@article{21270,
abstract = {The one-dimensional Fröhlich model describing the motion of a single electron interacting with optical phonons is a paradigmatic model of quantum many-body physics. We predict the existence of an arbitrarily large number of bound excited states in the strong-coupling limit and calculate their excitation energies. Numerical simulations of a discretized model demonstrate the complete amelioration of the projector Monte Carlo sign problem by walker annihilation in an infinite Hilbert space. They reveal the threshold for the occurrence of the first bound excited states at a value of 𝛼≈1.73 for the dimensionless coupling constant. This puts the threshold into the regime of intermediate interaction strength. We find a significant spectral weight and increased phonon number of the bound excited state at threshold.},
author = {Taylor, J. and Čufar, M. and Mitrouskas, David Johannes and Seiringer, Robert and Pahl, E. and Brand, J.},
issn = {2469-9969},
journal = {Physical Review B},
number = {18},
publisher = {American Physical Society},
title = {{Bound excited states of Fröhlich polarons in one dimension}},
doi = {10.1103/s9p9-jflq},
volume = {112},
year = {2025},
}
@article{21271,
abstract = {For general non-Hermitian large random matrices X and deterministic deformation matrices A, we prove that the local eigenvalue statistics of A+X close to the typical edge points of its spectrum are universal. Furthermore, we show that, under natural assumptions, on A the spectrum of A+X does not have outliers at a distance larger than the natural fluctuation scale of the eigenvalues. As a consequence, the number of eigenvalues in each component of Spec(A+X) is deterministic.},
author = {Campbell, Andrew J and Cipolloni, Giorgio and Erdös, László and Ji, Hong Chang},
issn = {2168-894X},
journal = {The Annals of Probability},
number = {6},
pages = {2256--2308},
publisher = {Institute of Mathematical Statistics},
title = {{On the spectral edge of non-Hermitian random matrices}},
doi = {10.1214/25-aop1761},
volume = {53},
year = {2025},
}
@inproceedings{21272,
abstract = {Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a Monte Carlo (MC)-based algorithm that updates spins one at a time. Yet, these localized updates can cause the system to become trapped in local minima. Cluster algorithms (CAs) were developed to address this limitation and have demonstrated considerable success in studying ferromagnetic systems; however, they tend to encounter percolation issues when applied to generic spin glasses. In this work, we introduce a novel CA designed to tackle these challenges by leveraging precomputed two-point correlations, aiming solve combinatorial optimization problems in the form of Max-Cut more efficiently. In our approach, clusters are formed probabilistically based on these correlations. Various classical and quantum algorithms can be employed to generate correlations that embody information about the energy landscape of the problem. By utilizing this information, the algorithm aims to identify groups of spins whose simultaneous flipping induces large transitions in configuration space with high acceptance probability - even at low energy levels - thereby escaping local minima more effectively. Notably, clusters generated using correlations from the Quantum Approximate Optimization Algorithm exhibit high acceptance rates at low temperatures. These acceptance rates often increase with circuit depth, accelerating the algorithm and enabling more efficient exploration of the solution space.},
author = {Eder, Peter J. and Kerschbaumer, Aron and Finžgar, Jernej Rudi and Medina Ramos, Raimel A and Schuetz, Martin J. A. and Katzgraber, Helmut G. and Braun, Sarah and Mendl, Christian B.},
booktitle = {2025 IEEE International Conference on Quantum Computing and Engineering},
location = {Albuquerque, NM, United States},
publisher = {IEEE},
title = {{Quantum-guided cluster algorithms for combinatorial optimization}},
doi = {10.1109/qce65121.2025.00033},
year = {2025},
}
@inproceedings{21280,
abstract = {We give an algorithm that, with high probability, maintains a (1-ε)-approximate s-t maximum flow in undirected, uncapacitated n-vertex graphs undergoing m edge insertions in Õ(m+ n F^*/ε) total update time, where F^{*} is the maximum flow on the final graph. This is the first algorithm to achieve polylogarithmic amortized update time for dense graphs (m = Ω(n²)), and more generally, for graphs where F^* = Õ(m/n). At the heart of our incremental algorithm is the residual graph sparsification technique of Karger and Levine [SICOMP '15], originally designed for computing exact maximum flows in the static setting. Our main contributions are (i) showing how to maintain such sparsifiers for approximate maximum flows in the incremental setting and (ii) generalizing the cut sparsification framework of Fung et al. [SICOMP '19] from undirected graphs to balanced directed graphs.},
