@article{1873,
  abstract     = {We consider partially observable Markov decision processes (POMDPs) with limit-average payoff, where a reward value in the interval [0,1] is associated with every transition, and the payoff of an infinite path is the long-run average of the rewards. We consider two types of path constraints: (i) a quantitative constraint defines the set of paths where the payoff is at least a given threshold λ1ε(0,1]; and (ii) a qualitative constraint which is a special case of the quantitative constraint with λ1=1. We consider the computation of the almost-sure winning set, where the controller needs to ensure that the path constraint is satisfied with probability 1. Our main results for qualitative path constraints are as follows: (i) the problem of deciding the existence of a finite-memory controller is EXPTIME-complete; and (ii) the problem of deciding the existence of an infinite-memory controller is undecidable. For quantitative path constraints we show that the problem of deciding the existence of a finite-memory controller is undecidable. We also present a prototype implementation of our EXPTIME algorithm and experimental results on several examples.},
  author       = {Chatterjee, Krishnendu and Chmelik, Martin},
  journal      = {Artificial Intelligence},
  pages        = {46 -- 72},
  publisher    = {Elsevier},
  title        = {{POMDPs under probabilistic semantics}},
  doi          = {10.1016/j.artint.2014.12.009},
  volume       = {221},
  year         = {2015},
}

@inbook{18734,
  abstract     = {In this Introduction, we outline expectations for when and how the hydrogen and helium atoms in the universe turned from neutral to ionized, focusing on the earliest, least well understood stages, and emphasize the most important open questions. We include a historical summary, and highlight the role of reionization as one of the few milestones in the evolution of the universe since the Big Bang, and its status as a unique probe of the beginning stages of structure formation.},
  author       = {Haiman, Zoltán},
  booktitle    = {Understanding the Epoch of Cosmic Reionization},
  editor       = {Mesinger, Andrei},
  isbn         = {9783319219561},
  issn         = {2214-7985},
  pages        = {1--22},
  publisher    = {Springer Nature},
  title        = {{Cosmic Reionization and the First Nonlinear Structures in the Universe}},
  doi          = {10.1007/978-3-319-21957-8_1},
  year         = {2015},
}

@article{1874,
  abstract     = {The hippocampal region, comprising the hippocampal formation and the parahippocampal region, has been one of the most intensively studied parts of the brain for decades. Better understanding of its functional diversity and complexity has led to an increased demand for specificity in experimental procedures and manipulations. In view of the complex 3D structure of the hippocampal region, precisely positioned experimental approaches require a fine-grained architectural description that is available and readable to experimentalists lacking detailed anatomical experience. In this paper, we provide the first cyto- and chemoarchitectural description of the hippocampal formation and parahippocampal region in the rat at high resolution and in the three standard sectional planes: coronal, horizontal and sagittal. The atlas uses a series of adjacent sections stained for neurons and for a number of chemical marker substances, particularly parvalbumin and calbindin. All the borders defined in one plane have been cross-checked against their counterparts in the other two planes. The entire dataset will be made available as a web-based interactive application through the Rodent Brain WorkBench (http://www.rbwb.org) which, together with this paper, provides a unique atlas resource.},
  author       = {Boccara, Charlotte and Kjønigsen, Lisa and Hammer, Ingvild and Bjaalie, Jan and Leergaard, Trygve and Witter, Menno},
  journal      = {Hippocampus},
  number       = {7},
  pages        = {838 -- 857},
  publisher    = {Wiley},
  title        = {{A three-plane architectonic atlas of the rat hippocampal region}},
  doi          = {10.1002/hipo.22407},
  volume       = {25},
  year         = {2015},
}

