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Full-Text Articles in Social and Behavioral Sciences
Ideals Of Largest Weight In Constructions Based On Directed Graphs, A V. Kelarev, Willy Susilo, Mirka Miller, Joe Ryan
Ideals Of Largest Weight In Constructions Based On Directed Graphs, A V. Kelarev, Willy Susilo, Mirka Miller, Joe Ryan
Faculty of Engineering and Information Sciences - Papers: Part A
We introduce a new construction based on directed graphs. It provides a common generalization of the incidence rings and Munn semirings. Our main theorem describes all ideals of the largest possible weight in this construction. Several previous results can be obtained as corollaries to our new main theorem.
Topological Spaces Associated To Higher-Rank Graphs, Alexander Kumjian, David Pask, Aidan Sims, Michael F. Whittaker
Topological Spaces Associated To Higher-Rank Graphs, Alexander Kumjian, David Pask, Aidan Sims, Michael F. Whittaker
Faculty of Engineering and Information Sciences - Papers: Part A
We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that identifying isomorphic co-hereditary subgraphs in a disjoint union of two rank-k graphs gives rise to pullbacks of the associated C*-algebras. We describe a combinatorial version of the connected-sum operation and apply it to the rank-2-graph realisations of the four basic surfaces to deduce that every compact 2-manifold is the topological realisation of a rank-2 graph. We also show how to construct k-spheres and wedges of k-spheres as …
Von Neumann Algebras Of Strongly Connected Higher-Rank Graphs, Marcelo Laca, Nadia S. Larsen, Sergey Neshveyev, Aidan Sims, Samuel B. Webster
Von Neumann Algebras Of Strongly Connected Higher-Rank Graphs, Marcelo Laca, Nadia S. Larsen, Sergey Neshveyev, Aidan Sims, Samuel B. Webster
Faculty of Engineering and Information Sciences - Papers: Part A
We investigate the factor types of the extremal KMS states for the preferred dynamics on the Toeplitz algebra and the Cuntz-Krieger algebra of a strongly connected finite (Formula presented.)-graph. For inverse temperatures above 1, all of the extremal KMS states are of type (Formula presented.). At inverse temperature 1, there is a dichotomy: if the (Formula presented.)-graph is a simple (Formula presented.)-dimensional cycle, we obtain a finite type (Formula presented.) factor; otherwise we obtain a type III factor, whose Connes invariant we compute in terms of the spectral radii of the coordinate matrices and the degrees of cycles in the …
Aperiodicity And Primitive Ideals Of Row-Finite K-Graphs, Sooran Kang, David Pask
Aperiodicity And Primitive Ideals Of Row-Finite K-Graphs, Sooran Kang, David Pask
Faculty of Engineering and Information Sciences - Papers: Part A
We describe the primitive ideal space of the C*-algebra of a row-finite k-graph with no sources when every ideal is gauge invariant. We characterize which spectral spaces can occur, and compute the primitive ideal space of two examples. In order to do this we prove some new results on aperiodicity. Our computations indicate that when every ideal is gauge invariant, the primitive ideal space only depends on the 1-skeleton of the k-graph in question. 2014 World Scientific Publishing Company.
Kms States On The C-Algebras Of Reducible Graphs, Astrid An Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
Kms States On The C-Algebras Of Reducible Graphs, Astrid An Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We consider the dynamics on the C-algebras of finite graphs obtained by lifting the gauge action to an action of the real line. Enomoto, Fujii and Watatani [KMS states for gauge action on OA. Math. Japon. 29 (1984), 607-619] proved that if the vertex matrix of the graph is irreducible, then the dynamics on the graph algebra admits a single Kubo-Martin-Schwinger (KMS) state. We have previously studied the dynamics on the Toeplitz algebra, and explicitly described a finite-dimensional simplex of KMS states for inverse temperatures above a critical value. Here we study the KMS states for graphs with reducible vertex …
Kms States On C*-Algebras Associated To Higher-Rank Graphs, Astrid An Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
Kms States On C*-Algebras Associated To Higher-Rank Graphs, Astrid An Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
Consider a higher rank graph of rank k. Both the Cuntz-Krieger algebra and Toeplitz-Cuntz-Krieger algebra of the graph carry natural gauge actions of the torus Tk, and restricting these guage actions to one parameter subgroups of Tk gives dynamical systems involving actions of the real line. We study the KMS states of these dynamical systems. We find that for large inverse temperatures B, the simplex of KMS B states of the Toeplitz-Cuntz-Krieger algebra has dimension d one less than the number of vertices in the graph. We also show that there is a preferred dynamics for which there is a …
Group Actions On Labeled Graphs And Their C*-Algebras, Teresa Bates, David Pask, Paulette Willis
Group Actions On Labeled Graphs And Their C*-Algebras, Teresa Bates, David Pask, Paulette Willis
Faculty of Engineering and Information Sciences - Papers: Part A
We introduce the notion of the action of a group on a labeled graph and the quotient object, also a labeled graph. We define a skew product labeled graph and use it to prove a version of the Gross–Tucker theorem for labeled graphs. We then apply these results to the C -algebra associated to a labeled graph and provide some applications in non-Abelian duality.
