92 research outputs found
Explicit formulas for a continuous stochastic maturation model. Application to anticancer drug pharmacokinetics/pharmacodynamics
We present a continuous time model of maturation and survival, obtained as
the limit of a compartmental evolution model when the number of compartments
tends to infinity. We establish in particular an explicit formula for the law
of the system output under inhomogeneous killing and when the input follows a
time-inhomogeneous Poisson process. This approach allows the discussion of
identifiability issues which are of difficult access for finite compartmental
models. The article ends up with an example of application for anticancer drug
pharmacokinetics/pharmacodynamics.Comment: Revised version, accepted for publication in Stochastic Models
(Taylor & Francis
Dynamics for a non-linear and non-autonomous compartmental system
We study the long-time behavior of the amount of material within the compartments of a compartmental system for which the flow of material does not have to be instantaneous and may even take an infinite time to occur. Results on the estructure of minimal sets for monotone skew-product semiflows, previously obtained by the authors, are applied to this description
Analyzing Linear Communication Networks using the Ribosome Flow Model
The Ribosome Flow Model (RFM) describes the unidirectional movement of
interacting particles along a one-dimensional chain of sites. As a site becomes
fuller, the effective entry rate into this site decreases. The RFM has been
used to model and analyze mRNA translation, a biological process in which
ribosomes (the particles) move along the mRNA molecule (the chain), and decode
the genetic information into proteins.
Here we propose the RFM as an analytical framework for modeling and analyzing
linear communication networks. In this context, the moving particles are
data-packets, the chain of sites is a one dimensional set of ordered buffers,
and the decreasing entry rate to a fuller buffer represents a kind of
decentralized backpressure flow control. For an RFM with homogeneous link
capacities, we provide closed-form expressions for important network metrics
including the throughput and end-to-end delay. We use these results to analyze
the hop length and the transmission probability (in a contention access mode)
that minimize the end-to-end delay in a multihop linear network, and provide
closed-form expressions for the optimal parameter values
Equivalence of finite dimensional input-output models of solute transport and diffusion in geosciences
We show that for a large class of finite dimensional input-output positive
systems that represent networks of transport and diffusion of solute in
geological media, there exist equivalent multi-rate mass transfer and multiple
interacting continua representations, which are quite popular in geo-sciences.
Moreover, we provide explicit methods to construct these equivalent
representations. The proofs show that controllability property is playing a
crucial role for obtaining equivalence. These results contribute to our
fundamental understanding on the effect of fine-scale geological structures on
the transfer and dispersion of solute, and, eventually, on their interaction
with soil microbes and minerals
Transit times and mean ages for nonautonomous and autonomous compartmental systems
We develop a theory for transit times and mean ages for nonautonomous
compartmental systems. Using the McKendrick-von F\"orster equation, we show
that the mean ages of mass in a compartmental system satisfy a linear
nonautonomous ordinary differential equation that is exponentially stable. We
then define a nonautonomous version of transit time as the mean age of mass
leaving the compartmental system at a particular time and show that our
nonautonomous theory generalises the autonomous case. We apply these results to
study a nine-dimensional nonautonomous compartmental system modeling the
terrestrial carbon cycle, which is a modification of the Carnegie-Ames-Stanford
approach (CASA) model, and we demonstrate that the nonautonomous versions of
transit time and mean age differ significantly from the autonomous quantities
when calculated for that model
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