19,670 research outputs found

    Narrow scope for resolution-limit-free community detection

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    Detecting communities in large networks has drawn much attention over the years. While modularity remains one of the more popular methods of community detection, the so-called resolution limit remains a significant drawback. To overcome this issue, it was recently suggested that instead of comparing the network to a random null model, as is done in modularity, it should be compared to a constant factor. However, it is unclear what is meant exactly by "resolution-limit-free", that is, not suffering from the resolution limit. Furthermore, the question remains what other methods could be classified as resolution-limit-free. In this paper we suggest a rigorous definition and derive some basic properties of resolution-limit-free methods. More importantly, we are able to prove exactly which class of community detection methods are resolution-limit-free. Furthermore, we analyze which methods are not resolution-limit-free, suggesting there is only a limited scope for resolution-limit-free community detection methods. Finally, we provide such a natural formulation, and show it performs superbly

    Testing Cluster Structure of Graphs

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    We study the problem of recognizing the cluster structure of a graph in the framework of property testing in the bounded degree model. Given a parameter ε\varepsilon, a dd-bounded degree graph is defined to be (k,ϕ)(k, \phi)-clusterable, if it can be partitioned into no more than kk parts, such that the (inner) conductance of the induced subgraph on each part is at least ϕ\phi and the (outer) conductance of each part is at most cd,kε4ϕ2c_{d,k}\varepsilon^4\phi^2, where cd,kc_{d,k} depends only on d,kd,k. Our main result is a sublinear algorithm with the running time O~(npoly(ϕ,k,1/ε))\widetilde{O}(\sqrt{n}\cdot\mathrm{poly}(\phi,k,1/\varepsilon)) that takes as input a graph with maximum degree bounded by dd, parameters kk, ϕ\phi, ε\varepsilon, and with probability at least 23\frac23, accepts the graph if it is (k,ϕ)(k,\phi)-clusterable and rejects the graph if it is ε\varepsilon-far from (k,ϕ)(k, \phi^*)-clusterable for ϕ=cd,kϕ2ε4logn\phi^* = c'_{d,k}\frac{\phi^2 \varepsilon^4}{\log n}, where cd,kc'_{d,k} depends only on d,kd,k. By the lower bound of Ω(n)\Omega(\sqrt{n}) on the number of queries needed for testing graph expansion, which corresponds to k=1k=1 in our problem, our algorithm is asymptotically optimal up to polylogarithmic factors.Comment: Full version of STOC 201

    Superstatistical random-matrix-theory approach to transition intensities in mixed systems

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    We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution of the reduced transition probabilities that applies to systems undergoing a transition out of chaos. The obtained distribution fits the results of a previous nuclear shell model calculations for some electromagnetic transitions that deviate from the Porter-Thomas distribution. It agrees with the experimental reduced transition probabilities for the 26A nucleus better than the commonly used chi-squared distribution.Comment: 14 pages, 3 figure

    Estimating the reproductive number, total outbreak size, and reporting rates for Zika epidemics in South and Central America

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    As South and Central American countries prepare for increased birth defects from Zika virus outbreaks and plan for mitigation strategies to minimize ongoing and future outbreaks, understanding important characteristics of Zika outbreaks and how they vary across regions is a challenging and important problem. We developed a mathematical model for the 2015 Zika virus outbreak dynamics in Colombia, El Salvador, and Suriname. We fit the model to publicly available data provided by the Pan American Health Organization, using Approximate Bayesian Computation to estimate parameter distributions and provide uncertainty quantification. An important model input is the at-risk susceptible population, which can vary with a number of factors including climate, elevation, population density, and socio-economic status. We informed this initial condition using the highest historically reported dengue incidence modified by the probable dengue reporting rates in the chosen countries. The model indicated that a country-level analysis was not appropriate for Colombia. We then estimated the basic reproduction number, or the expected number of new human infections arising from a single infected human, to range between 4 and 6 for El Salvador and Suriname with a median of 4.3 and 5.3, respectively. We estimated the reporting rate to be around 16% in El Salvador and 18% in Suriname with estimated total outbreak sizes of 73,395 and 21,647 people, respectively. The uncertainty in parameter estimates highlights a need for research and data collection that will better constrain parameter ranges.Comment: 35 pages, 16 figure

    Design, analysis, and testing of high frequency passively damped struts

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    Objectives of the research are: (1) to develop design requirements for damped struts to stabilize control system in the high frequency cross-over and spill-over range; (2) to design, fabricate and test viscously damped strut and viscoelastically damped strut; (3) to verify accuracy of design and analysis methodology of damped struts; and (4) to design and build test apparatus, and develop data reduction algorithm to measure strut complex stiffness. In order to meet the stringent performance requirements of the SPICE experiment, the active control system is used to suppress the dynamic responses of the low order structural modes. However, the control system also inadvertently drives some of the higher order modes unstable in the cross-over and spill-over frequency range. Passive damping is a reliable and effective way to provide damping to stabilize the control system. It also improves the robustness of the control system. Damping is designed into the SPICE testbed as an integral part of the control-structure technology

    Shuttle STS-2 mission communication systems RF coverage and performance predictions. Volume 1: Ascent

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    The RF communications capabilities and nominally expected performance for the ascent phase of the second orbital flight of the shuttle are provided. Predicted performance is given mainly in the form of plots of signal strength versus elapsed mission time for the STDN (downlink) and shuttle orbiter (uplink) receivers for the S-band PM and FM, and UHF systems. Performance of the NAV and landing RF systems is treated for RTLS abort, since in this case the spacecraft will loop around and return to the launch site. NAV and landing RF systems include TACAN, MSBLS, and C-band altimeter. Signal strength plots were produced by a computer program which combines the spacecraft trajectory, antenna patterns, transmit and receive performance characteristics, and system mathematical models. When available, measured spacecraft parameters were used in the predictions; otherwise, specified values were used. Specified ground station parameter values were also used. Thresholds and other criteria on the graphs are explained
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