Skew-Products Of Higher-Rank Graphs And Crossed Products By Semigroups, Benjamin Maloney, David Pask, Iain Raeburn
Skew-Products Of Higher-Rank Graphs And Crossed Products By Semigroups, Benjamin Maloney, David Pask, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the C ∗-algebra of the graph. We show that the crossed product by this action is stably isomorphic to the C ∗-algebra of a quotient graph. Our main tool is Laca’s dilation theory for endomorphic actions of Ore semigroups on C ∗-algebras, which embeds such an action in an automorphic action of the enveloping group on a larger C ∗-algebra.
Mean Curvature Flow Of Entire Graphs In A Half-Space With A Free Boundary, V.-M Wheeler
Mean Curvature Flow Of Entire Graphs In A Half-Space With A Free Boundary, V.-M Wheeler
Faculty of Engineering and Information Sciences - Papers: Part A
We study the mean curvature flow of graphs with prescribed contact angle on a fixed, smooth hyperplane in Euclidean space. We obtain long time existence and convergence to a self similar solution of the mean curvature flow orthogonal to the fixed hyperplane.
Twisted C-Algebras Associated To Finitely Aligned Higher-Rank Graphs, Aidan Sims, Benjamin Whitehead, Michael Whittaker
Twisted C-Algebras Associated To Finitely Aligned Higher-Rank Graphs, Aidan Sims, Benjamin Whitehead, Michael Whittaker
Faculty of Engineering and Information Sciences - Papers: Part A
We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties. We establish versions of the usual uniqueness theorems and the classification of gauge-invariant ideals. We show that all twisted relative Cuntz- Krieger algebras associated to finitely aligned higher-rank graphs are nuclear and satisfy the UCT, and that for twists that lift to real-valued cocycles, the K-theory of a twisted relative Cuntz-Krieger algebra is independent of the twist. In the final section, we identify a sufficient condition for simplicity of twisted Cuntz-Krieger algebras associated to higher-rank graphs which are …
An Elementary Approach To C*-Algebras Associated To Topological Graphs, Hui Li, David Pask, Aidan Sims
An Elementary Approach To C*-Algebras Associated To Topological Graphs, Hui Li, David Pask, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We develop notions of a representation of a toopological grapph E and of a covariant representation of a topological graph E which do onot require the machinery of C* -correspondences and Cuntz-Pimsner alegebars. We show that the C* -algebra generated by a universal representation of E is isomorphic to the Toeplitz algebra of Katsura's topological-graph bimodule, and that the C* palgebra generated by a universal covariant representation of E is isomorphic to Katsura's topological graph C* -algebra. We exhibit our resluts by constructing the isomorphism between the C* -algebra of the row-finite directed graph E with no sources and the …
Progressive Mode-Seeking On Graphs For Sparse Feature Matching, Chao Wang, Lei Wang, Lingqiao Liu
Progressive Mode-Seeking On Graphs For Sparse Feature Matching, Chao Wang, Lei Wang, Lingqiao Liu
Faculty of Engineering and Information Sciences - Papers: Part A
Sparse feature matching poses three challenges to graph-based methods: (1) the combinatorial nature makes the number of possible matches huge; (2) most possible matches might be outliers; (3) high computational complexity is often incurred. In this paper, to resolve these issues, we propose a simple, yet surprisingly effective approach to explore the huge matching space in order to significantly boost true matches while avoiding outliers. The key idea is to perform mode-seeking on graphs progressively based on our proposed guided graph density. We further design a density-aware sampling technique to considerably accelerate mode-seeking. Experimental study on various benchmark data sets …
Kms States On The C*-Algebras Of Finite Graphs, Astrid An Huef, Marcelo Laca, Iain F. Raeburn, Aidan D. Sims
Kms States On The C*-Algebras Of Finite Graphs, Astrid An Huef, Marcelo Laca, Iain F. Raeburn, Aidan D. Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We consider a finite directed graph E, and the gauge action on its Toeplitz-Cuntz-Krieger algebra, viewed as an action of R. For inverse temperatures larger than a critical value βc, we give an explicit construction of all the KMSβ states. If the graph is strongly connected, then there is a unique KMSβc state, and this state factors through the quotient map onto C*(E). Our approach is direct and relatively elementary.
