@inproceedings{17098,
  abstract     = {Turn-based discounted-sum games are two-player zero-sum games played on finite directed graphs. The vertices of the graph are partitioned between player 1 and player 2. Plays are infinite walks on the graph where the next vertex is decided by a player that owns the current vertex. Each edge is assigned an integer weight and the payoff of a play is the discounted-sum of the weights of the play. The goal of player 1 is to maximize the discounted-sum payoff against the adversarial player 2. These games lie in NP ∩ coNP and are among the rare combinatorial problems that belong to this complexity class and the existence of a polynomial-time algorithm is a major open question. Since breaking the general exponential barrier has been a challenging problem, faster parameterized algorithms have been considered. If the discount factor is expressed in unary, then discounted-sum games can be solved in polynomial time. However, if the discount factor is arbitrary (or expressed in binary), but the weights are in unary, none of the existing approaches yield a sub-exponential bound. Our main result is a new analysis technique for a classical algorithm (namely, the strategy iteration algorithm) that present a new runtime bound which is [EQUATION] for game graphs with n vertices and absolute weights of at most W. In particular, our result yields a deterministic sub-exponential bound for games with weights that are constant or represented in unary.},
  author       = {Asadi, Ali and Chatterjee, Krishnendu and Svoboda, Jakub and Saona Urmeneta, Raimundo J},
  booktitle    = {39th Annual ACM/IEEE Symposium on Logic in Computer Science},
  isbn         = {9798400706608},
  issn         = {1043-6871},
  location     = {Tallinn, Estonia},
  publisher    = {Association for Computing Machinery},
  title        = {{Deterministic sub-exponential algorithm for discounted-sum games with unary weights}},
  doi          = {10.1145/3661814.3662080},
  year         = {2024},
}

@inproceedings{19510,
  abstract     = {We propose a new variant of the Adam optimizer [Kingma and Ba, 2014] called
MICROADAM that specifically minimizes memory overheads, while maintaining
theoretical convergence guarantees. We achieve this by compressing the gradient
information before it is fed into the optimizer state, thereby reducing its memory
footprint significantly. We control the resulting compression error via a novel
instance of the classical error feedback mechanism from distributed optimization [Seide et al., 2014, Alistarh et al., 2018, Karimireddy et al., 2019] in which
the error correction information is itself compressed to allow for practical memory
gains. We prove that the resulting approach maintains theoretical convergence
guarantees competitive to those of AMSGrad, while providing good practical performance. Specifically, we show that MICROADAM can be implemented efficiently
on GPUs: on both million-scale (BERT) and billion-scale (LLaMA) models, MICROADAM provides practical convergence competitive to that of the uncompressed
Adam baseline, with lower memory usage and similar running time. Our code is
available at https://github.com/IST-DASLab/MicroAdam.},
  author       = {Modoranu, Ionut-Vlad and Safaryan, Mher and Malinovsky, Grigory and Kurtic, Eldar and Robert, Thomas and Richtárik, Peter and Alistarh, Dan-Adrian},
  booktitle    = {38th Conference on Neural Information Processing Systems},
  issn         = {1049-5258},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{MICROADAM: Accurate adaptive optimization with low space overhead and provable convergence}},
  doi          = {10.52202/079017-0001},
  volume       = {37},
  year         = {2024},
}

@article{18654,
  abstract     = {We compute the rotational anisotropy of the free energy of 𝛼−RuCl3 in an external magnetic field. This quantity, known as the magnetotropic susceptibility, 𝑘, relates to the second derivative of the free energy with respect to the angle of rotation. We have used approximation-free, auxiliary-field quantum Monte Carlo simulations for a realistic model of 𝛼−RuCl3 and optimized the path integral to alleviate the negative sign problem. This allows us to reach temperatures down to 30K—an energy scale below the dominant Kitaev coupling. We demonstrate that the magnetotropic spin susceptibility in this model of 𝛼−RuCl3 displays scaling behavior 𝑘=𝑇⁢𝑓⁡(𝐵/𝑇) at high temperatures. Once the uniform susceptibility departs from the Curie law (i.e., at the energy scale of the exchange interactions), it appears to transition to an emergent scalinglike behavior, characterized by a different function 𝑓 at lower temperatures, stemming from the locality of torque fluctuations. We observe a remarkable numerical match between experiment and simulations and we also find qualitative agreement with the pure Kitaev model. In comparison, for the XXZ Heisenberg Hamiltonian, the scaling 𝑘=𝑇⁢𝑓⁡(𝐵/𝑇) breaks down at a temperature scale where the uniform spin susceptibility deviates from the Curie law and never reemerges at low temperatures.},
  author       = {Sato, Toshihiro and Ramshaw, B. J. and Modic, Kimberly A and Assaad, Fakher F.},
  issn         = {2469-9969},
  journal      = {Physical Review B},
  number       = {20},
  publisher    = {American Physical Society},
  title        = {{Scale-invariant magnetic anisotropy in α-RuCl3: A quantum Monte Carlo study}},
  doi          = {10.1103/PhysRevB.110.L201114},
  volume       = {110},
  year         = {2024},
}

