5,708 research outputs found
Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces
Model sets (or cut and project sets) provide a familiar and commonly used
method of constructing and studying nonperiodic point sets. Here we extend this
method to situations where the internal spaces are no longer Euclidean, but
instead spaces with p-adic topologies or even with mixed Euclidean/p-adic
topologies.
We show that a number of well known tilings precisely fit this form,
including the chair tiling and the Robinson square tilings. Thus the scope of
the cut and project formalism is considerably larger than is usually supposed.
Applying the powerful consequences of model sets we derive the diffractive
nature of these tilings.Comment: 11 pages, 2 figures; dedicated to Peter Kramer on the occasion of his
65th birthda
Oriented Response Networks
Deep Convolution Neural Networks (DCNNs) are capable of learning
unprecedentedly effective image representations. However, their ability in
handling significant local and global image rotations remains limited. In this
paper, we propose Active Rotating Filters (ARFs) that actively rotate during
convolution and produce feature maps with location and orientation explicitly
encoded. An ARF acts as a virtual filter bank containing the filter itself and
its multiple unmaterialised rotated versions. During back-propagation, an ARF
is collectively updated using errors from all its rotated versions. DCNNs using
ARFs, referred to as Oriented Response Networks (ORNs), can produce
within-class rotation-invariant deep features while maintaining inter-class
discrimination for classification tasks. The oriented response produced by ORNs
can also be used for image and object orientation estimation tasks. Over
multiple state-of-the-art DCNN architectures, such as VGG, ResNet, and STN, we
consistently observe that replacing regular filters with the proposed ARFs
leads to significant reduction in the number of network parameters and
improvement in classification performance. We report the best results on
several commonly used benchmarks.Comment: Accepted in CVPR 2017. Source code available at http://yzhou.work/OR
A Diffusive Strategic Dynamics for Social Systems
We propose a model for the dynamics of a social system, which includes
diffusive effects and a biased rule for spin-flips, reproducing the effect of
strategic choices. This model is able to mimic some phenomena taking place
during marketing or political campaigns. Using a cost function based on the
Ising model defined on the typical quenched interaction environments for social
systems (Erdos-Renyi graph, small-world and scale-free networks), we find, by
numerical simulations, that a stable stationary state is reached, and we
compare the final state to the one obtained with standard dynamics, by means of
total magnetization and magnetic susceptibility. Our results show that the
diffusive strategic dynamics features a critical interaction parameter strictly
lower than the standard one. We discuss the relevance of our findings in social
systems.Comment: Major revisions; to appear on the Journal of Statistical Physic
Topological signatures in CMB temperature anisotropy maps
We propose an alternative formalism to simulate CMB temperature maps in
CDM universes with nontrivial spatial topologies. This formalism
avoids the need to explicitly compute the eigenmodes of the Laplacian operator
in the spatial sections. Instead, the covariance matrix of the coefficients of
the spherical harmonic decomposition of the temperature anisotropies is
expressed in terms of the elements of the covering group of the space. We
obtain a decomposition of the correlation matrix that isolates the topological
contribution to the CMB temperature anisotropies out of the simply connected
contribution. A further decomposition of the topological signature of the
correlation matrix for an arbitrary topology allows us to compute it in terms
of correlation matrices corresponding to simpler topologies, for which closed
quadrature formulae might be derived. We also use this decomposition to show
that CMB temperature maps of (not too large) multiply connected universes must
show ``patterns of alignment'', and propose a method to look for these
patterns, thus opening the door to the development of new methods for detecting
the topology of our Universe even when the injectivity radius of space is
slightly larger than the radius of the last scattering surface. We illustrate
all these features with the simplest examples, those of flat homogeneous
manifolds, i.e., tori, with special attention given to the cylinder, i.e.,
topology.Comment: 25 pages, 7 eps figures, revtex4, submitted to PR
A genetic-algorithms based evolutionary computational neural network for modelling spatial interaction data
Building a feedforward computational neural network model (CNN) involves two distinct tasks: determination of the network topology and weight estimation. The specification of a problem adequate network topology is a key issue and the primary focus of this contribution. Up to now, this issue has been either completely neglected in spatial application domains, or tackled by search heuristics (see Fischer and Gopal 1994). With the view of modelling interactions over geographic space, this paper considers this problem as a global optimization problem and proposes a novel approach that embeds backpropagation learning into the evolutionary paradigm of genetic algorithms. This is accomplished by interweaving a genetic search for finding an optimal CNN topology with gradient-based backpropagation learning for determining the network parameters. Thus, the model builder will be relieved of the burden of identifying appropriate CNN-topologies that will allow a problem to be solved with simple, but powerful learning mechanisms, such as backpropagation of gradient descent errors. The approach has been applied to the family of three inputs, single hidden layer, single output feedforward CNN models using interregional telecommunication traffic data for Austria, to illustrate its performance and to evaluate its robustness.
Propagation dynamics on networks featuring complex topologies
Analytical description of propagation phenomena on random networks has
flourished in recent years, yet more complex systems have mainly been studied
through numerical means. In this paper, a mean-field description is used to
coherently couple the dynamics of the network elements (nodes, vertices,
individuals...) on the one hand and their recurrent topological patterns
(subgraphs, groups...) on the other hand. In a SIS model of epidemic spread on
social networks with community structure, this approach yields a set of ODEs
for the time evolution of the system, as well as analytical solutions for the
epidemic threshold and equilibria. The results obtained are in good agreement
with numerical simulations and reproduce random networks behavior in the
appropriate limits which highlights the influence of topology on the processes.
Finally, it is demonstrated that our model predicts higher epidemic thresholds
for clustered structures than for equivalent random topologies in the case of
networks with zero degree correlation.Comment: 10 pages, 5 figures, 1 Appendix. Published in Phys. Rev. E (mistakes
in the PRE version are corrected here
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