17,182 research outputs found
Reduction of Second-Order Network Systems with Structure Preservation
This paper proposes a general framework for structure-preserving model
reduction of a secondorder network system based on graph clustering. In this
approach, vertex dynamics are captured by the transfer functions from inputs to
individual states, and the dissimilarities of vertices are quantified by the
H2-norms of the transfer function discrepancies. A greedy hierarchical
clustering algorithm is proposed to place those vertices with similar dynamics
into same clusters. Then, the reduced-order model is generated by the
Petrov-Galerkin method, where the projection is formed by the characteristic
matrix of the resulting network clustering. It is shown that the simplified
system preserves an interconnection structure, i.e., it can be again
interpreted as a second-order system evolving over a reduced graph.
Furthermore, this paper generalizes the definition of network controllability
Gramian to second-order network systems. Based on it, we develop an efficient
method to compute H2-norms and derive the approximation error between the
full-order and reduced-order models. Finally, the approach is illustrated by
the example of a small-world network
Joint Centrality Distinguishes Optimal Leaders in Noisy Networks
We study the performance of a network of agents tasked with tracking an
external unknown signal in the presence of stochastic disturbances and under
the condition that only a limited subset of agents, known as leaders, can
measure the signal directly. We investigate the optimal leader selection
problem for a prescribed maximum number of leaders, where the optimal leader
set minimizes total system error defined as steady-state variance about the
external signal. In contrast to previously established greedy algorithms for
optimal leader selection, our results rely on an expression of total system
error in terms of properties of the underlying network graph. We demonstrate
that the performance of any given set of leaders depends on their influence as
determined by a new graph measure of centrality of a set. We define the of a set of nodes in a network graph such that a leader set with
maximal joint centrality is an optimal leader set. In the case of a single
leader, we prove that the optimal leader is the node with maximal information
centrality. In the case of multiple leaders, we show that the nodes in the
optimal leader set balance high information centrality with a coverage of the
graph. For special cases of graphs, we solve explicitly for optimal leader
sets. We illustrate with examples.Comment: Conditionally accepted to IEEE TCN
Hamiltonian System Approach to Distributed Spectral Decomposition in Networks
Because of the significant increase in size and complexity of the networks,
the distributed computation of eigenvalues and eigenvectors of graph matrices
has become very challenging and yet it remains as important as before. In this
paper we develop efficient distributed algorithms to detect, with higher
resolution, closely situated eigenvalues and corresponding eigenvectors of
symmetric graph matrices. We model the system of graph spectral computation as
physical systems with Lagrangian and Hamiltonian dynamics. The spectrum of
Laplacian matrix, in particular, is framed as a classical spring-mass system
with Lagrangian dynamics. The spectrum of any general symmetric graph matrix
turns out to have a simple connection with quantum systems and it can be thus
formulated as a solution to a Schr\"odinger-type differential equation. Taking
into account the higher resolution requirement in the spectrum computation and
the related stability issues in the numerical solution of the underlying
differential equation, we propose the application of symplectic integrators to
the calculation of eigenspectrum. The effectiveness of the proposed techniques
is demonstrated with numerical simulations on real-world networks of different
sizes and complexities
New technologies and procurement and negotiation process support
The aim of this work is to present innovative IT solutions which can
be widely applied in the area of procurement processes and accompanying
negotiations, thereby contributing to the assessment of their practical
applicability. Particular attention has been placed on Ariba Networks, a
platform for procurement management.
This work sources the latest literature in this field as well
as research conducted in one of the largest worldwide companies operating
in the Polish market of fast moving consumable goods.Preparation and printing funded by the National Agency for Research and Development under project âKreator InnowacyjnoĆci â wparcie dla PrzedsiÄbiorczoĆci akademickiej
Surface networks
© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and ânatural â data structures because they store a surface as a framework of âsurface â elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou
Mean-field analysis of the q-voter model on networks
We present a detailed investigation of the behavior of the nonlinear q-voter
model for opinion dynamics. At the mean-field level we derive analytically, for
any value of the number q of agents involved in the elementary update, the
phase diagram, the exit probability and the consensus time at the transition
point. The mean-field formalism is extended to the case that the interaction
pattern is given by generic heterogeneous networks. We finally discuss the case
of random regular networks and compare analytical results with simulations.Comment: 20 pages, 10 figure
Online Learning of Dynamic Parameters in Social Networks
This paper addresses the problem of online learning in a dynamic setting. We
consider a social network in which each individual observes a private signal
about the underlying state of the world and communicates with her neighbors at
each time period. Unlike many existing approaches, the underlying state is
dynamic, and evolves according to a geometric random walk. We view the scenario
as an optimization problem where agents aim to learn the true state while
suffering the smallest possible loss. Based on the decomposition of the global
loss function, we introduce two update mechanisms, each of which generates an
estimate of the true state. We establish a tight bound on the rate of change of
the underlying state, under which individuals can track the parameter with a
bounded variance. Then, we characterize explicit expressions for the steady
state mean-square deviation(MSD) of the estimates from the truth, per
individual. We observe that only one of the estimators recovers the optimal
MSD, which underscores the impact of the objective function decomposition on
the learning quality. Finally, we provide an upper bound on the regret of the
proposed methods, measured as an average of errors in estimating the parameter
in a finite time.Comment: 12 pages, To appear in Neural Information Processing Systems (NIPS)
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