An autonomous mobile robot requires a robust onboard controller that makes intelligent responses in dynamic environments. Current solutions tend to lead to unnecessarily complex solutions that only work in niche envir...
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An autonomous mobile robot requires a robust onboard controller that makes intelligent responses in dynamic environments. Current solutions tend to lead to unnecessarily complex solutions that only work in niche environments. Evolutionary techniques such as genetic programming (GP) can successfully be used to automatically program the controller, minimizing the limitations arising from explicit or implicit human design criteria, based on the robot's experience of the world. Grammatical evolution (GE) is a recent evolutionary algorithm that has been applied to various problems, particularly those for which GP has performed. We formulate robot control as vector-valued function estimation and present a novel generative grammar for vector-valued functions. A consideration of the crossover operator leads us to propose a design criterion for the application of GE to vector-valued function estimation, along with a second novel generative grammar which meets this criterion. The suitability of these grammars for vector-valued function estimation is assessed empirically on a simulated task for the Khepera robot. (C) 2013 Elsevier Inc. All rights reserved.
For vector-valued Dirichlet class on the unit disc D in the complex plane, we get the inclusion relation between vector-valued Dirichlet class and vector-valued Hardy space, and then obtain an exact rate of best polyn...
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ISBN:
(纸本)9781315685892;9781138028005
For vector-valued Dirichlet class on the unit disc D in the complex plane, we get the inclusion relation between vector-valued Dirichlet class and vector-valued Hardy space, and then obtain an exact rate of best polynomial approximation and of upper bounds for the deviations of Fejer means in the metric of vector-valued Hardy space.
This article discusses McShane and strong McShane integration theory in the class of vector-valued functions endowed with the Alexiewicz norm, their relations, and properties as the fundamental theorem of calculus. We...
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This article discusses McShane and strong McShane integration theory in the class of vector-valued functions endowed with the Alexiewicz norm, their relations, and properties as the fundamental theorem of calculus. We extend this theory to some Stieltjes-type integrals via a bounded bilinear operator, such as McShane-Stieltjes, strong McShane-Stieltjes, and Riemann-McShane-Stieltjes and give some relations with the non-Stieltjes integrals via the integration by parts. Finally, we establish some versions of the Riesz representation Theorem for each space of functions that characterizes the respective dual spaces of the McShane and strong McShane integrable functions.
Let L-theta be the circular cone in R-n which includes a second-order cone as a special case. For any function f from R to R, one can define a corresponding vector-valued function f(c)(x) on R-n by applying f to the s...
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Let L-theta be the circular cone in R-n which includes a second-order cone as a special case. For any function f from R to R, one can define a corresponding vector-valued function f(c)(x) on R-n by applying f to the spectral values of the spectral decomposition of x is an element of R-n with respect to L-theta. We show that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, directional differentiability, Frechet differentiability, continuous differentiability, as well as semismoothness. These results will play a crucial role in designing solution methods for optimization problem associated with the circular cone. (C) 2013 Elsevier Ltd. All rights reserved.
We exhibit a real Banach space M such that C(K, M) is almost transitive if K is the Cantor set, the growth of the integers in its Stone-Cech compactification or the maximal ideal space of L(infinity). For finite K, th...
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We exhibit a real Banach space M such that C(K, M) is almost transitive if K is the Cantor set, the growth of the integers in its Stone-Cech compactification or the maximal ideal space of L(infinity). For finite K, the space C(K, M) = M(vertical bar K vertical bar) is even transitive.
We study Hilbert spaces (sic)(2)(E, G), where E subset of R-d is a measurable set, vertical bar E vertical bar > 0 and for almost every t is an element of E the matrix G(t) (see (3)) is a Hermitian positive-definit...
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We study Hilbert spaces (sic)(2)(E, G), where E subset of R-d is a measurable set, vertical bar E vertical bar > 0 and for almost every t is an element of E the matrix G(t) (see (3)) is a Hermitian positive-definite matrix. We find necessary and sufficient conditions for which the projection operators T-k(f)(.) = f(k)(.)e(k), 1 <= k <= n are bounded. The obtained results allow us to translate various questions in the spaces (sic)(2)(E, G) to weighted norm inequalities with weights which are the diagonal elements of the matrix G(t). In Section 3 we study the properties of the system (phi(m)(t)e(j), 1 <= j <= n;m is an element of N) in the space, (sic)(2)(E, G), where Phi = (phi(m))(m=1)(infinity), is a complete orthonormal system defined on a measurable set E subset of R. We concentrate our study on two classical systems: the Haar and the trigonometric systems. Simultaneous approximations of n elements F-1, ..., F-n of some Banach spaces X-1, ..., X-n with respect to a system psi which is a basis in any of those spaces are studied. (C) 2013 Elsevier Inc. All rights reserved.
Let K-n be the Lorentz/second-order cone in R-n. For any function f from R to R, one can define a corresponding function f(soc)(x) on R-n by applying f to the spectral values of the spectral decomposition of x is an e...
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Let K-n be the Lorentz/second-order cone in R-n. For any function f from R to R, one can define a corresponding function f(soc)(x) on R-n by applying f to the spectral values of the spectral decomposition of x is an element of R-n with respect to K-n. We show that this vector-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Frechet differentiability, continuous differentiability, as well as (rho-order) semismoothness. These results are useful for designing and analyzing smoothing methods and nonsmooth methods for solving second-order cone programs and complementarity problems.
Let K-n be the Lorentz/second-order cone in R-n. For any function f from R to R, one can define a corresponding function f(soc)(x) on R-n by applying f to the spectral values of the spectral decomposition of x is an e...
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Let K-n be the Lorentz/second-order cone in R-n. For any function f from R to R, one can define a corresponding function f(soc)(x) on R-n by applying f to the spectral values of the spectral decomposition of x is an element of R-n with respect to K-n. We show that this vector-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Frechet differentiability, continuous differentiability, as well as (rho-order) semismoothness. These results are useful for designing and analyzing smoothing methods and nonsmooth methods for solving second-order cone programs and complementarity problems.
In this note an analytic representation is given for continuous linear operators from C(X) into a linear normed space Y where C(X) is the space of continuous functions on [0, 1 ] with values in a linear normed space X...
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Exact forms of Taylor expansion for vector-valued functions have been incorrectly used in many statistical publications. We offer two methods to correct this error.
Exact forms of Taylor expansion for vector-valued functions have been incorrectly used in many statistical publications. We offer two methods to correct this error.
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