@inproceedings{8089, abstract = {We consider the classical problem of invariant generation for programs with polynomial assignments and focus on synthesizing invariants that are a conjunction of strict polynomial inequalities. We present a sound and semi-complete method based on positivstellensaetze, i.e. theorems in semi-algebraic geometry that characterize positive polynomials over a semi-algebraic set. On the theoretical side, the worst-case complexity of our approach is subexponential, whereas the worst-case complexity of the previous complete method (Kapur, ACA 2004) is doubly-exponential. Even when restricted to linear invariants, the best previous complexity for complete invariant generation is exponential (Colon et al, CAV 2003). On the practical side, we reduce the invariant generation problem to quadratic programming (QCLP), which is a classical optimization problem with many industrial solvers. We demonstrate the applicability of our approach by providing experimental results on several academic benchmarks. To the best of our knowledge, the only previous invariant generation method that provides completeness guarantees for invariants consisting of polynomial inequalities is (Kapur, ACA 2004), which relies on quantifier elimination and cannot even handle toy programs such as our running example.}, author = {Chatterjee, Krishnendu and Fu, Hongfei and Goharshady, Amir Kafshdar and Goharshady, Ehsan Kafshdar}, booktitle = {Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation}, isbn = {9781450376136}, location = {London, United Kingdom}, pages = {672--687}, publisher = {Association for Computing Machinery}, title = {{Polynomial invariant generation for non-deterministic recursive programs}}, doi = {10.1145/3385412.3385969}, year = {2020}, } @inproceedings{8193, abstract = {Multiple-environment Markov decision processes (MEMDPs) are MDPs equipped with not one, but multiple probabilistic transition functions, which represent the various possible unknown environments. While the previous research on MEMDPs focused on theoretical properties for long-run average payoff, we study them with discounted-sum payoff and focus on their practical advantages and applications. MEMDPs can be viewed as a special case of Partially observable and Mixed observability MDPs: the state of the system is perfectly observable, but not the environment. We show that the specific structure of MEMDPs allows for more efficient algorithmic analysis, in particular for faster belief updates. We demonstrate the applicability of MEMDPs in several domains. In particular, we formalize the sequential decision-making approach to contextual recommendation systems as MEMDPs and substantially improve over the previous MDP approach.}, author = {Chatterjee, Krishnendu and Chmelik, Martin and Karkhanis, Deep and Novotný, Petr and Royer, Amélie}, booktitle = {Proceedings of the 30th International Conference on Automated Planning and Scheduling}, issn = {23340843}, location = {Nancy, France}, pages = {48--56}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Multiple-environment Markov decision processes: Efficient analysis and applications}}, volume = {30}, year = {2020}, } @inproceedings{8272, abstract = {We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit both randomness as well as angelic and demonic non-determinism. Lexicographic order allows to consider multiple objectives with a strict preference order over the satisfaction of the objectives. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. We establish determinacy of such games and present strategy and computational complexity results. For strategy complexity, we show that lexicographically optimal strategies exist that are deterministic and memory is only required to remember the already satisfied and violated objectives. For a constant number of objectives, we show that the relevant decision problem is in NP∩coNP , matching the current known bound for single objectives; and in general the decision problem is PSPACE -hard and can be solved in NEXPTIME∩coNEXPTIME . We present an algorithm that computes the lexicographically optimal strategies via a reduction to computation of optimal strategies in a sequence of single-objectives games. We have implemented our algorithm and report experimental results on various case studies.}, author = {Chatterjee, Krishnendu and Katoen, Joost P and Weininger, Maximilian and Winkler, Tobias}, booktitle = {International Conference on Computer Aided Verification}, isbn = {9783030532901}, issn = {16113349}, pages = {398--420}, publisher = {Springer Nature}, title = {{Stochastic games with lexicographic reachability-safety objectives}}, doi = {10.1007/978-3-030-53291-8_21}, volume = {12225}, year = {2020}, } @inproceedings{8324, abstract = {The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected sensitivity. A previous approach develops a relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded. In this work, we consider probabilistic while loops where the number of iterations is not fixed, but randomized and depends on the initial input values. We present a sound approach for proving expected sensitivity of such programs. Our sound approach is martingale-based and can be automated through existing martingale-synthesis algorithms. Furthermore, our approach is compositional for sequential composition of while loops under a mild side condition. We demonstrate the effectiveness of our approach on several classical examples from Gambler's Ruin, stochastic hybrid systems and stochastic gradient descent. We also present experimental results showing that our automated approach can handle various probabilistic programs in the literature.