Motifs in Temporal Networks

Networks are a fundamental tool for modeling complex systems in a variety of domains including social and communication networks as well as biology and neuroscience. Small subgraph patterns in networks, called network motifs, are crucial to understanding the structure and function of these systems. However, the role of network motifs in temporal networks, which contain many timestamped links between the nodes, is not yet well understood. Here we develop a notion of a temporal network motif as an elementary unit of temporal networks and provide a general methodology for counting such motifs. We define temporal network motifs as induced subgraphs on sequences of temporal edges, design fast algorithms for counting temporal motifs, and prove their runtime complexity. Our fast algorithms achieve up to 56.5x speedup compared to a baseline method. Furthermore, we use our algorithms to count temporal motifs in a variety of networks. Results show that networks from different domains have significantly different motif counts, whereas networks from the same domain tend to have similar motif counts. We also find that different motifs occur at different time scales, which provides further insights into structure and function of temporal networks

Tensor Spectral Clustering for Partitioning Higher-order Network Structures

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.Comment: SDM 201

Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification

This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned on a given class is Gaussian with a zero mean and a low-rank covariance matrix. We also assume that the classifier knows only a mismatched version of the parameters of input distribution in lieu of the true parameters. By constructing an asymptotic low-noise expansion of an upper bound to the error probability of such a mismatched classifier, we provide sufficient conditions for reliable classification in the low-noise regime that are able to sharply predict the absence of a classification error floor. Such conditions are a function of the geometry of the true signal distribution, the geometry of the mismatched signal distributions as well as the interplay between such geometries, namely, the principal angles and the overlap between the true and the mismatched signal subspaces. Numerical results demonstrate that our conditions for reliable classification can sharply predict the behavior of a mismatched classifier both with synthetic data and in a motion segmentation and a hand-written digit classification applications.Comment: 17 pages, 7 figures, submitted to IEEE Transactions on Signal Processin

Comments on the diphoton excess: critical reappraisal of effective field theory interpretations

We consider the diphoton excess observed by ATLAS and CMS using the most up-to-date data and estimate the preferred enhancement in the production rate between 8 TeV and 13 TeV. Within the framework of effective field theory (EFT), we then show that for both spin-0 and spin-2 Standard Model (SM) gauge-singlet resonances, two of the three processes S to ZZ, S to Z gamma, and S to WW must occur with a non-zero rate. Moreover, we demonstrate that these branching ratios are highly correlated in the EFT. Couplings of S to additional SM states may be constrained and differentiated by comparing the S production rates with and without the vector-boson fusion (VBF) cuts. We find that for a given VBF to inclusive production ratio there is maximum rate of S to gauge bosons, b b-bar, and lighter quark anti-quark pairs. Simultaneous measurements of the width and the VBF ratio may be able to point towards the existence of hidden decays.Comment: 31 pages, 8 figures; version as publishe

Association between anticholinergic burden and dementia in UK Biobank

Abstract Background Previous studies on the relationship between anticholinergic drugs and dementia have reported heterogeneous results. This variability could be due to different anticholinergic scales and differential effects of distinct classes of drugs. Methods Using Cox proportional hazards models, we computed the association between annual anticholinergic burden (AChB) and the risk of dementia in UK Biobank with linked general practitioner prescription records between the years 2000 and 2015 (n = 171,775). Results AChB according to most anticholinergic scales (standardized odds ratio range: 1.027–1.125) and the slope of the AChB trajectory (hazard ratio = 1.094; 95% confidence interval: 1.068–1.119) were predictive of dementia. However, the association between AChB and dementia held only for some classes of drugs, especially antidepressants, antiepileptics, and antidiuretics. Discussion The heterogeneity in previous findings may partially be due to different effects for different classes of drugs. Future studies should establish differences in more detail and further examine the practicality of a general measure of AChB relating to the risk of dementia

Ultrafast dynamics of coherent optical phonons and nonequilibrium electrons in transition metals

The femtosecond optical pump-probe technique was used to study dynamics of photoexcited electrons and coherent optical phonons in transition metals Zn and Cd as a function of temperature and excitation level. The optical response in time domain is well fitted by linear combination of a damped harmonic oscillation because of excitation of coherent $E_{2g}$ phonon and a subpicosecond transient response due to electron-phonon thermalization. The electron-phonon thermalization time monotonically increases with temperature, consistent with the thermomodulation scenario, where at high temperatures the system can be well explained by the two-temperature model, while below $\approx$ 50 K the nonthermal electron model needs to be applied. As the lattice temperature increases, the damping of the coherent $E_{2g}$ phonon increases, while the amplitudes of both fast electronic response and the coherent $E_{2g}$ phonon decrease. The temperature dependence of the damping of the $E_{2g}$ phonon indicates that population decay of the coherent optical phonon due to anharmonic phonon-phonon coupling dominates the decay process. We present a model that accounts for the observed temperature dependence of the amplitude assuming the photoinduced absorption mechanism, where the signal amplitude is proportional to the photoinduced change in the quasiparticle density. The result that the amplitude of the $E_{2g}$ phonon follows the temperature dependence of the amplitude of the fast electronic transient indicates that under the resonant condition both electronic and phononic responses are proportional to the change in the dielectric function.Comment: 10 pages, 9 figures, to appear in Physical Review