@article{1878,
  abstract     = {Petrocoptis is a small genus of chasmophytic plants endemic to the Iberian Peninsula, with some localized populations in the French Pyrenees. Within the genus, a dozen species have been recognized based on morphological diversity, most of them with limited distribution area, in small populations and frequently with potential threats to their survival. To date, however, a molecular evaluation of the current systematic treatments has not been carried out. The aim of the present study is to infer phylogenetic relationships among its subordinate taxa by using plastidial rps16 intron and nuclear internal transcribed spacer (ITS) DNA sequences; and evaluate the phylogenetic placement of the genus Petrocoptis within the family Caryophyllaceae. The monophyly of Petrocoptis is supported by both ITS and rps16 intron sequence analyses. Furthermore, time estimates using BEAST analyses indicate a Middle to Late Miocene diversification (10.59 Myr, 6.44–15.26 Myr highest posterior densities [HPD], for ITS; 14.30 Myr, 8.61–21.00 Myr HPD, for rps16 intron).},
  author       = {Cires Rodriguez, Eduardo and Prieto, José},
  journal      = {Journal of Plant Research},
  number       = {2},
  pages        = {223 -- 238},
  publisher    = {Springer},
  title        = {{Phylogenetic relationships of Petrocoptis A. Braun ex Endl. (Caryophyllaceae), a discussed genus from the Iberian Peninsula}},
  doi          = {10.1007/s10265-014-0691-6},
  volume       = {128},
  year         = {2015},
}

@article{1879,
  abstract     = {When electron microscopy (EM) was introduced in the 1930s it gave scientists their first look into the nanoworld of cells. Over the last 80 years EM has vastly increased our understanding of the complex cellular structures that underlie the diverse functions that cells need to maintain life. One drawback that has been difficult to overcome was the inherent lack of volume information, mainly due to the limit on the thickness of sections that could be viewed in a transmission electron microscope (TEM). For many years scientists struggled to achieve three-dimensional (3D) EM using serial section reconstructions, TEM tomography, and scanning EM (SEM) techniques such as freeze-fracture. Although each technique yielded some special information, they required a significant amount of time and specialist expertise to obtain even a very small 3D EM dataset. Almost 20 years ago scientists began to exploit SEMs to image blocks of embedded tissues and perform serial sectioning of these tissues inside the SEM chamber. Using first focused ion beams (FIB) and subsequently robotic ultramicrotomes (serial block-face, SBF-SEM) microscopists were able to collect large volumes of 3D EM information at resolutions that could address many important biological questions, and do so in an efficient manner. We present here some examples of 3D EM taken from the many diverse specimens that have been imaged in our core facility. We propose that the next major step forward will be to efficiently correlate functional information obtained using light microscopy (LM) with 3D EM datasets to more completely investigate the important links between cell structures and their functions.},
  author       = {Kremer, A and Lippens, Stefaan and Bartunkova, Sonia and Asselbergh, Bob and Blanpain, Cendric and Fendrych, Matyas and Goossens, A and Holt, Matthew and Janssens, Sophie and Krols, Michiel and Larsimont, Jean and Mc Guire, Conor and Nowack, Moritz and Saelens, Xavier and Schertel, Andreas and Schepens, B and Slezak, M and Timmerman, Vincent and Theunis, Clara and Van Brempt, Ronald and Visser, Y and Guérin, Christophe},
  journal      = {Journal of Microscopy},
  number       = {2},
  pages        = {80 -- 96},
  publisher    = {Wiley-Blackwell},
  title        = {{Developing 3D SEM in a broad biological context}},
  doi          = {10.1111/jmi.12211},
  volume       = {259},
  year         = {2015},
}

@article{1880,
  abstract     = {We investigate the relation between Bose-Einstein condensation (BEC) and superfluidity in the ground state of a one-dimensional model of interacting bosons in a strong random potential. We prove rigorously that in a certain parameter regime the superfluid fraction can be arbitrarily small while complete BEC prevails. In another regime there is both complete BEC and complete superfluidity, despite the strong disorder},
  author       = {Könenberg, Martin and Moser, Thomas and Seiringer, Robert and Yngvason, Jakob},
  journal      = {New Journal of Physics},
  publisher    = {IOP Publishing},
  title        = {{Superfluid behavior of a Bose-Einstein condensate in a random potential}},
  doi          = {10.1088/1367-2630/17/1/013022},
  volume       = {17},
  year         = {2015},
}

@inproceedings{1882,
  abstract     = {We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations.},
  author       = {Fahrenberg, Uli and Kretinsky, Jan and Legay, Axel and Traonouez, Louis},
  location     = {Bertinoro, Italy},
  pages        = {306 -- 324},
  publisher    = {Springer},
  title        = {{Compositionality for quantitative specifications}},
  doi          = {10.1007/978-3-319-15317-9_19},
  volume       = {8997},
  year         = {2015},
}

