally atop a special class of reviving initial states related to quantum many-body scars and are capable of carrying energy. Exhibiting long coherence times, these states constitute a form of non-ergodic quantum dynamics and can be efficiently implemented on Rydberg atom simulators. In this work, in addition to a phenomenological description of solitons, we identify their counterpart in a classical nonlinear dynamical system, demonstrate their potential use in quantum information transfer, and conjecture their relevance for anomalous energy transport reported in numerical studies of Rydberg atom arrays.}, author = {Kerschbaumer, Aron}, publisher = {Institute of Science and Technology Austria}, title = {{Research Data: "Quasi-solitons in Rydberg atom chains"}}, doi = {10.15479/AT-ISTA-21960}, year = {2026}, } @article{22941, abstract = {Argonaute proteins mediate RNA interference in eukaryotes and nucleic‐acid defence in prokaryotes. Although these systems operate in distinct biological contexts and produce diverse downstream outcomes, they share a conserved structural architecture and mechanism of guide‐dependent target recognition. Here, we argue that Argonautes function as programmable surveillance platforms that kinetically sample nucleic acids, engage targets through sequential pairing and conformational checkpoints, and couple recognition to functional outputs through regulated structural transitions. Rather than representing distinct recognition mechanisms, the diverse targeting behaviours observed across Argonaute families reflect different implementations of this shared framework, in which guide biogenesis, target accessibility, pairing requirements and effector coupling are weighted differently according to biological context. Viewing Argonautes through this common operational logic reconciles apparent differences in specificity, mismatch tolerance and target selection across systems, while providing a unified conceptual framework for understanding their evolution and guiding the engineering of programmable nucleic‐acid recognition technologies.}, author = {Bravo, Jack Peter Kelly}, issn = {1873-3468}, journal = {FEBS Letters}, publisher = {Wiley}, title = {{‘Guide and Prejudice’ -  How Argonautes recognize targets across domains of life}}, doi = {10.1002/1873-3468.70450}, year = {2026}, } @article{21501, abstract = {Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy—known as zero modes—stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a U(1) particle-conservation symmetry. We use the U(1) East, which lacks inversion symmetry, and the inversion-symmetric U(1) East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a parametric increase in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single-particle physics and introduce the notion of collective bound states, a special kind of nonergodic eigenstates that are robust to enlarging the system size. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models and in a two-dimensional model, the U(1) North-East, and in the pairflip model, a system without particle conservation. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models. }, author = {Nicolau Jimenez, Eulalia and Ljubotina, Marko and Serbyn, Maksym}, issn = {2691-3399}, journal = {PRX Quantum}, publisher = {American Physical Society}, title = {{Fragmentation, zero modes, and collective bound states in constrained models}}, doi = {10.1103/sl79-1xgb}, volume = {7}, year = {2026}, } @inproceedings{22245, abstract = {A single-commodity congestion approximator for a graph is a compact data structure that approximately predicts the edge congestion required to route any set of single-commodity flow demands in a network. A hierarchical congestion approximator (HCA) consists of a laminar family of cuts in the graph and has numerous applications in approximating cut and flow problems in graphs, designing efficient routing schemes, and managing distributed networks. There is a tradeoff between the running time for computing an HCA and its approximation quality. The best polynomial-time construction in an n-node graph gives an HCA with approximation quality O(log1.5n loglogn). Among near-linear time algorithms, the best previous result achieves approximation quality O(log4 n). We improve upon the latter result by giving the first near-linear time algorithm for computing an HCA with approximation quality O(log2 n loglogn). Additionally, our algorithm can be implemented in the parallel setting with polylogarithmic span and near-linear work, achieving the same approximation quality. This improves upon the best previous such algorithm, which has an O(log9n) approximation quality. We also present a lower bound of Ω(logn) for the approximation guarantee of hierarchical congestion approximators. Crucial for achieving a near-linear running time is a new partitioning routine that, unlike previous such routines, manages to avoid recursing on large subgraphs. To achieve the improved approximation quality, we introduce the new concept of border routability of a cut and provide an improved sparsest cut oracle for general vertex weights.