@unpublished{21399, abstract = {We report on the Equational Theories Project (ETP), an online collaborative pilot project to explore new ways to collaborate in mathematics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}, } @unpublished{21427, abstract = {While tumor malignancy has been extensively studied under the prism of genetic and epigenetic heterogeneity, tumor cell states also critically depend on reciprocal interactions with the microenvironment. This raises the hitherto untested possibility that heterogeneity of the untransformed tumor stroma can actively fuel malignant progression. As biological heterogeneity is inherently difficult to control, we adopted a reductionist approach and let tumor cells invade micro-engineered environments harboring obstacles with precision-controlled geometry. We find that not only the presence of obstacles, but more surprisingly their spatial disorder, causes a drastic shift from a collective to a single-cell mode of invasion – comparable in strength to cadherin loss. Combining live-imaging and perturbation experiments with minimal biophysical modeling, we demonstrate that cell detachments result both from local geometrical constraints and a global integration of spatial disorder over time. We show that different types of microenvironments map onto different universality classes of invasion dynamics - homogeneous substrates follow Kardar–Parisi–Zhang (KPZ) scaling, while disordered ones exhibit exponents consistent with KPZ with quenched disorder (KPZq). Our findings highlight generic physical principles for how the mode of cancer cell invasion depends on environmental heterogeneity, with potential implications to understand tumor evolution in vivo.}, author = {Dunajova, Zuzana and Tasciyan, Saren and Majek, Juraj and Merrin, Jack and Sahai, Erik and Sixt, Michael K and Hannezo, Edouard B}, publisher = {bioRxiv}, title = {{Substrate heterogeneity promotes cancer cell dissemination through interface roughening}}, doi = {10.1101/2025.05.20.655037}, year = {2025}, } @unpublished{21435, abstract = {Multiferroic materials, in which electric polarization and magnetic order coexist and couple, offer rich opportunities for both fundamental discovery and technology. However, multiferroicity remains rare due to conflicting electronic requirements for ferroelectricity and magnetism. One route to circumvent this challenge is to exploit the noncollinear ordering of spin cycloids, whose symmetry permits the emergence of polar order. In this work, we introduce another pathway to multiferroic order in which strain generates polarization in materials that host nonpolar spin spirals. To demonstrate this phenomenon, we chose the spin spiral in the well-studied helimagnet Cr1/3NbS2. To detect the induced polarization, we introduce the technique of magnetoelectric birefringence (MEB), an optical probe that enables spatially-resolved and unambiguous detection of polar order. By combining MEB imaging with strain engineering, we confirm the onset of a polar vector at the magnetic transition, establishing strained Cr1/3NbS2 as a type-II multiferroic.}, author = {Sun, Y. and Ahn, Y. and Sapkota, D. and Arachchige, H. S. and Xue, R. and Mozaffari, S. and Mandrus, D. G. and Zhao, L. and Orenstein, J. and Sunko, Veronika}, booktitle = {arXiv}, title = {{Strain-induced multiferroicity in Cr1/3NbS2}}, doi = {10.48550/arXiv.2510.11619}, year = {2025}, } @inproceedings{21474, abstract = {Rendering novel, relit views of a human head, given a monocular portrait image as input, is an inherently underconstrained problem. The traditional graphics solution is to explicitly decompose the input image into geometry, material and lighting via differentiable rendering; but this is constrained by the multiple assumptions and approximations of the underlying models and parameterizations of these scene components. We propose 3DPR, an image-based relighting model that leverages generative priors learnt from multi-view One-Light-at-A-Time (OLAT) images captured in a light stage. We introduce a new diverse and large-scale multi-view 4K OLAT dataset of 139 subjects to learn a high-quality prior over