@inproceedings{19511,
  abstract     = {We introduce QuaRot, a new Quantization scheme based on Rotations, which is able to quantize LLMs end-to-end, including all weights, activations, and KV cache in 4 bits. QuaRot rotates LLMs in a way that removes outliers from the hidden state without changing the output, making quantization easier. This computational invariance is applied to the hidden state (residual) of the LLM, as well as to the activations of the feed-forward components, aspects of the attention mechanism, and to the KV cache. The result is a quantized model where all matrix multiplications are performed in 4 bits, without any channels identified for retention in higher precision. Our 4-bit quantized LLAMA2-70B model has losses of at most 0.47 WikiText-2 perplexity and retains 99% of the zero-shot performance. We also show that QuaRot can provide lossless 6 and 8 bit LLAMA-2 models without any calibration data using round-to-nearest quantization. Code is available at github.com/spcl/QuaRot.},
  author       = {Ashkboos, Saleh and Mohtashami, Amirkeivan and Croci, Maximilian L. and Li, Bo and Cameron, Pashmina and Jaggi, Martin and Alistarh, Dan-Adrian and Hoefler, Torsten and Hensman, James},
  booktitle    = {38th Conference on Neural Information Processing Systems},
  issn         = {1049-5258},
  location     = {Vancouver, Canada},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{QuaRot: Outlier-free 4-bit inference in rotated LLMs}},
  doi          = {10.52202/079017-3180},
  volume       = {37},
  year         = {2024},
}

@article{15003,
  abstract     = {Magnetic frustration allows to access novel and intriguing properties of magnetic systems and has been explored mainly in planar triangular-like arrays of magnetic ions. In this work, we describe the phosphide Ce6Ni6P17, where the Ce+3 ions accommodate in a body-centered cubic lattice of Ce6 regular octahedra. From measurements of magnetization, specific heat, and resistivity, we determine a rich phase diagram as a function of temperature and magnetic field in which different magnetic phases are found. Besides clear evidence of magnetic frustration is obtained from entropy analysis. At zero field, a second-order antiferromagnetic transition occurs at TN1≈1 K followed by a first-order transition at TN2≈0.45 K. With magnetic field new magnetic phases appear, including a weakly first-order transition which ends in a classical critical point and a third magnetic phase. We also study the exact solution of the spin-1/2 Heisenberg model in an octahedron which allows us a qualitative understanding of the phase diagram and compare with the experimental results.},
  author       = {Franco, D. G. and Avalos, R. and Hafner, D. and Modic, Kimberly A and Prots, Yu and Stockert, O. and Hoser, A. and Moll, P. J.W. and Brando, M. and Aligia, A. A. and Geibel, C.},
  issn         = {2469-9969},
  journal      = {Physical Review B},
  number       = {5},
  publisher    = {American Physical Society},
  title        = {{Frustrated magnetism in octahedra-based Ce6 Ni6 P17}},
  doi          = {10.1103/PhysRevB.109.054405},
  volume       = {109},
  year         = {2024},
}

@article{18926,
  abstract     = {We study weak solutions to mean curvature flow satisfying Young’s angle condition for general contact angles α ∈ (0, π). First, we construct BV solutions by using the Allen-Cahn approximation with boundary contact energy as proposed by Owen and Sternberg. Second, we prove the weak-strong uniqueness and stability for this solution concept. The main ingredient for both results is a relative energy, which can also be interpreted as a tilt excess. },
  author       = {Hensel, Sebastian and Laux, Tim},
  issn         = {0022-2518},
  journal      = {Indiana University Mathematics Journal},
  number       = {1},
  pages        = {111--148},
  publisher    = {Indiana University Mathematics Journal},
  title        = {{BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness}},
  doi          = {10.1512/iumj.2024.73.9701},
  volume       = {73},
  year         = {2024},
}