author = {Goranci, Gramoz and Henzinger, Monika H and Räcke, Harald and Sricharan, A.},
booktitle = {52nd International Colloquium on Automata, Languages, and Programming},
isbn = {9783959773720},
location = {Aarhus, Denmark},
pages = {91:1--91:20},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Incremental approximate maximum flow via residual graph sparsification}},
doi = {10.4230/lipics.icalp.2025.91},
volume = {334},
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{21317,
abstract = {Accreting white dwarfs (WDs) in close binary systems, commonly known as cataclysmic variables (CVs), with orbital periods below the canonical period minimum (≈80 minutes) are rare. Such short periods can only be reached if the donor star in the CV is either significantly evolved before initiating mass transfer to the WD or is metal-poor. We present optical photometry and spectroscopy of Gaia19bxc, a high-amplitude variable identified as a polar CV with an exceptionally short orbital period of 64.42 minutes—well below the canonical CV period minimum. High-speed photometry confirms persistent double-peaked variability consistent with cyclotron beaming, thus indicating the presence of a magnetic WD. Phase-resolved Keck/Low-Resolution Imaging Spectrometer (LRIS) spectroscopy reveals strong hydrogen and helium emission lines but no donor features, indicating the accretor is a magnetic WD and the donor is hydrogen-rich, but cold and faint. The absence of a detectable donor and the low inferred temperature (≲3500 K) disfavor an evolved donor scenario. Instead, the short period and the system’s halo-like kinematics suggest Gaia19bxc may be the first known metal-poor polar. Because metal-poor donors are more compact than solar-metallicity donors of the same mass, they can reach shorter minimum periods. Gaia19bxc is one of only a handful of known metal-poor CVs below the canonical period minimum and has the shortest period of any such magnetic system discovered to date.},
author = {Galiullin, Ilkham and Rodriguez, Antonio C. and El-Badry, Kareem and Caiazzo, Ilaria and Szkody, Paula and Nagarajan, Pranav and Whitebook, Samuel},
issn = {2041-8213},
journal = {The Astrophysical Journal Letters},
number = {2},
publisher = {IOP Publishing},
title = {{Optical spectroscopy of the most compact accreting binary harboring a magnetic White Dwarf and a hydrogen-rich donor}},
doi = {10.3847/2041-8213/adff82},
volume = {990},
year = {2025},
}
@article{21318,
abstract = {Matter waves have been observed in double-slit experiments with microscopic objects, such as atoms or molecules. The wave function describing the motion of these objects must extend over a distance comparable to the slit separation, much larger than the characteristic size of the objects. Preparing such states for more massive objects, such as mechanical oscillators, remains an outstanding challenge. Here we delocalize the quantum ground state of an optically levitated nanosphere by modulating the stiffness of the confining potential. We show a more than threefold increase of the initial coherence length, which corresponds to mechanical momentum squeezing of more than 7 dB. Our work is a stepping stone toward the generation of coherence lengths comparable to the object size, a crucial regime for macroscopic quantum experiments.},
author = {Rossi, M. and Militaru, Andrei and Carlon Zambon, N. and Riera-Campeny, A. and Romero-Isart, O. and Frimmer, M. and Novotny, L.},
issn = {1079-7114},
journal = {Physical Review Letters},
number = {8},
publisher = {American Physical Society},
title = {{Quantum delocalization of a levitated nanoparticle}},
doi = {10.1103/2yzc-fsm3},
volume = {135},
year = {2025},
}
@inproceedings{21320,
abstract = {Prophet inequalities are a central object of study in optimal stopping theory. In the iid model, a gambler sees values in an online fashion, sampled independently from a given distribution. Upon observing each value, the gambler either accepts it as a reward, or irrevocably rejects it and proceeds to observe the next value. The goal of the gambler, who cannot see the future, is to maximise the expected value of the reward while competing against the expectation of a prophet (the offline maximum). In other words, one seeks to maximise the gambler-to-prophet ratio of the expectations.
