Index sets and parametric reductions

2001 ◽  
Vol 40 (5) ◽  
pp. 329-348
Author(s):  
Rod G. Downey ◽  
Michael R. Fellows
Keyword(s):  
Index Sets

Index sets for ω-languages

2003 ◽  
Vol 49 (1) ◽  
pp. 22-33 ◽  
Author(s):  
Douglas Czenzer ◽  
Jeffrey B. Remmel
Keyword(s):  
Index Sets

scholarly journals Index sets and universal numberings

2011 ◽  
Vol 77 (4) ◽  
pp. 760-773 ◽  
Author(s):  
Sanjay Jain ◽  
Frank Stephan ◽  
Jason Teutsch
Keyword(s):  
Index Sets

scholarly journals ON THE EDGE-BALANCED INDEX SETS OF PRODUCT GRAPHS

2012 ◽  
Vol 0 (0) ◽  
Author(s):  
Elliot Krop ◽  
Sin-Min Lee ◽  
Christopher Raridan
Keyword(s):  
Product Graphs ◽  
Index Sets

scholarly journals A note on decidable categoricity and index sets

2020 ◽  
Vol 17 ◽  
pp. 1013-1026
Author(s):  
N. A. Bazhenov ◽  
M. I. Marchuk
Keyword(s):  
Index Sets

scholarly journals Index sets and Boolean operations

1982 ◽  
Vol 84 (4) ◽  
pp. 568-568 ◽  
Author(s):  
Douglas E. Miller
Keyword(s):  
Boolean Operations ◽  
Index Sets

An adaptive sparse polynomial-chaos technique based on anisotropic indices

2020 ◽  
Vol 39 (3) ◽  
pp. 691-707
Author(s):  
Christos Salis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros Zygiridis
Keyword(s):  
Polynomial Chaos ◽  
Computational Cost ◽  
Uncertainty Assessment ◽  
Design Parameters ◽  
Test Problems ◽  
Content Type ◽  
Sparse Polynomial ◽  
Index Sets ◽  
The Mean ◽  
Expansion Coefficients

Purpose The fabrication of electromagnetic (EM) components may induce randomness in several design parameters. In such cases, an uncertainty assessment is of high importance, as simulating the performance of those devices via deterministic approaches may lead to a misinterpretation of the extracted outcomes. This paper aims to present a novel heuristic for the sparse representation of the polynomial chaos (PC) expansion of the output of interest, aiming at calculating the involved coefficients with a small computational cost. Design/methodology/approach This paper presents a novel heuristic that aims to develop a sparse PC technique based on anisotropic index sets. Specifically, this study’s approach generates those indices by using the mean elementary effect of each input. Accurate outcomes are extracted in low computational times, by constructing design of experiments (DoE) which satisfy the D-optimality criterion. Findings The method proposed in this study is tested on three test problems; the first one involves a transmission line that exhibits several random dielectrics, while the second and the third cases examine the effects of various random design parameters to the transmission coefficient of microwave filters. Comparisons with the Monte Carlo technique and other PC approaches prove that accurate outcomes are obtained in a smaller computational cost, thus the efficiency of the PC scheme is enhanced. Originality/value This paper introduces a new sparse PC technique based on anisotropic indices. The proposed method manages to accurately extract the expansion coefficients by locating D-optimal DoE.

From index sets to randomness in ∅n: random reals and possibly infinite computations part II

2009 ◽  
Vol 74 (1) ◽  
pp. 124-156 ◽  
Author(s):  
Verónica Becher ◽  
Serge Grigorieff
Keyword(s):  
Large Class ◽  
Turing Machine ◽  
Index Sets ◽  
Random Reals

AbstractWe obtain a large class of significant examples of n-random reals (i.e., Martin-Löf random in oracle ∅(n−1)) à la Chaitin. Any such real is defined as the probability that a universal monotone Turing machine performing possibly infinite computations on infinite (resp. finite large enough, resp. finite self-delimited) inputs produces an output in a given set . In particular, we develop methods to transfer many-one completeness results of index sets to n-randomness of associated probabilities.

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