@unpublished{17101,
  abstract     = {This paper considers a class of two-player zero-sum games on directed graphs whose vertices are equipped with random payoffs of bounded support known by both players.
Starting from a fixed vertex, players take turns to move a token along the edges of the graph.
On the one hand, for acyclic directed graphs of bounded degree and sub-exponential expansion, we show that the value of the game converges almost surely to a constant at an exponential rate dominated in terms of the expansion.
On the other hand, for the infinite d-ary tree that does not fall into the previous class of graphs, we show convergence at a double-exponential rate in terms of the expansion.},
  author       = {Attia, Luc and Lichev, Lyuben and Mitsche, Dieter and Saona Urmeneta, Raimundo J and Ziliotto, Bruno},
  booktitle    = {arXiv},
  title        = {{Zero-sum random games on directed graphs}},
  doi          = {10.48550/arXiv.2401.16252},
  year         = {2024},
}

@inproceedings{15006,
  abstract     = {Graphical games are a useful framework for modeling the interactions of (selfish) agents who are connected via an underlying topology and whose behaviors influence each other. They have wide applications ranging from computer science to economics and biology. Yet, even though an agent’s payoff only depends on the actions of their direct neighbors in graphical games, computing the Nash equilibria and making statements about the convergence time of "natural" local dynamics in particular can be highly challenging. In this work, we present a novel approach for classifying complexity of Nash equilibria in graphical games by establishing a connection to local graph algorithms, a subfield of distributed computing. In particular, we make the observation that the equilibria of graphical games are equivalent to locally verifiable labelings (LVL) in graphs; vertex labelings which are verifiable with constant-round local algorithms. This connection allows us to derive novel lower bounds on the convergence time to equilibrium of best-response dynamics in graphical games. Since we establish that distributed convergence can sometimes be provably slow, we also introduce and give bounds on an intuitive notion of "time-constrained" inefficiency of best responses. We exemplify how our results can be used in the implementation of mechanisms that ensure convergence of best responses to a Nash equilibrium. Our results thus also give insight into the convergence of strategy-proof algorithms for graphical games, which is still not well understood.},
  author       = {Hirvonen, Juho and Schmid, Laura and Chatterjee, Krishnendu and Schmid, Stefan},
  booktitle    = {27th International Conference on Principles of Distributed Systems},
  isbn         = {9783959773089},
  issn         = {1868-8969},
  location     = {Tokyo, Japan},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{On the convergence time in graphical games: A locality-sensitive approach}},
  doi          = {10.4230/LIPIcs.OPODIS.2023.11},
  volume       = {286},
  year         = {2024},
}

@inproceedings{17402,
  abstract     = {We present version 2.0 of the Partial Exploration Tool (PET), a tool for verification of probabilistic systems. We extend the previous version by adding support for stochastic games, based on a recent unified framework for sound value iteration algorithms. Thereby, PET2 is the first tool implementing a sound and efficient approach for solving stochastic games with objectives of the type reachability/safety and mean payoff. We complement this approach by developing and implementing a partial-exploration based variant for all three objectives. Our experimental evaluation shows that PET2 offers the most efficient partial-exploration based algorithm and is the most viable tool on SGs, even outperforming unsound tools.},
  author       = {Meggendorfer, Tobias and Weininger, Maximilian},
  booktitle    = {36th International Conference on Computer Aided Verification},
  isbn         = {9783031656323},
  issn         = {1611-3349},
  location     = {Montreal, Canada},
  pages        = {359--372},
  publisher    = {Springer Nature},
  title        = {{Playing games with your PET: Extending the Partial Exploration Tool to stochastic games}},
  doi          = {10.1007/978-3-031-65633-0_16},
  volume       = {14683},
  year         = {2024},
}

