Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

A Simple Generative Model of Collective Online Behaviour

Human activities increasingly take place in online environments, providing novel opportunities for relating individual behaviours to population-level outcomes. In this paper, we introduce a simple generative model for the collective behaviour of millions of social networking site users who are deciding between different software applications. Our model incorporates two distinct components: one is associated with recent decisions of users, and the other reflects the cumulative popularity of each application. Importantly, although various combinations of the two mechanisms yield long-time behaviour that is consistent with data, the only models that reproduce the observed temporal dynamics are those that strongly emphasize the recent popularity of applications over their cumulative popularity. This demonstrates---even when using purely observational data without experimental design---that temporal data-driven modelling can effectively distinguish between competing microscopic mechanisms, allowing us to uncover new aspects of collective online behaviour.Comment: Updated, with new figures and Supplementary Informatio

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Modeling the Daily Variations of the Coronal X-ray Spectral Irradiance with Two Temperatures and Two Emission Measures

The Miniature X-ray Solar Spectrometer (MinXSS-1) CubeSat observed solar X-rays between 0.5 and 10 keV. A two-temperature, two-emission measure model is fit to each daily averaged spectrum. These daily average temperatures and emission measures are plotted against the corresponding daily solar 10.7 cm radio flux (F10.7) value and a linear correlation is found between each that we call the Schwab Woods Mason (SWM) model. The linear trends show that one can estimate the solar spectrum between 0.5 keV and 10 keV based on the F10.7 measurement alone. The cooler temperature component of this model represents the quiescent sun contribution to the spectra and is essentially independent of solar activity, meaning the daily average quiescent sun is accurately described by a single temperature (1.70 MK) regardless of solar intensity and only the emission measure corresponding to this temperature needs to be adjusted for higher or lower solar intensity. The warmer temperature component is shown to represent active region contributions to the spectra and varies between 5 MK to 6 MK. GOES XRS-B data between 1-8 Angstroms is used to validate this model and it is found that the ratio between the SWM model irradiance and the GOES XRS-B irradiance is close to unity on average. MinXSS-1 spectra during quiescent solar conditions have very low counts beyond around 3 keV. The SWM model can generate MinXSS-1 or DAXSS spectra at very high spectral resolution and with extended energy ranges to fill in gaps between measurements and extend predictions back to 1947

Connexin36 knockout mice display increased sensitivity to pentylenetetrazol-induced seizure-like behaviors

Large-scale synchronous firing of neurons during seizures is modulated by electrotonic coupling between neurons via gap junctions. To explore roles for connexin36 (Cx36) gap junctions in seizures, we examined the seizure threshold of connexin36 knockout (Cx36KO) mice using a pentylenetetrazol (PTZ) model

Parametric search and optimisation of fast displacement hull forms using rans simulations of full-scale flow

Abstract. A methodology to derive parametric hull design candidates with a specified displacement and initial stability is introduced. A gradient-free search and optimisation algorithm coupled to a RANS CFD solver is then used to identify efficient pure-displacement hull shapes with minimal hydrodynamic resistance operating in the transition speed region without relying on dynamic lift

The Swift-UVOT ultraviolet and visible grism calibration

We present the calibration of the Swift UVOT grisms, of which there are two, providing low-resolution field spectroscopy in the ultraviolet and optical bands respectively. The UV grism covers the range 1700-5000 Angstrom with a spectral resolution of 75 at 2600 Angstrom for source magnitudes of u=10-16 mag, while the visible grism covers the range 2850-6600 Angstrom with a spectral resolution of 100 at 4000 Angstrom for source magnitudes of b=12-17 mag. This calibration extends over all detector positions, for all modes used during operations. The wavelength accuracy (1-sigma) is 9 Angstrom in the UV grism clocked mode, 17 Angstrom in the UV grism nominal mode and 22 Angstrom in the visible grism. The range below 2740 Angstrom in the UV grism and 5200 Angstrom in the visible grism never suffers from overlapping by higher spectral orders. The flux calibration of the grisms includes a correction we developed for coincidence loss in the detector. The error in the coincidence loss correction is less than 20%. The position of the spectrum on the detector only affects the effective area (sensitivity) by a few percent in the nominal modes, but varies substantially in the clocked modes. The error in the effective area is from 9% in the UV grism clocked mode to 15% in the visible grism clocked mode .Comment: 27 pages, 31 figures; MNRAS accepted 23 February 201

Comparing the Activity Profiles of Wheelchair Rugby Using a Miniaturised Data Logger and Radio-Frequency Tracking System

Copyright © 2014 Barry Mason et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Testing the proposed link between cosmic rays and cloud cover

A decrease in the globally averaged low level cloud cover, deduced from the ISCCP infra red data, as the cosmic ray intensity decreased during the solar cycle 22 was observed by two groups. The groups went on to hypothesise that the decrease in ionization due to cosmic rays causes the decrease in cloud cover, thereby explaining a large part of the presently observed global warming. We have examined this hypothesis to look for evidence to corroborate it. None has been found and so our conclusions are to doubt it. From the absence of corroborative evidence, we estimate that less than 23%, at the 95% confidence level, of the 11-year cycle change in the globally averaged cloud cover observed in solar cycle 22 is due to the change in the rate of ionization from the solar modulation of cosmic rays