
Universal Lossless Compression of Graphical Data
Graphical data is comprised of a graph with marks on its edges and verti...
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Percolation Threshold Results on  Graphs: an Empirical Process Approach
In this paper we define a directed percolation over ErdosRenyi graphs a...
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Distributed Compression of Graphical Data
In contrast to time series, graphical data is data indexed by the nodes ...
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From SharmaMittal to vonNeumann Entropy of a Graph
In this article, we introduce the SharmaMittal entropy of a graph, whic...
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Characterization of Time Series Via Rényi ComplexityEntropy Curves
One of the most useful tools for distinguishing between chaotic and stoc...
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Tensor entropy for uniform hypergraphs
In this paper, we develop a new notion of entropy for uniform hypergraph...
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Learning opacity in Stratal Maximum Entropy Grammar
Opaque phonological patterns are sometimes claimed to be difficult to le...
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A Notion of Entropy for Stochastic Processes on Marked Rooted Graphs
In this document, we introduce a notion of entropy for stochastic processes on marked rooted graphs. For this, we employ the framework of local weak limit theory for sparse marked graphs, also known as the objective method, due to Benjamini, Schramm, Aldous, Steele and Lyons. Our contribution is a generalization of the notion of entropy introduced by Bordenave and Caputo to graphs which carry marks on their vertices and edges. The theory of time series is the engine driving an enormous range of applications in areas such as control theory, communications, information theory and signal processing. It is to be expected that a theory of stationary stochastic processes indexed by combinatorial structures, in particular graphs, would eventually have a similarly wideranging impact.
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