578 research outputs found
Communication Network Design: Balancing Modularity and Mixing via Optimal Graph Spectra
By leveraging information technologies, organizations now have the ability to
design their communication networks and crowdsourcing platforms to pursue
various performance goals, but existing research on network design does not
account for the specific features of social networks, such as the notion of
teams. We fill this gap by demonstrating how desirable aspects of
organizational structure can be mapped parsimoniously onto the spectrum of the
graph Laplacian allowing the specification of structural objectives and build
on recent advances in non-convex programming to optimize them. This design
framework is general, but we focus here on the problem of creating graphs that
balance high modularity and low mixing time, and show how "liaisons" rather
than brokers maximize this objective
COMMUNITY DETECTION IN COMPLEX NETWORKS AND APPLICATION TO DENSE WIRELESS SENSOR NETWORKS LOCALIZATION
Complex network analysis is applied in numerous researches. Features and characteristics of complex networks provide information associated with a network feature called community structure. Naturally, nodes with similar attributes will be more likely to form a community. Community detection is described as the process by which complex network data are analyzed to uncover organizational properties, and structure; and ultimately to enable extraction of useful information. Analysis of Wireless Sensor Networks (WSN) is considered as one of the most important categories of network analysis due to their enormous and emerging applications. Most WSN applications are location-aware, which entails precise localization of the deployed sensor nodes. However, localization of sensor nodes in very dense network is a challenging task. Among various challenges associated with localization of dense WSNs, anchor node selection is shown as a prominent open problem. Optimum anchor selection impacts overall sensor node localization in terms of accuracy and consumed energy. In this thesis, various approaches are developed to address both overlapping and non-overlapping community detection. The proposed approaches target small-size to very large-size networks in near linear time, which is important for very large, densely-connected networks. Performance of the proposed techniques are evaluated over real-world data-sets with up to 106 nodes and syntactic networks via Newman\u27s Modularity and Normalized Mutual Information (NMI). Moreover, the proposed community detection approaches are extended to develop a novel criterion for range-free anchor selection in WSNs. Our approach uses novel objective functions based on nodes\u27 community memberships to reveal a set of anchors among all available permutations of anchors-selection sets. The performance---the mean and variance of the localization error---of the proposed approach is evaluated for a variety of node deployment scenarios and compared with random anchor selection and the full-ranging approach. In order to study the effectiveness of our algorithm, the performance is evaluated over several simulations that randomly generate network configurations. By incorporating our proposed criteria, the accuracy of the position estimate is improved significantly relative to random anchor selection localization methods. Simulation results show that the proposed technique significantly improves both the accuracy and the precision of the location estimation
Assortative-Constrained Stochastic Block Models
Stochastic block models (SBMs) are often used to find assortative community
structures in networks, such that the probability of connections within
communities is higher than in between communities. However, classic SBMs are
not limited to assortative structures. In this study, we discuss the
implications of this model-inherent indifference towards assortativity or
disassortativity, and show that this characteristic can lead to undesirable
outcomes for networks which are presupposedy assortative but which contain a
reduced amount of information. To circumvent this issue, we introduce a
constrained SBM that imposes strong assortativity constraints, along with
efficient algorithmic approaches to solve it. These constraints significantly
boost community recovery capabilities in regimes that are close to the
information-theoretic threshold. They also permit to identify
structurally-different communities in networks representing cerebral-cortex
activity regions
Local to Global: A Distributed Quantum Approximate Optimization Algorithm for Pseudo-Boolean Optimization Problems
With the rapid advancement of quantum computing, Quantum Approximate
Optimization Algorithm (QAOA) is considered as a promising candidate to
demonstrate quantum supremacy, which exponentially solves a class of Quadratic
Unconstrained Binary Optimization (QUBO) problems. However, limited qubit
availability and restricted coherence time challenge QAOA to solve large-scale
pseudo-Boolean problems on currently available Near-term Intermediate Scale
Quantum (NISQ) devices. In this paper, we propose a distributed QAOA which can
solve a general pseudo-Boolean problem by converting it to a simplified Ising
model. Different from existing distributed QAOAs' assuming that local solutions
are part of a global one, which is not often the case, we introduce community
detection using Louvian algorithm to partition the graph where subgraphs are
further compressed by community representation and merged into a higher level
subgraph. Recursively and backwards, local solutions of lower level subgraphs
are updated by heuristics from solutions of higher level subgraphs. Compared
with existing methods, our algorithm incorporates global heuristics into local
solutions such that our algorithm is proven to achieve a higher approximation
ratio and outperforms across different graph configurations. Also, ablation
studies validate the effectiveness of each component in our method.Comment: 12 pages, 6 figure
Stochastic Block Models are a Discrete Surface Tension
Networks, which represent agents and interactions between them, arise in
myriad applications throughout the sciences, engineering, and even the
humanities. To understand large-scale structure in a network, a common task is
to cluster a network's nodes into sets called "communities", such that there
are dense connections within communities but sparse connections between them. A
popular and statistically principled method to perform such clustering is to
use a family of generative models known as stochastic block models (SBMs). In
this paper, we show that maximum likelihood estimation in an SBM is a network
analog of a well-known continuum surface-tension problem that arises from an
application in metallurgy. To illustrate the utility of this relationship, we
implement network analogs of three surface-tension algorithms, with which we
successfully recover planted community structure in synthetic networks and
which yield fascinating insights on empirical networks that we construct from
hyperspectral videos.Comment: to appear in Journal of Nonlinear Scienc
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