Archive for the ‘Dynamic Updating’ Category

Dynamical Systems on Networks: A Tutorial

Thursday, May 14th, 2015

Dynamical Systems on Networks: A Tutorial by Mason A. Porter and James P. Gleeson.

Abstract:

We give a tutorial for the study of dynamical systems on networks. We focus especially on “simple” situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.

At thirty-nine (39) pages and two hundred and sixty-three references, the authors leave the reader with an overview of the field and the tools to go further.

I am intrigued by the closer by the authors:


Finally, many networks are multiplex (i.e., include multiple types of edges) or have other multilayer features [16, 136]. The existence of multiple layers over which dynamics can occur and the possibility of both structural and dynamical correlations between layers offers another rich set of opportunities to study dynamical systems on networks. The investigation of dynamical systems on multilayer networks is only in its infancy, and this area is also loaded with a rich set of problems [16, 136, 144, 205].

Topic maps can have multiple type of edges and multiple layers.

For further reading on those topics see:

The structure and dynamics of multilayer networks by S. Boccaletti, G. Bianconi, R. Criado, C.I. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang, M. Zanin.

Abstract:

In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.

Multilayer Networks by Mikko Kivelä, Alexandre Arenas, Marc Barthelemy, James P. Gleeson, Yamir Moreno, Mason A. Porter.

Abstract:

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such “multilayer” features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize “traditional” network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.

This may have been where we collectively went wrong in marketing topic maps. Yes, yes it is true that topic maps could do multilayer networks but network theory has made $billions with an overly simplistic model that bears little resemblance to reality.

As computation resources improve and closer to reality models, at least somewhat closer, become popular, something between simplistic networks and the full generality of topic maps could be successful.

How to Execute the Research Paper

Saturday, December 3rd, 2011

How to Execute the Research Paper by Anita de Waard.

I had to create the category, “dynamic updating,” to at least partially capture what Anita describes in this presentation. I would have loved to be present to see it in person!

The gist of the presentation is that we need to create mechanisms to support research papers being dynamically linked to the literature and other resources. One example that Anita uses is linking a patient’s medical records to reports in literature with professional tools for the diagnostician.

It isn’t clear how Linked Data (no matter how generously described by Jeni Tennison) could be the second technology for making research papers linked to other data. In part because as Jeni points out, URIs are simply more names for some subject. We don’t know if that name is for the resource or something the resource represents. Makes reliable linking rather difficult.

BTW, the web lost its ability to grow in a “gradual and sustainable way” when RDF/Linked Data introduced the notion that URIs cannot be allowed to fail. If you try to reason based on something that fails, the reasoner falls on its side. Not nearly as robust as allowing semantic 404’s.

Anita’s third step, an integrated workflow is certainly the goal to which we should be striving. I am less convinced about the mechanisms, such as generating linked data stores in addition to the documents we already have, are the way forward. For documents, for instance, why do we need to repeat data they already possess? Why can’t documents represent their contents themselves? Oh, because that isn’t how Linked Data/RDF stores work.

Still, I would highly recommend this slide deck and that you catch any presentation by Anita that you can.