@article{1883,
  abstract     = {We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ-α. Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)2. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.
},
  author       = {Keller-Schmidt, Stephanie and Tugrul, Murat and Eguíluz, Víctor and Hernandez Garcia, Emilio and Klemm, Konstantin},
  journal      = {Physical Review E Statistical Nonlinear and Soft Matter Physics},
  number       = {2},
  publisher    = {American Institute of Physics},
  title        = {{Anomalous scaling in an age-dependent branching model}},
  doi          = {10.1103/PhysRevE.91.022803},
  volume       = {91},
  year         = {2015},
}

@article{1885,
  abstract     = {The concept of positional information is central to our understanding of how cells determine their location in a multicellular structure and thereby their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine the features of expression patterns that affect positional information quantitatively. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with nearly single-cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail. },
  author       = {Tkacik, Gasper and Dubuis, Julien and Petkova, Mariela and Gregor, Thomas},
  journal      = {Genetics},
  number       = {1},
  pages        = {39 -- 59},
  publisher    = {Genetics Society of America},
  title        = {{Positional information, positional error, and readout precision in morphogenesis: A mathematical framework}},
  doi          = {10.1534/genetics.114.171850},
  volume       = {199},
  year         = {2015},
}

@article{1938,
  abstract     = {We numerically investigate the distribution of extrema of 'chaotic' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy, which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2.},
  author       = {Pausinger, Florian and Steinerberger, Stefan},
  journal      = {Physics Letters, Section A},
  number       = {6},
  pages        = {535 -- 541},
  publisher    = {Elsevier},
  title        = {{On the distribution of local extrema in quantum chaos}},
  doi          = {10.1016/j.physleta.2014.12.010},
  volume       = {379},
  year         = {2015},
}

@article{1940,
  abstract     = {We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying signals subject to gene regulatory noise? Here we extend our information-theoretic framework for gene regulation to spatially extended systems. As an example, we consider a lattice of nuclei responding to a concentration field of a transcriptional regulator (the &quot;input&quot;) by expressing a single diffusible target gene. When input concentrations are low, diffusive coupling markedly improves information transmission; optimal gene activation functions also systematically change. A qualitatively new regulatory strategy emerges where individual cells respond to the input in a nearly step-like fashion that is subsequently averaged out by strong diffusion. While motivated by early patterning events in the Drosophila embryo, our framework is generically applicable to spatially coupled stochastic gene expression models.},
  author       = {Sokolowski, Thomas R and Tkacik, Gasper},
  journal      = {Physical Review E Statistical Nonlinear and Soft Matter Physics},
  number       = {6},
  publisher    = {American Institute of Physics},
  title        = {{Optimizing information flow in small genetic networks. IV. Spatial coupling}},
  doi          = {10.1103/PhysRevE.91.062710},
  volume       = {91},
  year         = {2015},
}

@article{1944,
  author       = {Rakusová, Hana and Fendrych, Matyas and Friml, Jirí},
  journal      = {Current Opinion in Plant Biology},
  number       = {2},
  pages        = {116 -- 123},
  publisher    = {Elsevier},
  title        = {{Intracellular trafficking and PIN-mediated cell polarity during tropic responses in plants}},
  doi          = {10.1016/j.pbi.2014.12.002},
  volume       = {23},
  year         = {2015},
}

@article{473,
  abstract     = {We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction strength behaves as 1/T. We proceed by characterizing the interacting Gibbs state as minimizing a functional counting the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional analogue of phase-space semiclassical analysis, using fine properties of the quantum relative entropy, the link between quantum de Finetti measures and upper/lower symbols in a coherent state basis, as well as Berezin-Lieb type inequalities. Our results cover the measure built on the defocusing nonlinear Schrödinger functional on a finite interval, as well as smoother interactions in dimensions d 2.},
  author       = {Lewin, Mathieu and Phan Thanh, Nam and Rougerie, Nicolas},
  journal      = {Journal de l'Ecole Polytechnique - Mathematiques},
  pages        = {65 -- 115},
  publisher    = {Ecole Polytechnique},
  title        = {{Derivation of nonlinear gibbs measures from many-body quantum mechanics}},
  doi          = {10.5802/jep.18},
  volume       = {2},
  year         = {2015},
}