}, author = {Wang, Peixin and Fu, Hongfei and Chatterjee, Krishnendu and Deng, Yuxin and Xu, Ming}, booktitle = {Proceedings of the ACM on Programming Languages}, issn = {2475-1421}, number = {POPL}, publisher = {ACM}, title = {{Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time}}, doi = {10.1145/3371093}, volume = {4}, year = {2020}, } @inproceedings{8533, abstract = {Game of Life is a simple and elegant model to study dynamical system over networks. The model consists of a graph where every vertex has one of two types, namely, dead or alive. A configuration is a mapping of the vertices to the types. An update rule describes how the type of a vertex is updated given the types of its neighbors. In every round, all vertices are updated synchronously, which leads to a configuration update. While in general, Game of Life allows a broad range of update rules, we focus on two simple families of update rules, namely, underpopulation and overpopulation, that model several interesting dynamics studied in the literature. In both settings, a dead vertex requires at least a desired number of live neighbors to become alive. For underpopulation (resp., overpopulation), a live vertex requires at least (resp. at most) a desired number of live neighbors to remain alive. We study the basic computation problems, e.g., configuration reachability, for these two families of rules. For underpopulation rules, we show that these problems can be solved in polynomial time, whereas for overpopulation rules they are PSPACE-complete.}, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Jecker, Ismael R and Svoboda, Jakub}, booktitle = {45th International Symposium on Mathematical Foundations of Computer Science}, isbn = {9783959771597}, issn = {18688969}, location = {Prague, Czech Republic}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Simplified game of life: Algorithms and complexity}}, doi = {10.4230/LIPIcs.MFCS.2020.22}, volume = {170}, year = {2020}, } @inproceedings{8534, abstract = {A regular language L of finite words is composite if there are regular languages L₁,L₂,…,L_t such that L = ⋂_{i = 1}^t L_i and the index (number of states in a minimal DFA) of every language L_i is strictly smaller than the index of L. Otherwise, L is prime. Primality of regular languages was introduced and studied in [O. Kupferman and J. Mosheiff, 2015], where the complexity of deciding the primality of the language of a given DFA was left open, with a doubly-exponential gap between the upper and lower bounds. We study primality for unary regular languages, namely regular languages with a singleton alphabet. A unary language corresponds to a subset of ℕ, making the study of unary prime languages closer to that of primality in number theory. We show that the setting of languages is richer. In particular, while every composite number is the product of two smaller numbers, the number t of languages necessary to decompose a composite unary language induces a strict hierarchy. In addition, a primality witness for a unary language L, namely a word that is not in L but is in all products of languages that contain L and have an index smaller than L’s, may be of exponential length. Still, we are able to characterize compositionality by structural properties of a DFA for L, leading to a LogSpace algorithm for primality checking of unary DFAs.}, author = {Jecker, Ismael R and Kupferman, Orna and Mazzocchi, Nicolas}, booktitle = {45th International Symposium on Mathematical Foundations of Computer Science}, isbn = {9783959771597}, issn = {18688969}, location = {Prague, Czech Republic}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Unary prime languages}}, doi = {10.4230/LIPIcs.MFCS.2020.51}, volume = {170}, year = {2020}, } @inproceedings{8600, abstract = {A vector addition system with states (VASS) consists of a finite set of states and counters. A transition changes the current state to the next state, and every counter is either incremented, or decremented, or left unchanged. A state and value for each counter is a configuration; and a computation is an infinite sequence of configurations with transitions between successive configurations. A probabilistic VASS consists of a VASS along with a probability distribution over the transitions for each state. Qualitative properties such as state and configuration reachability have been widely studied for VASS. In this work we consider multi-dimensional long-run average objectives for VASS and probabilistic