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- Gyllenberg, Mats, et al.
(författare)
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A nonlinear structured population model of tumor growth with quiescence
- 1990
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Ingår i: Journal of Mathematical Biology. - 0303-6812 .- 1432-1416. ; 28:6, s. 671-694
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Tidskriftsartikel (refereegranskat)abstract
- A nonlinear structured cell population model of tumor growth is considered. The model distinguishes between two types of cells within the tumor: proliferating and quiescent. Within each class the behavior of individual cells depends on cell size, whereas the probabilities of becoming quiescent and returning to the proliferative cycle are in addition controlled by total tumor size. The asymptotic behavior of solutions of the full nonlinear model, as well as some linear special cases, is investigated using spectral theory of a positive semigroup of operators
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- Gyllenberg, Mats, et al.
(författare)
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Asynchronous exponential growth of semigroups of nonlinear operators
- 1992
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Ingår i: Journal of Mathematical Analysis and Applications. - 0022-247X .- 1096-0813. ; 167:2, s. 443-467
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Tidskriftsartikel (refereegranskat)abstract
- The property of asynchronous exponential growth is analyzed for the abstract nonlinear differential equation z′(t) = Az(t) + F(z(t)), t ≥ 0, z(0) = x ε{lunate} X, where A is the infinitesimal generator of a semigroup of linear operators in the Banach space X and F is a nonlinear operator in X. Asynchronous exponential growth means that the nonlinear semigroup S(t), t ≥ 0 associated with this problem has the property that there exists λ > 0 and a nonlinear operator Q in X such that the range of Q lies in a one-dimensional subspace of X and limt → ∞ e-λtS(t)x = Qx for all x ε{lunate} X. It is proved that if the linear semigroup generated by A has asynchronous exponential growth and F satisfies ∥F(x)∥ ≤ f(∥x∥) ∥x∥, where f: R+ → R+ and ∝∞( f(r) r) dr < ∞, then the nonlinear semigroup S(t), t ≥ 0 has asynchronous exponential growth. The method of proof is a linearization about infinity. Examples from structured population dynamics are given to illustrate the results
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- 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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- Gyllenberg, Mats, et al.
(författare)
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Non-uniqueness in probabilistic numerical identification of bacteria
- 1994
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 31:2, s. 542-548
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Tidskriftsartikel (refereegranskat)abstract
- In this note we point out an inherent difficulty in numerical identification of bacteria. The problem is that of uniqueness of the taxonomic structure or, in mathematical terms, the lack of statistical identifiability of finite mixtures of multivariate Bernoulli probability distributions shown here.
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- Gyllenberg, Mats, et al.
(författare)
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Non-uniqueness of numerical taxonomic structures
- 1993
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Ingår i: Binary Computing in Microbiology. - 0266-304X. ; 5:4, s. 138-144
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Tidskriftsartikel (refereegranskat)abstract
- The most important methods of numerical taxonomy in microbiology are based on so called reference matrices giving the frequencies of positive binary features of the different taxa. Microbiologists seem to have been tacitly assuming that every well-defined classification method, that is, every algorithm for constructing a reference matrix from data, leads to a unique classification (reference matrix). We use a mathematical result-that a finite mixture of multivariate Bernoulli distributions is always unidentifiable-to disprove this assumption. We show that the same classification method applied to the same data can always lead to different classifications. This result is of importance for the foundations of computational microbial taxonomy. It is illustrated by simple examples from the two main methods of classification and identification: the one where classification is performed first and then followed by identification, and cumulative classification where classification and identification are carried out simultaneously. The consequences of the non-uniqueness result for microbiological practice are discussed
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