@article{477,
  abstract     = {Dendritic cells are potent antigen-presenting cells endowed with the unique ability to initiate adaptive immune responses upon inflammation. Inflammatory processes are often associated with an increased production of serotonin, which operates by activating specific receptors. However, the functional role of serotonin receptors in regulation of dendritic cell functions is poorly understood. Here, we demonstrate that expression of serotonin receptor 5-HT7 (5-HT7TR) as well as its downstream effector Cdc42 is upregulated in dendritic cells upon maturation. Although dendritic cell maturation was independent of 5-HT7TR, receptor stimulation affected dendritic cell morphology through Cdc42-mediated signaling. In addition, basal activity of 5-HT7TR was required for the proper expression of the chemokine receptor CCR7, which is a key factor that controls dendritic cell migration. Consistent with this, we observed that 5-HT7TR enhances chemotactic motility of dendritic cells in vitro by modulating their directionality and migration velocity. Accordingly, migration of dendritic cells in murine colon explants was abolished after pharmacological receptor inhibition. Our results indicate that there is a crucial role for 5-HT7TR-Cdc42-mediated signaling in the regulation of dendritic cell morphology and motility, suggesting that 5-HT7TR could be a new target for treatment of a variety of inflammatory and immune disorders.},
  author       = {Holst, Katrin and Guseva, Daria and Schindler, Susann and Sixt, Michael K and Braun, Armin and Chopra, Himpriya and Pabst, Oliver and Ponimaskin, Evgeni},
  journal      = {Journal of Cell Science},
  number       = {15},
  pages        = {2866 -- 2880},
  publisher    = {Company of Biologists},
  title        = {{The serotonin receptor 5-HT7R regulates the morphology and migratory properties of dendritic cells}},
  doi          = {10.1242/jcs.167999},
  volume       = {128},
  year         = {2015},
}

@article{523,
  abstract     = {We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multi-dimensional mean-payoff games that are known to be coNP-complete, multi-dimensional total-payoff games are undecidable. We introduce conservative approximations of these objectives, where the payoff is considered over a local finite window sliding along a play, instead of the whole play. For single dimension, we show that (i) if the window size is polynomial, deciding the winner takes polynomial time, and (ii) the existence of a bounded window can be decided in NP ∩ coNP, and is at least as hard as solving mean-payoff games. For multiple dimensions, we show that (i) the problem with fixed window size is EXPTIME-complete, and (ii) there is no primitive-recursive algorithm to decide the existence of a bounded window.},
  author       = {Chatterjee, Krishnendu and Doyen, Laurent and Randour, Mickael and Raskin, Jean},
  journal      = {Information and Computation},
  number       = {6},
  pages        = {25 -- 52},
  publisher    = {Elsevier},
  title        = {{Looking at mean-payoff and total-payoff through windows}},
  doi          = {10.1016/j.ic.2015.03.010},
  volume       = {242},
  year         = {2015},
}

@article{524,
  abstract     = {We consider concurrent games played by two players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study the most fundamental objective for concurrent games, namely, mean-payoff or limit-average objective, where a reward is associated to each transition, and the goal of player 1 is to maximize the long-run average of the rewards, and the objective of player 2 is strictly the opposite (i.e., the games are zero-sum). The path constraint for player 1 could be qualitative, i.e., the mean-payoff is the maximal reward, or arbitrarily close to it; or quantitative, i.e., a given threshold between the minimal and maximal reward. We consider the computation of the almost-sure (resp. positive) winning sets, where player 1 can ensure that the path constraint is satisfied with probability 1 (resp. positive probability). Almost-sure winning with qualitative constraint exactly corresponds to the question of whether there exists a strategy to ensure that the payoff is the maximal reward of the game. Our main results for qualitative path constraints are as follows: (1) we establish qualitative determinacy results that show that for every state either player 1 has a strategy to ensure almost-sure (resp. positive) winning against all player-2 strategies, or player 2 has a spoiling strategy to falsify almost-sure (resp. positive) winning against all player-1 strategies; (2) we present optimal strategy complexity results that precisely characterize the classes of strategies required for almost-sure and positive winning for both players; and (3) we present quadratic time algorithms to compute the almost-sure and the positive winning sets, matching the best known bound of the algorithms for much simpler problems (such as reachability objectives). For quantitative constraints we show that a polynomial time solution for the almost-sure or the positive winning set would imply a solution to a long-standing open problem (of solving the value problem of turn-based deterministic mean-payoff games) that is not known to be solvable in polynomial time.},
  author       = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus},
  journal      = {Information and Computation},
  number       = {6},
  pages        = {2 -- 24},
  publisher    = {Elsevier},
  title        = {{Qualitative analysis of concurrent mean payoff games}},
  doi          = {10.1016/j.ic.2015.03.009},
  volume       = {242},
  year         = {2015},
}