VASS. For a counter, the cost of a configuration is the value of the counter; and the long-run average value of a computation for the counter is the long-run average of the costs of the configurations in the computation. The multi-dimensional long-run average problem given a VASS and a threshold value for each counter, asks whether there is a computation such that for each counter the long-run average value for the counter does not exceed the respective threshold. For probabilistic VASS, instead of the existence of a computation, we consider whether the expected long-run average value for each counter does not exceed the respective threshold. Our main results are as follows: we show that the multi-dimensional long-run average problem (a) is NP-complete for integer-valued VASS; (b) is undecidable for natural-valued VASS (i.e., nonnegative counters); and (c) can be solved in polynomial time for probabilistic integer-valued VASS, and probabilistic natural-valued VASS when all computations are non-terminating.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, booktitle = {31st International Conference on Concurrency Theory}, isbn = {9783959771603}, issn = {18688969}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Multi-dimensional long-run average problems for vector addition systems with states}}, doi = {10.4230/LIPIcs.CONCUR.2020.23}, volume = {171}, year = {2020}, } @article{8671, abstract = {We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory. We also demonstrate that one can induce a natural belief structure on one set, given a belief structure on another set, if the two sets are related by a partial monotone S-approximation space. }, author = {Shakiba, A. and Goharshady, Amir Kafshdar and Hooshmandasl, M.R. and Alambardar Meybodi, M.}, issn = {2008-9473}, journal = {Iranian Journal of Mathematical Sciences and Informatics}, number = {2}, pages = {117--128}, publisher = {Iranian Academic Center for Education, Culture and Research}, title = {{A note on belief structures and s-approximation spaces}}, doi = {10.29252/ijmsi.15.2.117}, volume = {15}, year = {2020}, } @inproceedings{8728, abstract = {Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there are many techniques for computing these objectives in general MCs/MDPs, they have not been thoroughly studied in terms of parameterized algorithms, particularly when treewidth is used as the parameter. This is in sharp contrast to qualitative objectives for MCs, MDPs and graph games, for which treewidth-based algorithms yield significant complexity improvements. In this work, we show that treewidth can also be used to obtain faster algorithms for the quantitative problems. For an MC with n states and m transitions, we show that each of the classical quantitative objectives can be computed in O((n+m)⋅t2) time, given a tree decomposition of the MC with width t. Our results also imply a bound of O(κ⋅(n+m)⋅t2) for each objective on MDPs, where κ is the number of strategy-iteration refinements required for the given input and objective. Finally, we make an experimental evaluation of our new algorithms on low-treewidth MCs and MDPs obtained from the DaCapo benchmark suite. Our experiments show that on low-treewidth MCs and MDPs, our algorithms outperform existing well-established methods by one or more orders of magnitude.}, author = {Asadi, Ali and Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Mohammadi, Kiarash and Pavlogiannis, Andreas}, booktitle = {Automated Technology for Verification and Analysis}, isbn = {9783030591519}, issn = {1611-3349}, location = {Hanoi, Vietnam}, pages = {253--270}, publisher = {Springer Nature}, title = {{Faster algorithms for quantitative analysis of MCs and MDPs with small treewidth}}, doi = {10.1007/978-3-030-59152-6_14}, volume = {12302}, year = {2020}, } @article{8767, abstract = {Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where “properly colored” means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.}, author = {Kaveh, Kamran and McAvoy, Alex and Chatterjee, Krishnendu and Nowak, Martin A.}, issn = {1553-7358}, journal = {PLOS Computational Biology}, keywords = {Ecology, Modelling and Simulation, Computational Theory and Mathematics, Genetics, Ecology, Evolution, Behavior and Systematics, Molecular Biology, Cellular and Molecular Neuroscience}, number = {11}, publisher = {Public Library of Science}, title = {{The Moran process on 2-chromatic graphs}}, doi = {10.1371/journal.pcbi.1008402}, volume = {16}, year = {2020}, } @article{8788, abstract = {We consider a real-time setting where an environment releases sequences of firm-deadline tasks, and an online scheduler chooses on-the-fly the ones to execute on a single processor so as to maximize cumulated utility. The competitive ratio is a well-known performance measure for the scheduler: it gives the worst-case ratio, among all possible choices for the environment, of the cumulated utility of the online scheduler versus an offline scheduler that knows these choices in advance. Traditionally, competitive analysis is performed by hand, while