1,773 research outputs found
Nonparametric Bayes Modeling of Populations of Networks
Replicated network data are increasingly available in many research fields.
In connectomic applications, inter-connections among brain regions are
collected for each patient under study, motivating statistical models which can
flexibly characterize the probabilistic generative mechanism underlying these
network-valued data. Available models for a single network are not designed
specifically for inference on the entire probability mass function of a
network-valued random variable and therefore lack flexibility in characterizing
the distribution of relevant topological structures. We propose a flexible
Bayesian nonparametric approach for modeling the population distribution of
network-valued data. The joint distribution of the edges is defined via a
mixture model which reduces dimensionality and efficiently incorporates network
information within each mixture component by leveraging latent space
representations. The formulation leads to an efficient Gibbs sampler and
provides simple and coherent strategies for inference and goodness-of-fit
assessments. We provide theoretical results on the flexibility of our model and
illustrate improved performance --- compared to state-of-the-art models --- in
simulations and application to human brain networks
Design of Easily Synchronizable Oscillator Networks Using the Monte Carlo Optimization Method
Starting with an initial random network of oscillators with a heterogeneous
frequency distribution, its autonomous synchronization ability can be largely
improved by appropriately rewiring the links between the elements. Ensembles of
synchronization-optimized networks with different connectivities are generated
and their statistical properties are studied
Economic Small-World Behavior in Weighted Networks
The small-world phenomenon has been already the subject of a huge variety of
papers, showing its appeareance in a variety of systems. However, some big
holes still remain to be filled, as the commonly adopted mathematical
formulation suffers from a variety of limitations, that make it unsuitable to
provide a general tool of analysis for real networks, and not just for
mathematical (topological) abstractions. In this paper we show where the major
problems arise, and how there is therefore the need for a new reformulation of
the small-world concept. Together with an analysis of the variables involved,
we then propose a new theory of small-world networks based on two leading
concepts: efficiency and cost. Efficiency measures how well information
propagates over the network, and cost measures how expensive it is to build a
network. The combination of these factors leads us to introduce the concept of
{\em economic small worlds}, that formalizes the idea of networks that are
"cheap" to build, and nevertheless efficient in propagating information, both
at global and local scale. This new concept is shown to overcome all the
limitations proper of the so-far commonly adopted formulation, and to provide
an adequate tool to quantitatively analyze the behaviour of complex networks in
the real world. Various complex systems are analyzed, ranging from the realm of
neural networks, to social sciences, to communication and transportation
networks. In each case, economic small worlds are found. Moreover, using the
economic small-world framework, the construction principles of these networks
can be quantitatively analyzed and compared, giving good insights on how
efficiency and economy principles combine up to shape all these systems.Comment: 17 pages, 10 figures, 4 table
Parallel solution of power system linear equations
At the heart of many power system computations lies the solution of a large sparse set of linear equations. These equations arise from the modelling of the network and are the cause of a computational bottleneck in power system analysis applications. Efficient sequential techniques have been developed to solve these equations but the solution is still too slow for applications such as real-time dynamic simulation and on-line security analysis. Parallel computing techniques have been explored in the attempt to find faster solutions but the methods developed to date have not efficiently exploited the full power of parallel processing. This thesis considers the solution of the linear network equations encountered in power system computations. Based on the insight provided by the elimination tree, it is proposed that a novel matrix structure is adopted to allow the exploitation of parallelism which exists within the cutset of a typical parallel solution. Using this matrix structure it is possible to reduce the size of the sequential part of the problem and to increase the speed and efficiency of typical LU-based parallel solution. A method for transforming the admittance matrix into the required form is presented along with network partitioning and load balancing techniques. Sequential solution techniques are considered and existing parallel methods are surveyed to determine their strengths and weaknesses. Combining the benefits of existing solutions with the new matrix structure allows an improved LU-based parallel solution to be derived. A simulation of the improved LU solution is used to show the improvements in performance over a standard LU-based solution that result from the adoption of the new techniques. The results of a multiprocessor implementation of the method are presented and the new method is shown to have a better performance than existing methods for distributed memory multiprocessors
Different approaches to community detection
A precise definition of what constitutes a community in networks has remained
elusive. Consequently, network scientists have compared community detection
algorithms on benchmark networks with a particular form of community structure
and classified them based on the mathematical techniques they employ. However,
this comparison can be misleading because apparent similarities in their
mathematical machinery can disguise different reasons for why we would want to
employ community detection in the first place. Here we provide a focused review
of these different motivations that underpin community detection. This
problem-driven classification is useful in applied network science, where it is
important to select an appropriate algorithm for the given purpose. Moreover,
highlighting the different approaches to community detection also delineates
the many lines of research and points out open directions and avenues for
future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in
network clustering and blockmodeling, and based on an extended version of The
many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4
(2017) by the same author
Systemic risk assessment through high order clustering coefficient
In this article we propose a novel measure of systemic risk in the context of
financial networks. To this aim, we provide a definition of systemic risk which
is based on the structure, developed at different levels, of clustered
neighbours around the nodes of the network. The proposed measure incorporates
the generalized concept of clustering coefficient of order of a node
introduced in Cerqueti et al. (2018). Its properties are also explored in terms
of systemic risk assessment. Empirical experiments on the time-varying global
banking network show the effectiveness of the presented systemic risk measure
and provide insights on how systemic risk has changed over the last years, also
in the light of the recent financial crisis and the subsequent more stringent
regulation for globally systemically important banks.Comment: Submitte
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