200,659 research outputs found
Non-Conservative Diffusion and its Application to Social Network Analysis
The random walk is fundamental to modeling dynamic processes on networks.
Metrics based on the random walk have been used in many applications from image
processing to Web page ranking. However, how appropriate are random walks to
modeling and analyzing social networks? We argue that unlike a random walk,
which conserves the quantity diffusing on a network, many interesting social
phenomena, such as the spread of information or disease on a social network,
are fundamentally non-conservative. When an individual infects her neighbor
with a virus, the total amount of infection increases. We classify diffusion
processes as conservative and non-conservative and show how these differences
impact the choice of metrics used for network analysis, as well as our
understanding of network structure and behavior. We show that Alpha-Centrality,
which mathematically describes non-conservative diffusion, leads to new
insights into the behavior of spreading processes on networks. We give a
scalable approximate algorithm for computing the Alpha-Centrality in a massive
graph. We validate our approach on real-world online social networks of Digg.
We show that a non-conservative metric, such as Alpha-Centrality, produces
better agreement with empirical measure of influence than conservative metrics,
such as PageRank. We hope that our investigation will inspire further
exploration into the realms of conservative and non-conservative metrics in
social network analysis
Corporate competition: A self-organized network
A substantial number of studies have extended the work on universal properties in physical systems to complex networks in social, biological, and technological systems. In this paper, we present a complex networks perspective on interfirm organizational networks by mapping, analyzing and modeling the spatial structure of a large interfirm competition network across a variety of sectors and industries within the United States. We propose two micro-dynamic models that are able to reproduce empirically observed characteristics of competition networks as a natural outcome of a minimal set of general mechanisms governing the formation of competition networks. Both models, which utilize different approaches yet apply common principles to network formation give comparable results. There is an asymmetry between companies that are considered competitors, and companies that consider others as their competitors. All companies only consider a small number of other companies as competitors; however, there are a few companies that are considered as competitors by many others. Geographically, the density of corporate headquarters strongly correlates with local population density, and the probability two firms are competitors declines with geographic distance. We construct these properties by growing a corporate network with competitive links using random incorporations modulated by population density and geographic distance. Our new analysis, methodology and empirical results are relevant to various phenomena of social and market behavior, and have implications to research fields such as economic geography, economic sociology, and regional economic development.Organizational networks; Interfirm competition; Economic geography; Social networks; Spatial networks; Network dynamics; Firm size dynamics
Multiscale modeling of oscillations and spiral waves in Dictyostelium populations
Unicellular organisms exhibit elaborate collective behaviors in response to
environmental cues. These behaviors are controlled by complex biochemical
networks within individual cells and coordinated through cell-to-cell
communication. Describing these behaviors requires new mathematical models that
can bridge scales -- from biochemical networks within individual cells to
spatially structured cellular populations. Here, we present a family of
multiscale models for the emergence of spiral waves in the social amoeba
Dictyostelium discoideum. Our models exploit new experimental advances that
allow for the direct measurement and manipulation of the small signaling
molecule cAMP used by Dictyostelium cells to coordinate behavior in cellular
populations. Inspired by recent experiments, we model the Dictyostelium
signaling network as an excitable system coupled to various pre-processing
modules. We use this family of models to study spatially unstructured
populations by constructing phase diagrams that relate the properties of
population-level oscillations to parameters in the underlying biochemical
network. We then extend our models to include spatial structure and show how
they naturally give rise to spiral waves. Our models exhibit a wide range of
novel phenomena including a density dependent frequency change, bistability,
and dynamic death due to slow cAMP dynamics. Our modeling approach provides a
powerful tool for bridging scales in modeling of Dictyostelium populations
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