automated techniques are rare and only handle static environments with independent tasks. We present a quantitative-verification framework for precedence-aware competitive analysis, where task releases may depend on preceding scheduling choices, i.e., the environment can respond to scheduling decisions dynamically . We consider two general classes of precedences: 1) follower precedences force the release of a dependent task upon the completion of a set of precursor tasks, while and 2) pairing precedences modify the characteristics of a dependent task provided the completion of a set of precursor tasks. Precedences make competitive analysis challenging, as the online and offline schedulers operate on diverging sequences. We make a formal presentation of our framework, and use a GPU-based implementation to analyze ten well-known schedulers on precedence-based application examples taken from the existing literature: 1) a handshake protocol (HP); 2) network packet-switching; 3) query scheduling (QS); and 4) a sporadic-interrupt setting. Our experimental results show that precedences and task parameters can vary drastically the best scheduler. Our framework thus supports application designers in choosing the best scheduler among a given set automatically.}, author = {Pavlogiannis, Andreas and Schaumberger, Nico and Schmid, Ulrich and Chatterjee, Krishnendu}, issn = {19374151}, journal = {IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems}, number = {11}, pages = {3981--3992}, publisher = {IEEE}, title = {{Precedence-aware automated competitive analysis of real-time scheduling}}, doi = {10.1109/TCAD.2020.3012803}, volume = {39}, year = {2020}, } @article{8789, abstract = {Cooperation is a ubiquitous and beneficial behavioural trait despite being prone to exploitation by free-riders. Hence, cooperative populations are prone to invasions by selfish individuals. However, a population consisting of only free-riders typically does not survive. Thus, cooperators and free-riders often coexist in some proportion. An evolutionary version of a Snowdrift Game proved its efficiency in analysing this phenomenon. However, what if the system has already reached its stable state but was perturbed due to a change in environmental conditions? Then, individuals may have to re-learn their effective strategies. To address this, we consider behavioural mistakes in strategic choice execution, which we refer to as incompetence. Parametrising the propensity to make such mistakes allows for a mathematical description of learning. We compare strategies based on their relative strategic advantage relying on both fitness and learning factors. When strategies are learned at distinct rates, allowing learning according to a prescribed order is optimal. Interestingly, the strategy with the lowest strategic advantage should be learnt first if we are to optimise fitness over the learning path. Then, the differences between strategies are balanced out in order to minimise the effect of behavioural uncertainty.}, author = {Kleshnina, Maria and Streipert, Sabrina and Filar, Jerzy and Chatterjee, Krishnendu}, issn = {22277390}, journal = {Mathematics}, number = {11}, publisher = {MDPI}, title = {{Prioritised learning in snowdrift-type games}}, doi = {10.3390/math8111945}, volume = {8}, year = {2020}, } @article{6918, abstract = {We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge of the network is operable with its associated probability and the problem is to determine the probability of having at least one source-to-target path that is entirely composed of operable edges. This problem is known to be NP-hard. We provide a novel scalable algorithm to solve the Network Reliability problem when the treewidth of the underlying network is small. We also show our algorithm’s applicability for real-world transit networks that have small treewidth, including the metro networks of major cities, such as London and Tokyo. Our algorithm leverages tree decompositions to shrink the original graph into much smaller graphs, for which reliability can be efficiently and exactly computed using a brute force method. To the best of our knowledge, this is the first exact algorithm for Network Reliability that can scale to handle real-world instances of the problem.}, author = {Goharshady, Amir Kafshdar and Mohammadi, Fatemeh}, issn = {09518320}, journal = {Reliability Engineering and System Safety}, publisher = {Elsevier}, title = {{An efficient algorithm for computing network reliability in small treewidth}}, doi = {10.1016/j.ress.2019.106665}, volume = {193}, year = {2020}, } @phdthesis{7196, abstract = {In this thesis we study certain mathematical aspects of evolution. The two primary forces that drive an evolutionary process are mutation and selection. Mutation generates new variants in a population. Selection chooses among the variants depending on the reproductive rates of individuals. Evolutionary processes are intrinsically random – a new mutation that is initially present in the population at low frequency can go extinct, even if it confers a reproductive