Community detection in complex networks using Extremal Optimization

We propose a novel method to find the community structure in complex networks based on an extremal optimization of the value of modularity. The method outperforms the optimal modularity found by the existing algorithms in the literature. We present the results of the algorithm for computer simulated and real networks and compare them with other approaches. The efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks.Comment: 4 pages, 4 figure

Impact of region-of-interest delineation methods, reconstruction algorithms, and intra- and inter-operator variability on internal dosimetry estimates using PET

Purpose Human dosimetry studies play a central role in radioligand development for positron emission tomography (PET). Drawing regions of interest (ROIs) on the PET images is used to measure the dose in each organ. In the study aspects related to ROI delineation methods were evaluated for two radioligands of different biodistribution (intestinal vs urinary). Procedures PET images were simulated from a human voxel-based phantom. Several ROI delineation methods were tested: antero-posterior projections (AP), 3D sub-samples of the organs (S), and a 3D volume covering the whole-organ (W). Inter- and intra-operator variability ROI drawing was evaluated by using human data. Results The effective dose estimates using S and W methods were comparable to the true values. AP methods overestimated (49 %) the dose for the radioligand with intestinal biodistribution. Moreover, the AP method showed the highest inter-operator variability: 11 ± 1 %. Conclusions The sub-sampled organ method showed the best balance between quantitative accuracy and inter- and intra-operator variability.Postprint (author's final draft

Enhance the Efficiency of Heuristic Algorithm for Maximizing Modularity Q

Modularity Q is an important function for identifying community structure in complex networks. In this paper, we prove that the modularity maximization problem is equivalent to a nonconvex quadratic programming problem. This result provide us a simple way to improve the efficiency of heuristic algorithms for maximizing modularity Q. Many numerical results demonstrate that it is very effective.Comment: 9 pages, 3 figure

The problem of shot selection in basketball

In basketball, every time the offense produces a shot opportunity the player with the ball must decide whether the shot is worth taking. In this paper, I explore the question of when a team should shoot and when they should pass up the shot by considering a simple theoretical model of the shot selection process, in which the quality of shot opportunities generated by the offense is assumed to fall randomly within a uniform distribution. I derive an answer to the question "how likely must the shot be to go in before the player should take it?", and show that this "lower cutoff" for shot quality $f$ depends crucially on the number $n$ of shot opportunities remaining (say, before the shot clock expires), with larger $n$ demanding that only higher-quality shots should be taken. The function $f(n)$ is also derived in the presence of a finite turnover rate and used to predict the shooting rate of an optimal-shooting team as a function of time. This prediction is compared to observed shooting rates from the National Basketball Association (NBA), and the comparison suggests that NBA players tend to wait too long before shooting and undervalue the probability of committing a turnover.Comment: 7 pages, 2 figures; comparison to NBA data adde

Size reduction of complex networks preserving modularity

The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the NP-hard class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining invariant its modularity. This size reduction allows the heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complex-networks by using the Extremal Optimization algorithm, before and after the size reduction, showing the improvement obtained. We speculate that the proposed analytical size reduction could be extended to an exact coarse graining of the network in the scope of real-space renormalization.Comment: 14 pages, 2 figure

An evolving network model with community structure

Many social and biological networks consist of communities—groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting community structures in real-world complex networks. In this paper, we propose an evolving network model which exhibits community structure. The network model is based on the inner-community preferential attachment and inter-community preferential attachment mechanisms. The degree distributions of this network model are analysed based on a mean-field method. Theoretical results and numerical simulations indicate that this network model has community structure and scale-free properties