This model has been studied with infinite, finite and unknown number of values. When the gambler faces a random number of values, the model is said to have a random horizon. We consider the model in which the gambler is given a priori knowledge of the horizon’s distribution. Alijani et al. (2020) designed a single-threshold algorithm achieving a ratio of 1/2 when the random horizon has an increasing hazard rate and is independent of the values. We prove that with a single threshold, a ratio of 1/2 is actually achievable for several larger classes of horizon distributions, with the largest being known as the 𝒢 class in reliability theory. Moreover, we show that this does not extend to its dual, the ̅𝒢 class (which includes the decreasing hazard rate class), while it can be extended to low-variance horizons. Finally, we construct the first example of a family of horizons, for which multiple thresholds are necessary to achieve a nonzero ratio. We establish that the Secretary Problem optimal stopping rule provides one such algorithm, paving the way towards the study of the model beyond single-threshold algorithms.},
author = {Giambartolomei, Giordano and Mallmann-Trenn, Frederik and Saona Urmeneta, Raimundo J},
booktitle = {52nd International Colloquium on Automata, Languages, and Programming},
isbn = {9783959773720},
location = {Aarhus, Denmark},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{IID prophet inequality with random horizon: Going beyond increasing hazard rates}},
doi = {10.4230/LIPIcs.ICALP.2025.87},
volume = {334},
year = {2025},
}
@article{21321,
abstract = {The development of cost-effective and high-performance thermoelectric (TE) materials faces significant challenges, particularly in improving the properties of promising copper-based TE materials such as Cu3SbSe4, which are limited by their poor electrical conductivity. This study presents a detailed comparative analysis of three strategies to promote the electrical transport properties of Cu3SbSe4 through Sn doping: conventional Sn atomic doping, surface treatment with SnSe molecular complexes, and blending with SnSe nanocrystals to form nanocomposites, all followed by annealing and hot pressing under identical conditions. Our results reveal that a surface treatment using SnSe molecular complexes significantly enhances TE performance over atomic doping and nanocomposite formation, achieving a power factor of 1.1 mW·m−1·K−2 and a maximum dimensionless figure of merit zT value of 0.80 at 640 K, representing an excellent performance among Cu3SbSe4-based materials produced via solution-processing methods. This work highlights the effectiveness of surface engineering in optimizing the transport properties of nanostructured materials, demonstrating the versatility and cost-efficiency of solution-based technologies in the development of advanced nanostructured materials for application in the field of TE among others.},
author = {Xiao, Shanshan and Zhao, Mingjun and Li, Mingquan and Wan, Shanhong and Genç, Aziz and Huang, Lulu and Chen, Lei and Zhang, Yu and Ibáñez, Maria and Lim, Khak Ho and Hong, Min and Liu, Yu and Cabot, Andreu},
issn = {1998-0000},
journal = {Nano Research},
number = {1},
publisher = {Tsinghua University Press},
title = {{Band and defect engineering in solution-processed nanocrystal building blocks to promote transport properties in nanomaterials: The case of thermoelectric Cu 3SbSe 4}},
doi = {10.26599/nr.2025.94907072},
volume = {18},
year = {2025},
}
@inproceedings{21323,
abstract = {We present a unifying framework for proving the knowledge-soundness of KZG-like polynomial commitment schemes, encompassing both univariate and multivariate variants. By conceptualizing the proof technique of Lipmaa, Parisella, and Siim for the univariate KZG scheme (EUROCRYPT 2024), we present tools and falsifiable hardness assumptions that permit black-box extraction of the multivariate KZG scheme. Central to our approach is the notion of a canonical Proof-of-Knowledge of a Polynomial (PoKoP) of a polynomial commitment scheme, which we use to capture the extractability notion required in constructions of practical zk-SNARKs. We further present an explicit polynomial decomposition lemma for multivariate polynomials, enabling a more direct analysis of interpolating extractors and bridging the gap between univariate and multivariate commitments. Our results provide the first standard-model proofs of extractability for the multivariate KZG scheme and many of its variants under falsifiable assumptions.},
author = {Belohorec, Juraj and Dvořák, Pavel and Hoffmann, Charlotte and Hubáček, Pavel and Mašková, Kristýna and Pastyřík, Martin},
booktitle = {45th Annual International Cryptology Conference},
isbn = {9783032018861},
issn = {1611-3349},
location = {Santa Barbara, CA, United States},
pages = {584--616},
publisher = {Springer Nature},
title = {{On extractability of the KZG family of polynomial commitment schemes}},
doi = {10.1007/978-3-032-01887-8_19},
volume = {16005},
year = {2025},
}
@inproceedings{21324,
