7 research outputs found
Generative modeling of the enteric nervous system employing point pattern analysis and graph construction
We describe a generative network model of the architecture of the enteric
nervous system (ENS) in the colon employing data from images of human and mouse
tissue samples obtained through confocal microscopy. Our models combine spatial
point pattern analysis with graph generation to characterize the spatial and
topological properties of the ganglia (clusters of neurons and glial cells),
the inter-ganglionic connections, and the neuronal organization within the
ganglia. We employ a hybrid hardcore-Strauss process for spatial patterns and a
planar random graph generation for constructing the spatially embedded network.
We show that our generative model may be helpful in both basic and
translational studies, and it is sufficiently expressive to model the ENS
architecture of individuals who vary in age and health status. Increased
understanding of the ENS connectome will enable the use of neuromodulation
strategies in treatment and clarify anatomic diagnostic criteria for people
with bowel motility disorders.Comment: 17 pages, 5 figure
Spatial networks with wireless applications
Many networks have nodes located in physical space, with links more common
between closely spaced pairs of nodes. For example, the nodes could be wireless
devices and links communication channels in a wireless mesh network. We
describe recent work involving such networks, considering effects due to the
geometry (convex,non-convex, and fractal), node distribution,
distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina
Computationally efficient inference for latent position network models
Latent position models are widely used for the analysis of networks in a
variety of research fields. In fact, these models possess a number of desirable
theoretical properties, and are particularly easy to interpret. However,
statistical methodologies to fit these models generally incur a computational
cost which grows with the square of the number of nodes in the graph. This
makes the analysis of large social networks impractical. In this paper, we
propose a new method characterised by a linear computational complexity, which
can be used to fit latent position models on networks of several tens of
thousands nodes. Our approach relies on an approximation of the likelihood
function, where the amount of noise introduced by the approximation can be
arbitrarily reduced at the expense of computational efficiency. We establish
several theoretical results that show how the likelihood error propagates to
the invariant distribution of the Markov chain Monte Carlo sampler. In
particular, we demonstrate that one can achieve a substantial reduction in
computing time and still obtain a good estimate of the latent structure.
Finally, we propose applications of our method to simulated networks and to a
large coauthorships network, highlighting the usefulness of our approach.Comment: 39 pages, 10 figures, 1 tabl
Fast generation of spatially embedded random networks
Date of publication 15 Mar. 2017Spatially Embedded Random Networks such as the Waxman random graph have been used in many settings for synthesizing networks. Prior to our work, there existed no software for generating these efficiently. Existing techniques are O(n²) where n is the number of nodes in the network; in this paper we present an O(n+e) algorithm, where e is the number of edges.Eric Parsonage and Matthew Rougha