180,111 research outputs found
Lumping of Degree-Based Mean Field and Pair Approximation Equations for Multi-State Contact Processes
Contact processes form a large and highly interesting class of dynamic
processes on networks, including epidemic and information spreading. While
devising stochastic models of such processes is relatively easy, analyzing them
is very challenging from a computational point of view, particularly for large
networks appearing in real applications. One strategy to reduce the complexity
of their analysis is to rely on approximations, often in terms of a set of
differential equations capturing the evolution of a random node, distinguishing
nodes with different topological contexts (i.e., different degrees of different
neighborhoods), like degree-based mean field (DBMF), approximate master
equation (AME), or pair approximation (PA). The number of differential
equations so obtained is typically proportional to the maximum degree kmax of
the network, which is much smaller than the size of the master equation of the
underlying stochastic model, yet numerically solving these equations can still
be problematic for large kmax. In this paper, we extend AME and PA, which has
been proposed only for the binary state case, to a multi-state setting and
provide an aggregation procedure that clusters together nodes having similar
degrees, treating those in the same cluster as indistinguishable, thus reducing
the number of equations while preserving an accurate description of global
observables of interest. We also provide an automatic way to build such
equations and to identify a small number of degree clusters that give accurate
results. The method is tested on several case studies, where it shows a high
level of compression and a reduction of computational time of several orders of
magnitude for large networks, with minimal loss in accuracy.Comment: 16 pages with the Appendi
Fast Neural Network Predictions from Constrained Aerodynamics Datasets
Incorporating computational fluid dynamics in the design process of jets,
spacecraft, or gas turbine engines is often challenged by the required
computational resources and simulation time, which depend on the chosen
physics-based computational models and grid resolutions. An ongoing problem in
the field is how to simulate these systems faster but with sufficient accuracy.
While many approaches involve simplified models of the underlying physics,
others are model-free and make predictions based only on existing simulation
data. We present a novel model-free approach in which we reformulate the
simulation problem to effectively increase the size of constrained pre-computed
datasets and introduce a novel neural network architecture (called a cluster
network) with an inductive bias well-suited to highly nonlinear computational
fluid dynamics solutions. Compared to the state-of-the-art in model-based
approximations, we show that our approach is nearly as accurate, an order of
magnitude faster, and easier to apply. Furthermore, we show that our method
outperforms other model-free approaches
Complete Characterization of Stability of Cluster Synchronization in Complex Dynamical Networks
Synchronization is an important and prevalent phenomenon in natural and
engineered systems. In many dynamical networks, the coupling is balanced or
adjusted in order to admit global synchronization, a condition called Laplacian
coupling. Many networks exhibit incomplete synchronization, where two or more
clusters of synchronization persist, and computational group theory has
recently proved to be valuable in discovering these cluster states based upon
the topology of the network. In the important case of Laplacian coupling,
additional synchronization patterns can exist that would not be predicted from
the group theory analysis alone. The understanding of how and when clusters
form, merge, and persist is essential for understanding collective dynamics,
synchronization, and failure mechanisms of complex networks such as electric
power grids, distributed control networks, and autonomous swarming vehicles. We
describe here a method to find and analyze all of the possible cluster
synchronization patterns in a Laplacian-coupled network, by applying methods of
computational group theory to dynamically-equivalent networks. We present a
general technique to evaluate the stability of each of the dynamically valid
cluster synchronization patterns. Our results are validated in an electro-optic
experiment on a 5 node network that confirms the synchronization patterns
predicted by the theory.Comment: 6 figure
Improvements in the reconstruction of time-varying gene regulatory networks: dynamic programming and regularization by information sharing among genes
<b>Method:</b> Dynamic Bayesian networks (DBNs) have been applied widely to reconstruct the structure of regulatory processes from time series data, and they have established themselves as a standard modelling tool in computational systems biology. The conventional approach is based on the assumption of a homogeneous Markov chain, and many recent research efforts have focused on relaxing this restriction. An approach that enjoys particular popularity is based on a combination of a DBN with a multiple changepoint process, and the application of a Bayesian inference scheme via reversible jump Markov chain Monte Carlo (RJMCMC). In the present article, we expand this approach in two ways. First, we show that a dynamic programming scheme allows the changepoints to be sampled from the correct conditional distribution, which results in improved convergence over RJMCMC. Second, we introduce a novel Bayesian clustering and information sharing scheme among nodes, which provides a mechanism for automatic model complexity tuning.
<b>Results:</b> We evaluate the dynamic programming scheme on expression time series for Arabidopsis thaliana genes involved in circadian regulation. In a simulation study we demonstrate that the regularization scheme improves the network reconstruction accuracy over that obtained with recently proposed inhomogeneous DBNs. For gene expression profiles from a synthetically designed Saccharomyces cerevisiae strain under switching carbon metabolism we show that the combination of both: dynamic programming and regularization yields an inference procedure that outperforms two alternative established network reconstruction methods from the biology literature
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