@phdthesis{20167, author = {Schön, Hanna}, isbn = {978-3-99078-061-9}, issn = {2663-337X}, pages = {171}, publisher = {Institute of Science and Technology Austria}, title = {{The ER complex SUTU-7/MACO-1 regulates the fate of mRNAs encoding GPCRs}}, doi = {10.15479/AT-ISTA-20167}, year = {2025}, } @article{20187, abstract = {Very long-chain fatty acids (VLCFAs), being constituents of different types of lipids, are critical factors in plant development, presumably due to their impact on the endomembrane system. The VLCFAs are synthesized in the endoplasmic reticulum by a heterotetrameric enzymatic complex including β-ketoacyl CoA reductase 1 (KCR1), whose mutant is lethal. Here, we describe the ectopic shoot meristems (esm) mutant, a viable kcr1 allele presumably affecting surface properties of the KCR1 protein. This kcr1-2 mutant shows reduced fatty acyl elongation that impacts VLCFAs. The kcr1-2 plants show severe defects during different stages of development, which all correlate with defects in polar localization and subcellular trafficking of PIN auxin transporters and resulting asymmetric auxin distribution. Detailed analysis of KCR1 expression and patterning defects in kcr1-2 suggests that KCR1 plays a role in delineating boundaries around meristematic and specialized differentiating tissues, including root and shoot meristems, initiating lateral roots, lateral root primordia, and trichomes. In these contexts, KCR1-produced VLCFAs may act in a non-cell-autonomous manner. Viable kcr1-2 represents a useful tool to study VLCFA roles in plant development and highlights VLCFAs as critical developmental factors at the interface of cell polarity and tissue development.}, author = {Babic, David and Abualia, Rashed and Fiedler, Lukas and Qi, Linlin and Tellier, Frédérique and Smoljan, Adrijana and Rakusova, Hana and Valošek, Petr and Han, Huibin and Benková, Eva and Faure, Jean Denis and Friml, Jiří}, issn = {1365-313X}, journal = {Plant Journal}, number = {3}, publisher = {Wiley}, title = {{Biosynthesis of very long-chain fatty acids is required for Arabidopsis auxin-mediated embryonic and post-embryonic development}}, doi = {10.1111/tpj.70396}, volume = {123}, year = {2025}, } @phdthesis{20362, author = {Babic, David}, issn = {2663-337X}, pages = {116}, publisher = {Institute of Science and Technology Austria}, title = {{Mechanisms of auxin-mediated early embryogenesis in Arabidopsis thaliana}}, doi = {10.15479/AT-ISTA-20362}, year = {2025}, } @phdthesis{20415, author = {Lee, Seungho}, issn = {2663-337X}, pages = {144}, publisher = {Institute of Science and Technology Austria}, title = {{Nanoparticle-based precursors toward advanced crystalline inorganic solids}}, doi = {10.15479/AT-ISTA-20415}, year = {2025}, } @phdthesis{20364, author = {Giannini, Caterina}, issn = {2663-337X}, keywords = {Auxin Signaling, Plant Development}, pages = {151}, publisher = {Institute of Science and Technology Austria}, title = {{Nuclear and cell surface auxin signaling in A. thaliana developmental transitions}}, doi = {10.15479/AT-ISTA-20364}, year = {2025}, } @phdthesis{20441, abstract = {Epithelial spreading plays a pivotal role in the development of organisms especially those such as zebrafish which require the epithelial enveloping layer (EVL) to spread to cover the substantial yolk surface during gastrulation. Epiboly requires the transition of the epithelium with cuboidal cells to form a thin, flat squamous epithelial sheet. During this transition, the cells show tissue-scale mechanosensation with mechanisms such as direct mechanical control over the axis of cell division. Cytoskeletal intermediate filaments play a crucial role in vertebrate cells, not only facilitating mechanical stability but also helping facilitate the mechanosensitive response of the cell. Mechanosenstivity displayed by intermediate filaments is due not just to their interesting physical properties but also to their interactions with other cytoskeletal elements such as actin and microtubules. Keratin is the predominant intermediate filament expressed in the EVL. It expresses concomitantly with the gastrulation movements of the developing embryo. Our work focuses on understanding the role and dynamics of the keratin cytoskeletal network in modulating the physical aspects of EVL spreading. We demonstrated with the combination of physical characterisation and manipulations of the EVL, utilising a variety of biophysical tools and microscopy, the mechanistic role of keratin in tissue spreading. Generating novel genetic morphants and mutants, we probe the effect that the loss of the keratin network has on the physiology of the epithelium and the developing embryo. We show that the changing organisation of the keratin network is important for changing EVL physical properties as the stress imposed on the EVL increases during epiboly. By modelling the epithelium, we study how the mechanical heterogeneity in an