@article{17162,
  abstract     = {Cost analysis, also known as resource usage analysis, is the task of finding bounds on the total cost of a program and is a well-studied problem in static analysis. In this work, we consider two classical quantitative problems in cost analysis for probabilistic programs. The first problem is to find a bound on the expected total cost of the program. This is a natural measure for the resource usage of the program and can also be directly applied to average-case runtime analysis. The second problem asks for a tail bound, i.e. ‍given a threshold t the goal is to find a probability bound p such that ℙ[total cost ≥ t] ≤ p. Intuitively, given a threshold t on the resource, the problem is to find the likelihood that the total cost exceeds this threshold.
First, for expectation bounds, a major obstacle in previous works on cost analysis is that they can handle only non-negative costs or bounded variable updates. In contrast, we provide a new variant of the standard notion of cost martingales, that allows us to find expectation bounds for a class of programs with general positive or negative costs and no restriction on the variable updates. More specifically, our approach is applicable as long as there is a lower bound on the total cost incurred along every path.
Second, for tail bounds, all previous methods are limited to programs in which the expected total cost is finite. In contrast, we present a novel approach, based on a combination of our martingale-based method for expectation bounds with a quantitative safety analysis, to obtain a solution to the tail bound problem that is applicable even to programs with infinite expected cost. Specifically, this allows us to obtain runtime tail bounds for programs that do not terminate almost-surely.
In summary, we provide a novel combination of martingale-based cost analysis and quantitative safety analysis that is able to find expectation and tail cost bounds for probabilistic programs, without the restrictions of non-negative costs, bounded updates, or finiteness of the expected total cost. Finally, we provide experimental results showcasing that our approach can solve instances that were beyond the reach of previous methods.},
  author       = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Meggendorfer, Tobias and Zikelic, Dorde},
  issn         = {2475-1421},
  journal      = {Proceedings of the ACM on Programming Languages},
  number       = {OOPSLA1},
  publisher    = {Association for Computing Machinery},
  title        = {{Quantitative bounds on resource usage of probabilistic programs}},
  doi          = {10.1145/3649824},
  volume       = {8},
  year         = {2024},
}

@inproceedings{19512,
  abstract     = {Differential privacy with gradual expiration models the setting where data items
arrive in a stream and at a given time t the privacy loss guaranteed for a data item
seen at time (t − d) is εg(d), where g is a monotonically non-decreasing function.
We study the fundamental continual (binary) counting problem where each data
item consists of a bit, and the algorithm needs to output at each time step the sum of
all the bits streamed so far. For a stream of length T and privacy without expiration
continual counting is possible with maximum (over all time steps) additive error
O(log2
(T)/ε) and the best known lower bound is Ω(log(T)/ε); closing this gap
is a challenging open problem.
We show that the situation is very different for privacy with gradual expiration by
giving upper and lower bounds for a large set of expiration functions g. Specifically,
our algorithm achieves an additive error of O(log(T)/ε) for a large set of privacy
expiration functions. We also give a lower bound that shows that if C is the additive
error of any ε-DP algorithm for this problem, then the product of C and the privacy
expiration function after 2C steps must be Ω(log(T)/ε). Our algorithm matches
this lower bound as its additive error is O(log(T)/ε), even when g(2C) = O(1).
Our empirical evaluation shows that we achieve a slowly growing privacy loss
with significantly smaller empirical privacy loss for large values of d than a natural
baseline algorithm.},
  author       = {Andersson, Joel Daniel and Henzinger, Monika H and Pagh, Rasmus and Steiner, Teresa Anna and Upadhyay, Jalaj},
  booktitle    = {38th Conference on Neural Information Processing Systems},
  issn         = {1049-5258},
  location     = {Vancouver, Canada},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{Continual counting with gradual privacy expiration}},
  doi          = {10.52202/079017-0299},
  volume       = {37},
  year         = {2024},
}

@inproceedings{19515,
  abstract     = {Neural models learn data representations that lie on low-dimensional manifolds,
yet modeling the relation between these representational spaces is an ongoing challenge. By integrating spectral geometry principles into neural modeling, we show
that this problem can be better addressed in the functional domain, mitigating complexity, while enhancing interpretability and performances on downstream tasks.
To this end, we introduce a multi-purpose framework to the representation learning
community, which allows to: (i) compare different spaces in an interpretable way
and measure their intrinsic similarity; (ii) find correspondences between them, both
in unsupervised and weakly supervised settings, and (iii) to effectively transfer
representations between distinct spaces. We validate our framework on various
applications, ranging from stitching to retrieval tasks, and on multiple modalities,
demonstrating that Latent Functional Maps can serve as a swiss-army knife for
representation alignment},
  author       = {Fumero, Marco and Pegoraro, Marco and Maiorca, Valentino and Locatello, Francesco and Rodolà, Emanuele},
  booktitle    = {38th Conference on Neural Information Processing Systems},
  issn         = {1049-5258},
  location     = {Vancouver, Canada},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{Latent functional maps: A spectral framework for representation alignment}},
  doi          = {10.52202/079017-2115},
  volume       = {37},
  year         = {2024},
}

@misc{23140,
  abstract     = {The artefact for the OOPSLA 2024 paper "Quantitative Bounds on Resource Usage of Probabilistic Programs".