abstract = {Learning models have been shown to rely on spurious correlations between non-predictive features and the associated labels in the training data, with negative implications on robustness, bias and fairness. In this work, we provide a statistical characterization of this phenomenon for high-dimensional regression, when the data contains a predictive core feature x and a spurious feature y. Specifically, we quantify the amount of spurious correlations C learned via linear regression, in terms of the data covariance and the strength λ of the ridge regularization. As a consequence, we first capture the simplicity of y through the spectrum of its covariance, and its correlation with x through the Schur complement of the full data covariance. Next, we prove a trade-off between C and the in-distribution test loss L, by showing that the value of λ that minimizes L lies in an interval where C is increasing. Finally, we investigate the effects of over-parameterization via the random features model, by showing its equivalence to regularized linear regression. Our theoretical results are supported by numerical experiments on Gaussian, Color-MNIST, and CIFAR-10 datasets.},
author = {Bombari, Simone and Mondelli, Marco},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
issn = {2640-3498},
location = {Vancouver, Canada},
pages = {4839--4873},
publisher = {ML Research Press},
title = {{Spurious correlations in high dimensional regression: The roles of regularization, simplicity bias and over-parameterization}},
volume = {267},
year = {2025},
}
@inproceedings{21325,
abstract = {Test-time training (TTT) methods explicitly update the weights of a model to adapt to the specific test instance, and they have found success in a variety of settings, including most recently language modeling and reasoning. To demystify this success, we investigate a gradient-based TTT algorithm for in-context learning, where we train a transformer model on the in-context demonstrations provided in the test prompt. Specifically, we provide a comprehensive theoretical characterization of linear transformers when the update rule is a single gradient step. Our theory (i) delineates the role of alignment between pretraining distribution and target task, (ii) demystifies how TTT can alleviate distribution shift, and (iii) quantifies the sample complexity of TTT including how it can significantly reduce the eventual sample size required for in-context learning. As our empirical contribution, we study the benefits of TTT for TabPFN, a tabular foundation model. In line with our theory, we demonstrate that TTT significantly reduces the required sample size for tabular classification (3 to 5 times fewer) unlocking substantial inference efficiency with a negligible training cost.},
author = {Gozeten, Halil Alperen and Ildiz, Muhammed Emrullah and Zhang, Xuechen and Soltanolkotabi, Mahdi and Mondelli, Marco and Oymak, Samet},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
issn = {2640-3498},
location = {Vancouver, Canada},
pages = {20266--20295},
publisher = {ML Research Press},
title = {{Test-time training provably improves transformers as in-context learners}},
volume = {267},
year = {2025},
}
@inproceedings{21326,
abstract = {Neural Collapse is a phenomenon where the last-layer representations of a well-trained neural network converge to a highly structured geometry. In this paper, we focus on its first (and most basic) property, known as NC1: the within-class variability vanishes. While prior theoretical studies establish the occurrence of NC1 via the data-agnostic unconstrained features model, our work adopts a data-specific perspective, analyzing NC1 in a three-layer neural network, with the first two layers operating in the mean-field regime and followed by a linear layer. In particular, we establish a fundamental connection between NC1 and the loss landscape: we prove that points with small empirical loss and gradient norm (thus, close to being stationary) approximately satisfy NC1, and the closeness to NC1 is controlled by the residual loss and gradient norm. We then show that (i) gradient flow on the mean squared error converges to NC1 solutions with small empirical loss, and (ii) for well-separated data distributions, both NC1 and vanishing test loss are achieved simultaneously. This aligns with the empirical observation that NC1 emerges during training while models attain near-zero test error. Overall, our results demonstrate that NC1 arises from gradient training due to the properties of the loss landscape, and they show the co-occurrence of NC1 and small test error for certain data distributions.},
author = {Wu, Diyuan and Mondelli, Marco},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
issn = {2640-3498},
location = {Vancouver, Canada},
pages = {67499--67536},
publisher = {ML Research Press},
title = {{Neural collapse beyond the unconstrained features model: Landscape, dynamics, and generalization in the mean-field regime}},
volume = {267},
year = {2025},
}
@inproceedings{21327,
