@misc{5382,
abstract = {We consider two-player stochastic games played on a finite state space for an infinite num- ber of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine a probability distribution over the successor states. We also consider the important special case of turn-based stochastic games where players make moves in turns, rather than concurrently. We study concurrent games with ω-regular winning conditions specified as parity objectives. The value for player 1 for a parity objective is the maximal probability with which the player can guarantee the satisfaction of the objective against all strategies of the opponent. We study the problem of continuity and robustness of the value function in concurrent and turn-based stochastic parity games with respect to imprecision in the transition probabilities. We present quantitative bounds on the difference of the value function (in terms of the imprecision of the transition probabilities) and show the value continuity for structurally equivalent concurrent games (two games are structurally equivalent if the support of the transition func- tion is same and the probabilities differ). We also show robustness of optimal strategies for structurally equivalent turn-based stochastic parity games. Finally we show that the value continuity property breaks without the structurally equivalent assumption (even for Markov chains) and show that our quantitative bound is asymptotically optimal. Hence our results are tight (the assumption is both necessary and sufficient) and optimal (our quantitative bound is asymptotically optimal).},
author = {Chatterjee, Krishnendu},
issn = {2664-1690},
pages = {18},
publisher = {IST Austria},
title = {{Robustness of structurally equivalent concurrent parity games}},
doi = {10.15479/AT:IST-2011-0006},
year = {2011},
}
@misc{5387,
abstract = {We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode ω-regular specifications, and the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition re- quires that the resource level never drops below 0, and the mean-payoff condi- tion requires that the limit-average value of the resource consumption is within a threshold. While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for mean- payoff parity MDPs, the problem is solvable in polynomial time, improving a recent PSPACE bound.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{Energy and mean-payoff parity Markov decision processes}},
doi = {10.15479/AT:IST-2011-0001},
year = {2011},
}
@inproceedings{3336,
abstract = {We introduce TopoCut: a new way to integrate knowledge about topological properties (TPs) into random field image segmentation model. Instead of including TPs as additional constraints during minimization of the energy function, we devise an efficient algorithm for modifying the unary potentials such that the resulting segmentation is guaranteed with the desired properties. Our method is more flexible in the sense that it handles more topology constraints than previous methods, which were only able to enforce pairwise or global connectivity. In particular, our method is very fast, making it for the first time possible to enforce global topological properties in practical image segmentation tasks.},
author = {Chen, Chao and Freedman, Daniel and Lampert, Christoph},
booktitle = {CVPR: Computer Vision and Pattern Recognition},
location = {Colorado Springs, CO, USA},
pages = {2089 -- 2096},
publisher = {IEEE},
title = {{Enforcing topological constraints in random field image segmentation}},
doi = {10.1109/CVPR.2011.5995503},
year = {2011},
}
@article{3267,
abstract = {We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We study the problem with different measures: volume, diameter and radius. For volume, that is, the 1-norm of a cycle, two main results are presented. First, we prove that the problem is NP-hard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NP-hard to approximate even when the Betti number is O(1). The latter result leads to the inapproximability of the problem of computing the nonbounding cycle with the smallest volume and computing cycles representing a homology basis with the minimal total volume. As for the other two measures defined by pairwise geodesic distance, diameter and radius, we show that the localization problem is NP-hard for diameter but is polynomial for radius. Our work is restricted to homology over the ℤ2 field.},
author = {Chen, Chao and Freedman, Daniel},
journal = {Discrete & Computational Geometry},
number = {3},
pages = {425 -- 448},
publisher = {Springer},
title = {{Hardness results for homology localization}},
doi = {10.1007/s00454-010-9322-8},
volume = {45},
year = {2011},
}
@inproceedings{3298,
