105 research outputs found
Distributed Reconstruction of Nonlinear Networks: An ADMM Approach
In this paper, we present a distributed algorithm for the reconstruction of
large-scale nonlinear networks. In particular, we focus on the identification
from time-series data of the nonlinear functional forms and associated
parameters of large-scale nonlinear networks. Recently, a nonlinear network
reconstruction problem was formulated as a nonconvex optimisation problem based
on the combination of a marginal likelihood maximisation procedure with
sparsity inducing priors. Using a convex-concave procedure (CCCP), an iterative
reweighted lasso algorithm was derived to solve the initial nonconvex
optimisation problem. By exploiting the structure of the objective function of
this reweighted lasso algorithm, a distributed algorithm can be designed. To
this end, we apply the alternating direction method of multipliers (ADMM) to
decompose the original problem into several subproblems. To illustrate the
effectiveness of the proposed methods, we use our approach to identify a
network of interconnected Kuramoto oscillators with different network sizes
(500~100,000 nodes).Comment: To appear in the Preprints of 19th IFAC World Congress 201
Bounding stationary averages of polynomial diffusions via semidefinite programming
We introduce an algorithm based on semidefinite programming that yields
increasing (resp. decreasing) sequences of lower (resp. upper) bounds on
polynomial stationary averages of diffusions with polynomial drift vector and
diffusion coefficients. The bounds are obtained by optimising an objective,
determined by the stationary average of interest, over the set of real vectors
defined by certain linear equalities and semidefinite inequalities which are
satisfied by the moments of any stationary measure of the diffusion. We
exemplify the use of the approach through several applications: a Bayesian
inference problem; the computation of Lyapunov exponents of linear ordinary
differential equations perturbed by multiplicative white noise; and a
reliability problem from structural mechanics. Additionally, we prove that the
bounds converge to the infimum and supremum of the set of stationary averages
for certain SDEs associated with the computation of the Lyapunov exponents, and
we provide numerical evidence of convergence in more general settings
Shaping Pulses to Control Bistable Biological Systems
In this paper we study how to shape temporal pulses to switch a bistable
system between its stable steady states. Our motivation for pulse-based control
comes from applications in synthetic biology, where it is generally difficult
to implement real-time feedback control systems due to technical limitations in
sensors and actuators. We show that for monotone bistable systems, the
estimation of the set of all pulses that switch the system reduces to the
computation of one non-increasing curve. We provide an efficient algorithm to
compute this curve and illustrate the results with a genetic bistable system
commonly used in synthetic biology. We also extend these results to models with
parametric uncertainty and provide a number of examples and counterexamples
that demonstrate the power and limitations of the current theory. In order to
show the full potential of the framework, we consider the problem of inducing
oscillations in a monotone biochemical system using a combination of temporal
pulses and event-based control. Our results provide an insight into the
dynamics of bistable systems under external inputs and open up numerous
directions for future investigation.Comment: 14 pages, contains material from the paper in Proc Amer Control Conf
2015, (pp. 3138-3143) and "Shaping pulses to control bistable systems
analysis, computation and counterexamples", which is due to appear in
Automatic
Approximations of countably-infinite linear programs over bounded measure spaces
We study a class of countably-infinite-dimensional linear programs (CILPs)
whose feasible sets are bounded subsets of appropriately defined weighted
spaces of measures. We show how to approximate the optimal value, optimal
points, and minimal points of these CILPs by solving finite-dimensional linear
programs. The errors of our approximations converge to zero as the size of the
finite-dimensional program approaches that of the original problem and are easy
to bound in practice. We discuss the use of our methods in the computation of
the stationary distributions, occupation measures, and exit distributions of
Markov~chains
Hybrid Graph: A Unified Graph Representation with Datasets and Benchmarks for Complex Graphs
Graphs are widely used to encapsulate a variety of data formats, but
real-world networks often involve complex node relations beyond only being
pairwise. While hypergraphs and hierarchical graphs have been developed and
employed to account for the complex node relations, they cannot fully represent
these complexities in practice. Additionally, though many Graph Neural Networks
(GNNs) have been proposed for representation learning on higher-order graphs,
they are usually only evaluated on simple graph datasets. Therefore, there is a
need for a unified modelling of higher-order graphs, and a collection of
comprehensive datasets with an accessible evaluation framework to fully
understand the performance of these algorithms on complex graphs. In this
paper, we introduce the concept of hybrid graphs, a unified definition for
higher-order graphs, and present the Hybrid Graph Benchmark (HGB). HGB contains
23 real-world hybrid graph datasets across various domains such as biology,
social media, and e-commerce. Furthermore, we provide an extensible evaluation
framework and a supporting codebase to facilitate the training and evaluation
of GNNs on HGB. Our empirical study of existing GNNs on HGB reveals various
research opportunities and gaps, including (1) evaluating the actual
performance improvement of hypergraph GNNs over simple graph GNNs; (2)
comparing the impact of different sampling strategies on hybrid graph learning
methods; and (3) exploring ways to integrate simple graph and hypergraph
information. We make our source code and full datasets publicly available at
https://zehui127.github.io/hybrid-graph-benchmark/.Comment: Preprint. Under review. 16 pages, 5 figures, 11 table
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