@article{532,
  abstract     = {Ethylene is a gaseous phytohormone that plays vital roles in plant growth and development. Previous studies uncovered EIN2 as an essential signal transducer linking ethylene perception on ER to transcriptional regulation in the nucleus through a “cleave and shuttle” model. In this study, we report another mechanism of EIN2-mediated ethylene signaling, whereby EIN2 imposes the translational repression of EBF1 and EBF2 mRNA. We find that the EBF1/2 3′ UTRs mediate EIN2-directed translational repression and identify multiple poly-uridylates (PolyU) motifs as functional cis elements of 3′ UTRs. Furthermore, we demonstrate that ethylene induces EIN2 to associate with 3′ UTRs and target EBF1/2 mRNA to cytoplasmic processing-body (P-body) through interacting with multiple P-body factors, including EIN5 and PABs. Our study illustrates translational regulation as a key step in ethylene signaling and presents mRNA 3′ UTR functioning as a “signal transducer” to sense and relay cellular signaling in plants.},
  author       = {Li, Wenyang and Ma, Mengdi and Feng, Ying and Li, Hongjiang and Wang, Yichuan and Ma, Yutong and Li, Mingzhe and An, Fengying and Guo, Hongwei},
  journal      = {Cell},
  number       = {3},
  pages        = {670 -- 683},
  publisher    = {Cell Press},
  title        = {{EIN2-directed translational regulation of ethylene signaling in arabidopsis}},
  doi          = {10.1016/j.cell.2015.09.037},
  volume       = {163},
  year         = {2015},
}

@misc{5430,
  abstract     = {We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean- payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m = O ( n ) ) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a mul- tiplicative factor of ∊ in time O ( n · log( n/∊ )) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O ( n · log( | a · b · n | )) = O ( n · log( n · W )) , when the output is a b , as compared to the previously best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O ( n 2 · m ) time and the associated decision problem can be solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n · W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O ( n · log n ) time, improving the previous known O ( n 4 · log( n · W )) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.},
  author       = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
  issn         = {2664-1690},
  pages        = {31},
  publisher    = {IST Austria},
  title        = {{Faster algorithms for quantitative verification in constant treewidth graphs}},
  doi          = {10.15479/AT:IST-2015-319-v1-1},
  year         = {2015},
}

@misc{5431,
  abstract     = {We consider finite-state concurrent stochastic games, played by k>=2 players for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. We consider reachability objectives that given a target set of states require that some state in the target set is visited, and the dual safety objectives that given a target set require that only states in the target set are visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed.

 Our main results are as follows: We show that in two-player zero-sum concurrent stochastic games (with reachability objective for one player and the complementary safety objective for the other player): (i) the optimal bound on the patience of optimal and epsilon-optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary. In general we study the class of non-zero-sum games admitting epsilon-Nash equilibria. We show that if there is at least one player with reachability objective, then doubly-exponential patience is needed in general for epsilon-Nash equilibrium strategies, whereas in contrast if all players have safety objectives, then the optimal bound on patience for epsilon-Nash equilibrium strategies is only exponential.},
  author       = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Hansen, Kristoffer},
  issn         = {2664-1690},
  pages        = {25},
  publisher    = {IST Austria},
  title        = {{The patience of concurrent stochastic games with safety and reachability objectives}},
  doi          = {10.15479/AT:IST-2015-322-v1-1},
  year         = {2015},
}

@misc{5432,
  abstract     = {Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom in the context of evolution.The replacement graph specifies who competes with whom for reproduction. 
The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. 
Our main results are:
(1) We show that the qualitative question is NP-complete and the quantitative approximation question is #P-hard in the special case when the interaction and the replacement graphs coincide and even with the restriction that the resident individuals do not reproduce (which corresponds to an invading population taking over an empty structure).
(2) We show that in general the qualitative question is PSPACE-complete and the quantitative approximation question is PSPACE-hard and can be solved in exponential time.
},
  author       = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Nowak, Martin},
  issn         = {2664-1690},
  pages        = {29},
  publisher    = {IST Austria},
  title        = {{The complexity of evolutionary games on graphs}},
  doi          = {10.15479/AT:IST-2015-323-v1-1},
  year         = {2015},
}