abstract = {We present a new algorithm for enforcing incompressibility for Smoothed Particle Hydrodynamics (SPH) by preserving uniform density across the domain. We propose a hybrid method that uses a Poisson solve on a coarse grid to enforce a divergence free velocity ﬁeld, followed by a local density correction of the particles. This avoids typical grid artifacts and maintains the Lagrangian nature of SPH by directly transferring pressures onto particles. Our method can be easily integrated with existing SPH techniques such as the incompressible PCISPH method as well as weakly compressible SPH by adding an additional force term. We show that this hybrid method accelerates convergence towards uniform density and permits a signiﬁcantly larger time step compared to earlier approaches while producing similar results. We demonstrate our approach in a variety of scenarios with signiﬁcant pressure gradients such as splashing liquids.},
author = {Raveendran, Karthik and Wojtan, Christopher J and Turk, Greg},
editor = {Spencer, Stephen},
location = {Vancouver, Canada},
pages = {33 -- 42},
publisher = {ACM},
title = {{Hybrid smoothed particle hydrodynamics}},
doi = {10.1145/2019406.2019411},
year = {2011},
}
@inproceedings{3301,
abstract = {The chemical master equation is a differential equation describing the time evolution of the probability distribution over the possible “states” of a biochemical system. The solution of this equation is of interest within the systems biology field ever since the importance of the molec- ular noise has been acknowledged. Unfortunately, most of the systems do not have analytical solutions, and numerical solutions suffer from the course of dimensionality and therefore need to be approximated. Here, we introduce the concept of tail approximation, which retrieves an approximation of the probabilities in the tail of a distribution from the total probability of the tail and its conditional expectation. This approximation method can then be used to numerically compute the solution of the chemical master equation on a subset of the state space, thus fighting the explosion of the state space, for which this problem is renowned.},
author = {Henzinger, Thomas A and Mateescu, Maria},
publisher = {Tampere International Center for Signal Processing},
title = {{Tail approximation for the chemical master equation}},
year = {2011},
}
@inproceedings{3313,
abstract = {Interpreting an image as a function on a compact sub- set of the Euclidean plane, we get its scale-space by diffu- sion, spreading the image over the entire plane. This gener- ates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian ker- nel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods.},
author = {Chen, Chao and Edelsbrunner, Herbert},
booktitle = {Proceedings of the IEEE International Conference on Computer Vision},
location = {Barcelona, Spain},
publisher = {IEEE},
title = {{Diffusion runs low on persistence fast}},
doi = {10.1109/ICCV.2011.6126271},
year = {2011},
}
@unpublished{3363,
abstract = {We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, Büchi, coBüchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs for probabilistic finite automata and present a complete characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems for probabilistic automata on infinite words.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Tracol, Mathieu},
pages = {19},
publisher = {ArXiv},
title = {{The decidability frontier for probabilistic automata on infinite words}},
year = {2011},
}
@inproceedings{3349,
abstract = {Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model various open systems in computer science, as for instance turn-based or concurrent moves, and deterministic or stochastic transitions. In this paper, we are interested in turn-based games, and specifically in deterministic parity games and stochastic reachability games (also known as simple stochastic games). We present a simple, direct and efficient reduction from deterministic parity games to simple stochastic games: it yields an arena whose size is linear up to a logarithmic factor in size of the original arena.},
author = {Chatterjee, Krishnendu and Fijalkow, Nathanaël},
location = {Minori, Italy},
pages = {74 -- 86},
publisher = {EPTCS},
title = {{A reduction from parity games to simple stochastic games}},
doi = {10.4204/EPTCS.54.6},
volume = {54},
year = {2011},
}
@inproceedings{3351,
abstract = {In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the limit-average or the discounted sum of the rewards along the path. Besides their simple definition, these two payoff functions enjoy the property that memoryless optimal strategies always exist. In an attempt to construct other simple payoff functions, we define a class of payoff functions which compute an (infinite) weighted average of the rewards. This new class contains both the limit-average and the discounted sum functions, and we show that they are the only members of this class which induce memoryless optimal strategies, showing that there is essentially no other simple payoff functions.},
author = {Chatterjee, Krishnendu and Doyen, Laurent and Singh, Rohit},
editor = {Owe, Olaf and Steffen, Martin and Telle, Jan Arne},
location = {Oslo, Norway},
pages = {148 -- 159},
publisher = {Springer},
title = {{On memoryless quantitative objectives}},
doi = {10.1007/978-3-642-22953-4_13},
volume = {6914},
year = {2011},
}