the distribution of high-frequency face reflectance. We leverage the latent space of a pre-trained generative head model that provides a rich prior over face geometry learnt from in-the-wild image datasets. The input portrait is first embedded in the latent manifold of such a model through an encoder-based inversion process. Then a novel triplane-based reflectance network trained on our lightstage data is used to synthesize high-fidelity OLAT images to enable image-based relighting. Our reflectance network operates in the latent space of the generative head model, crucially enabling a relatively small number of lightstage images to train the reflectance model. Combining the generated OLATs according to a given HDRI environment maps yields physically accurate environmental relighting results. Through quantitative and qualitative evaluations, we demonstrate that 3DPR outperforms previous methods, particularly in preserving identity and in capturing lighting effects such as specularities, self-shadows, and subsurface scattering.}, author = {Rao, Pramod and Meka, Abhimitra and Zhou, Xilong and Fox, Gereon and Mallikarjun, B. R. and Zhan, Fangneng and Weyrich, Tim and Bickel, Bernd and Pfister, Hanspeter and Matusik, Wojciech and Beeler, Thabo and Elgharib, Mohamed and Habermann, Marc and Theobalt, Christian}, booktitle = {Proceedings SIGGRAPH Asia 2025 Conference Papers 2025}, isbn = {9798400721373}, location = {Hong Kong, Hong Kong}, publisher = {Association for Computing Machinery}, title = {{3DPR: Single image 3D portrait relighting with generative priors}}, doi = {10.1145/3757377.3763962}, year = {2025}, } @misc{21668, abstract = {This artifact allows to review and reproduce the experiments from the paper *A Revised Practitioner's Guide to MDP Model Checking Algorithms*. The package contains all original logfiles and derived data used to generate the plots as in the paper. Furthermore, the artifact contains the model checking tools `Storm` and `mcsta` in the version exercised in the paper, the used Docker container, as well as benchmark instances and execution scripts to reproduce the experiments. See also the artifact of the conference paper: https://zenodo.org/records/7509474}, author = {Hartmanns, Arnd and Junges, Sebastian and Quatmann, Tim and Weininger, Maximilian}, publisher = {Zenodo}, title = {{Benchmark data for the revised practitioner's guide to MDP model checking algorithms}}, doi = {10.5281/ZENODO.14500423}, year = {2025}, } @article{21706, abstract = {Consider a quadratic polynomial Q(ξ1, . . . , ξn) of independent Rademacher random variables ξ1, . . . , ξn. To what extent can Q(ξ1, . . . , ξn) concentrate on a single value? This quadratic version of the classical Littlewood–Offord problem was popularised by Costello, Tao and Vu in their study of symmetric random matrices. In this paper, we obtain an essentially optimal bound for this problem, as conjectured by Nguyen and Vu. Specifically, if Q(ξ1, . . . , ξn) ‘robustly depends on at least m of the ξi’ in the sense that there is no way to pin down the value of Q(ξ1, . . . , ξn) by fixing values for fewer than m of the variables ξi, then we have Pr[Q(ξ1, . . . , ξn) = 0] ≤ O(1/√m). This also implies a similar result in the case where ξ1, . . . , ξn have arbitrary distributions. Our proof combines a number of ideas that may be of independent interest, including an inductive decoupling scheme that reduces quadratic anticoncentration problems to high-dimensional linear anticoncentration problems. Also, one application of our main result is the resolution of a conjecture of Alon, Hefetz, Krivelevich and Tyomkyn related to graph inducibility. }, author = {Kwan, Matthew Alan and Sauermann, Lisa}, issn = {1570-5846}, journal = {Compositio Mathematica}, number = {12}, pages = {3089--3139}, publisher = {Cambridge University Press}, title = {{Resolution of the quadratic Littlewood–Offord problem}}, doi = {10.1112/S0010437X25102789}, volume = {161}, year = {2025}, } @article{21724, abstract = {The next generation of weak-gravitational-lensing surveys has the potential to place stringent constraints on cosmological parameters. However, their