},
  author       = {  Žikelić, Đorđe},
  publisher    = {Zenodo},
  title        = {{Artefact for: Quantitative Bounds on Resource Usage of Probabilistic Programs}},
  doi          = {10.5281/zenodo.10457565},
  year         = {2024},
}

@article{15083,
  abstract     = {Direct reciprocity is a powerful mechanism for cooperation in social dilemmas. The very logic of reciprocity, however, seems to require that individuals are symmetric, and that everyone has the same means to influence each others’ payoffs. Yet in many applications, individuals are asymmetric. Herein, we study the effect of asymmetry in linear public good games. Individuals may differ in their endowments (their ability to contribute to a public good) and in their productivities (how effective their contributions are). Given the individuals’ productivities, we ask which allocation of endowments is optimal for cooperation. To this end, we consider two notions of optimality. The first notion focuses on the resilience of cooperation. The respective endowment distribution ensures that full cooperation is feasible even under the most adverse conditions. The second notion focuses on efficiency. The corresponding endowment distribution maximizes group welfare. Using analytical methods, we fully characterize these two endowment distributions. This analysis reveals that both optimality notions favor some endowment inequality: More productive players ought to get higher endowments. Yet the two notions disagree on how unequal endowments are supposed to be. A focus on resilience results in less inequality. With additional simulations, we show that the optimal endowment allocation needs to account for both the resilience and the efficiency of cooperation.},
  author       = {Hübner, Valentin and Staab, Manuel and Hilbe, Christian and Chatterjee, Krishnendu and Kleshnina, Maria},
  issn         = {1091-6490},
  journal      = {Proceedings of the National Academy of Sciences of the United States of America},
  number       = {10},
  publisher    = {National Academy of Sciences},
  title        = {{Efficiency and resilience of cooperation in asymmetric social dilemmas}},
  doi          = {10.1073/pnas.2315558121},
  volume       = {121},
  year         = {2024},
}

@article{15297,
  abstract     = {Populations evolve by accumulating advantageous mutations. Every population has some spatial structure that can be modeled by an underlying network. The network then influences the probability that new advantageous mutations fixate. Amplifiers of selection are networks that increase the fixation probability of advantageous mutants, as compared to the unstructured fully-connected network. Whether or not a network is an amplifier depends on the choice of the random process that governs the evolutionary dynamics. Two popular choices are Moran process with Birth-death updating and Moran process with death-Birth updating. Interestingly, while some networks are amplifiers under Birth-death updating and other networks are amplifiers under death-Birth updating, so far no spatial structures have been found that function as an amplifier under both types of updating simultaneously. In this work, we identify networks that act as amplifiers of selection under both versions of the Moran process. The amplifiers are robust, modular, and increase fixation probability for any mutant fitness advantage in a range r ∈ (1, 1.2). To complement this positive result, we also prove that for certain quantities closely related to fixation probability, it is impossible to improve them simultaneously for both versions of the Moran process. Together, our results highlight how the two versions of the Moran process differ and what they have in common.},
  author       = {Svoboda, Jakub and Joshi, Soham Shrikant and Tkadlec, Josef and Chatterjee, Krishnendu},
  issn         = {1553-7358},
  journal      = {PLoS Computational Biology},
  number       = {3},
  publisher    = {Public Library of Science},
  title        = {{Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating}},
  doi          = {10.1371/journal.pcbi.1012008},
  volume       = {20},
  year         = {2024},
}

@misc{15108,
  abstract     = {in the research article "Efficiency and resilience of cooperation in asymmetric social dilemmas" (by Valentin Hübner, Manuel Staab, Christian Hilbe, Krishnendu Chatterjee, and Maria Kleshnina).

