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Epistasis On Finite And Infinite Spaces
"... The main purpose of this text is to present a brief overview of recent results on epistasis. The first part of the note introduces epistasis and deals with epistasis on finite search spaces. It covers both minimally epistatic, i.e., linear, and maximally epistatic functions. The second part introduc ..."
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introduces epistasis and excess values on infinite search spaces. Some properties of this generalization are discussed, among them the fact that epistasis, under certain circumstances, reduces to the L 2 norm. We do not aim to go into the mathematical details here, instead referring to recently published
Independent products in infinite spaces.
 Journal of Mathematical Analysis and Applications,
, 2015
"... Abstract Probabilistic independence, intended as the mutual irrelevance of given variables, can be solidly founded on a notion of selfconsistency of an uncertainty model, in particular when probabilities go imprecise. There is nothing in this approach that prevents it from being adopted in very ge ..."
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characterise the main notions, including some of factorisation and productivity, in the general case where both spaces can be infinite and show that, however, there are situationseven in the case of precise probabilitywhere no independent product exists. This is not the case as soon as at least one space
Avoiding paradox with infinite space
, 2003
"... We argue that whether the universe is infinite or finite is less important than often supposed. Paradoxes of repeating behaviour in the infinite, or eternal inflationary, universe can be alleviated by a realistic definition of differing lives: not simply permutations of various quantum states. We al ..."
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We argue that whether the universe is infinite or finite is less important than often supposed. Paradoxes of repeating behaviour in the infinite, or eternal inflationary, universe can be alleviated by a realistic definition of differing lives: not simply permutations of various quantum states. We
Is there paradox with infinite space?
, 2004
"... We argue that an infinite universe should not necessarily be avoided on philosophical grounds. Paradoxes of repeating behaviour in the infinite, or eternal inflationary, universe can be alleviated by a realistic definition of differing lives: not simply permutations of various quantum states. We als ..."
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We argue that an infinite universe should not necessarily be avoided on philosophical grounds. Paradoxes of repeating behaviour in the infinite, or eternal inflationary, universe can be alleviated by a realistic definition of differing lives: not simply permutations of various quantum states. We
Concentrated Force in an Infinite Space of Transversely Isotropic Material By
, 1988
"... An exact closed form solution for the displacements and stresses in a transversely isotropic infinite space due to concentrated point forces is presented, which contains the solution for the corresponding granular material as its special case and the wellknown threedimensional Ke vin solution as i ..."
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An exact closed form solution for the displacements and stresses in a transversely isotropic infinite space due to concentrated point forces is presented, which contains the solution for the corresponding granular material as its special case and the wellknown threedimensional Ke vin solution
Surface deformation due to shear and tensile faults in a halfspace
, 1985
"... A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a halfspace for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms r ..."
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Cited by 727 (1 self)
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A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a halfspace for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms
A theory of timed automata
, 1999
"... Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis of ..."
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Cited by 2651 (32 self)
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using finitely many realvalued clock variables. Automated analysis of timed automata relies on the construction of a finite quotient of the infinite space of clock valuations. Over the years, the formalism has been extensively studied leading to many results establishing connections to circuits
Quantum field theory on noncommutative spaces
"... A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommuta ..."
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Cited by 396 (26 self)
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, noncommutative YangMills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an indepth study of the gauge group of noncommutative YangMills theory. Some of the more mathematical ideas and
Convolution Kernels on Discrete Structures
, 1999
"... We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes the fa ..."
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Cited by 506 (0 self)
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the theory of infinitely divisible positive definite functions. Fundamentals of this theory and the theory of reproducing kernel Hilbert spaces are reviewed and applied in establishing the validity of the method.
The algorithmic analysis of hybrid systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 778 (71 self)
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to linear hybrid systems. In particular, we consider symbolic modelchecking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We
Results 1  10
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