9,613 research outputs found
Unevenness of Loop Location in Complex Networks
The loop structure plays an important role in many aspects of complex
networks and attracts much attention. Among the previous works, Bianconi et al
find that real networks often have fewer short loops as compared to random
models. In this paper, we focus on the uneven location of loops which makes
some parts of the network rich while some other parts sparse in loops. We
propose a node removing process to analyze the unevenness and find rich loop
cores can exist in many real networks such as neural networks and food web
networks. Finally, an index is presented to quantify the unevenness of loop
location in complex networks.Comment: 7 pages, 6 figure
Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition
In this paper, we study chance constrained mixed integer program with
consideration of recourse decisions and their incurred cost, developed on a
finite discrete scenario set. Through studying a non-traditional bilinear mixed
integer formulation, we derive its linear counterparts and show that they could
be stronger than existing linear formulations. We also develop a variant of
Jensen's inequality that extends the one for stochastic program. To solve this
challenging problem, we present a variant of Benders decomposition method in
bilinear form, which actually provides an easy-to-use algorithm framework for
further improvements, along with a few enhancement strategies based on
structural properties or Jensen's inequality. Computational study shows that
the presented Benders decomposition method, jointly with appropriate
enhancement techniques, outperforms a commercial solver by an order of
magnitude on solving chance constrained program or detecting its infeasibility
Enhancing network robustness for malicious attacks
In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], the authors
proposed a simple measure for network robustness under malicious attacks on
nodes. With a greedy algorithm, they found the optimal structure with respect
to this quantity is an onion structure in which high-degree nodes form a core
surrounded by rings of nodes with decreasing degree. However, in real networks
the failure can also occur in links such as dysfunctional power cables and
blocked airlines. Accordingly, complementary to the node-robustness measurement
(), we propose a link-robustness index (). We show that solely
enhancing cannot guarantee the improvement of . Moreover, the
structure of -optimized network is found to be entirely different from
that of onion network. In order to design robust networks resistant to more
realistic attack condition, we propose a hybrid greedy algorithm which takes
both the and into account. We validate the robustness of our
generated networks against malicious attacks mixed with both nodes and links
failure. Finally, some economical constraints for swapping the links in real
networks are considered and significant improvement in both aspects of
robustness are still achieved.Comment: 6 pages, 6 figure
Temporal effects in trend prediction: identifying the most popular nodes in the future
Prediction is an important problem in different science domains. In this
paper, we focus on trend prediction in complex networks, i.e. to identify the
most popular nodes in the future. Due to the preferential attachment mechanism
in real systems, nodes' recent degree and cumulative degree have been
successfully applied to design trend prediction methods. Here we took into
account more detailed information about the network evolution and proposed a
temporal-based predictor (TBP). The TBP predicts the future trend by the node
strength in the weighted network with the link weight equal to its exponential
aging. Three data sets with time information are used to test the performance
of the new method. We find that TBP have high general accuracy in predicting
the future most popular nodes. More importantly, it can identify many potential
objects with low popularity in the past but high popularity in the future. The
effect of the decay speed in the exponential aging on the results is discussed
in detail
Inferring network topology via the propagation process
Inferring the network topology from the dynamics is a fundamental problem, with wide applications in geology, biology, and even counter-terrorism. Based on the propagation process, we present a simple method to uncover the network topology. A numerical simulation on artificial networks shows that our method enjoys a high accuracy in inferring the network topology. We find that the infection rate in the propagation process significantly influences the accuracy, and that each network corresponds to an optimal infection rate. Moreover, the method generally works better in large networks. These finding are confirmed in both real social and nonsocial networks. Finally, the method is extended to directed networks, and a similarity measure specific for directed networks is designed
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