We used different implementations for the case of two and three players, both described below.},
  author       = {Hübner, Valentin and Kleshnina, Maria},
  publisher    = {Zenodo},
  title        = {{Computer code for "Efficiency and resilience of cooperation in asymmetric social dilemmas"}},
  doi          = {10.5281/ZENODO.10639167},
  year         = {2024},
}

@inproceedings{18155,
  abstract     = {We study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). We first present novel sound and complete witnesses for LTL verification over imperative programs. Our witnesses are applicable to both verification (proving) and refutation (finding bugs) settings. We then consider LTL formulas in which atomic propositions can be polynomial constraints and turn our focus to polynomial arithmetic programs, i.e. programs in which every assignment and guard consists only of polynomial expressions. For this setting, we provide an efficient algorithm to automatically synthesize such LTL witnesses. Our synthesis procedure is both sound and semi-complete. Finally, we present experimental results demonstrating the effectiveness of our approach and that it can handle programs which were beyond the reach of previous state-of-the-art tools.},
  author       = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Goharshady, Ehsan and Karrabi, Mehrdad and Zikelic, Dorde},
  booktitle    = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
  isbn         = {9783031711619},
  issn         = {1611-3349},
  location     = {Milan, Italy},
  pages        = {600--619},
  publisher    = {Springer Nature},
  title        = {{Sound and complete witnesses for template-based verification of LTL properties on polynomial programs}},
  doi          = {10.1007/978-3-031-71162-6_31},
  volume       = {14933},
  year         = {2024},
}

@misc{22798,
  abstract     = {This repository contains the artifact of the paper titled "Sound and Complete Witnesses for Template-based Verification of LTL Properties on Polynomial Programs" accepted at FM 2024.

The task of verifying an LTL formula on a program can be reduced to verifying a Büchi specification on the product transition system. This tool takes a non-deterministic transition system together with a Büchi specification as input and based on user preferences tries to either (i) prove the existence of a run in the program that satisfies the Büchi condition or (ii) demonstrate that every run of the program satisfies the Büchi condition.
 
The tool is written in Java and works well with openjdk 11 on Ubuntu 22.04. Running all the experiments can take weeks to finish. We have provided a script for running the strongest configuration of our tool which solves most of the benchmarks and takes less than 48 hours. Detailed guidance is given in the readme file.},
  author       = {Chatterjee, Krishnendu and   Kafshdar Goharshady, Amir and Kafshdar Goharshady, Ehsan and Karrabi, Mehrdad and Žikelić, Ðorđe},
  publisher    = {Repository},
  title        = {{Data for Sound and Complete Witnesses for Template-based Verification of LTL Properties on Polynomial Programs}},
  doi          = {10.5281/zenodo.12518216},
  year         = {2024},
}

@article{18703,
  abstract     = {Spatial games provide a simple and elegant mathematical model to study the evolution of cooperation in networks. In spatial games, individuals reside in vertices, adopt simple strategies, and interact with neighbors to receive a payoff. Depending on their own and neighbors’ payoffs, individuals can change their strategy. The payoff is determined by the Prisoners’ Dilemma, a classical matrix game, where players cooperate or defect. While cooperation is the desired behavior, defection provides a higher payoff for a selfish individual. There are many theoretical and empirical studies related to the role of the network in the evolution of cooperation. However, the fundamental question of whether there exist networks that for low initial cooperation rate ensure a high chance of fixation, i.e., cooperation spreads across the whole population, has remained elusive for spatial games with strong selection. In this work, we answer this fundamental question in the affirmative by presenting network structures that ensure high fixation probability for cooperators in the strong selection regime. Besides, our structures have many desirable properties: (a) they ensure the spread of cooperation even for a low initial density of cooperation and high temptation of defection, (b) they have constant degrees, and (c) the number of steps, until cooperation spreads, is at most quadratic in the size of the network.},
  author       = {Svoboda, Jakub and Chatterjee, Krishnendu},
  issn         = {1091-6490},
  journal      = {Proceedings of the National Academy of Sciences of the United States of America},
  number       = {50},
  publisher    = {National Academy of Sciences},
  title        = {{Density amplifiers of cooperation for spatial games}},
  doi          = {10.1073/pnas.2405605121},
  volume       = {121},
  year         = {2024},
}

@article{18630,
  abstract     = {Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.},
  author       = {Chatterjee, Krishnendu and Doyen, Laurent},
  issn         = {1860-5974},
  journal      = {Logical Methods in Computer Science},
  number       = {4},
  pages        = {11:1--11:34},
  publisher    = {EPI Sciences},
  title        = {{Stochastic processes with expected stopping time}},
  doi          = {10.46298/lmcs-20(4:11)2024},
  volume       = {20},
  year         = {2024},
}