11,396 research outputs found
A weighted configuration model and inhomogeneous epidemics
A random graph model with prescribed degree distribution and degree dependent
edge weights is introduced. Each vertex is independently equipped with a random
number of half-edges and each half-edge is assigned an integer valued weight
according to a distribution that is allowed to depend on the degree of its
vertex. Half-edges with the same weight are then paired randomly to create
edges. An expression for the threshold for the appearance of a giant component
in the resulting graph is derived using results on multi-type branching
processes. The same technique also gives an expression for the basic
reproduction number for an epidemic on the graph where the probability that a
certain edge is used for transmission is a function of the edge weight. It is
demonstrated that, if vertices with large degree tend to have large (small)
weights on their edges and if the transmission probability increases with the
edge weight, then it is easier (harder) for the epidemic to take off compared
to a randomized epidemic with the same degree and weight distribution. A recipe
for calculating the probability of a large outbreak in the epidemic and the
size of such an outbreak is also given. Finally, the model is fitted to three
empirical weighted networks of importance for the spread of contagious diseases
and it is shown that can be substantially over- or underestimated if the
correlation between degree and weight is not taken into account
The military and administrative reforms of the emperor Gallienus
The military and administrative reforms of Gallienus affected the tactical organisation of the army, the composition and structure of the officer corps, and the social composition of the provincial administration. Gallienus' tactical reforms created a powerful body of cavalry, which represented the culmination to a century of increasing mobility and depth in defence. This "battlecavalry" was not the direct ancestor of the later comitatenses. but its tactical value and elite status paved the way for a "dual" system of defence involving frontier garrisons and centralised field-armies. His reforms of the officer corps involved the replacement of senatorial officers by equestrians, and the introduction of the protectorate. He hoped thereby to bind military commanders more closely to himself. The administrative reforms involved increasing the number of equestrian governors. Though senatorial governorships continued to occur, senators were henceforth without any real military power. Whether Gallienus ever issued an "edict" to this effect is uncertain, as is the motive behind the reform. Most scholars see in it an attempt to improve the quality of military leadership, but there is little evidence for this. It is preferable to agree with Aurelius Victor, that Gallienus feared the senators, and so deprived them of their commands. Together, Gallienus' creation of the "battlecavalry" and his reforms of the officer corps and provincial administration created the pre-conditions for the recovery of the Roman empire under the Illyrian emperors, and laid the foundations to the "Military Monarchy" of the later Roman empire
Room temperature spin relaxation in GaAs/AlGaAs multiple quantum wells
We have explored the dependence of electron spin relaxation in undoped GaAs/AlGaAs quantum wells on well width (confinement energy) at 300 K. For wide wells, the relaxation rate tends to the intrinsic bulk value due to the D'yakonov-Perel (DP) mechanism with momentum scattering by phonons. In narrower wells, there is a strong dependence of relaxation rate on well width, as expected for the DP mechanism, but also considerable variation between samples from different sources, which we attribute to differences in sample interface morphology. (C) 1998 American Institute of Physics. [S0003-6951(98)02541-8].</p
High-velocity feature of the class I methanol maser in G309.38-0.13
The Australia Telescope Compact Array (ATCA) has been used to map class I
methanol masers at 36 and 44 GHz in G309.38-0.13. Maser spots are found at nine
locations in an area of 50''x30'', with both transitions reliably detected at
only two locations. The brightest spot is associated with shocked gas traced by
4.5 micron emission. The data allowed us to make a serendipitous discovery of a
high-velocity 36-GHz spectral feature, which is blue-shifted by about 30 km/s
from the peak velocity at this frequency, but spatially located close to
(within a few arcseconds of) the brightest maser spot. We interpret this as
indicating an outflow parallel to the line of sight. Such a high velocity
spread of maser features, which has not been previously reported in the class I
methanol masers associated with a single molecular cloud, suggests that the
outflow most likely interacts with a moving parcel of gas.Comment: 6 pages, 2 figures, accepted by MNRAS Letter
Characterizing the Initial Phase of Epidemic Growth on some Empirical Networks
A key parameter in models for the spread of infectious diseases is the basic
reproduction number , which is the expected number of secondary cases a
typical infected primary case infects during its infectious period in a large
mostly susceptible population. In order for this quantity to be meaningful, the
initial expected growth of the number of infectious individuals in the
large-population limit should be exponential.
We investigate to what extent this assumption is valid by performing repeated
simulations of epidemics on selected empirical networks, viewing each epidemic
as a random process in discrete time. The initial phase of each epidemic is
analyzed by fitting the number of infected people at each time step to a
generalised growth model, allowing for estimating the shape of the growth. For
reference, similar investigations are done on some elementary graphs such as
integer lattices in different dimensions and configuration model graphs, for
which the early epidemic behaviour is known.
We find that for the empirical networks tested in this paper, exponential
growth characterizes the early stages of the epidemic, except when the network
is restricted by a strong low-dimensional spacial constraint, such as is the
case for the two-dimensional square lattice. However, on finite integer
lattices of sufficiently high dimension, the early development of epidemics
shows exponential growth.Comment: To be included in the conference proceedings for SPAS 2017
(International Conference on Stochastic Processes and Algebraic Structures),
October 4-6, 201
Intensity enhancement of O VI ultraviolet emission lines in solar spectra due to opacity
Opacity is a property of many plasmas, and it is normally expected that if an
emission line in a plasma becomes optically thick, its intensity ratio to that
of another transition that remains optically thin should decrease. However,
radiative transfer calculations undertaken both by ourselves and others predict
that under certain conditions the intensity ratio of an optically thick to thin
line can show an increase over the optically thin value, indicating an
enhancement in the former. These conditions include the geometry of the
emitting plasma and its orientation to the observer. A similar effect can take
place between lines of differing optical depth. Previous observational studies
have focused on stellar point sources, and here we investigate the
spatially-resolved solar atmosphere using measurements of the I(1032 A)/I(1038
A) intensity ratio of O VI in several regions obtained with the Solar
Ultraviolet Measurements of Emitted Radiation (SUMER) instrument on board the
Solar and Heliospheric Observatory (SoHO) satellite. We find several I(1032
A)/I(1038 A) ratios observed on the disk to be significantly larger than the
optically thin value of 2.0, providing the first detection (to our knowledge)
of intensity enhancement in the ratio arising from opacity effects in the solar
atmosphere. Agreement between observation and theory is excellent, and confirms
that the O VI emission originates from a slab-like geometry in the solar
atmosphere, rather than from cylindrical structures.Comment: 17 pages, 4 figures, ApJ Letters, in pres
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