1,199 research outputs found
On the analysis of mixed-index time fractional differential equation systems
In this paper we study the class of mixed-index time fractional differential
equations in which different components of the problem have different time
fractional derivatives on the left hand side. We prove a theorem on the
solution of the linear system of equations, which collapses to the well-known
Mittag-Leffler solution in the case the indices are the same, and also
generalises the solution of the so-called linear sequential class of time
fractional problems. We also investigate the asymptotic stability properties of
this class of problems using Laplace transforms and show how Laplace transforms
can be used to write solutions as linear combinations of generalised
Mittag-Leffler functions in some cases. Finally we illustrate our results with
some numerical simulations.Comment: 21 pages, 6 figures (some are made up of sub-figures - there are 15
figures or sub-figures
Vectorised simulations for stochastic differential equations
Often when solving stochastic differential equations numerically, many simulations must be generated. For example, this approach is required when computing the statistics of the numerical solution, or when verifying the strong order of convergence of a numerical method (when a range of step sizes is also required). Such computational effort can be very slow, and this paper discusses an approach to vectorise the simulation calculations and hence produce an efficient implementation. The numerical simulations here were performed in MATLAB but the techniques are equally applicable in a high performance computing environment using, for example, Fortran 90
Using a library of chemical reactions to fit systems of ordinary differential equations to agent-based models: a machine learning approach
In this paper we introduce a new method based on a library of chemical
reactions for constructing a system of ordinary differential equations from
stochastic simulations arising from an agent-based model. The advantage of this
approach is that this library respects any coupling between systems components,
whereas the SINDy algorithm (introduced by Brunton, Proctor and Kutz) treats
the individual components as decoupled from one another. Another advantage of
our approach is that we can use a non-negative least squares algorithm to find
the non-negative rate constants in a very robust, stable and simple manner. We
illustrate our ideas on an agent-based model of tumour growth on a 2D lattice.Comment: 16 page
DBI Galileon and Late time acceleration of the universe
We consider 1+3 dimensional maximally symmetric Minkowski brane embedded in a
1+4 dimensional maximally symmetric Minkowski background. The resulting 1+3
dimensional effective field theory is of DBI (Dirac-Born-Infeld) Galileon type.
We use this model to study the late time acceleration of the universe. We study
the deviation of the model from the concordance \Lambda CDM behaviour. Finally
we put constraints on the model parameters using various observational data.Comment: 16 pages, 7 eps figures, Latex Style, new references added, corrected
missing reference
Population of human ventricular cell models calibrated with in vivo measurements unravels ionic mechanisms of cardiac alternans
Cardiac alternansis an important risk factor in cardiac physiology, and is related to the initiation of many pathophysiological conditions. However, the mechanisms underlying the generation of alternans remain unclear. In this study, we used a population of computational human ventricle models based onthe O’Hara model [1] to explore the effect of 11 key factors experimentally reported to be related to alternans. In vivo experimental datasets coming from patients undergoing cardiac surgery were used in the calibration of our in silico population of models. The calibrated models in the population were divided into two groups (Normal and Alternans) depending on alternans occurrence. Our results showed that there were significant differences in the following 5 ionic currents between the two groups: fast sodium current, sodium calcium exchanger current, sodium potassium pump current, sarcoplasmic reticulum (SR) calcium release flux and SR calcium reuptake flux. Further analysis indicated that fast sodium current and SR calcium uptake were the two most significant currents that contributed to voltage and calcium alternans generation, respectively
Chronology Protection in Galileon Models and Massive Gravity
Galileon models are a class of effective field theories that have recently
received much attention. They arise in the decoupling limit of theories of
massive gravity, and in some cases they have been treated in their own right as
scalar field theories with a specific nonlinearly realized global symmetry
(Galilean transformation). It is well known that in the presence of a source,
these Galileon theories admit superluminal propagating solutions, implying that
as quantum field theories they must admit a different notion of causality than
standard local Lorentz invariant theories. We show that in these theories it is
easy to construct closed timelike curves (CTCs) within the {\it naive} regime
of validity of the effective field theory. However, on closer inspection we see
that the CTCs could never arise since the Galileon inevitably becomes
infinitely strongly coupled at the onset of the formation of a CTC. This
implies an infinite amount of backreaction, first on the background for the
Galileon field, signaling the break down of the effective field theory, and
subsequently on the spacetime geometry, forbidding the formation of the CTC.
Furthermore the background solution required to create CTCs becomes unstable
with an arbitrarily fast decay time. Thus Galileon theories satisfy a direct
analogue of Hawking's chronology protection conjecture.Comment: 34 pages, no figure
Supernova Brightening from Chameleon-Photon Mixing
Measurements of standard candles and measurements of standard rulers give an
inconsistent picture of the history of the universe. This discrepancy can be
explained if photon number is not conserved as computations of the luminosity
distance must be modified. I show that photon number is not conserved when
photons mix with chameleons in the presence of a magnetic field. The strong
magnetic fields in a supernova mean that the probability of a photon converting
into a chameleon in the interior of the supernova is high, this results in a
large flux of chameleons at the surface of the supernova. Chameleons and
photons also mix as a result of the intergalactic magnetic field. These two
effects combined cause the image of the supernova to be brightened resulting in
a model which fits both observations of standard candles and observations of
standard rulers.Comment: 17 pages, 3 figure
Simple non-mydriatic retinal photography is feasible and demonstrates retinal microvascular dilation in Chronic Obstructive Pulmonary Disease (COPD).
BACKGROUND: Chronic Obstructive Pulmonary Disease (COPD) is associated with an increased risk of myocardial infarction and stroke but it remains unclear how to identify microvascular changes in this population. OBJECTIVES: We hypothesized that simple non-mydriatic retinal photography is feasible and can be used to assess microvascular damage in COPD. METHODS: Novel Vascular Manifestations of COPD was a prospective study comparing smokers with and without COPD, matched for age. Non-mydriatic, retinal fundus photographs were assessed using semi-automated software. RESULTS: Retinal images from 24 COPD and 22 control participants were compared. Cases were of similar age to controls (65.2 vs. 63.1 years, p = 0.38), had significantly lower Forced Expiratory Volume in one second (FEV1) (53.4 vs 100.1% predicted; p < 0.001) and smoked more than controls (41.7 vs. 29.6 pack years; p = 0.04). COPD participants had wider mean arteriolar (155.6 ±15 uM vs. controls [142.2 ± 12 uM]; p = 0.002) and venular diameters (216.8 ±20.7 uM vs. [201.3± 19.1 uM]; p = 0.012). Differences in retinal vessel caliber were independent of confounders, odds ratios (OR) = 1.08 (95% confidence intervals [CI] = 1.02, 1.13; p = 0.007) and OR = 1.05 (CI = 1.01, 1.09; p = 0.011) per uM increase in arteriolar and venular diameter respectively. FEV1 remained significantly associated with retinal vessel dilatation r = -0.39 (p = 0.02). CONCLUSIONS: Non-mydriatic retinal imaging is easily facilitated. We found significant arteriole and venous dilation in COPD compared to age-matched smokers without COPD associated with lung function independent of standard cardiovascular risk factors. Retinal microvascular changes are known to be strongly associated with future vascular events and retinal photography offers potential to identify this risk. TRIAL REGISTRATION: clinicaltrials.gov NCT02060292
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