210 research outputs found
Potential-Density Basis Sets for Galactic Disks
A class of complete potential-density basis sets in cylindrical (R,phi,z)
coordinates is presented. This class is suitable for stability studies of
galactic disks in three dimensions and includes basis sets tailored for disks
with vertical density profiles that are exponential (exp(-|z|/\zn)), Gaussian
(exp(-(z/\zn)^2) or locally isothermal (sech^2(z/\zn)). The basis sets are
non-discrete and non-biorthogonal; however, the extra numerical computations
required (compared with discrete biorthogonal sets) are explained and
constitute a small overhead. The method of construction (and proof of
completeness) is simple and can be used to construct basis sets for other
density distributions that are best described in circular or elliptic
cylindrical coordinates. When combined with a basis set designed for spheroidal
systems, the basis sets presented here can be used to study the stability of
realistic disks embedded in massive halos.Comment: Accepted for publication in The Astrophysical Journal, 13 pages,
plain TeX, uses mtexsis.tex, no figure
THE OPTIMAL N-BODY METHOD FOR STABILITY STUDIES OF GALAXIES
The stability of a galaxy model is most easily assessed through N-body
simulation. Particle-mesh codes have been widely used for this purpose, since
they enable the largest numbers of particles to be employed. We show that the
functional expansion technique, originally proposed by Clutton-Brock for other
simulation problems, is in fact superior for stability work. For simulations of
linear evolution it is not much slower than grid methods using the same number
of particles, and reproduces analytical results with much greater accuracy.
This success rests on its ability to represent global modes with a modest
number of basis functions; grid methods may be more effective for other
applications, however. Our conclusions are based on implementations of
functional expansion and grid algorithms for disk galaxies.Comment: Accepted for publication in The Astrophysical Journal, to appear
October 1, 1995; 16 pages including 4 figures, self-unpacking uuencoded
gzipped postscript, also available by email from [email protected]
Bifurcations and chaotic dynamics in a tumour-immune-virus system
Despite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunity-dependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.Publisher PDFPeer reviewe
Evaluating undercounts in epidemics: response to Maruotti et al. 2022
Maruotti et al. 2022 used a mark-recapture approach to estimate bounds on the
true number of monkeypox infections in various countries. These approaches are
fundamentally flawed; it is impossible to estimate undercounting based solely
on a single stream of reported cases. Simulations based on a Richards curve for
cumulative incidence show that, for reasonable epidemic parameters, the
proposed methods estimate bounds on the ascertainment ratio of roughly independently of the true ascertainment ratio. These methods
should not be used
Generation of potential/surface density pairs in flat disks Power law distributions
We report a simple method to generate potential/surface density pairs in flat
axially symmetric finite size disks. Potential/surface density pairs consist of
a ``homogeneous'' pair (a closed form expression) corresponding to a uniform
disk, and a ``residual'' pair. This residual component is converted into an
infinite series of integrals over the radial extent of the disk. For a certain
class of surface density distributions (like power laws of the radius), this
series is fully analytical. The extraction of the homogeneous pair is
equivalent to a convergence acceleration technique, in a matematical sense. In
the case of power law distributions, the convergence rate of the residual
series is shown to be cubic inside the source. As a consequence, very accurate
potential values are obtained by low order truncation of the series. At zero
order, relative errors on potential values do not exceed a few percent
typically, and scale with the order N of truncation as 1/N**3. This method is
superior to the classical multipole expansion whose very slow convergence is
often critical for most practical applications.Comment: Accepted for publication in Astronomy & Astrophysics 7 pages, 8
figures, F90-code available at
http://www.obs.u-bordeaux1.fr/radio/JMHure/intro2applawd.htm
Pandemic Paradox: Early Life H2N2 Pandemic Influenza Infection Enhanced Susceptibility to Death during the 2009 H1N1 Pandemic.