epithelium can feed back into a mechanical loop to the maturation of the keratin network and hence affect the mechanics of the epithelium. However, unlike what would be predicted by the effect of intermediate filaments in acting as a security belt and increasing the resistance of the epithelium, we observe that loss of keratin leads to a delay in the EVL movement. Using both local aspirations of the YSL and EVL ablations, we demonstrate the mechanistic facilitation of actin mechanosensation in a keratin-dependent manner. Furthermore, using chemical inhibitors of microtubule polymerisation, we provide insight into the mechanisms underlying the organisation and distribution of keratin. Interestingly, the phenotype observed upon this loss of microtubules shows that keratins interact with the nucleus through microtubular interactions. Together with these diverse observations, we describe the mechanosensory feedback between resilience and that is critical for uniform and robust spreading of the epithelium.}, author = {Naik, Suyash}, isbn = {978-3-99078-069-5}, issn = {2663-337X}, pages = {105}, publisher = {Institute of Science and Technology Austria}, title = {{Keratins act as global coordinators of tissue spreading through mechanosensitive feedback}}, doi = {10.15479/AT-ISTA-20441}, year = {2025}, } @phdthesis{20485, author = {Misova, Michaela}, isbn = {978-3-99078-068-8}, issn = {2663-337X}, pages = {155}, publisher = {Institute of Science and Technology Austria}, title = {{Dissecting gap junction biology using the C. elegans nervous system}}, doi = {10.15479/AT-ISTA-20485}, year = {2025}, } @phdthesis{19853, abstract = {The internal dynamical properties of red giant stars have been explored extensively in recent years as a result of the increase in high precision data availability from the space missions Kepler and TESS (Transiting Exoplanet Survey Satellite), and in this exploration, it has been discovered that some of these stars are not behaving as expected. Red giants are stars that have evolved off of the main sequence after having completed fusing hydrogen into helium in their core. Observational data shows that the cores are rotating significantly slower than models can recreate consistently across evolutionary stages. This discrepancy has prompted investigation into the efficiency of angular momentum transport mechanisms and mixing processes including meridional circulation, shear instability, internal gravity waves, Tayler-Spruit dynamo, fossil magnetic fields etc., to explain this behavior. Analyzing seismic oscillations in stars, via asteroseismology, is a powerful tool as it is the only way in which the deep stellar interior can be probed and subsequently characterized; this is possible as global oscillations modulating the stellar surface are effected by internal processes. For red giants, p-modes (pressure modes; resonating through the entire star) and g-modes (gravity-modes; resonating in the radiative interior) couple to create mixed modes. These mixed modes give access to the otherwise hidden stellar interior as g-modes couple to p-modes, delivering information from the interior to the surface. Internal magnetic signatures have been observationally confirmed in red giant stars via asteroseismology and characterized in two ways. One being that dipole mixed modes with ℓ = 1 will display a global asymmetric frequency shift of its azimuthal components; where the m = 0 and m = ±1 components of the ℓ = 1 dipole mode will be shifted by two different power laws, respectively. And the other being a reduced visibility of dipole mixed mode amplitudes in the power spectra, where stars presenting with this feature are denoted as suppressed. Several studies of the suppressed dipole mixed mode amplitudes have been carried out, but thus far, no dedicated studies of the asymmetric frequency shifts of suppressed red giants have been conducted; one reason being that the asymmetric frequency shifts cannot be characterized when the dipole mixed mode amplitudes are severely reduced in many of the suppressed stars. Sincefullysuppressedstarsdonothavedetectablemixed-modestoevaluate, partiallysuppressed stars, that is, red giant stars presenting with suppressed dipole mixed modes in select parts of their power spectra rather than across the entire spectra, will be the subject of this study as the respective mode amplitudes are still visible at high frequencies. As such, this study will search for asymmetric frequency shifts on the dipole mixed modes of partially suppressed red giant stars; the aim here is to investigate if both mode suppression and magnetic shifting of dipole mixed modes occur simultaneously. Thisstudywillbeconductedbycreatingapipelinetoestimatepriorsofasteroseismicparameters, use the priors to model the power spectra with the stellar modeling code sloscillations_ISTA, and perform a Bayesian fit of the parameters with the simulated data on the star KIC 6975038, a target with partially suppressed dipolar mode amplitudes identified in the literature, to fit its magnetic parameters. I present a novel method to model the stellar power spectra of partially suppressed red giants by application of a sigmoid profile to the ℓ= 1 dipolar mode component of the spectra. With the results of this study I aim at constraining the cause of this partial dipole mode amplitude suppression, allowing for more detailed studies regarding their astrophysical nature. Furthermore, the long term hope for the method used in this study will be to expand the sample of partially suppressed red giants and fit their asteroseismic parameters accordingly.