scholarly journals THE CLASSIFICATION PROBLEM FOR AUTOMORPHISMS OF C*-ALGEBRAS

2015 ◽  
Vol 21 (4) ◽  
pp. 402-424 ◽  
Author(s):  
MARTINO LUPINI
Keyword(s):  
Complexity Theory ◽  
Classification Problem ◽  
C Algebras ◽  
Borel Complexity ◽  
Recent Developments

AbstractWe present an overview of the recent developments in the study of the classification problem for automorphisms of C*-algebras from the perspective of Borel complexity theory.

CROSSED PRODUCT C*-ALGEBRAS AND ALGEBRAIC TOPOLOGY

1996 ◽  
Vol 08 (04) ◽  
pp. 623-637
Author(s):  
JUDITH A. PACKER
Keyword(s):  
Algebraic Topology ◽  
Equivariant Cohomology ◽  
Automorphism Groups ◽  
Crossed Product ◽  
Fiber Bundles ◽  
Topological Invariants ◽  
C Algebras ◽  
Recent Developments ◽  
Continuous Trace ◽  
Cech Cohomology

We discuss some recent developments that illustrate the interplay between the theory of crossed products of continuous trace C*-algebras and algebraic topology, summarizing results relating topological invariants coming from the theory of fiber bundles to continuous trace C*-algebras and their automorphism groups and the structure of the associated crossed product C*-algebras. This survey article starts from the classical theory of Dixmier, Douady, and Fell, and discusses the more recent work of Echterhoff, Phillips, Raeburn, Rosenberg, and Williams, among others. The topological invariants involved are Čech cohomology, the cohomology of locally compact groups with Borel cochains of C. Moore, and the recently introduced equivariant cohomology theory of Crocker, Kumjian, Raeburn and Williams.

Seeds of Change and Emancipation: Towards a Cognitive Mapping of Globilisation in Literature

2011 ◽  
Vol 4 (3) ◽  
pp. 61-71
Author(s):  
Antonio Cuadrado-Fernandez
Keyword(s):  
Complexity Theory ◽  
Cognitive Linguistics ◽  
Cognitive Mapping ◽  
Dynamic Environment ◽  
Human Perception ◽  
Global Capitalism ◽  
Environmental Crisis ◽  
Human Beings ◽  
Recent Developments ◽  
The Impact

200 years of industrial capitalism, and 500 years of colonialism, have caused the worst human and environmental crisis in the history of human kind. Rapid and unprecedented depletion of natura resources, global warming, the exploitation of human beings, the global economic crises, and the military might needed to enforce the free flow of capital, al these call for a common, emancipatory articulation of local struggles. However, the creation of a larger empowering discourse requires the formation of a cognitive mapping whereby different local struggles can identify and map the structural source of their oppression. In this paper I argue that recent approaches to globalisation from the perspective of complexity theory and recent developments in cognitive linguistics and poetics, can help to construct a cognitive mapping of contemporary postcolonial poetry that enables us to scrutinise the impact of global capitalism on the loca context. Complexity theory and cognitive theories regard language as rooted in human perception of a complex and dynamic environment. Cognitive mapping articulates the reader's bodily experience to the writer's embodied conceptualisations of the effects of global capitalism on their land. In this way modernity can be redefined in more democratic terms that incorporate the voice of the marginalised and the oppressed.

On the uniformization of plane direction fields, and of second-order partial differential operators

1973 ◽  
Vol 73 (1) ◽  
pp. 87-109 ◽  
Author(s):  
Robert Finn
Keyword(s):  
Elliptic Equations ◽  
Differential Operators ◽  
Classification Problem ◽  
Second Order ◽  
Generalized Solutions ◽  
Partial Differential ◽  
Uniformization Theorem ◽  
Partial Differential Operators ◽  
Recent Developments ◽  
Direction Fields

One of the topics covered by most textbooks on partial differential equations is the classification problem for second-order equations in the plane. In a typical treatment, it is shown that under some smoothness conditions on the coefficients, hyperbolic and parabolic equations can be reduced locally to normal form (uniformized) by an elementary procedure. For elliptic equations, the procedure fails unless an extraneous hypothesis (analyticity of the coefficients) is introduced. It is then pointed out that a different and much deeper method (essentially the general uniformization theorem) is effective for the elliptic case and even yields a global result. It is striking, but not surprising in view of recent developments on generalized solutions, that the alternate (global) procedure for elliptic equations requires much less smoothness of the coefficients than is needed for a sensible local result in the other cases.

scholarly journals Nonstationary Signal Analysis with Kernel Machines

2010 ◽  
pp. 223-241
Author(s):  
Paul Honeine ◽  
Cédric Richard ◽  
Patrick Flandrin
Keyword(s):  
Machine Learning ◽  
Pattern Recognition ◽  
Signal Analysis ◽  
Selection Criterion ◽  
Reproducing Kernels ◽  
Classification Problem ◽  
Optimal Time ◽  
Nonstationary Signal ◽  
Time Frequency ◽  
Recent Developments

