87,843 research outputs found
Singularities in ternary mixtures of k-core percolation
Heterogeneous k-core percolation is an extension of a percolation model which
has interesting applications to the resilience of networks under random damage.
In this model, the notion of node robustness is local, instead of global as in
uniform k-core percolation. One of the advantages of k-core percolation models
is the validity of an analytical mathematical framework for a large class of
network topologies. We study ternary mixtures of node types in random networks
and show the presence of a new type of critical phenomenon. This scenario may
have useful applications in the stability of large scale infrastructures and
the description of glass-forming systems.Comment: To appear in Complex Networks, Studies in Computational Intelligence,
Proceedings of CompleNet 201
Robustness: a New Form of Heredity Motivated by Dynamic Networks
We investigate a special case of hereditary property in graphs, referred to
as {\em robustness}. A property (or structure) is called robust in a graph
if it is inherited by all the connected spanning subgraphs of . We motivate
this definition using two different settings of dynamic networks. The first
corresponds to networks of low dynamicity, where some links may be permanently
removed so long as the network remains connected. The second corresponds to
highly-dynamic networks, where communication links appear and disappear
arbitrarily often, subject only to the requirement that the entities are
temporally connected in a recurrent fashion ({\it i.e.} they can always reach
each other through temporal paths). Each context induces a different
interpretation of the notion of robustness.
We start by motivating the definition and discussing the two interpretations,
after what we consider the notion independently from its interpretation, taking
as our focus the robustness of {\em maximal independent sets} (MIS). A graph
may or may not admit a robust MIS. We characterize the set of graphs \forallMIS
in which {\em all} MISs are robust. Then, we turn our attention to the graphs
that {\em admit} a robust MIS (\existsMIS). This class has a more complex
structure; we give a partial characterization in terms of elementary graph
properties, then a complete characterization by means of a (polynomial time)
decision algorithm that accepts if and only if a robust MIS exists. This
algorithm can be adapted to construct such a solution if one exists
Evolution of complex modular biological networks
Biological networks have evolved to be highly functional within uncertain
environments while remaining extremely adaptable. One of the main contributors
to the robustness and evolvability of biological networks is believed to be
their modularity of function, with modules defined as sets of genes that are
strongly interconnected but whose function is separable from those of other
modules. Here, we investigate the in silico evolution of modularity and
robustness in complex artificial metabolic networks that encode an increasing
amount of information about their environment while acquiring ubiquitous
features of biological, social, and engineering networks, such as scale-free
edge distribution, small-world property, and fault-tolerance. These networks
evolve in environments that differ in their predictability, and allow us to
study modularity from topological, information-theoretic, and gene-epistatic
points of view using new tools that do not depend on any preconceived notion of
modularity. We find that for our evolved complex networks as well as for the
yeast protein-protein interaction network, synthetic lethal pairs consist
mostly of redundant genes that lie close to each other and therefore within
modules, while knockdown suppressor pairs are farther apart and often straddle
modules, suggesting that knockdown rescue is mediated by alternative pathways
or modules. The combination of network modularity tools together with genetic
interaction data constitutes a powerful approach to study and dissect the role
of modularity in the evolution and function of biological networks.Comment: 28 pages, 10 figures, 8 supplemental figures, and one supplementary
table. Final version to appear in PLoS Comp Bi
Power network and smart grids analysis from a graph theoretic perspective
The growing size and complexity of power systems has given raise to the use of complex network theory in their modelling, analysis, and synthesis. Though most of the previous studies in this area have focused on distributed control through well established protocols like synchronization and consensus, recently, a few fundamental concepts from graph theory have also been applied, for example in symmetry-based cluster synchronization. Among the existing notions of graph theory, graph symmetry is the focus of this proposal. However, there are other development around some concepts from complex network theory such as graph clustering in the study.
In spite of the widespread applications of symmetry concepts in many real world complex networks, one can rarely find an article exploiting the symmetry in power systems. In addition, no study has been conducted in analysing controllability and robustness for a power network employing graph symmetry. It has been verified that graph symmetry promotes robustness but impedes controllability. A largely absent work, even in other fields outside power systems, is the simultaneous investigation of the symmetry effect on controllability and robustness.
The thesis can be divided into two section. The first section, including Chapters 2-3, establishes the major theoretical development around the applications of graph symmetry in power networks. A few important topics in power systems and smart grids such as controllability and robustness are addressed using the symmetry concept. These topics are directed toward solving specific problems in complex power networks. The controllability analysis will lead to new algorithms elaborating current controllability benchmarks such as the maximum matching and the minimum dominant set. The resulting algorithms will optimize the number of required driver nodes indicated as FACTS devices in power networks. The second topic, robustness, will be tackled by the symmetry analysis of the network to investigate three aspects of network robustness: robustness of controllability, disturbance decoupling, and fault tolerance against failure in a network element.
In the second section, including Chapters 4-8, in addition to theoretical development, a few novel applications are proposed for the theoretical development proposed in both sections one and two. In Chapter 4, an application for the proposed approaches is introduced and developed. The placement of flexible AC transmission systems (FACTS) is investigated where the cybersecurity of the associated data exchange under the wide area power networks is also considered. A new notion of security, i.e. moderated-k-symmetry, is introduced to leverage on the symmetry characteristics of the network to obscure the network data from the adversary perspective. In chapters 5-8, the use of graph theory, and in particular, graph symmetry and centrality, are adapted for the complex network of charging stations. In Chapter 5, the placement and sizing of charging stations (CSs) of the network of electric vehicles are addressed by proposing a novel complex network model of the charging stations. The problems of placement and sizing are then reformulated in a control framework and the impact of symmetry on the number and locations of charging stations is also investigated. These results are developed in Chapters 6-7 to robust placement and sizing of charging stations for the Tesla network of Sydney where the problem of extending the capacity having a set of pre-existing CSs are addressed. The role of centrality in placement of CSs is investigated in Chapter 8. Finally, concluding remarks and future works are presented in Chapter 9
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