}, author = {Smith, Kanah}, issn = {2791-4585}, keywords = {asteroseismology, stellar physics, red giant, magnetism, suppressed}, pages = {38}, publisher = {Institute of Science and Technology Austria}, title = {{Exploring internal magnetism in partially suppressed red giant stars}}, doi = {10.15479/AT-ISTA-19853}, year = {2025}, } @phdthesis{20551, abstract = {The space of codimension-2 shapes, such as curves in 3D and surfaces in 4D, is an infinite-dimensional manifold. This thesis explores geometric structures and dynamics on this space, with emphasis on their implications for physics, particularly hydrodynamics. Our investigation ranges from theoretical studies of infinite-dimensional symplectic and prequantum geometry to numerical computation of the time evolution of shapes. The thesis presents four main contributions. In the first part, we introduce implicit representations of codimension-2 shapes using a class of complex-valued functions, and prove that the space of these implicit representations forms a prequantum bundle over the codimension-2 shape space. This reveals a new geometric interpretation of the canonical symplectic structure on the codimension-2 shape space. In the second part, we use implicit representations to develop a simulation method for the dynamics of space curves. To handle chaotic systems such as vortex filaments in hydrodynamics, we exploit the infinite degrees of freedom, hidden in both the configuration and dynamics of implicit representations. In the third part, we introduce new symplectic structures on the space of space curves, which generalize the only previously known symplectic structure on this space, allowing for new Hamiltonian dynamics of space curves. In the fourth part, we apply a symplectic viewpoint to a differential geometric problem with practical applications. We derive a new area formula for spherical polygons via prequantization. }, author = {Ishida, Sadashige}, isbn = {978-3-99078-070-1}, issn = {2663-337X}, pages = {141}, publisher = {Institute of Science and Technology Austria}, title = {{Symplectic-prequantum structures and dynamics on the codimension-2 shape space}}, doi = {10.15479/AT-ISTA-20551}, year = {2025}, } @unpublished{20580, abstract = {This paper explores the geometry of the space of codimension-2 submanifolds. We implicitly represent these submanifolds by a class of complex-valued functions. This reveals a prequantum bundle structure over the space of submanifolds, equipped with the well-known Marsden-Weinstein symplectic structure. This bundle allows a new physical interpretation of the Marsden-Weinstein structure as the curvature of a connection form, which measures the average of volumes swept by the deformation of the S^1-family of hypersurfaces, defined as the phases of a complex function implicitly representing a submanifold.}, author = {Chern, Albert and Ishida, Sadashige}, booktitle = {arXiv}, title = {{Implicit representations of codimension-2 submanifolds and their prequantum structure}}, doi = {10.48550/ARXIV.2507.11727}, year = {2025}, } @phdthesis{20357, author = {Ruzickova, Natalia}, isbn = {978-3-99078-066-4}, issn = {2663-337X}, keywords = {gene regulation, networks, omnigenic model, pancreas, collective behaviour}, pages = {160}, publisher = {Institute of Science and Technology Austria}, title = {{Effect propagation in biological networks}}, doi = {10.15479/AT-ISTA-20357}, year = {2025}, } @phdthesis{20147, abstract = {Quantitative properties offer a framework for specifying and verifying system behaviors beyond the traditional boolean perspective. For example, while a boolean property may specify whether a server eventually grants every request it receives, a quantitative one may map each server execution to its average response time. This quantitative view is relatively well-studied in the context of static verification. However, although such properties often appear in practice as performance or robustness measures in a dynamic verification context, a general theoretical framework for their analysis and classification from a monitoring perspective is still missing. In this thesis, we aim to develop such a framework that takes resource-precision tradeoffs of monitors as a central consideration. We present the first theory