Remarks On Some Fundamental Results About Higher-Rank Graphs And Their C*-Algebras, Robert Hazlewood, Iain Raeburn, Aidan Sims, Samuel B. G Webster
Remarks On Some Fundamental Results About Higher-Rank Graphs And Their C*-Algebras, Robert Hazlewood, Iain Raeburn, Aidan Sims, Samuel B. G Webster
Faculty of Engineering and Information Sciences - Papers: Part A
Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the k-graph associated with a given skeleton and collection of squares and show that two k-graphs are isomorphic if and only if there is an isomorphism of their skeletons which preserves commuting squares. We use this to prove directly that each k-graph. is isomorphic to the quotient of the path category of its skeleton by the equivalence relation determined by the commuting squares, and show that this extends to a homeomorphism of …
Projection Of Undirected And Non-Positional Graphs Using Self Organizing Maps, Markus Hagenbuchner, Shujia Zhang, Ah Chung Tsoi, Alessandro Sperduti
Projection Of Undirected And Non-Positional Graphs Using Self Organizing Maps, Markus Hagenbuchner, Shujia Zhang, Ah Chung Tsoi, Alessandro Sperduti
Faculty of Engineering and Information Sciences - Papers: Part A
Kohonen's Self-Organizing Map is a popular method which allows the projection of high dimensional data onto a low dimensional display space. Models of Self-Organizing Maps for the treatment of graphs have also been defined and studied. This paper proposes an extension to the GraphSOM model which substantially improves the stability of the model, and, as a side effect, allows for an acceleration of training. The proposed extension is based on a soft encoding of the information needed to represent the vertices of an input graph. Experimental results demonstrate the advantages of the proposed extension.
Lmmse Turbo Equalization Based On Factor Graphs, Qinghua Guo, Li Ping
Lmmse Turbo Equalization Based On Factor Graphs, Qinghua Guo, Li Ping
Faculty of Engineering and Information Sciences - Papers: Part A
In this paper, a vector-form factor graph representation is derived for intersymbol interference (ISI) channels. The resultant graphs have a tree-structure that avoids the short cycle problem in existing graph approaches. Based on a joint Gaussian approximation, we establish a connection between the LLR (log-likelihood ratio) estimator for a linear system driven by binary inputs and the LMMSE (linear minimum mean-square error) estimator for a linear system driven by Gaussian inputs. This connection facilitates the application of the recently proposed Gaussian message passing technique to the cycle-free graphs for ISI channels. We also show the equivalence between the proposed approach …
A Dual Graph Construction For Higher-Rank Graphs, And K-Theory For Finite 2-Graphs, Stephen Allen, David Pask, Aidan Sims
A Dual Graph Construction For Higher-Rank Graphs, And K-Theory For Finite 2-Graphs, Stephen Allen, David Pask, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
Given a k-graph Λ and an element p of Nk, we define the dual k-graph, pΛ. We show that when Λ is row-finite and has no sources, the C*-algebras C*(Λ) and C*(pΛ) coincide. We use this isomorphism to apply Robertson and Steger's results to calculate the K-theory of C*(Λ) when Λ is finite and strongly connected and satisfies the aperiodicity condition.