advantage. The overall rate of evolution is largely determined by two quantities: the probability that an invading advantageous mutation spreads through the population (called fixation probability) and the time until it does so (called fixation time). Both those quantities crucially depend not only on the strength of the invading mutation but also on the population structure. In this thesis, we aim to understand how the underlying population structure affects the overall rate of evolution. Specifically, we study population structures that increase the fixation probability of advantageous mutants (called amplifiers of selection). Broadly speaking, our results are of three different types: We present various strong amplifiers, we identify regimes under which only limited amplification is feasible, and we propose population structures that provide different tradeoffs between high fixation probability and short fixation time.}, author = {Tkadlec, Josef}, issn = {2663-337X}, pages = {144}, publisher = {Institute of Science and Technology Austria}, title = {{A role of graphs in evolutionary processes}}, doi = {10.15479/AT:ISTA:7196}, year = {2020}, } @article{7212, abstract = {The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many amplifiers exist for the Birth-death Moran process, some of them substantially increasing the fixation probability or even guaranteeing fixation in the limit of large population size. On the other hand, no amplifiers are known for the death-Birth Moran process, and computer-assisted exhaustive searches have failed to discover amplification. In this work we resolve this disparity, by showing that any amplification under death-Birth updating is necessarily bounded and transient. Our boundedness result states that even if a population structure does amplify selection, the resulting fixation probability is close to that of the well-mixed population. Our transience result states that for any population structure there exists a threshold r⋆ such that the population structure ceases to amplify selection if the mutant fitness advantage r is larger than r⋆. Finally, we also extend the above results to δ-death-Birth updating, which is a combination of Birth-death and death-Birth updating. On the positive side, we identify population structures that maintain amplification for a wide range of values r and δ. These results demonstrate that amplification of natural selection depends on the specific mechanisms of the evolutionary process.}, author = {Tkadlec, Josef and Pavlogiannis, Andreas and Chatterjee, Krishnendu and Nowak, Martin A.}, issn = {15537358}, journal = {PLoS computational biology}, publisher = {Public Library of Science}, title = {{Limits on amplifiers of natural selection under death-Birth updating}}, doi = {10.1371/journal.pcbi.1007494}, volume = {16}, year = {2020}, } @article{7343, abstract = {Coinfections with multiple pathogens can result in complex within‐host dynamics affecting virulence and transmission. While multiple infections are intensively studied in solitary hosts, it is so far unresolved how social host interactions interfere with pathogen competition, and if this depends on coinfection diversity. We studied how the collective disease defences of ants – their social immunity – influence pathogen competition in coinfections of same or different fungal pathogen species. Social immunity reduced virulence for all pathogen combinations, but interfered with spore production only in different‐species coinfections. Here, it decreased overall pathogen sporulation success while increasing co‐sporulation on individual cadavers and maintaining a higher pathogen diversity at the community level. Mathematical modelling revealed that host sanitary care alone can modulate competitive outcomes between pathogens, giving advantage to fast‐germinating, thus less grooming‐sensitive ones. Host social interactions can hence modulate infection dynamics in coinfected group members, thereby altering pathogen communities at the host level and population level.}, author = {Milutinovic, Barbara and Stock, Miriam and Grasse, Anna V and Naderlinger, Elisabeth and Hilbe, Christian and Cremer, Sylvia}, issn = {1461-0248}, journal = {Ecology Letters}, number = {3}, pages = {565--574}, publisher = {Wiley}, title = {{Social immunity modulates competition between coinfecting pathogens}}, doi = {10.1111/ele.13458}, volume = {23}, year = {2020}, } @inproceedings{7346, abstract = {The Price of Anarchy (PoA) is a well-established game-theoretic concept to shed light on coordination issues arising in open distributed systems. Leaving agents to selfishly optimize comes with the risk of ending up in sub-optimal states (in terms of performance and/or costs), compared to a centralized system design. However, the PoA relies on strong assumptions about agents' rationality (e.g., resources and information) and interactions, whereas in many distributed systems agents interact locally with bounded resources. They do so repeatedly over time (in contrast to "one-shot games"), and their strategies may evolve. Using