abstract = {Proteins exist as a dynamic ensemble of multiple conformations, and these motions are often crucial for their functions. However, current structure prediction methods predominantly yield a single conformation, overlooking the conformational heterogeneity revealed by diverse experimental modalities. Here, we present a framework for building experiment-grounded protein structure generative models that infer conformational ensembles consistent with measured experimental data. The key idea is to treat stateof-the-art protein structure predictors (e.g., AlphaFold3) as sequence-conditioned structural priors, and cast ensemble modeling as posterior inference of protein structures given experimental measurements. Through extensive real-data experiments, we demonstrate the generality of our method to incorporate a variety of experimental measurements. In particular, our framework uncovers previously unmodeled conformational heterogeneity from crystallographic densities, and generates high-accuracy NMR ensembles orders of magnitude faster than the status quo. Notably, we demonstrate that our ensembles outperform AlphaFold3 (Abramson et al., 2024) and sometimes better fit experimental data than publicly deposited structures to the Protein Data Bank (PDB, Burley et al. (2017)). We believe that this approach will unlock building predictive models that fully embrace experimentally observed conformational diversity.},
author = {Maddipatla, Sai A and Sellam, Nadav E and Bojan, Meital I and Vedula, Sanketh and Schanda, Paul and Marx, Ailie and Bronstein, Alexander},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
issn = {2640-3498},
location = {Vancouver, Canada},
pages = {42366 -- 42393},
publisher = {ML Research Press},
title = {{Inverse problems with experiment-guided AlphaFold}},
volume = {267},
year = {2025},
}
@inproceedings{21328,
abstract = {Multi-index models provide a popular framework to investigate the learnability of functions with low-dimensional structure and, also due to their connections with neural networks, they have been object of recent intensive study. In this paper, we focus on recovering the subspace spanned by the signals via spectral estimators – a family of methods routinely used in practice, often as a warm-start for iterative algorithms. Our main technical contribution is a precise asymptotic characterization of the performance of spectral methods, when sample size and input dimension grow proportionally and the dimension p of the space to recover is fixed. Specifically, we locate the top-p eigenvalues of the spectral matrix and establish the overlaps between the corresponding eigenvectors (which give the spectral estimators) and a basis of the signal subspace. Our analysis unveils a phase transition phenomenon in which, as the sample complexity grows, eigenvalues escape from the bulk of the spectrum and, when that happens, eigenvectors recover directions of the desired subspace. The precise characterization we put forward enables the optimization of the data preprocessing, thus allowing to identify the spectral estimator that requires the minimal sample size for weak recovery.},
author = {Kovačević, Filip and Yihan, Zhang and Mondelli, Marco},
booktitle = {Proceedings of 38th Conference on Learning Theory},
issn = {2640-3498},
location = {Lyon, France},
pages = {3354--3404},
publisher = {ML Research Press},
title = {{Spectral estimators for multi-index models: Precise asymptotics and optimal weak recovery}},
volume = {291},
year = {2025},
}
@article{21343,
abstract = {The large sieve is used to estimate the density of quadratic polynomials Q ∈ Z[x],
such that there exists an odd degree polynomial defined over Z which has resultant ±1 with Q.
Given a monic polynomial R ∈ Z[x] of odd degree, this is used to show that for almost all
quadratic polynomials Q ∈ Z[x], there exists a prime p such that Q and R share a common
root in Fp. Using recent work of Landesman, an application to the average size of the odd part
of the class group of quadratic number fields is also given},
author = {Browning, Timothy D and Chan, Yik Tung},
issn = {2270-518X},
journal = {Journal de l'ecole polytechnique mathematiques},
pages = {1677--1691},
publisher = {Ecole polytechnique},
title = {{Solubility of a resultant equation and applications}},
doi = {10.5802/jep.320},
volume = {12},
year = {2025},
}
@unpublished{21399,
abstract = {We report on the Equational Theories Project (ETP), an online collaborative pilot project to explore new ways to collaborate in mathematics with machine assistance. The project successfully determined all 22 028 942 edges of the implication graph between the 4694 simplest equational laws on magmas, by a combination of human-generated and automated proofs, all validated by the formal proof assistant language Lean. As a result of this project, several new constructions of magmas satisfying specific laws were discovered, and several auxiliary questions were also addressed, such as the effect of restricting attention to finite magmas.},
author = {Bolan, Matthew and Breitner, Joachim and Brox, Jose and Carlini, Nicholas and Carneiro, Mario and Doorn, Floris van and Dvorak, Martin and Goens, Andrés and Hill, Aaron and Husum, Harald and Mejia, Hernán Ibarra and Kocsis, Zoltan A. and Floch, Bruno Le and Bar-on, Amir and Luccioli, Lorenzo and McNeil, Douglas and Meiburg, Alex and Monticone, Pietro and Nielsen, Pace P. and Osazuwa, Emmanuel Osalotioman and Paolini, Giovanni and Petracci, Marco and Reinke, Bernhard and Renshaw, David and Rossel, Marcus and Roux, Cody and Scanvic, Jérémy and Srinivas, Shreyas and Tadipatri, Anand Rao and Tao, Terence and Tsyrklevich, Vlad and Vaquerizo-Villar, Fernando and Weber, Daniel and Zheng, Fan},
booktitle = {arXiv},
title = {{The equational theories project: Advancing collaborative mathematical research at scale}},