analysis is limited by systematics such as the intrinsic alignments of galaxies, which alter weak-lensing convergence and can lead to biases in cosmological parameter estimations. For the first time, in this work, we investigate the impact of intrinsic alignments on non-Gaussian statistics of the weak-lensing field using galaxy shapes derived from the IllustrisTNG hydrodynamical simulation. We create two catalogs of ray-traced convergence maps: one that includes the measured intrinsic shape of each galaxy and another where all galaxies are randomly rotated to eliminate intrinsic alignments. We compare a range of weak-lensing statistics between the two catalogs, including the shear–shear correlation function, the map-level angular power spectrum, one-point, peak count, and minimum distribution functions, and Minkowski functionals. For each statistic, we assess the level of statistical distinguishability between catalogs for a set of future survey angular areas. Our results reveal strong small-scale correlation in the alignment of galaxies and statistically significant boosts in weak-lensing convergence in both positive and negative directions for high-significance peaks and minima, respectively. We note that our analysis is at a fixed number density of ˜ 5 arcmin^-2, drawn from a single realization of initial conditions, and does not include observational uncertainties or supersample covariance contributions. Weak-lensing analyses utilizing non-Gaussian statistics must account for intrinsic alignments to avoid significantly compromised cosmological inferences.}, author = {Lee, Max E. and Haiman, Zoltán and Pandey, Shivam and Genel, Shy}, issn = {1538-4357}, journal = {The Astrophysical Journal}, number = {1}, publisher = {IOP Publishing}, title = {{The effect of intrinsic alignments on weak-lensing statistics in hydrodynamical simulations}}, doi = {10.3847/1538-4357/ae1ca7}, volume = {996}, year = {2025}, } @article{21727, abstract = {We present a comprehensive analysis of the MIRI Extremely Red Object Virgil, a Lyα emitter at zspec = 6.6379 ± 0.0035 with the photometric properties of a Little Red Dot. Leveraging new JWST/MIRI imaging from the MIDIS and PAHSPECS programs, we confirm Virgil’s extraordinary nature among galaxies in JADES/GOODS-South, exhibiting a strikingly red NIRCam-to-MIRI color (F444W–F1500W = 2.84 ± 0.04 mag). Deep NIRSpec/PRISM spectroscopy from the OASIS program offers key insights into the host galaxy, revealing properties of an average star-forming galaxy during Cosmic Reionization, such as a subsolar metallicity, low-to-moderate dust content, and a relatively high ionization parameter and electron temperature. By estimating the star formation rate of Virgil from UV and Hα, we find evidence that the galaxy is either entering or fading out of a bursty episode. Although line-ratio diagnostics employed at high z would classify Virgil as an active galactic nucleus (AGN), this classification becomes ambiguous once redshift evolution is considered. Nonetheless, Virgil occupies the same parameter space as recently confirmed AGNs at similar redshifts. The new deep MIRI data at 15 μm reinforce the AGN nature of Virgil, as inferred from multiple spectral energy distribution (SED) fitting codes. Virgil’s rising infrared SED and UV excess resemble those of Dust-Obscured Galaxies (DOGs) studied with Spitzer at Cosmic Noon, particularly blue-excess HotDOGs. Our results highlight the need for a multiwavelength approach incorporating MIRI to uncover such extreme sources at z ≳ 6 and to shed light on the interplay between galaxy evolution and early black hole growth during Cosmic Reionization.