| 1. |
- Bellman, R., et al.
(författare)
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On Structural Identifiability
- 1970
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Ingår i: Mathematical Biosciences. - 0025-5564. ; 7, s. 329-339
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Tidskriftsartikel (refereegranskat)abstract
- In this article we introduce a new concept, structural identifiability, which plays a central role in identification problems. The concept is useful when answering questions such as: To what extent is it possible to get insight into the internal structure of a system from input-output measurements? What experiments are necessary in order to determine the internal couplings uniquely? The definition of the concept of an identifiable structure is given. Criteria as well as certain identifiable structures are discussed. Particular emphasis is given to compartmental models.
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| 2. |
- Hagander, Per, et al.
(författare)
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Incompatibility Alleles; Characteristics of a 1-Locus System
- 1974
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564. ; 20, s. 145-154
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Tidskriftsartikel (refereegranskat)abstract
- The 1-locus incompatibility system that is usually assumed to be present in the red clover is investigated. The allele fluctuations from one generation to the other are demonstrated. A mathematical state model is deduced for arbitrary numbers of alleles in the population, and its steady-state behaviour and stability are discussed. The eigenvalues of the linearized models as well as simulations show that the large systems react slowly to disturbances while the three-allele system oscillates around its equilibrium.
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| 3. |
- Hagander, Per, et al.
(författare)
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Models for the Insulin Response to Intravenous Glucose
- 1978
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564. ; 42, s. 15-29
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Tidskriftsartikel (refereegranskat)abstract
- The Grodsky packet storage model describes many features of insulin release, but at present more or less arbitrary simplifications are necessary. The consequences of various simplifications are discussed, especially with regard to identification of parameters thought to be of importance for glucose tolerance. In particular, the insulin release dynamics of the ordinary intravenous glucose tolerance test is examined. The proposed model contains the following features: It considers arterial rather than venous blood glucose concentration as the stimulus, it takes the glucose injection time into account, and it contains a positive derivative term during the rise of the glucose concentration. When the insulin elimination-rate time constant is fixed to an a priori value, model fitting gives a clear quantification of the sensitivity of early and late insulin release to glucose.
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| 4. |
- Hagander, Per
(författare)
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Random Effects in Biomedical Flow Systems
- 1977
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564. ; 36:3-4, s. 243-255
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Tidskriftsartikel (refereegranskat)abstract
- The random effects in tracer kinetics and cell cycle kinetics are usually described by the particle residence time. An analytical framework is developed, and the importance of the statistical independence of the residence times is emphasized.
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| 5. |
- Johansson, Rolf, et al.
(författare)
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Multi-Stimulus Multi-Response Posturography
- 2001
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Ingår i: Mathematical Biosciences. - 0025-5564. ; 174:1, s. 41-59
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Tidskriftsartikel (refereegranskat)abstract
- In this study a method for the analysis of simultaneous multiple measurements of kinematics and stabilizing forces related to human postural dynamics is proposed. Each subject in a group of normal subjects (n=10) was tested with eyes-open and eyes-closed with simultaneous but uncorrelated vestibular and proprioceptive stimuli in order to investigate the contributions of individual sensory feedback loops. Statistical analysis was made by means of multi-input multi-output identification of a transfer function from stimuli to stabilizing forces of the feet and the resulting body position, the transfer function being compatible with a biomechanical model formulated as a stabilized segmented inverted pendulum subject to feedback of body sway and position. Each individual model estimated is effective in predicting a subject's response to new stimuli and in describing the interacting effects of stimuli on body kinetics. The proposed methodology responds to the current needs of data analysis of multi-stimulus multi-response experiments.
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| 6. |
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| 7. |
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| 8. |
- Gyllenberg, M., et al.
(författare)
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Bayesian predictiveness, exchangeability and sufficientness in bacterial taxonomy
- 2002
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Ingår i: Mathematical Biosciences. - 0025-5564 .- 1879-3134. ; 177-178, s. 161-184
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We present a theory of classification and predictive identification of bacteria. Bacterial strains are characterized by a binary vector and the taxonomy is specified by attaching a label to each vector. The theory is developed from only two basic assumptions, viz. that the sequence of pairs of feature vectors and the attached labels is judged (infinitely) exchangeable and predictively sufficient. We derive expressions for the training error and the probability of identification error and show that latter is an affine function of the former. We prove the law of large numbers for identification matrices, which contain the fundamental information of bacterial data. We prove the Bayesian risk consistency of the predictive identification rule given by the theory and show that the training error is a consistent estimate of the generalization error. © 2002 Published by Elsevier Science Inc.
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| 9. |
- Gyllenberg, Mats, et al.
(författare)
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Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model
- 1993
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 118:1, s. 25-49
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Tidskriftsartikel (refereegranskat)abstract
- A discrete model for a metapopulation consisting of two local populations connected by migration is described and analyzed. It is assumed that the local populations grow according to the logistic law, that both populations have the same emigration rate, and that migrants choose their new habitat patch at random. Mathematically this leads to a coupled system of two logistic equations. A complete characterization of fixed point and two-periodic orbits is given, and a bifurcation analysis is performed. The region in the parameter plane where the diagonal is a global attractor is determined. In the symmetric case, where both populations have the same growth rate, the analysis is rigorous with complete proofs. In the nonsymmetric case, where the populations grow at different rates, the results are obtained numerically. The results are interpreted biologically. Particular attention is given to the sense in which migration has a stabilizing and synchronizing effect on local dynamics.
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| 10. |
- Nåsell, Ingemar
(författare)
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Stochastic models of some endemic infections
- 2002
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Ingår i: Mathematical Biosciences. - 0025-5564 .- 1879-3134. ; 179:1, s. 1-19
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Tidskriftsartikel (refereegranskat)abstract
- Stochastic models are established and studied for several endemic infections with demography. Approximations of quasi-stationary distributions and of times to extinction are derived for stochastic versions of SI, SIS, SIR, and SIRS models. The approximations are valid for sufficiently large population sizes. Conditions for validity of the approximations are given for each of the models. These are also conditions for validity of the corresponding deterministic model. It is noted that some deterministic models are unacceptable approximations of the stochastic models for a large range of realistic parameter values.
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