3,321 research outputs found
On the genericity properties in networked estimation: Topology design and sensor placement
In this paper, we consider networked estimation of linear, discrete-time
dynamical systems monitored by a network of agents. In order to minimize the
power requirement at the (possibly, battery-operated) agents, we require that
the agents can exchange information with their neighbors only \emph{once per
dynamical system time-step}; in contrast to consensus-based estimation where
the agents exchange information until they reach a consensus. It can be
verified that with this restriction on information exchange, measurement fusion
alone results in an unbounded estimation error at every such agent that does
not have an observable set of measurements in its neighborhood. To over come
this challenge, state-estimate fusion has been proposed to recover the system
observability. However, we show that adding state-estimate fusion may not
recover observability when the system matrix is structured-rank (-rank)
deficient.
In this context, we characterize the state-estimate fusion and measurement
fusion under both full -rank and -rank deficient system matrices.Comment: submitted for IEEE journal publicatio
Controlling edge dynamics in complex networks
The interaction of distinct units in physical, social, biological and
technological systems naturally gives rise to complex network structures.
Networks have constantly been in the focus of research for the last decade,
with considerable advances in the description of their structural and dynamical
properties. However, much less effort has been devoted to studying the
controllability of the dynamics taking place on them. Here we introduce and
evaluate a dynamical process defined on the edges of a network, and demonstrate
that the controllability properties of this process significantly differ from
simple nodal dynamics. Evaluation of real-world networks indicates that most of
them are more controllable than their randomized counterparts. We also find
that transcriptional regulatory networks are particularly easy to control.
Analytic calculations show that networks with scale-free degree distributions
have better controllability properties than uncorrelated networks, and
positively correlated in- and out-degrees enhance the controllability of the
proposed dynamics.Comment: Preprint. 24 pages, 4 figures, 2 tables. Source code available at
http://github.com/ntamas/netctr
Twin subgraphs and core-semiperiphery-periphery structures
A standard approach to reduce the complexity of very large networks is to
group together sets of nodes into clusters according to some criterion which
reflects certain structural properties of the network. Beyond the well-known
modularity measures defining communities, there are criteria based on the
existence of similar or identical connection patterns of a node or sets of
nodes to the remainder of the network. A key notion in this context is that of
structurally equivalent or twin nodes, displaying exactly the same connection
pattern to the remainder of the network.
The first goal of this paper is to extend this idea to subgraphs of arbitrary
order of a given network, by means of the notions of T-twin and F-twin
subgraphs. This is motivated by the need to provide a systematic approach to
the analysis of core-semiperiphery-periphery (CSP) structures, a notion which
somehow lacks a formal treatment in the literature. The goal is to provide an
analytical framework accommodating and extending the idea that the unique
(ideal) core-periphery (CP) structure is a 2-partitioned K2. We provide a
formal definition of CSP structures in terms of core eccentricities and
periphery degrees, with semiperiphery vertices acting as intermediaries. The
T-twin and F-twin notions then make it possible to reduce the large number of
resulting structures by identifying isomorphic substructures which share the
connection pattern to the remainder of the graph, paving the way for the
decomposition and enumeration of CSP structures. We compute the resulting CSP
structures up to order six.
We illustrate the scope of our results by analyzing a subnetwork of the
network of 1994 metal manufactures trade. Our approach can be further applied
in complex network theory and seems to have many potential extensions
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