of monitorability for quantitative properties where monitors can be naturally approximate and compared regarding their precision and resource use. In particular, we show that additional monitor resources such as registers or states lead to strictly better approximations for some properties. To enable such analyses in a machine-model independent way, we describe an abstract notion of monitors that can be instantiated with concrete models of monitors. Within this framework, we study how abstract monitors behave and identify classes of properties amenable to approximate monitoring with resource-precision considerations. We then extend the boolean safety-liveness dichotomy and safety-progress hierarchy to the quantitative setting with a monitoring perspective. In particular, we prove that every property is the pointwise minimum of a safety property and a liveness property, and properties that are both safe and co-safe can be approximately monitored arbitrarily precisely using only finitely many states. We also study the classes of quantitative properties definable by finite-state quantitative automata and provide algorithms for deciding their safety or liveness as well as their safety-liveness decompositions. Finally, we present the first general-purpose tool for automating the analysis, verification, and monitoring of quantitative automata. -------------------------------------------------------------------------------------------------------------------------------------------------------------- In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of ISTA's products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to http://www.ieee.org/publications_standards/publications/rights/rights_link.html to learn how to obtain a License from RightsLink. }, author = {Sarac, Naci E}, issn = {2663-337X}, pages = {149}, publisher = {Institute of Science and Technology Austria}, title = {{A monitoring-oriented theory and classification of quantitative specifications}}, doi = {10.15479/AT-ISTA-20147}, year = {2025}, } @article{20342, abstract = {Safety and liveness stand as fundamental concepts in formal languages, playing a key role in verification. The safety-liveness classification of boolean properties characterizes whether a given property can be falsified by observing a finite prefix of an infinite computation trace (always for safety, never for liveness). In the quantitative setting, properties are arbitrary functions from infinite words to partially-ordered domains. Extending this paradigm to the quantitative domain, where properties are arbitrary functions mapping infinite words to partially-ordered domains, we introduce and study the notions of quantitative safety and liveness. First, we formally define quantitative safety and liveness, and prove that our definitions induce conservative quantitative generalizations of both the safety-progress hierarchy and the safety-liveness decomposition of boolean properties. Consequently, like their boolean counterparts, quantitative properties can be min-decomposed into safety and liveness parts, or alternatively, max-decomposed into co-safety and co-liveness parts. We further establish a connection between quantitative safety and topological continuity and provide alternative characterizations of quantitative safety and liveness in terms of their boolean analogs. Second, we instantiate our framework with the specific classes of quantitative properties expressed by automata. These quantitative automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totally-ordered domain of real numbers. For all common value functions, we provide a procedure for deciding whether a given automaton is safe or live, we show how to construct its safety closure, and we present a min-decomposition into safe and live automata.}, author = {Boker, Udi and Henzinger, Thomas A and Mazzocchi, Nicolas Adrien and Sarac, Naci E}, issn = {1860-5974}, journal = {Logical Methods in Computer Science}, number = {2}, publisher = {EPI Sciences}, title = {{ Safety and liveness of quantitative properties and automata}}, doi = {10.46298/lmcs-21(2:2)2025}, volume = {21}, year = {2025}, } @phdthesis{20741, abstract = {Life on Earth emerged when biomacromolecules were membrane-enclosed in a confined space where many essential chemical reactions were more likely to happen and thereby accelerate evolution. These kinds of membranes separated internal reactions from the outside chaos while staying flexible so that those primordial cells can move, adopt their shape and, most importantly, propagate. Such membrane plasticity still remains a defining feature of all modern cell types. This remarkable ability to change their shape is most prominently observed during their propagation (i.e., cell division). Throughout division, a cell undergoes drastic change in its shape, usually at the middle of the cell, pulling the two opposite membrane sides inward, closer to each