a more realistic evolutionary game model, this paper introduces a realized evolutionary Price of Anarchy (ePoA). The ePoA allows an exploration of equilibrium selection in dynamic distributed systems with multiple equilibria, based on local interactions of simple memoryless agents. Considering a fundamental game related to virus propagation on networks, we present analytical bounds on the ePoA in basic network topologies and for different strategy update dynamics. In particular, deriving stationary distributions of the stochastic evolutionary process, we find that the Nash equilibria are not always the most abundant states, and that different processes can feature significant off-equilibrium behavior, leading to a significantly higher ePoA compared to the PoA studied traditionally in the literature. }, author = {Schmid, Laura and Chatterjee, Krishnendu and Schmid, Stefan}, booktitle = {Proceedings of the 23rd International Conference on Principles of Distributed Systems}, location = {Neuchâtel, Switzerland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The evolutionary price of anarchy: Locally bounded agents in a dynamic virus game}}, doi = {10.4230/LIPIcs.OPODIS.2019.21}, volume = {153}, year = {2020}, } @article{15055, abstract = {Markov decision processes (MDPs) are the defacto framework for sequential decision making in the presence of stochastic uncertainty. A classical optimization criterion for MDPs is to maximize the expected discounted-sum payoff, which ignores low probability catastrophic events with highly negative impact on the system. On the other hand, risk-averse policies require the probability of undesirable events to be below a given threshold, but they do not account for optimization of the expected payoff. We consider MDPs with discounted-sum payoff with failure states which represent catastrophic outcomes. The objective of risk-constrained planning is to maximize the expected discounted-sum payoff among risk-averse policies that ensure the probability to encounter a failure state is below a desired threshold. Our main contribution is an efficient risk-constrained planning algorithm that combines UCT-like search with a predictor learned through interaction with the MDP (in the style of AlphaZero) and with a risk-constrained action selection via linear programming. We demonstrate the effectiveness of our approach with experiments on classical MDPs from the literature, including benchmarks with an order of 106 states.}, author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Novotný, Petr and Vahala, Jiří}, issn = {2374-3468}, journal = {Proceedings of the 34th AAAI Conference on Artificial Intelligence}, keywords = {General Medicine}, location = {New York, NY, United States}, number = {06}, pages = {9794--9801}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Reinforcement learning of risk-constrained policies in Markov decision processes}}, doi = {10.1609/aaai.v34i06.6531}, volume = {34}, year = {2020}, } @inproceedings{15082, abstract = {Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points two plane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which is disjoint compatible to both M1 and M2. We show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameter of this graph is either 4 or 5, independent of n.}, author = {Aichholzer, Oswin and Obmann, Julia and Patak, Pavel and Perz, Daniel and Tkadlec, Josef}, booktitle = {36th European Workshop on Computational Geometry}, location = {Würzburg, Germany, Virtual}, title = {{Disjoint tree-compatible plane perfect matchings}}, year = {2020}, } @misc{13060, abstract = {Coinfections with multiple pathogens can result in complex within-host dynamics affecting virulence and transmission. Whilst multiple infections are intensively studied in solitary hosts, it is so far unresolved how social host interactions interfere with pathogen competition, and if this depends on coinfection diversity. We studied how the collective disease defenses of ants – their social immunity ­– influence pathogen competition in coinfections of same or different fungal pathogen species. Social immunity reduced virulence for all pathogen combinations, but interfered with spore production only in different-species coinfections. Here, it decreased overall pathogen sporulation success, whilst simultaneously increasing co-sporulation on individual cadavers and maintaining a higher pathogen diversity at the community-level. Mathematical modeling revealed that host sanitary care alone can modulate competitive outcomes between pathogens, giving advantage to fast-germinating, thus less grooming-sensitive ones. Host social interactions can hence modulate infection dynamics in coinfected group members, thereby altering pathogen communities at the host- and population-level.}, author = {Milutinovic, Barbara and Stock, Miriam and Grasse, Anna V and Naderlinger, Elisabeth and Hilbe, Christian and Cremer, Sylvia}, publisher = {Dryad}, title = {{Social immunity modulates competition between coinfecting pathogens}}, doi = {10.5061/DRYAD.CRJDFN318}, year = {2020}, }