4,958 research outputs found

    The Graph Curvature Calculator and the curvatures of cubic graphs

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    We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-\'Emery curvature everywhere. We show in both curvature notions that the non-negatively curved graphs are the prism graphs and the M\"obius ladders. We also highlight an online tool for calculating the curvature of graphs under several variants of these curvature notions that we use in the classification. As a consequence of the classification result we show, that non-negatively curved cubic expanders do not exist

    Multi-level Visualization of Concurrent and Distributed Computation in Erlang

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    This paper describes a prototype visualization system for concurrent and distributed applications programmed using Erlang, providing two levels of granularity of view. Both visualizations are animated to show the dynamics of aspects of the computation. At the low level, we show the concurrent behaviour of the Erlang schedulers on a single instance of the Erlang virtual machine, which we call an Erlang node. Typically there will be one scheduler per core on a multicore system. Each scheduler maintains a run queue of processes to execute, and we visualize the migration of Erlang concurrent processes from one run queue to another as work is redistributed to fully exploit the hardware. The schedulers are shown as a graph with a circular layout. Next to each scheduler we draw a variable length bar indicating the current size of the run queue for the scheduler. At the high level, we visualize the distributed aspects of the system, showing interactions between Erlang nodes as a dynamic graph drawn with a force model. Speci?cally we show message passing between nodes as edges and lay out nodes according to their current connections. In addition, we also show the grouping of nodes into “s_groups” using an Euler diagram drawn with circles

    Requirements for Topology in 3D GIS

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    Topology and its various benefits are well understood within the context of 2D Geographical Information Systems. However, requirements in three-dimensional (3D) applications have yet to be defined, with factors such as lack of users' familiarity with the potential of such systems impeding this process. In this paper, we identify and review a number of requirements for topology in 3D applications. The review utilises existing topological frameworks and data models as a starting point. Three key areas were studied for the purposes of requirements identification, namely existing 2D topological systems, requirements for visualisation in 3D and requirements for 3D analysis supported by topology. This was followed by analysis of application areas such as earth sciences and urban modelling which are traditionally associated with GIS, as well as others including medical, biological and chemical science. Requirements for topological functionality in 3D were then grouped and categorised. The paper concludes by suggesting that these requirements can be used as a basis for the implementation of topology in 3D. It is the aim of this review to serve as a focus for further discussion and identification of additional applications that would benefit from 3D topology. © 2006 The Authors. Journal compilation © 2006 Blackwell Publishing Ltd

    Affective graphs: the visual appeal of linked data

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    The essence and value of Linked Data lies in the ability of humans and machines to query, access and reason upon highly structured and formalised data. Ontology structures provide an unambiguous description of the structure and content of data. While a multitude of software applications and visualization systems have been developed over the past years for Linked Data, there is still a significant gap that exists between applications that consume Linked Data and interfaces that have been designed with significant focus on aesthetics. Though the importance of aesthetics in affecting the usability, effectiveness and acceptability of user interfaces have long been recognised, little or no explicit attention has been paid to the aesthetics of Linked Data applications. In this paper, we introduce a formalised approach to developing aesthetically pleasing semantic web interfaces by following aesthetic principles and guidelines identified from literature. We apply such principles to design and develop a generic approach of using visualizations to support exploration of Linked Data, in an interface that is pleasing to users. This provides users with means to browse ontology structures, enriched with statistics of the underlying data, facilitating exploratory activities and enabling visual query for highly precise information needs. We evaluated our approach in three ways: an initial objective evaluation comparing our approach with other well-known interfaces for the semantic web and two user evaluations with semantic web researchers

    Dynamic Influence Networks for Rule-based Models

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    We introduce the Dynamic Influence Network (DIN), a novel visual analytics technique for representing and analyzing rule-based models of protein-protein interaction networks. Rule-based modeling has proved instrumental in developing biological models that are concise, comprehensible, easily extensible, and that mitigate the combinatorial complexity of multi-state and multi-component biological molecules. Our technique visualizes the dynamics of these rules as they evolve over time. Using the data produced by KaSim, an open source stochastic simulator of rule-based models written in the Kappa language, DINs provide a node-link diagram that represents the influence that each rule has on the other rules. That is, rather than representing individual biological components or types, we instead represent the rules about them (as nodes) and the current influence of these rules (as links). Using our interactive DIN-Viz software tool, researchers are able to query this dynamic network to find meaningful patterns about biological processes, and to identify salient aspects of complex rule-based models. To evaluate the effectiveness of our approach, we investigate a simulation of a circadian clock model that illustrates the oscillatory behavior of the KaiC protein phosphorylation cycle.Comment: Accepted to TVCG, in pres
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