5,148 research outputs found
KK-DUALITY FOR SELF-SIMILAR GROUPOID ACTIONS ON GRAPHS
No full textWe extend Nekrashevych’s KK-duality for C∗-algebras of regular, recurrent, contracting self-similar group actions to regular, contracting self-similar groupoid actions on a graph, removing the recurrence condition entirely and generalising from a finite alphabet to a finite graph. More precisely, given a regular and contracting self-similar groupoid (G, E) acting faithfully on a finite directed graph E, we associate two C∗-algebras, O(G, E) and Ô(G, E), to it and prove that they are strongly Morita equivalent to the stable and unstable Ruelle C*-algebras of a Smale space arising from a Wieler solenoid of the self-similar limit space. That these algebras are Spanier-Whitehead dual in KK-theory follows from the general result for Ruelle algebras of irreducible Smale spaces proved by Kaminker, Putnam, and the last author
Adaptive classification with ellipsoidal regions for multidimensional pattern classification problems
No full textThis paper presents an adaptive classification method that utilizes ellipsoidal regions for multidimensional pattern classification problems with continuous input variables. The classification method fits a finite number of the ellipsoidal regions to data pattern by using adaptive operations iteratively. The method adaptively expands, rotates, shrinks, and/ or moves the ellipsoidal regions while each ellipsoidal region is separately handled with a fitness value assigned. The adaptation procedure is combined with a variable selection process in the outer loop, where significant input variables for the ellipsoids are determined by using a stepwise selection method. The performance of the method is evaluated on well-known classification problems from the UCI machine learning repository. The evaluation result shows that the proposed method can exert equivalent or superior performance, with smaller number of rules, to other classification methods such as fuzzy rules, decision trees, or neural networks. © 2004 Elsevier B.V. All rights reserved
ALL-ELECTRON RELATIVISTIC SCF CALCULATIONS FOR LIGHT-ATOMS AND DIATOMIC-MOLECULES - CORRECT NONRELATIVISTIC LIMIT CALCULATIONS WITH A RELATIVISTIC METHOD
No full textProcedures to perform reliable relativistic self-consistent-field (RSCF) calculations are described. Using light atoms and molecules, it is demonstrated that the present method always yields correct nonrelativistic limit by employing a sufficiently large value for the speed of light in RSCF calculations. Many problems associated with analytic expansions of the Dirac equations can be computationally avoided by kinetically balancing the basis sets for large and small component spinors. Results of RSCF calculations for Ne, Kr, H2, and LiH indicate very small relativistic effects for these systems as expected. Trends found is these molecules, however, may be useful in understanding relativistic effects for molecules with similar valence electronic structures and heavier atoms
K-theory for group C*-algebras
No full textThese notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C*-algebras, equivariant K-homology and KK-theory in the context of the Baum-Connes conjectur
[[alternative]]Shape and KK Masses
No full text[[abstract]]我們討論在六維時空模型中，額外維度空間的形狀對現象學的影響。兩個以週期性條件緊緻化的維度可以夾角Θ，此角對Kaluza-Klein態的質量有很大影響。我們特別考慮Θ<<1的情況，大部分的KK態質量會比Θ=90°時大很多，但是有一群KK態的質量會相較下小很多，我們討論這些Light KK態的KK數n1、n2滿足哪些條件，並以一個具體Θ為例找出最輕的一些KK態，這些態通常具有蠻大的KK數。如果在Universal Extra Dimension模型中來討論，KK數守恆會造成許多Light KK態無法衰變，而形成穩定粒子，這些粒子可能成為黑物質。
A classification method using a hybrid genetic algorithm combined with an adaptive procedure for the pool of ellipsoids
No full textThis paper presents a hybrid classification method that utilizes genetic algorithms (GAs) and adaptive operations of ellipsoidal regions for multidimensional pattern classification problems with continuous features. The classification method fits a finite number of the ellipsoidal regions to data pattern by using hybrid GAs, the combination of local improvement procedures and GAs. The local improvement method adaptively expands, rotates, shrinks, and/or moves the ellipsoids while each ellipsoid is separately handled with a fitness value assigned during the GA operations. A set of significant features for the ellipsoids are automatically determined in the hybrid GA procedure by introducing "don't care" bits to encode the chromosomes. The performance of the method is evaluated on well-known data sets and a real field classification problem originated from a deflection yoke production line. The evaluation results show that the proposed method can exert superior performance to other classification methods such as k nearest neighbor, decision trees, or neural networks
Robust Design Concept in Possibility Theory And Optimization For System With Both Random And Fuzzy Input Variables
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