}, author = {Henzinger, Monika H and Münk, Robin and Räcke, Harald}, booktitle = {58th Annual ACM Symposium on Theory of Computing}, isbn = {9798400725364}, issn = {0737-8017}, keywords = {Congestion Approximators, Hierarchical Graph Decompositions}, location = {Salt Lake City, UT, United States}, pages = {1417--1428}, publisher = {ACM}, title = {{An improved quality hierarchical congestion approximator in near-linear time}}, doi = {10.1145/3798129.3800851}, year = {2026}, } @inproceedings{21921, abstract = {A variety of problems in geometry processing boil down to finding the most parallel field relative to a connection. Instances of this prototypical problem show up in computing direction fields and stripe patterns, quadrilateral meshing, and visualization of fluid flows. When the class of allowed fields includes those with topological defects, a relaxation is required to make the problem well-posed. We observe that these problems can be viewed as synchronization problems, which admit a natural semidefinite relaxation. We propose a unified method of solving all these problems via the efficient Burer-Monteiro factorization method. Geometrically, this amounts to lifting the field values to a higher-dimensional manifold, naturally resolving the singular nature of defects. Practically, we show that our convex relaxation method achieves better and more reliable optima than previous work employing alternative relaxations}, author = {Pacheco-Tallaj, Natalia and Couplet, Matteo and Chien, Edward and Palmer, David}, booktitle = {SIGGRAPH Conference Papers}, location = {Los Angeles, CA, United States}, publisher = {ACM}, title = {{Synchronizing fields with singularities}}, doi = {10.1145/3799902.3811225}, year = {2026}, } @phdthesis{22808, abstract = {As automated decision-makers have become ubiquitous in many domains of life, their decisions have become increasingly consequential. Recent years have shown that such systems can exhibit discriminatory behaviour against individuals and social groups alike, thereby amplifying existing biases and entrenching socio-economic disparities over time. Algorithmic fairness addresses this problem by developing methods to quantify and mitigate unfair behaviour. However, much of the existing literature studies fairness in a static pre-deployment setting and, therefore, neglects that automated decision-makers are often deployed in dynamic environments, where their behaviour and the populations they affect may change over time. This thesis addresses this gap through the lens of runtime verification. Instead of treating fairness as a property of a classifier together with a fixed input distribution, it reframes fairness as a property of the interaction trace between the decision-maker and its deployment environment. To evaluate such sequential fairness properties, the thesis develops runtime monitors that observe the evolving interaction between the system and the environment and issue verdicts after each new observation. Because, these monitors are designed to detect unfair behaviour during deployment, they complement fair training, auditing, verification, and enforcement by providing an additional layer of mathematically rigorous fairness assurance. In summary, the thesis develops quantitative, trace-based analogues of classical group and individual fairness measures and constructs monitors for them. This includes monitors for long-run group fairness over Markovian traces, for the time-varying welfare of a changing population in a dynamical system, and for the individual fairness of an arbitrary system generating a trace of inputs and outputs. To achieve this, the monitors combine ideas from runtime verification, sequential statistics, and nearest-neighbour search. In the group-fairness settings, monitoring is primarily a sequential statistical estimation problem: the monitor must construct statistically sound interval estimates of fairness values from dependent and partially observed interactions. In the individual-fairness setting, the main challenge is computational efficiency: the monitor must detect individual fairness violations by efficiently comparing the current decision with all previously observed decisions. }, author = {Kueffner, Konstantin}, isbn = {978-3-99078-089-3}, issn = {2663-337X}, pages = {183}, publisher = {Institute of Science and Technology Austria}, title = {{Monitoring algorithmic fairness in sequential decision making}}, doi = {10.15479/AT-ISTA-22808}, year = {2026}, } @phdthesis{22873, author = {Ehrmann, Andreas}, isbn = {978-3-99078-092-3}, issn = {2663-337X}, keywords = {PhD Thesis, functional nanomachines, biological functionality, nanotechnology, energy delivery, target behavior, dynamics, design principles, optimization, differentiable statistical physics, machine learning}, pages = {168}, publisher = {Institute of Science and Technology Austria}, title = {{Biological functionality without biochemistry: Designing nanomachines for target behavior}}, doi = {10.15479/AT-ISTA-22873}, year = {2026}, } @unpublished{22893, abstract = {Many biological machines function through controlled conformational transitions, yet designing synthetic nanostructures with prescribed dynamical behavior remains a major challenge. Here, we develop a modular inverse-design framework for bistable nanostructures whose function is controlled by an energy profile along a geometric reaction coordinate. Inspired by proteins with rigid domains connected by flexible hinges, we introduce a hinge-arm paradigm in which a small bistable hinge controls the energetics of a conformational transition, while rigid arms map this transition onto the separation between external binding sites. Specifically, we ask which features of a target energy profile can be programmed under different design constraints. We find that the energy barriers and the binding-site separations in the two metastable states can be readily designed, while controlling the location of the transition state or the full shape of the energy profile requires additional design freedom. Using a differentiable design framework, we find that some optimized solutions are numerically inexact but still display the functional behavior for which the target profile was selected, emphasizing the importance of function-based evaluation criteria. These results establish a practical hierarchy of designability for bistable nanostructures and provide a route toward synthetic nanomachines that couple conformational transitions to target behavior.}, author = {Ehrmann, Andreas and Krstić, Marija and Samadzadeh, Sahar and Goodrich, Carl Peter}, booktitle = {arXiv}, title = {{Designing bistable nanostructures for target behavior}}, doi = {10.48550/arXiv.2606.31620}, year = {2026}, }