Turbo Equalization Based On Factor Graphs, Qinghua Guo, Li Ping, Hans-Andrea Loeliger
Turbo Equalization Based On Factor Graphs, Qinghua Guo, Li Ping, Hans-Andrea Loeliger
Faculty of Engineering and Information Sciences - Papers: Part A
This paper presents a factor graph approach to turbo equalization. Unlike the existing linear MMSE turbo equalization methods, which operate with truncated windows (sliding or extending window), the proposed is a full-window approach with low complexity. This approach supports a high-speed parallel implementation technique, which makes it an attractive option in practice.
Cuntz-Krieger Algebras Of Infinite Graphs And Matrices, Iain Raeburn, Wojciech Szymanski
Cuntz-Krieger Algebras Of Infinite Graphs And Matrices, Iain Raeburn, Wojciech Szymanski
Faculty of Engineering and Information Sciences - Papers: Part A
We show that the Cuntz-Krieger algebras of infinite graphs and infinite {0,1}-matrices can be approximated by those of finite graphs. We then use these approximations to deduce the main uniqueness theorems for Cuntz-Krieger algebras and to compute their K-theory. Since the finite approximating graphs have sinks, we have to calculate the K-theory of Cuntz-Krieger algebras of graphs with sinks, and the direct methods we use to do this should be of independent interest.
Classification Theorems For The C*-Algebras Of Graphs With Sinks, Iain Raeburn, Mark Tomforde, Dana Williams
Classification Theorems For The C*-Algebras Of Graphs With Sinks, Iain Raeburn, Mark Tomforde, Dana Williams
Faculty of Engineering and Information Sciences - Papers: Part A
We consider graphs E which have been obtained by adding one or more sinks to a fixed directed graph G. We classify the C*-algebra of E up to a very strong equivalence relation, which insists, loosely speaking, that C*(G) is kept fixed. The main invariants are vectors WE: G0 → which describe how the sinks are attached to G; more precisely, the invariants are the classes of the WE in the cokernel of the map A – I, where A is the adjacency matrix of the graph …
Higher-Rank Graphs And Their C*-Algebras, Iain Raeburn, Aidan Sims, Trent Yeend
Higher-Rank Graphs And Their C*-Algebras, Iain Raeburn, Aidan Sims, Trent Yeend
Faculty of Engineering and Information Sciences - Papers: Part A
We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz-Krieger algebras. We describe a variant of the Cuntz-Krieger relations which applies to graphs with sources, and describe a local convexity condition which characterises the higher-rank graphs that admit a nontrivial Cuntz-Krieger family. We then prove versions of the uniqueness theorems and classifications of ideals for the C*-algebras generated by Cuntz-Krieger families.
Actions Of Z^K Associated To Higher Rank Graphs, Alexander Kumjian, David Pask
Actions Of Z^K Associated To Higher Rank Graphs, Alexander Kumjian, David Pask
Faculty of Engineering and Information Sciences - Papers: Part A
An action of Zk is associated to a higher rank graph Λ satisfying a mild assumption. This generalizes the construction of a topological Markov shift arising from a non-negative integer matrix. We show that the stable Ruelle algebra of Λ is strongly Morita equivalent to C∗(Λ). Hence, if Λ satisfies the aperiodicity condition, the stable Ruelle algebra is simple, stable and purely infinite.
The C*-Algebras Of Row-Finite Graphs, Teresa Bates, David Pask, Iain Raeburn, Wojciech Szymanski
The C*-Algebras Of Row-Finite Graphs, Teresa Bates, David Pask, Iain Raeburn, Wojciech Szymanski
Faculty of Engineering and Information Sciences - Papers: Part A
We prove versions of the fundamental theorems about Cuntz-Krieger algebras for the C*-algebras of row-finite graphs: directed graphs in which each vertex emits at most finitely many edges. Special cases of these results have previously been obtained using various powerful machines; our main point is that direct methods yield sharper results more easily.
The C*-Algebras Of Infinite Graphs, Neal J. Fowler, Marcelo Laca, Iain Raeburn
The C*-Algebras Of Infinite Graphs, Neal J. Fowler, Marcelo Laca, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
We associate C*-algebras to infinite directed graphs that are not necessarily locally finite. By realizing these algebras as Cuntz-Krieger algebras in the sense of Exel and Laca, we are able to give criteria for their uniqueness and simplicity, generalizing results of Kumjian, Pask, Raeburn, and Renault for locally finite directed graphs.