132,838 research outputs found
From regional pulse vaccination to global disease eradication: insights from a mathematical model of Poliomyelitis
Mass-vaccination campaigns are an important strategy in the global fight
against poliomyelitis and measles. The large-scale logistics required for these
mass immunisation campaigns magnifies the need for research into the
effectiveness and optimal deployment of pulse vaccination. In order to better
understand this control strategy, we propose a mathematical model accounting
for the disease dynamics in connected regions, incorporating seasonality,
environmental reservoirs and independent periodic pulse vaccination schedules
in each region. The effective reproduction number, , is defined and proved
to be a global threshold for persistence of the disease. Analytical and
numerical calculations show the importance of synchronising the pulse
vaccinations in connected regions and the timing of the pulses with respect to
the pathogen circulation seasonality. Our results indicate that it may be
crucial for mass-vaccination programs, such as national immunisation days, to
be synchronised across different regions. In addition, simulations show that a
migration imbalance can increase and alter how pulse vaccination should
be optimally distributed among the patches, similar to results found with
constant-rate vaccination. Furthermore, contrary to the case of constant-rate
vaccination, the fraction of environmental transmission affects the value of
when pulse vaccination is present.Comment: Added section 6.1, made other revisions, changed titl
Optimal phenotypic plasticity in a stochastic environment minimizes the cost/benefit ratio
This paper addresses the question of optimal phenotypic plasticity as a
response to environmental fluctuations while optimizing the cost/benefit ratio,
where the cost is energetic expense of plasticity, and benefit is fitness. The
dispersion matrix \Sigma of the genes' response (H = ln|\Sigma|) is used: (i)
in a numerical model as a metric of the phenotypic variance reduction in the
course of fitness optimization, then (ii) in an analytical model, in order to
optimize parameters under the constraint of limited energy availability.
Results lead to speculate that such optimized organisms should maximize their
exergy and thus the direct/indirect work they exert on the habitat. It is shown
that the optimal cost/benefit ratio belongs to an interval in which differences
between individuals should not substantially modify their fitness.
Consequently, even in the case of an ideal population, close to the optimal
plasticity, a certain level of genetic diversity should be long conserved, and
a part, still to be determined, of intra-populations genetic diversity probably
stem from environment fluctuations. Species confronted to monotonous factors
should be less plastic than vicariant species experiencing heterogeneous
environments. Analogies with the MaxEnt algorithm of E.T. Jaynes (1957) are
discussed, leading to the conjecture that this method may be applied even in
case of multivariate but non multinormal distributions of the responses
An optimization-based control strategy for energy efficiency of discrete manufacturing systems
In order to reduce the global energy consumption and avoid highest power peaks during operation of manufacturing systems, an optimization-based controller for selective switching on/off of peripheral devices in a test bench that emulates the energy consumption of a periodic system is proposed. First, energy consumption models for the test-bench devices are obtained based on data and subspace identification methods. Next, a control strategy is designed based on both optimization and receding horizon approach, considering the energy consumption models, operating constraints, and the real processes performed by peripheral devices. Thus, a control policy based on dynamical models of peripheral devices is proposed to reduce the energy consumption of the manufacturing systems without sacrificing the productivity. Afterward, the proposed strategy is validated in the test bench and comparing to a typical rule-based control scheme commonly used for these manufacturing systems. Based on the obtained results, reductions near 7% could be achieved allowing improvements in energy efficiency via minimization of the energy costs related to nominal power purchased.Peer ReviewedPostprint (author's final draft
Transfer of autocollimator calibration for use with scanning gantry profilometers for accurate determination of surface slope and curvature of state of the art x ray mirrors
X ray optics, desired for beamlines at free electron laser and diffraction limited storage ring x ray light sources, must have almost perfect surfaces, capable of delivering light to experiments without significant degradation of brightness and coherence. To accurately characterize such optics at an optical metrology lab, two basic types of surface slope profilometers are used the long trace profilers LTPs and nanometer optical measuring NOM like angular deflectometers, based on electronic autocollimator AC ELCOMAT 3000. The inherent systematic errors of the instrument s optical sensors set the principle limit to their measuring performance. Where autocollimator of a NOM like profiler may be calibrated at a unique dedicated facility, this is for a particular configuration of distance, aperture size, and angular range that does not always match the exact use in a scanning measurement with the profiler. Here we discuss the developed methodology, experimental set up, and numerical methods of transferring the calibration of one reference AC to the scanning AC of the Optical Surface Measuring System OSMS , recently brought to operation at the ALS Xray Optics Laboratory. We show that precision calibration of the OSMS performed in three steps, allows us to provide high confidence and accuracy low spatial frequency metrology and not print into measurements the inherent systematic error of tool in use. With the examples of the OSMS measurements with a state of the art x ray aspherical mirror, available from one of the most advanced vendors of X ray optics, we demonstrate the high efficacy of the developed calibration procedure. The results of our work are important for obtaining high reliability data, needed for sophisticated numerical simulations of beamline performance and optimization of beamline usage of the optics. This work was supported by the U. S. Department of Energy under contract number DE AC02 05CH1123
Phenotypic switching of populations of cells in a stochastic environment
In biology phenotypic switching is a common bet-hedging strategy in the face
of uncertain environmental conditions. Existing mathematical models often focus
on periodically changing environments to determine the optimal phenotypic
response. We focus on the case in which the environment switches randomly
between discrete states. Starting from an individual-based model we derive
stochastic differential equations to describe the dynamics, and obtain
analytical expressions for the mean instantaneous growth rates based on the
theory of piecewise deterministic Markov processes. We show that optimal
phenotypic responses are non-trivial for slow and intermediate environmental
processes, and systematically compare the cases of periodic and random
environments. The best response to random switching is more likely to be
heterogeneity than in the case of deterministic periodic environments, net
growth rates tend to be higher under stochastic environmental dynamics. The
combined system of environment and population of cells can be interpreted as
host-pathogen interaction, in which the host tries to choose environmental
switching so as to minimise growth of the pathogen, and in which the pathogen
employs a phenotypic switching optimised to increase its growth rate. We
discuss the existence of Nash-like mutual best-response scenarios for such
host-pathogen games.Comment: 17 pages, 6 figure
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