other, and, finally, culminating in pinching off to separate the cell into two daughter cells. To achieve this, a cell needs to employ a protein machinery, usually termed divisome, that can coordinate all necessary intracellular processes with membrane remodelling and synthesis of other extracellular structures that decorate a cell. The focus of this dissertation is a membrane-remodelling FtsZ system that is present across all domains of life. FtsZ forms filaments that further self-organize into ring-like structures at the cell septum and together with other division proteins perform cell envelope synthesis and constriction. However, there are still knowledge gaps in our mechanistic understanding of division in both archaea and bacteria. My work presented in this dissertation centres around a simple yet not well understood question: How is the divisome positioned correctly at the mid-cell? To achieve the proper positioning, the divisome needs to (i) be recruited to the mid-cell and (ii) localized orthogonally to the long cell axis. I tackle these processes in two different systems by applying an in vitro biochemical bottom-up reconstitution approach. I use purified components of Haloferax volcanii and Escherichia coli divisome to explore how divisome is recruited to the mid-cell in archaea and how the Z-ring positions orthogonally to the long cell axis in bacteria, respectively. Firstly, I collaborate with archaeal cell and structural biologists to explore the assembly of early division proteins in two FtsZ-containing archaeon H. volcanii, a standard model system for understudied archaeal organisms. I particularly address the hierarchy of interactions that allow a tripartite complex formation (SepF-CdpB1-CdpB2) and how the hierarchy of interactions ultimately leads to the recruitment of FtsZ filaments to the septum. This part of work has been published in (Nußbaum et al., 2024). In collaboration with evolutionary biologists, I shed light on ancient features that archaeal divisome has retained to this day and also speculate on a property that it might have lost during the course of evolution. Next, I switch my attention to E. coli divisome. Particularly, I address the FtsZ’s intrinsic biophysical property that drives the Z-ring diameter, and thereby the perpendicular orientation of the Z-ring to the long cell axis based on suggested membrane curvature sensing mechanism (Vanhille-Campos et al., 2024). This property allows formation of different Z-ring diameters that match the variety of cell diameters present in prokaryotes. The results showcase that the distribution of charged amino acids in the intrinsically disordered linker at the C-terminus (CTL) of FtsZ is the major determining factor of Z-ring diameter with inter-CTL interactions as an underlying mechanism. Finally, I thoroughly explain the methodology I used to address the abovementioned projects, and I finish with a discussion on how early archaeal divisome assembly and curvature sensing mechanism in bacteria, at first sight unrelated topics, are interconnected and important groundwork for both fundamental and translational research. }, author = {Kojic, Marko}, isbn = {978-3-99078-073-2}, issn = {2663-337X}, publisher = {Institute of Science and Technology Austria}, title = {{Towards understanding the assembly mechanisms of the Z-ring in Archaea and Bacteria}}, doi = {10.15479/AT-ISTA-20741}, year = {2025}, } @phdthesis{19903, abstract = {Cooperation, that is, one person paying a cost for another's benefit, is a fundamental principle without which no form of society could exist. The extent to which humans cooperate with each other is also an essential feature that differentiates them from other animals. Cooperation occurs even in the absence of altruistic motivations, when it is selfishly incentivised by the expectation of a future reward. For example, many economic interactions are well described that way. This kind of cooperation requires that people exhibit reciprocal behaviour that acts as a mechanism that rewards cooperation. With game-theoretic models, it is possible to formally study potential such mechanisms and under what conditions they can exist. This thesis contributes to this effort by analysing recently introduced models of cooperation that advance on previous work by taking into account the potential for pre-existing inequality among cooperating individuals as well as the different forms that reciprocity can take. Individuals may differ both intrinsically, in their abilities, as well as extrinsically, in the amount of resources they have available. Allowing for such differences in a model of cooperation helps to understand how inequality affects the potential for, and outcomes of, cooperation among unequals. In this thesis, it is shown that in the presence of intrinsic inequality, a similar unequal distribution of resources can increase the potential for cooperation. This effect is stronger the smaller