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- Anguelova, Milena, 1978, et al.
(författare)
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On analytic and algebraic observability of nonlinear delay systems
- 2010
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098. ; 46:4, s. 682-686
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Tidskriftsartikel (refereegranskat)abstract
- The observability of nonlinear delay systems has previously been defined in an algebraic setting by a rank condition on modules over noncommutative rings. We introduce an analytic definition of observability to ensure the local uniqueness of state and initial conditions that correspond to a given input-output behaviour. It is shown that an algebraically observable delay system can be reformulated as a system of ordinary differential equations. Analytic observability is then decided by the local uniqueness of solutions to a boundary value problem for this ODE system. (C) 2010 Elsevier Ltd. All rights reserved.
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| 2. |
- Henriksson, J., et al.
(författare)
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A Model of Sympatric Speciation Through Reinforcement
- 2010
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Ingår i: Kinetic and Related Models. - : American Institute of Mathematical Sciences (AIMS). - 1937-5093 .- 1937-5077. ; 3:1, s. 143-163
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Tidskriftsartikel (refereegranskat)abstract
- Sympatric speciation, i.e. the evolutionary split of one species into two in the same environment, has been a highly troublesome concept. It has been a questioned if it is actually possible. Even though there have been a number of reported results both in the wild and from controlled experiments in laboratories, those findings are both hard to get and hard to analyze, or even repeat. In the current study we propose a mathematical model which addresses the question of sympatric speciation and the evolution of reinforcement. Our aim has been to capture some of the essential features such as: phenotype, resources, competition, heritage, mutation, and reinforcement, in as simple a way as possible. Still, the resulting model is not too easy to grasp with purely analytical tools, so we have also complemented those studies with stochastic simulations. We present a few results that both illustrates the usefulness of such a model, but also rises new biological questions about sympatric speciation and reinforcement in particular.
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| 3. |
- Rodhe, P., et al.
(författare)
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Modelling of peripheral fluid accumulation after a crystalloid bolus in female volunteers - a mathematical study
- 2010
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Ingår i: Computational and Mathematical Methods in Medicine. - : Taylor and Francis. - 1748-670X .- 1748-6718. ; 11:4, s. 341-351
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Tidskriftsartikel (refereegranskat)abstract
- Objective. To simultaneously model plasma dilution and urinary output in female volunteers. Methods. Ten healthy female non-pregnant volunteers, aged 21-39 years (mean 29), with a bodyweight of 58-67kg (mean 62.5kg) participated. No oral fluid or food was allowed between midnight and completion of the experiment. The protocol included an infusion of acetated Ringer's solution, 25ml/kg over 30min. Blood samples (4ml) were taken every 5min during the first 120min, and thereafter the sampling rate was every 10min until the end of the experiment at 240min. A standard bladder catheter connected to a drip counter to monitor urine excretion continuously was used. The data were analysed by empirical calculations as well as by a mathematical model. Results. Maximum urinary output rate was found to be 19 (13-31) ml/min. The subjects were likely to accumulate three times as much of the infused fluid peripherally as centrally; 1/=2.7 (2.0-5.7). Elimination efficacy, Eeff, was 24 (5-35), and the basal elimination kb was 1.11 (0.28-2.90). The total time delay Ttot of urinary output was estimated as 17 (11-31) min. Conclusion. The experimental results showed a large variability in spite of a homogenous volunteer group. It was possible to compute the infusion amount, plasma dilution and simultaneous urinary output for each consecutive time point and thereby the empirical peripheral fluid accumulation. The variability between individuals may be explained by differences in tissue and hormonal responses to fluid boluses, which needs to be further explored.
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