Recent outbreaks of H5, H7, and H9 influenza A viruses in humans have served as a vivid reminder of the potentially devastating effects that a novel pandemic could exert on the modern world. Those who have survived infections with influenza viruses in the past have been protected from subsequent antigenically similar pandemics through adaptive immunity. For example, during the 2009 H1N1 "swine flu" pandemic, those exposed to H1N1 viruses that circulated between 1918 and the 1940s were at a decreased risk for mortality as a result of their previous immunity. It is also generally thought that past exposures to antigenically dissimilar strains of influenza virus may also be beneficial due to cross-reactive cellular immunity. However, cohorts born during prior heterosubtypic pandemics have previously experienced elevated risk of death relative to surrounding cohorts of the same population. Indeed, individuals born during the 1890 H3Nx pandemic experienced the highest levels of excess mortality during the 1918 "Spanish flu." Applying Serfling models to monthly mortality and influenza circulation data between October 1997 and July 2014 in the United States and Mexico, we show corresponding peaks in excess mortality during the 2009 H1N1 "swine flu" pandemic and during the resurgent 2013-2014 H1N1 outbreak for those born at the time of the 1957 H2N2 "Asian flu" pandemic. We suggest that the phenomenon observed in 1918 is not unique and points to exposure to pandemic influenza early in life as a risk factor for mortality during subsequent heterosubtypic pandemics.IMPORTANCE The relatively low mortality experienced by older individuals during the 2009 H1N1 influenza virus pandemic has been well documented. However, reported situations in which previous influenza virus exposures have enhanced susceptibility are rare and poorly understood. One such instance occurred in 1918-when those born during the heterosubtypic 1890 H3Nx influenza virus pandemic experienced the highest levels of excess mortality. Here, we demonstrate that this phenomenon was not unique to the 1918 H1N1 pandemic but that it also occurred during the contemporary 2009 H1N1 pandemic and 2013-2014 H1N1-dominated season for those born during the heterosubtypic 1957 H2N2 "Asian flu" pandemic. These data highlight the heretofore underappreciated phenomenon that, in certain instances, prior exposure to pandemic influenza virus strains can enhance susceptibility during subsequent pandemics. These results have important implications for pandemic risk assessment and should inform laboratory studies aimed at uncovering the mechanism responsible for this effect
Toward a comprehensive system for constructing compartmental epidemic models
Compartmental models are valuable tools for investigating infectious
diseases. Researchers building such models typically begin with a simple
structure where compartments correspond to individuals with different
epidemiological statuses, e.g., the classic SIR model which splits the
population into susceptible, infected, and recovered compartments. However, as
more information about a specific pathogen is discovered, or as a means to
investigate the effects of heterogeneities, it becomes useful to stratify
models further -- for example by age, geographic location, or pathogen strain.
The operation of constructing stratified compartmental models from a pair of
simpler models resembles the Cartesian product used in graph theory, but
several key differences complicate matters. In this article we give explicit
mathematical definitions for several so-called ``model products'' and provide
examples where each is suitable. We also provide examples of model
stratification where no existing model product will generate the desired
result
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Reconstructing influenza incidence by deconvolution of daily mortality time series
We propose a mathematically straightforward method to infer the incidence curve of an epidemic from a recorded daily death curve and time-to-death distribution; the method is based on the Richardson-Lucy deconvolution scheme from optics. We apply the method to reconstruct the incidence curves for the 1918 influenza epidemic in Philadelphia and New York State. The incidence curves are then used to estimate epidemiological quantities, such as daily reproductive numbers and infectivity ratios. We found that during a brief period before the official control measures were implemented in Philadelphia, the drop in the daily number of new infections due to an average infector was much larger than expected from the depletion of susceptibles during that period; this finding was subjected to extensive sensitivity analysis. Combining this with recorded evidence about public behavior, we conclude that public awareness and change in behavior is likely to have had a major role in the slowdown of the epidemic even in a city whose response to the 1918 influenza epidemic is considered to have been among the worst in the U.S
Quantum Computing of Classical Chaos: Smile of the Arnold-Schrodinger Cat
We show on the example of the Arnold cat map that classical chaotic systems
can be simulated with exponential efficiency on a quantum computer. Although
classical computer errors grow exponentially with time, the quantum algorithm
with moderate imperfections is able to simulate accurately the unstable chaotic
classical dynamics for long times. The algorithm can be easily implemented on
systems of a few qubits.Comment: revtex, 4 pages, 4 figure
An adaptive algorithm for n-body field expansions
An expansion of a density field or particle distribution in basis functions
which solve the Poisson equation both provides an easily parallelized n-body
force algorithm and simplifies perturbation theories. The expansion converges
quickly and provides the highest computational advantage if the lowest-order
potential-density pair in the basis looks like the unperturbed galaxy or
stellar system. Unfortunately, there are only a handful of such basis in the
literature which limits this advantage. This paper presents an algorithm for
deriving these bases to match a wide variety of galaxy models. The method is
based on efficient numerical solution of the Sturm-Liouville equation and can
be used for any geometry with a separable Laplacian. Two cases are described in
detail. First for the spherical case, the lowest order basis function pair may
be chosen to be exactly that of the underlying model. The profile may be cuspy
or have a core and truncated or of infinite extent. Secondly, the method yields
a three-dimensional cylindrical basis appropriate for studying galaxian disks.
In this case, the vertical and radial bases are coupled; the lowest order
radial part of the basis function can be chosen to match the underlying profile
only in the disk plane. Practically, this basis is still a very good match to
the overall disk profile and converges in a small number of terms.Comment: 16 pages, 5 figures, submitted to A
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