Exploring Temporal Networks with Greedy Walks

Temporal networks come with a wide variety of heterogeneities, from burstiness of event sequences to correlations between timings of node and link activations. In this paper, we set to explore the latter by using greedy walks as probes of temporal network structure. Given a temporal network (a sequence of contacts), greedy walks proceed from node to node by always following the first available contact. Because of this, their structure is particularly sensitive to temporal-topological patterns involving repeated contacts between sets of nodes. This becomes evident in their small coverage per step as compared to a temporal reference model -- in empirical temporal networks, greedy walks often get stuck within small sets of nodes because of correlated contact patterns. While this may also happen in static networks that have pronounced community structure, the use of the temporal reference model takes the underlying static network structure out of the equation and indicates that there is a purely temporal reason for the observations. Further analysis of the structure of greedy walks indicates that burst trains, sequences of repeated contacts between node pairs, are the dominant factor. However, there are larger patterns too, as shown with non-backtracking greedy walks. We proceed further to study the entropy rates of greedy walks, and show that the sequences of visited nodes are more structured and predictable in original data as compared to temporally uncorrelated references. Taken together, these results indicate a richness of correlated temporal-topological patterns in temporal networks

Dynamics of latent voters

We study the effect of latency on binary-choice opinion formation models. Latency is introduced into the models as an additional dynamic rule: after a voter changes its opinion, it enters a waiting period of stochastic length where no further changes take place. We first focus on the voter model and show that as a result of introducing latency, the average magnetization is not conserved, and the system is driven toward zero magnetization, independently of initial conditions. The model is studied analytically in the mean-field case and by simulations in one dimension. We also address the behavior of the Majority Rule model with added latency, and show that the competition between imitation and latency leads to a rich phenomenology

Limited resolution and multiresolution methods in complex network community detection

Detecting community structure in real-world networks is a challenging problem. Recently, it has been shown that the resolution of methods based on optimizing a modularity measure or a corresponding energy is limited; communities with sizes below some threshold remain unresolved. One possibility to go around this problem is to vary the threshold by using a tuning parameter, and investigate the community structure at variable resolutions. Here, we analyze the resolution limit and multiresolution behavior for two different methods: a q-state Potts method proposed by Reichard and Bornholdt, and a recent multiresolution method by Arenas, Fernandez, and Gomez. These methods are studied analytically, and applied to three test networks using simulated annealing.Comment: 6 pages, 2 figures.Minor changes from previous version, shortened a couple of page

Communities and beyond: mesoscopic analysis of a large social network with complementary methods

Community detection methods have so far been tested mostly on small empirical networks and on synthetic benchmarks. Much less is known about their performance on large real-world networks, which nonetheless are a significant target for application. We analyze the performance of three state-of-the-art community detection methods by using them to identify communities in a large social network constructed from mobile phone call records. We find that all methods detect communities that are meaningful in some respects but fall short in others, and that there often is a hierarchical relationship between communities detected by different methods. Our results suggest that community detection methods could be useful in studying the general mesoscale structure of networks, as opposed to only trying to identify dense structures.Comment: 11 pages, 10 figures. V2: typos corrected, one sentence added. V3: revised version, Appendix added. V4: final published versio

Improved approach for design of perfect reconstruction FIR QMF banks, with lossless lattice structures

A property of FIR (finite-impulse response) lossless systems is introduced, leading to substantial improvement in the sign procedure for perfect-reconstruction QMF (quadrature mirror filter) banks. The property enables the designer to initialize the coefficients of a lattice structure (which characterizes the analysis bank), in such a way as to speed up to the convergence. A design example is provided. Compared to other methods, the proposed method is shown to converge faster, and always leads to much improved attenuation characteristics for a given filter length

Eigenfilters for the design of special transfer functions with applications in multirate signal processing

Based on the multistage approach, a design procedure is presented for finding a spectral factor of an mth-band filter and for designing multistage decimation filters. The proposed design method finds spectral factors of mth-band FIR (finite-impulse response) filters without direct computation, and yields filters with much higher attenuation than would be possible by conventional methods. Such mth-band filters are used in filter-bank designs, including perfect-reconstruction systems