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- Wennberg, Bernt, 1961
(författare)
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Random many-particle systems: applications from biology, and propagation of chaos in abstract models
- 2012
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Ingår i: Rivista di Matematica della Università di Parma. ; 3:2, s. 291-344
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Konferensbidrag (refereegranskat)abstract
- The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric speciation, i.e. the process in which a genetically homogeneous population is split in two or more different species sharing the same habitat, and models for swarming animals. The second part of the paper deals with abstract many particle systems and methods for rigorously deriving mean field models.
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| 2. |
- Wennberg, Bernt, 1961, et al.
(författare)
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The Kac master equation with unbounded collision rate
- 2009
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Ingår i: Markov Processes and Related Fields. - 1024-2953. ; 15:2, s. 125-148
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Tidskriftsartikel (refereegranskat)abstract
- The Kac model is a Markov jump process on the sphere $\sum_{j=1}^{N} v_j^2$. The model was conceived as model for an N-particle system with pairwise interactions, and hence the jumps involve only pairs of coordinates, $(v_i, v_j )$. This paper deals with Kac models with unbounded jump rates. We prove that the processes are Feller processes, and introduce a diusion approximation that is useful for numerical simulation of the processes. We also study the spectral gap of the Markov generators, using the methods developed by Carlen, Carvalho and Loss.
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| 3. |
- Helgesson, Peter, 1985, et al.
(författare)
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The N-Player War of Attrition in the Limit of Infinitely Many Players
- 2015
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Ingår i: Dynamic Games and Applications. - : Springer Science and Business Media LLC. - 2153-0785 .- 2153-0793. ; 5:1, s. 65-93
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Tidskriftsartikel (refereegranskat)abstract
- The War of Attrition is a classical game theoretic model that was first introduced to mathematically describe certain non-violent animal behavior. The original setup considers two participating players in a one-shot game competing for a given prize by waiting. This model has later been extended to several different models allowing more than two players. One of the first of these N -player generalizations was due to Haigh and Cannings (Acta Appl Math 14:59–74, 1989) where two possible models are mainly discussed; one in which the game starts afresh with new strategies each time a player leaves the game, and one where the players have to stick with the strategy they chose initially. The first case is well understood whereas, for the second case, much is still left open. There are two main results in this paper. The first concerns the asymptotic behavior of the models as the number of players tend to infinity. In particular, we prove that the time evolution of the models coincide in the limit, thus providing a link between the two in the regime of infinitely many players. Secondly we prove, under certain conditions, existence and uniqueness of an ESS in the second model for any given number of players.
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| 4. |
- Mustafa, Dawan, 1985, et al.
(författare)
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The BGK Equation as the Limit of anN-Particle System
- 2020
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Ingår i: Journal of Statistical Physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 181, s. 715-737
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Tidskriftsartikel (refereegranskat)abstract
- The spatially homogeneous BGK equation is obtained as the limit of a model of a many particle system, similar to Mark Kac's charicature of the spatially homogeneous Boltzmann equation.
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| 5. |
- 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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| 6. |
- Mischler, S., et al.
(författare)
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A new approach to quantitative propagation of chaos for drift, diffusion and jump processes
- 2015
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Ingår i: Probability Theory and Related Fields. - : Springer Science and Business Media LLC. - 0178-8051 .- 1432-2064. ; 161:1-2, s. 1-59
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstract generator operators (consistency estimate) together with fine stability estimates on the flow of the limiting nonlinear equation (stability estimates). Then we apply this method to a Boltzmann collision jump process (for Maxwell molecules), to a McKean-Vlasov drift-diffusion process and to an inelastic Boltzmann collision jump process with (stochastic) thermal bath. To our knowledge, our approach yields the first such quantitative results for a combination of jump and diffusion processes. © 2013 Springer-Verlag Berlin Heidelberg.
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| 7. |
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| 8. |
- Anguelova, Milena, 1978, et al.
(författare)
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Input-Output Representation and Identifiability of Delay Parameters for Nonlinear Systems with Multiple Time-Delays
- 2009
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Ingår i: Lecture Notes in Control and Information Sciences: TOPICS IN TIME DELAY SYSTEMS: ANALYSIS, ALGORITHMS AND CONTROL; 7th IFAC Workshop on Time Delay Systems. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 0170-8643. - 9783642028960 ; 388, s. 243-253
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We have analyzed the identifiability of time-lag parameters in nonlinear delay systems using an algebraic framework. The identifiability is determined by the form of the system's input-output representation. The values of the time lags can be found directly from the input-output equations, if these can be obtained explicitly. Linear-algebraic criteria are formulated to decide the identifiability of the delay parameters when explicit computation of the input-output relations is not possible.
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| 9. |
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| 10. |
- Berglund, Martin, 1980, et al.
(författare)
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Improved Estimation of Human Lipoprotein Kinetics with Mixed Effects Models
- 2015
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Ingår i: PLoS ONE. - : Public Library of Science (PLoS). - 1932-6203. ; 10:9
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Tidskriftsartikel (refereegranskat)abstract
- Mathematical models may help the analysis of biological systems by providing estimates of otherwise un-measurable quantities such as concentrations and fluxes. The variability in such systems makes it difficult to translate individual characteristics to group behavior. Mixed effects models offer a tool to simultaneously assess individual and population behavior from experimental data. Lipoproteins and plasma lipids are key mediators for cardiovascular disease in metabolic disorders such as diabetes mellitus type 2. By the use of mathematical models and tracer experiments fluxes and production rates of lipoproteins may be estimated. We developed a mixed effects model to study lipoprotein kinetics in a data set of 15 healthy individuals and 15 patients with type 2 diabetes. We compare the traditional and the mixed effects approach in terms of group estimates at various sample and data set sizes. We conclude that the mixed effects approach provided better estimates using the full data set as well as with both sparse and truncated data sets. Sample size estimates showed that to compare lipoprotein secretion the mixed effects approach needed almost half the sample size as the traditional method.
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