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Articles 1 - 9 of 9
Full-Text Articles in Social and Behavioral Sciences
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.
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 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 …
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.
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.
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.
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 …
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 …
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 …