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Topological Complexity of . . .
, 2008
"... ... 10091026]. These languages are defined by local sentences and extend ωlanguages accepted by Büchi automata or defined by monadic second order sentences. We investigate their topological complexity. All locally finite ωlanguages are analytic sets, the class LOCω of locally finite ωlanguages m ..."
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... 10091026]. These languages are defined by local sentences and extend ωlanguages accepted by Büchi automata or defined by monadic second order sentences. We investigate their topological complexity. All locally finite ωlanguages are analytic sets, the class LOCω of locally finite ω
Topological Complexity of Motion Planning
 Discrete and Computational Geometry
, 2003
"... In this paper we study a notion of topological complexity TC(X) for the motion planning problem. TC(X) is a number which measures discontinuity of the process of motion planning in the configuration space X. More precisely, TC(X) is the minimal number k such that there are k different “motion planni ..."
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Cited by 72 (12 self)
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In this paper we study a notion of topological complexity TC(X) for the motion planning problem. TC(X) is a number which measures discontinuity of the process of motion planning in the configuration space X. More precisely, TC(X) is the minimal number k such that there are k different “motion
Topological complexity of configuration spaces
 Proc. Amer. Math. Soc
"... Abstract. The topological complexity TC(X) is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space X, viewed as configuration space of a mechanical system. In this paper we complete the computation of the topological complexity of ..."
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Cited by 4 (2 self)
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Abstract. The topological complexity TC(X) is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space X, viewed as configuration space of a mechanical system. In this paper we complete the computation of the topological complexity
ON HIGHER ANALOGS OF TOPOLOGICAL COMPLEXITY
, 909
"... Abstract. Farber introduced a notion of topological complexity TC(X) that is related to robotics. Here we introduce a series of numerical invariants TCn(X), n = 0, 1,... such that TC2(X) = TC(X) and TCn(X) ≤ TCn+1(X). For these higher complexities, we also define their symmetric version in spirit o ..."
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Cited by 4 (0 self)
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Abstract. Farber introduced a notion of topological complexity TC(X) that is related to robotics. Here we introduce a series of numerical invariants TCn(X), n = 0, 1,... such that TC2(X) = TC(X) and TCn(X) ≤ TCn+1(X). For these higher complexities, we also define their symmetric version in spirit
Topological complexity of blowup problems
 JOURNAL OF UNIVERSAL COMPUTER SCIENCE
, 2009
"... Consider the initial value problem of the firstorder ordinary differential equation d x(t) =f(t, x(t)), x(t0) =x0 dt where the locally Lipschitz continuous function f: R l+1 → R l with open domain and the initial datum (t0,x0) ∈ R l+1 are given. It is shown that the solution operator producing th ..."
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Cited by 3 (1 self)
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the maximal “time” interval of existence and the solution on it is computable. Furthermore, the topological complexity of the blowup problem is studied for functions f defined on the whole space. For each such function f the set Z of initial conditions (t0,x0) for which the positive solution does not blow up
Topological Complexity of the Range Searching
"... We prove an existence of a topological decision tree which solves the range searching problem for a system of real polynomials, in other words, the tree finds all feasible signs vectors of these polynomials, with the (topological) complexity logarithmic in the number of signs vectors. This answer ..."
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Cited by 7 (0 self)
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We prove an existence of a topological decision tree which solves the range searching problem for a system of real polynomials, in other words, the tree finds all feasible signs vectors of these polynomials, with the (topological) complexity logarithmic in the number of signs vectors
Evolving Neural Networks through Augmenting Topologies
 Evolutionary Computation
"... An important question in neuroevolution is how to gain an advantage from evolving neural network topologies along with weights. We present a method, NeuroEvolution of Augmenting Topologies (NEAT), which outperforms the best fixedtopology method on a challenging benchmark reinforcement learning task ..."
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Cited by 536 (112 self)
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An important question in neuroevolution is how to gain an advantage from evolving neural network topologies along with weights. We present a method, NeuroEvolution of Augmenting Topologies (NEAT), which outperforms the best fixedtopology method on a challenging benchmark reinforcement learning
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2148 (11 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled
Geometry of interfaces: topological complexity in biology and materials
"... materials Geometry of interfaces: topological complexity in biology and References ..."
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Cited by 1 (0 self)
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materials Geometry of interfaces: topological complexity in biology and References
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