}, author = {Rinaldi, Pierluigi and Pérez-González, Pablo G. and Rieke, George H. and Lyu, Jianwei and D’Eugenio, Francesco and Wu, Zihao and Carniani, Stefano and Looser, Tobias J. and Shivaei, Irene and Boogaard, Leindert A. and Diaz-Santos, Tanio and Colina, Luis and Östlin, Göran and Alberts, Stacey and Álvarez-Márquez, Javier and Annuziatella, Marianna and Aravena, Manuel and Bhatawdekar, Rachana and Bunker, Andrew J. and Caputi, Karina I. and Charlot, Stéphane and Crespo Gómez, Alejandro and Curti, Mirko and Eckart, Andreas and Gillman, Steven and Hainline, Kevin and Kumari, Nimisha and Hjorth, Jens and Iani, Edoardo and Inami, Hanae and Ji, Zhiyuan and Johnson, Benjamin D. and Jones, Gareth C. and Labiano, Álvaro and Maiolino, Roberto and Melinder, Jens and Moutard, Thibaud and Peissker, Florian and Rieke, Marcia and Robertson, Brant and Scholtz, Jan and Tacchella, Sandro and Van Der Werf, Paul P. and Walter, Fabian and Williams, Christina C. and Willott, Chris and Witstok, Joris and Übler, Hannah and Zhu, Yongda}, issn = {1538-4357}, journal = {The Astrophysical Journal}, number = {1}, publisher = {IOP Publishing}, title = {{Deciphering the nature of Virgil: An obscured active galactic nucleus lurking within an apparently normal Lyα emitter during cosmic reionization}}, doi = {10.3847/1538-4357/ae089c}, volume = {994}, year = {2025}, } @article{21768, abstract = {Let F∈Z[x1,…,xn] be a homogeneous form of degree d≥2, and V∗F the singular locus of the hypersurface {x∈AnC:F(x)=0}. A longstanding result of Birch states that there is a non-trivial integral solution to the equation F(x1,…,xn)=0 provided n>dimV∗F+(d−1)2d, and there is a non-singular solution in R and Qp for all primes p. We give a different formulation of this result. More precisely, we replace dimV∗F with a quantity HF defined in terms of the Hessian matrix of F. This quantity satisfies 0≤HF≤dimV∗F; therefore, we improve on the aforementioned result of Birch if HF}, author = {Ignatyev, Yuri and Papadopoulos, Stavros and Soretić, Mateja and Yeung, Jake and Lin, Tzi-Yang and Tanaka, Elly M and Peshkin, Leonid and Levine, Ariel J and Gabitto, Mariano I and Sweeney, Lora Beatrice Jaeger}, booktitle = {bioRxiv}, title = {{Innovations in spinal cord cell type heterogeneity across vertebrate evolution}}, doi = {10.1101/2025.10.09.680955}, year = {2025}, } @article{14278, abstract = {The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely, integrability close to the boundary, and prove a local version of this conjecture: a small perturbation of almost every ellipse that preserves integrability near the boundary, is itself an ellipse. We apply this result to study local spectral uniqueness of ellipses using the connection between the wave trace of the Laplacian and the dynamics near the boundary and establish local uniqueness for almost all of them.}, author = {Koval, Illya}, issn = {1432-1297}, journal = {Inventiones Mathematicae}, publisher = {Springer Nature}, title = {{Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse}}, doi = {10.1007/s00222-025-01397-y}, year = {2025}, } @article{14647, abstract = {In the developing vertebrate central nervous system, neurons and glia typically arise sequentially from common progenitors. Here, we report that the transcription factor Forkhead Box G1 (Foxg1) regulates gliogenesis in the mouse neocortex via distinct cell-autonomous roles in progenitors and postmitotic neurons that regulate different aspects of the gliogenic FGF signalling pathway. We demonstrate that loss of Foxg1 in cortical progenitors at neurogenic stages causes premature astrogliogenesis. We identify a novel FOXG1 target, the pro-gliogenic FGF pathway component Fgfr3, which is suppressed by FOXG1 cell-autonomously to maintain neurogenesis. Furthermore, FOXG1 can also suppress premature astrogliogenesis triggered by the augmentation of FGF signalling. We identify a second novel function of FOXG1 in regulating the expression of gliogenic cues in newborn neocortical upper-layer neurons. Loss of FOXG1 in postmitotic neurons non-autonomously enhances gliogenesis in the progenitors via FGF signalling. These results fit well with the model that newborn neurons secrete cues that trigger progenitors to produce the next wave of cell types, astrocytes. If FGF signalling is attenuated in Foxg1 null progenitors, they progress to oligodendrocyte production. Therefore, loss of FOXG1 transitions the progenitor to a gliogenic state, producing either astrocytes or oligodendrocytes depending on FGF signalling levels. Our results uncover how FOXG1 integrates extrinsic signalling via the FGF pathway to regulate the sequential generation of