1,713,961 research outputs found
Complex Networks
An outline of recent work on complex networks is given from the point of view
of a physicist. Motivation, achievements and goals are discussed with some of
the typical applications from a wide range of academic fields. An introduction
to the relevant literature and useful resources is also given.Comment: Review for Contemporary Physics, 31 page
Complex Networks
Introduction to the Special Issue on Complex Networks, Artificial Life
journal.Comment: 7 pages, in pres
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Complex networks
This chapter contains a brief introduction to complex networks, and in particular to small world and scale free networks. We show how to apply the replica method developed to analyse random matrices in statistical physics to calculate the spectral densities of the adjacency and Laplacian matrices of a scale free network. We use the effective medium approximation to treat networks with finite mean degree and discuss the local properties of random matrices associated with complex networks
Deep Complex Networks
At present, the vast majority of building blocks, techniques, and
architectures for deep learning are based on real-valued operations and
representations. However, recent work on recurrent neural networks and older
fundamental theoretical analysis suggests that complex numbers could have a
richer representational capacity and could also facilitate noise-robust memory
retrieval mechanisms. Despite their attractive properties and potential for
opening up entirely new neural architectures, complex-valued deep neural
networks have been marginalized due to the absence of the building blocks
required to design such models. In this work, we provide the key atomic
components for complex-valued deep neural networks and apply them to
convolutional feed-forward networks and convolutional LSTMs. More precisely, we
rely on complex convolutions and present algorithms for complex
batch-normalization, complex weight initialization strategies for
complex-valued neural nets and we use them in experiments with end-to-end
training schemes. We demonstrate that such complex-valued models are
competitive with their real-valued counterparts. We test deep complex models on
several computer vision tasks, on music transcription using the MusicNet
dataset and on Speech Spectrum Prediction using the TIMIT dataset. We achieve
state-of-the-art performance on these audio-related tasks
Sznajd Complex Networks
The Sznajd cellular automata corresponds to one of the simplest and yet most
interesting models of complex systems. While the traditional two-dimensional
Sznajd model tends to a consensus state (pro or cons), the assignment of the
contrary to the dominant opinion to some of its cells during the system
evolution is known to provide stabilizing feedback implying the overall system
state to oscillate around null magnetization. The current article presents a
novel type of geographic complex network model whose connections follow an
associated feedbacked Sznajd model, i.e. the Sznajd dynamics is run over the
network edges. Only connections not exceeding a maximum Euclidean distance
are considered, and any two nodes within such a distance are randomly selected
and, in case they are connected, all network nodes which are no further than
are connected to them. In case they are not connected, all nodes within
that distance are disconnected from them. Pairs of nodes are then randomly
selected and assigned to the contrary of the dominant connectivity. The
topology of the complex networks obtained by such a simple growth scheme, which
are typically characterized by patches of connected communities, is analyzed
both at global and individual levels in terms of a set of hierarchical
measurements introduced recently. A series of interesting properties are
identified and discussed comparatively to random and scale-free models with the
same number of nodes and similar connectivity.Comment: 10 pages, 4 figure
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