doi = {10.48550/arXiv.2512.07087},
year = {2025},
}
@inproceedings{21412,
abstract = {Payment channel networks (PCNs) are a promising technology that alleviates blockchain scalability by shifting the transaction load from the blockchain to the PCN. Nevertheless, the network topology has to be carefully designed to maximise the transaction throughput in PCNs. Additionally, users in PCNs also have to make optimal decisions on which transactions to forward and which to reject to prolong the lifetime of their channels. In this work, we consider an input sequence of transactions over p parties. Each transaction consists of a transaction size, source, and target, and can be either accepted or rejected (entailing a cost). The goal is to design a PCN topology among the p cooperating parties, along with the channel capacities, and then output a decision for each transaction in the sequence to minimise the cost of creating and augmenting channels, as well as the cost of rejecting transactions. Our main contribution is an 𝒪(p) approximation algorithm for the problem with p parties. We further show that with some assumptions on the distribution of transactions, we can reduce the approximation ratio to 𝒪(√p). We complement our theoretical analysis with an empirical study of our assumptions and approach in the context of the Lightning Network.},
author = {Chatterjee, Krishnendu and Křišťan, Jan Matyáš and Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle X},
booktitle = {39th International Symposium on Distributed Computing},
isbn = {9783959774024},
issn = {1868-8969},
location = {Berlin, Germany},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Boosting payment channel network liquidity with topology optimization and transaction selection}},
doi = {10.4230/LIPIcs.DISC.2025.23},
volume = {356},
year = {2025},
}
@article{21413,
abstract = {We present a general framework for applying learning algorithms and heuristical guidance to the verification of Markov decision processes (MDPs).
The primary goal of our techniques is to improve performance by avoiding an exhaustive exploration of the state space, instead focussing on particularly relevant areas of the system, guided by heuristics. Our work builds on the previous results of Br{á}zdil et al., significantly extending it as well as refining several details and fixing errors.
The presented framework focuses on probabilistic reachability, which is a core problem in verification, and is instantiated in two distinct scenarios.
The first assumes that full knowledge of the MDP is available, in particular precise transition probabilities. It performs a heuristic-driven partial exploration of the model, yielding precise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP without knowing the exact transition dynamics. Here, we obtain probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stopping criteria for the approximation. In particular, the latter is an extension of statistical model-checking (SMC) for unbounded properties in MDPs. In contrast to other related approaches, we do not restrict our attention to time-bounded (finite-horizon) or discounted properties, nor assume any particular structural properties of the MDP.},
author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Chmelik, Martin and Forejt, Vojtěch and Kretinsky, Jan and Kwiatkowska, Marta and Meggendorfer, Tobias and Parker, David and Ujma, Mateusz},
issn = {2751-4838},
journal = {TheoretiCS},
publisher = {TheoretiCS Foundation},
title = {{Learning algorithms for verification of Markov decision processes}},
doi = {10.46298/theoretics.25.10},
volume = {4},
year = {2025},
}
@article{17094,
abstract = {Contract-based design is a promising methodology for taming the complexity of developing sophisticated systems. A formal contract distinguishes between assumptions, which are constraints that the designer of a component puts on the environments in which the component can be used safely, and guarantees, which are promises that the designer asks from the team that implements the component. A theory of formal contracts can be formalized as an interface theory, which supports the composition and refinement of both assumptions and guarantees. Although there is a rich landscape of contract-based design methods that address functional and extra-functional properties, we present the first interface theory designed to ensure system-wide security properties. Our framework provides a refinement relation and a composition operation that support both incremental design and independent implementability. We develop our theory for both stateless and stateful interfaces. Additionally, we introduce information-flow contracts where assumptions and guarantees are sets of flow relations. We use these contracts to illustrate how to enrich information-flow interfaces with a semantic view. We illustrate the applicability of our framework with two examples inspired by the automotive domain.},
author = {Bartocci, Ezio and Ferrere, Thomas and Henzinger, Thomas A and Nickovic, Dejan and Oliveira da Costa, Ana},
issn = {1572-8102},
journal = {Formal Methods in System Design},
pages = {3--48},
publisher = {Springer Nature},
title = {{Information-flow interfaces}},
doi = {10.1007/s10703-024-00447-0},
volume = {66},
year = {2025},
}