neurons, astrocytes, and oligodendrocytes in the cerebral cortex. }, author = {Bose, Mahima and Suresh, Varun and Mishra, Urvi and Talwar, Ishita and Yadav, Anuradha and Biswas, Shiona and Hippenmeyer, Simon and Tole, Shubha}, issn = {2050-084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{Dual role of FOXG1 in regulating gliogenesis in the developing neocortex via the FGF signalling pathway}}, doi = {10.7554/elife.101851.3}, volume = {13}, year = {2025}, } @article{15016, abstract = {Amphibians, by virtue of their phylogenetic position, provide invaluable insights on nervous system evolution, development, and remodeling. The genetic toolkit for amphibians, however, remains limited. Recombinant adeno-associated viral vectors (AAVs) are a powerful alternative to transgenesis for labeling and manipulating neurons. Although successful in mammals, AAVs have never been shown to transduce amphibian cells efficiently. We screened AAVs in three amphibian species—the frogs Xenopus laevis and Pelophylax bedriagae and the salamander Pleurodeles waltl—and identified at least two AAV serotypes per species that transduce neurons. In developing amphibians, AAVs labeled groups of neurons generated at the same time during development. In the mature brain, AAVrg retrogradely traced long-range projections. Our study introduces AAVs as a tool for amphibian research, establishes a generalizable workflow for AAV screening in new species, and expands opportunities for cross-species comparisons of nervous system development, function, and evolution.}, author = {Jaeger, Eliza C.B. and Vijatovic, David and Deryckere, Astrid and Zorin, Nikol and Nguyen, Akemi L. and Ivanian, Georgiy and Woych, Jamie and Arnold, Rebecca C and Ortega Gurrola, Alonso and Shvartsman, Arik and Barbieri, Francesca and Toma, Florina-Alexandra and Gorbsky, Gary J. and Horb, Marko E. and Cline, Hollis T. and Shay, Timothy F. and Kelley, Darcy B. and Yamaguchi, Ayako and Shein-Idelson, Mark and Tosches, Maria Antonietta and Sweeney, Lora Beatrice Jaeger}, issn = {1878-1551}, journal = {Developmental Cell}, number = {5}, pages = {794--812.e6}, publisher = {Elsevier}, title = {{Adeno-associated viral tools to trace neural development and connectivity across amphibians}}, doi = {10.1016/j.devcel.2024.10.025}, volume = {60}, year = {2025}, } @article{15121, abstract = {We present an auction algorithm using multiplicative instead of constant weight updates to compute a (1-E)-approximate maximum weight matching (MWM) in a bipartite graph with n vertices and m edges in time 0(mE-1), beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM ’14] that runs in 0(mE-1 log E-1). Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a (1-E)-approximate maximum weight matching under (1) one-sided vertex deletions (with incident edges) and (2) one-sided vertex insertions (with incident edges sorted by weight) to the other side. The total time time used is 0(mE-1), where m is the sum of the number of initially existing and inserted edges.}, author = {Zheng, Da Wei and Henzinger, Monika H}, issn = {1436-4646}, journal = {Mathematical Programming}, pages = {881--894}, publisher = {Springer Nature}, title = {{Multiplicative auction algorithm for approximate maximum weight bipartite matching}}, doi = {10.1007/s10107-024-02066-3}, volume = {210}, year = {2025}, } @article{15128, abstract = {We prove a universal mesoscopic central limit theorem for linear eigenvalue statistics of a Wigner-type matrix inside the bulk of the spectrum with compactly supported twice continuously differentiable test functions. The main novel ingredient is an optimal local law for the two-point function $T(z,\zeta)$ and a general class of related quantities involving two resolvents at nearby spectral parameters.}, author = {Riabov, Volodymyr}, issn = {0246-0203}, journal = {Annales de l'institut Henri Poincare (B) Probability and Statistics}, number = {1}, pages = {129--154}, publisher = {Institute of Mathematical Statistics}, title = {{Mesoscopic eigenvalue statistics for Wigner-type matrices}}, doi = {10.1214/23-AIHP1438}, volume = {61}, 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}, }