This chapter introduces machine learning for nonstationary signal analysis and classification. It argues that machine learning based on the theory of reproducing kernels can be extended to nonstationary signal analysis and classification. The authors show that some specific reproducing kernels allow pattern recognition algorithm to operate in the time-frequency domain. Furthermore, the authors study the selection of the reproducing kernel for a nonstationary signal classification problem. For this purpose, the kernel-target alignment as a selection criterion is investigated, yielding the optimal time-frequency representation for a given classification problem. These links offer new perspectives in the field of nonstationary signal analysis, which can benefit from recent developments of statistical learning theory and pattern recognition.

scholarly journals On the classification problem for nuclear C∗-algebras

2008 ◽  
Vol 167 (3) ◽  
pp. 1029-1044 ◽  
Author(s):  
Andrew Toms
Keyword(s):  
Classification Problem ◽  
C Algebras

Cognition, Complexity, and Teacher Education

1997 ◽  
Vol 67 (1) ◽  
pp. 105-126 ◽  
Author(s):  
Brent Davis ◽  
Dennis Sumara
Keyword(s):  
Teacher Education ◽  
Elementary School ◽  
Inner City ◽  
Complexity Theory ◽  
Formal Education ◽  
Teacher Educators ◽  
School And Community ◽  
Recent Developments ◽  
Practice Of Teaching

Drawing on recent developments in complexity theory, ecology, and hermeneutics, Brent Davis and Dennis Sumara present an "enactivist" model of cognition and contrast it to popular notions of what it means to learn and think that pervade formal education. They illustrate their model by drawing from their experiences during a year-long study in a small, inner-city elementary school. According to this model, cognition does not occur in individual minds or brains, but in the possibility for shared action. An enactivist theory of cognition, the authors suggest, requires teachers and teacher educators to reconceive the practice of teaching by blurring the lines between knower and known, teacher and student, school and community.

scholarly journals Scalable Reordering Models for SMT based on Multiclass SVM

2015 ◽  
Vol 103 (1) ◽  
pp. 65-84 ◽  
Author(s):  
Abdullah Alrajeh ◽  
Mahesan Niranjan
Keyword(s):  
Large Scale ◽  
Statistical Machine Translation ◽  
Classification Problem ◽  
Training Data ◽  
Support Vector ◽  
Recent Developments ◽  
Dual Coordinate Descent ◽  
Baseline System ◽  
Multiclass Svm ◽  
Translation Systems

Abstract In state-of-the-art phrase-based statistical machine translation systems, modelling phrase reorderings is an important need to enhance naturalness of the translated outputs, particularly when the grammatical structures of the language pairs differ significantly. Posing phrase movements as a classification problem, we exploit recent developments in solving large-scale multiclass support vector machines. Using dual coordinate descent methods for learning, we provide a mechanism to shrink the amount of training data required for each iteration. Hence, we produce significant computational saving while preserving the accuracy of the models. Our approach is a couple of times faster than maximum entropy approach and more memory-efficient (50% reduction). Experiments were carried out on an Arabic-English corpus with more than a quarter of a billion words. We achieve BLEU score improvements on top of a strong baseline system with sparse reordering features.

scholarly journals Geometric Classification of Graph C*-algebras over Finite Graphs

2018 ◽  
Vol 70 (2) ◽  
pp. 294-353 ◽  
Author(s):  
Søren Eilers ◽  
Gunnar Restorff ◽  
Efren Ruiz ◽  
Adam P.W. Sørensen
Keyword(s):  
Standard Condition ◽  
Classification Problem ◽  
Complete Classification ◽  
Type I ◽  
Simple Graphs ◽  
Finite Graphs ◽  
C Algebras ◽  
Special Case

AbstractWe address the classification problem for graph C*-algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent special case. Contrasting earlier work, we do not assume that the graphs satisfy the standard condition (K), so that the graph C*-algebras may come with uncountably many ideals.We find that in this generality, stable isomorphism of graph C*-algebras does not coincide with the geometric notion of Cuntz move equivalence. However, adding a modest condition on the graphs, the two notions are proved to be mutually equivalent and equivalent to the C*-algebras having isomorphicK-theories. This proves in turn that under this condition, the graph C*-algebras are in fact classifiable byK-theory, providing, in particular, complete classification when the C* - algebras in question are either of real rank zero or type I/postliminal. The key ingredient in obtaining these results is a characterization of Cuntz move equivalence using the adjacency matrices of the graphs.Our results are applied to discuss the classification problem for the quantumlens spaces defined by Hong and Szymański, and to complete the classification of graph C*-algebras associated with all simple graphs with four vertices or less.

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