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Wireless sensor networks (WSNs) have attracted substantial research interest, especially in the context of performing monitoring and surveillance tasks. However, it is challenging to strike compelling trade-offs amongst the various…

Quantum adiabatic optimization has long been expected to outperform classical methods in solving NP-type problems. While this has been proven in certain experiments, its main applications still reside in academic problems where the size of…

We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…

This paper addresses the problem of mixed-membership estimation in networks, where the goal is to efficiently estimate the latent mixed-membership structure from the observed network. Recognizing the widespread availability and valuable…

Group Search Optimizer(GSO) is one of the best algorithms, is very new in the field of Evolutionary Computing. It is very robust and efficient algorithm, which is inspired by animal searching behaviour. The paper describes an application of…

Electromagnetismlike Optimization (EMO) is a global optimization algorithm, particularly well suited to solve problems featuring nonlinear and multimodal cost functions. EMO employs searcher agents that emulate a population of charged…

Modularity is a popular measure of community structure. However, maximizing the modularity can lead to many competing partitions, with almost the same modularity, that are poorly correlated with each other. It can also produce illusory…

The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block…

Revealing a community structure in a network or dataset is a central problem arising in many scientific areas. The modularity function $Q$ is an established measure quantifying the quality of a community, being identified as a set of nodes…

An efficient MCMC algorithm is presented to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modelling or block-clustering. The model is the stochastic blockmodel…

Using an intuitive concept of what constitutes a meaningful community, a novel metric is formulated for detecting non-overlapping communities in undirected, weighted heterogeneous networks. This metric, modularity density, is shown to be…

We introduce a metric space of clusterings, where clusterings are described by a binary vector indexed by the vertex-pairs. We extend this geometry to a hypersphere and prove that maximizing modularity is equivalent to minimizing the…

We study a graph based version of the Ohta-Kawasaki functional, which was originally introduced in a continuum setting to model pattern formation in diblock copolymer melts and has been studied extensively as a paradigmatic example of a…

Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null…

We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize 'perturbation modularity', defined as the autocovariance of…

Here we propose a new method to compare the modular structure of a pair of node-aligned networks. The majority of current methods, such as normalized mutual information, compare two node partitions derived from a community detection…

Graph-based machine learning has seen an increased interest over the last decade with many connections to other fields of applied mathematics. Learning based on partial differential equations, such as the phase-field Allen-Cahn equation,…

In this work we extend the class of Consensus-Based Optimization (CBO) metaheuristic methods by considering memory effects and a random selection strategy. The proposed algorithm iteratively updates a population of particles according to a…

Community detection is one of the fundamental problems of network analysis, for which a number of methods have been proposed. Most model-based or criteria-based methods have to solve an optimization problem over a discrete set of labels to…

Optimization is nothing but a mathematical technique which finds maxima or minima of any function of concern in some realistic region. Different optimization techniques are proposed which are competing for the best solution. Particle Swarm…