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892,483
The surprising complexity of generalized reachability games
, 2012
"... Abstract. Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such games is PSPACEcomplete, although it is fixedpara ..."
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Cited by 2 (0 self)
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Abstract. Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such games is PSPACEcomplete, although it is fixedparameter tractable with the number of reachability objectives as parameter. Moreover, we consider the memory requirements for both players and give matching upper and lower bounds on the size of winning strategies. In order to allow more efficient algorithms, we consider subclasses of generalized reachability games. We show that bounding the size of the reachability sets gives two natural subclasses where deciding the winner can be done efficiently. 1
Graph Clustering with Surprise: Complexity and Exact Solutions?
"... Abstract. Clustering graphs based on a comparison of the number of links within clusters and the expected value of this quantity in a random graph has gained a lot of attention and popularity in the last decade. Recently, Aldecoa and Maŕın proposed a related, but slightly different approach leading ..."
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leading to the quality measure surprise, and reported good behavior in the context of synthetic and real world benchmarks. We show that the problem of finding a clustering with optimum surprise is NPhard. Moreover, a bicriterial view on the problem permits to compute optimum solutions for small
The space complexity of approximating the frequency moments
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1996
"... The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, ..."
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Cited by 844 (12 self)
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The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly
Error and attack tolerance of complex networks
, 2000
"... Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network [1]. C ..."
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Cited by 1011 (7 self)
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Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network [1
Curvelets: a surprisingly effective nonadaptive representation of objects with edges
 IN CURVE AND SURFACE FITTING: SAINTMALO
, 2000
"... It is widely believed that to efficiently represent an otherwise smooth object with discontinuities along edges, one must use an adaptive representation that in some sense ‘tracks ’ the shape of the discontinuity set. This folkbelief — some would say folktheorem — is incorrect. At the very least ..."
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Cited by 395 (21 self)
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. By applying naive thresholding to the curvelet transform of such an object, one can form mterm approximations with rate of L 2 approximation rivaling the rate obtainable by complex adaptive schemes which attempt to ‘track ’ the discontinuity set. In this article we explain the basic issues of efficient m
Hierarchical Models of Object Recognition in Cortex
, 1999
"... The classical model of visual processing in cortex is a hierarchy of increasingly sophisticated representations, extending in a natural way the model of simple to complex cells of Hubel and Wiesel. Somewhat surprisingly, little quantitative modeling has been done in the last 15 years to explore th ..."
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Cited by 836 (84 self)
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The classical model of visual processing in cortex is a hierarchy of increasingly sophisticated representations, extending in a natural way the model of simple to complex cells of Hubel and Wiesel. Somewhat surprisingly, little quantitative modeling has been done in the last 15 years to explore
Very simple classification rules perform well on most commonly used datasets
 Machine Learning
, 1993
"... The classification rules induced by machine learning systems are judged by two criteria: their classification accuracy on an independent test set (henceforth "accuracy"), and their complexity. The relationship between these two criteria is, of course, of keen interest to the machin ..."
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Cited by 547 (5 self)
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The classification rules induced by machine learning systems are judged by two criteria: their classification accuracy on an independent test set (henceforth "accuracy"), and their complexity. The relationship between these two criteria is, of course, of keen interest
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 674 (15 self)
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and ap proximately 4000 findin nodes, with a number of ob served findings that varies per case. Due to the form of the noisyor CPTs the complexity of inference is ex ponential in the number of positive findings Results Initial experiments The experimental protocol for the PYRAMID network was as follows
Technological pedagogical content knowledge: A framework for integrating technology in teacher knowledge.
 Teachers College Record,
, 2006
"... Abstract This paper describes a framework for teacher knowledge for technology integration called technological pedagogical content knowledge (originally TPCK, now known as TPACK, or technology, pedagogy, and content knowledge). This framework builds on Lee Shulman's construct of pedagogical c ..."
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Cited by 416 (18 self)
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content knowledge (PCK) to include technology knowledge. The development of TPACK by teachers is critical to effective teaching with technology. The paper begins with a brief introduction to the complex, illstructured nature of teaching. The nature of technologies (both analog and digital) is considered
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