45 research outputs found
Fractional dynamics pharmacokinetics–pharmacodynamic models
While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics
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Fine-root turnover rates of European forests revisited: an analysis of data from sequential coring and ingrowth cores
Background and Aims
Forest trees directly contribute to carbon cycling in forest soils through the turnover of their fine roots. In this study we aimed to calculate root turnover rates of common European forest tree species and to compare them with most frequently published values.
Methods
We compiled available European data and applied various turnover rate calculation methods to the resulting database. We used Decision Matrix and Maximum-Minimum formula as suggested in the literature.
Results
Mean turnover rates obtained by the combination of sequential coring and Decision Matrix were 0.86 yr−1 for Fagus sylvatica and 0.88 yr−1 for Picea abies when maximum biomass data were used for the calculation, and 1.11 yr−1 for both species when mean biomass data were used. Using mean biomass rather than maximum resulted in about 30 % higher values of root turnover. Using the Decision Matrix to calculate turnover rate doubled the rates when compared to the Maximum-Minimum formula. The Decision Matrix, however, makes use of more input information than the Maximum-Minimum formula.
Conclusions
We propose that calculations using the Decision Matrix with mean biomass give the most reliable estimates of root turnover rates in European forests and should preferentially be used in models and C reporting
Loop Quantum Cosmology
Quantum gravity is expected to be necessary in order to understand situations
where classical general relativity breaks down. In particular in cosmology one
has to deal with initial singularities, i.e. the fact that the backward
evolution of a classical space-time inevitably comes to an end after a finite
amount of proper time. This presents a breakdown of the classical picture and
requires an extended theory for a meaningful description. Since small length
scales and high curvatures are involved, quantum effects must play a role. Not
only the singularity itself but also the surrounding space-time is then
modified. One particular realization is loop quantum cosmology, an application
of loop quantum gravity to homogeneous systems, which removes classical
singularities. Its implications can be studied at different levels. Main
effects are introduced into effective classical equations which allow to avoid
interpretational problems of quantum theory. They give rise to new kinds of
early universe phenomenology with applications to inflation and cyclic models.
To resolve classical singularities and to understand the structure of geometry
around them, the quantum description is necessary. Classical evolution is then
replaced by a difference equation for a wave function which allows to extend
space-time beyond classical singularities. One main question is how these
homogeneous scenarios are related to full loop quantum gravity, which can be
dealt with at the level of distributional symmetric states. Finally, the new
structure of space-time arising in loop quantum gravity and its application to
cosmology sheds new light on more general issues such as time.Comment: 104 pages, 10 figures; online version, containing 6 movies, available
at http://relativity.livingreviews.org/Articles/lrr-2005-11
Optimizing the breakaway position in cycle races using mathematical modelling
In long-distance competitive cycling, efforts to mitigate
the effects of air resistance can significantly reduce
the energy expended by the cyclist. A common method to
achieve such reductions is for the riders to cycle in one large
group, known as the peloton. However, to win a race a cyclist
must break away from the peloton, losing the advantage
of drag reduction and riding solo to cross the finish line
ahead of the other riders. If the rider breaks away too soon
then fatigue effects due to the extra pedal force required
to overcome the additional drag will result in them being
caught by the peloton. On the other hand, if the rider breaks
away too late then they will not maximize their time advantage
over the main field. In this paper, we derive a mathematical
model for the motion of the peloton and breakaway
rider and use asymptotic analysis techniques to derive analytical
solutions for their behaviour. The results are used to
predict the optimum time for a rider to break away that maximizes
the finish time ahead of the peloton for a given course
profile and rider statistics