792,893 research outputs found
Spatially embedded random networks
Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples
Transitions in spatial networks
Networks embedded in space can display all sorts of transitions when their
structure is modified. The nature of these transitions (and in some cases
crossovers) can differ from the usual appearance of a giant component as
observed for the Erdos-Renyi graph, and spatial networks display a large
variety of behaviors. We will discuss here some (mostly recent) results about
topological transitions, `localization' transitions seen in the shortest paths
pattern, and also about the effect of congestion and fluctuations on the
structure of optimal networks. The importance of spatial networks in real-world
applications makes these transitions very relevant and this review is meant as
a step towards a deeper understanding of the effect of space on network
structures.Comment: Corrected version and updated list of reference
Recurrent Spatial Transformer Networks
We integrate the recently proposed spatial transformer network (SPN)
[Jaderberg et. al 2015] into a recurrent neural network (RNN) to form an
RNN-SPN model. We use the RNN-SPN to classify digits in cluttered MNIST
sequences. The proposed model achieves a single digit error of 1.5% compared to
2.9% for a convolutional networks and 2.0% for convolutional networks with SPN
layers. The SPN outputs a zoomed, rotated and skewed version of the input
image. We investigate different down-sampling factors (ratio of pixel in input
and output) for the SPN and show that the RNN-SPN model is able to down-sample
the input images without deteriorating performance. The down-sampling in
RNN-SPN can be thought of as adaptive down-sampling that minimizes the
information loss in the regions of interest. We attribute the superior
performance of the RNN-SPN to the fact that it can attend to a sequence of
regions of interest
Spatial Social Networks
social networks;implementation;spatial cost topologies
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