7,772 research outputs found
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
Active Region Moss: Doppler Shifts from Hinode/EIS Observations
Studying the Doppler shifts and the temperature dependence of Doppler shifts
in moss regions can help us understand the heating processes in the core of the
active regions. In this paper we have used an active region observation
recorded by the Extreme-ultraviolet Imaging Spectrometer (EIS) onboard Hinode
on 12-Dec-2007 to measure the Doppler shifts in the moss regions. We have
distinguished the moss regions from the rest of the active region by defining a
low density cut-off as derived by Tripathi et al. (2010). We have carried out a
very careful analysis of the EIS wavelength calibration based on the method
described in Young et al. (2012). For spectral lines having maximum sensitivity
between log T = 5.85 and log T = 6.25 K, we find that the velocity distribution
peaks at around 0 km/s with an estimated error of 4-5 km/s. The width of the
distribution decreases with temperature. The mean of the distribution shows a
blue shift which increases with increasing temperature and the distribution
also shows asymmetries towards blue-shift. Comparing these results with
observables predicted from different coronal heating models, we find that these
results are consistent with both steady and impulsive heating scenarios.
However, the fact that there are a significant number of pixels showing
velocity amplitudes that exceed the uncertainty of 5 km s is suggestive
of impulsive heating. Clearly, further observational constraints are needed to
distinguish between these two heating scenarios.Comment: 21 pages (single column), 7 figures, Accepted for Publication in The
Astrophysical Journa
Alien Registration- Mason, James A. (Greenville, Piscataquis County)
https://digitalmaine.com/alien_docs/11406/thumbnail.jp
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
On Estimating the High-Energy Cutoff in the X-ray Spectra of Black Holes via Reflection Spectroscopy
The fundamental parameters describing the coronal spectrum of an accreting
black hole are the slope of the power-law continuum and the energy
at which it rolls over. Remarkably, this parameter can be accurately
measured for values as high as 1 MeV by modeling the spectrum of X-rays
reflected from a black hole accretion disk at energies below 100 keV. This is
possible because the details in the reflection spectrum, rich in fluorescent
lines and other atomic features, are very sensitive to the spectral shape of
the hardest coronal radiation illuminating the disk. We show that fitting
simultaneous NuSTAR (3-79 keV) and low-energy (e.g., Suzaku) data with the most
recent version of our reflection model RELXILL, one can obtain reasonable
constraints on at energies from tens of keV up to 1 MeV, for a source
as faint as 1 mCrab in a 100 ks observation.Comment: Accepted for publication in ApJL, 6 pages, 5 figure
A Simple, Consistent Estimate for Disturbance Components in Financial Models
Many recent papers have estimated components of the disturbance term in the "market model" of equity returns. In particular, several studies of regulatory changes and other policy events have decomposed the event effects in order to allow for heterogeneity across firms. In this paper we demonstrate that the econometric method applied in some papers yields biased and inconsistent estimates of the model parameters. We demonstrate the consistency of a simple and easily-implemented alternative method.Research Seminar in International Economics, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100855/1/ECON309.pd
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