the group is in which cooperation takes place. It is also shown that under particular assumptions, if the unequal members of a group vary the size of their contributions to a cooperative effort over time, they can thereby increase their efficiency and improve the collective outcome. Cooperative behaviour in a two-person interaction can be rewarded either by direct reciprocation whenever the same two people interact again, or indirectly by a third party who observed the interaction. In the latter case of indirect reciprocity, individuals are proximally rewarded by a good reputation, which ultimately translates to being rewarded with cooperative behaviour by others. This mechanism can enable selfishly motivated cooperation even in circumstances where individuals are unlikely to meet again, akin to how money facilitates trade. While these two forms of reciprocity have mostly been studied in isolation, this thesis analyses both direct and indirect reciprocity in a general model in order to compare their relative effectiveness under different circumstances. The contribution of this thesis is an extension of previous work regarding a specific kind of interaction, whose parameters allow for convenient mathematical analysis, to the most general set of possible interactions.}, author = {Hübner, Valentin}, issn = {2663-337X}, pages = {157}, publisher = {Institute of Science and Technology Austria}, title = {{Reciprocity and inequality in social dilemmas}}, doi = {10.15479/AT-ISTA-19903}, year = {2025}, } @phdthesis{20607, author = {Mondal, Soumyadip}, isbn = {978-3-99078-071-8}, issn = {2663-337X}, pages = {71}, publisher = {Institute of Science and Technology Austria}, title = {{Oxygen and sulfur redox : Conversion kinetics and phase equilibria}}, doi = {10.15479/AT-ISTA-20607}, year = {2025}, } @phdthesis{20449, author = {Bett, Vincent K}, issn = {2663-337X}, pages = {114}, publisher = {Institute of Science and Technology Austria}, title = {{Evolution and regulation of the Z chromosome}}, doi = {10.15479/AT-ISTA-20449}, year = {2025}, } @phdthesis{20777, author = {Zivadinovic, Predrag}, issn = {2663-337X}, pages = {104}, publisher = {Institute of Science and Technology Austria}, title = {{Scale-free activity as a basis for spatial learning and memory in the brain}}, doi = {10.15479/AT-ISTA-20777}, year = {2025}, } @phdthesis{20234, abstract = {Game Theory is the mathematical formalization of social dynamics - systems where agents interact over time and the evolution of the state of the system depends on the decisions of every player. This thesis takes the perspective of a single player and focuses on what they can guarantee in the worst case over the behavior of other players. In other words, we consider that the objective of every other player in the game is exactly the opposite to the player. We focus on sustained interactions over time, where the players repeatedly obtain quantitative rewards over time, and they are interested in maximizing their long-term performance. Formally, this thesis focuses on zero-sum games with the liminf average objective. Two fundamental questions that Game Theory aims to answer are the following. 1. How much can a player guarantee to obtain after the interaction? 2. How to act in order to obtain the previously mentioned guarantee? These questions are formalized by the concepts of "value" and "optimal strategies". We study their properties on games that exhibit one or more of the following properties. 1. Partial Observation: the players can not perfectly observe the current state of the system during the game. We consider the model of (finite) Partially Observable Markov Decision Processes and prove that finite-memory strategies are sufficient to approximately guarantee the value. 2. Perturbed Description: the formal description of the game is perturbed by a small parameter. We consider the model of (finite) Perturbed Matrix Games, and provide algorithms to check various robustness properties and to compute the parameterized value and optimal strategies. 3. Stochastic Transitions: the actions of the players determine the behavior of the evolution of the system, described as a probability distribution over the next state. We consider the model of (finite) Perturbed Stochastic Games and provide formulas for the marginal value. 4. Infinite States: the system can be in infinitely many states. We consider the model of Random Dynamic Games on a class of infinite graphs, prove the existence of the value, and quantify the concentration of finite-horizon values.}, author = {Saona Urmeneta, Raimundo J}, issn = {2663-337X}, pages = {125}, publisher = {Institute of Science and Technology Austria}, title = {{Robustness of solutions in game theory : Values and strategies in partially observable, perturbed, stochastic, and infinite games}}, doi = {10.15479/AT-ISTA-20234}, year = {2025}, } @article{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}, }