1,356 research outputs found
Topology Identification under Spatially Correlated Noise
This article addresses the problem of reconstructing the topology of a
network of agents interacting via linear dynamics, while being excited by
exogenous stochastic sources that are possibly correlated across the agents,
from time-series measurements alone. It is shown, under the assumption that the
correlations are affine in nature, such network of nodal interactions is
equivalent to a network with added agents, represented by nodes that are
latent, where no corresponding time-series measurements are available; however,
here all exogenous excitements are spatially (that is, across agents)
uncorrelated. Generalizing affine correlations, it is shown that, under
polynomial correlations, the latent nodes in the expanded networks can be
excited by clusters of noise sources, where the clusters are uncorrelated with
each other. The clusters can be replaced with a single noise source if the
latent nodes are allowed to have non-linear interactions. Finally, using the
sparse plus low-rank matrix decomposition of the imaginary part of the inverse
power spectral density matrix (IPSDM) of the time-series data, the topology of
the network is reconstructed. Under non conservative assumptions, the
correlation graph is retrieved.Comment: 14 pages, 5 figure
Graph Dynamical Networks for Unsupervised Learning of Atomic Scale Dynamics in Materials
Understanding the dynamical processes that govern the performance of
functional materials is essential for the design of next generation materials
to tackle global energy and environmental challenges. Many of these processes
involve the dynamics of individual atoms or small molecules in condensed
phases, e.g. lithium ions in electrolytes, water molecules in membranes, molten
atoms at interfaces, etc., which are difficult to understand due to the
complexity of local environments. In this work, we develop graph dynamical
networks, an unsupervised learning approach for understanding atomic scale
dynamics in arbitrary phases and environments from molecular dynamics
simulations. We show that important dynamical information can be learned for
various multi-component amorphous material systems, which is difficult to
obtain otherwise. With the large amounts of molecular dynamics data generated
everyday in nearly every aspect of materials design, this approach provides a
broadly useful, automated tool to understand atomic scale dynamics in material
systems.Comment: 25 + 7 pages, 5 + 3 figure
A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities
The hidden metric space behind complex network topologies is a fervid topic
in current network science and the hyperbolic space is one of the most studied,
because it seems associated to the structural organization of many real complex
systems. The Popularity-Similarity-Optimization (PSO) model simulates how
random geometric graphs grow in the hyperbolic space, reproducing strong
clustering and scale-free degree distribution, however it misses to reproduce
an important feature of real complex networks, which is the community
organization. The Geometrical-Preferential-Attachment (GPA) model was recently
developed to confer to the PSO also a community structure, which is obtained by
forcing different angular regions of the hyperbolic disk to have variable level
of attractiveness. However, the number and size of the communities cannot be
explicitly controlled in the GPA, which is a clear limitation for real
applications. Here, we introduce the nonuniform PSO (nPSO) model that,
differently from GPA, forces heterogeneous angular node attractiveness by
sampling the angular coordinates from a tailored nonuniform probability
distribution, for instance a mixture of Gaussians. The nPSO differs from GPA in
other three aspects: it allows to explicitly fix the number and size of
communities; it allows to tune their mixing property through the network
temperature; it is efficient to generate networks with high clustering. After
several tests we propose the nPSO as a valid and efficient model to generate
networks with communities in the hyperbolic space, which can be adopted as a
realistic benchmark for different tasks such as community detection and link
prediction
- …