| 1. |
- Aye, Tin Nwe, 1989-, et al.
(författare)
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Increasing effciency in the EBT algorithm
- 2019
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Ingår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180331 ; , s. 179-205
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Konferensbidrag (refereegranskat)abstract
- The Escalator Boxcar Train (EBT) is a commonly used method for solving physiologically structured population models. The main goal of this paper is to overcome computational disadvantages of the EBT method. We prove convergence, for a general class of EBT models in which we modify the original EBT formulation, allowing merging of cohorts. We show that this modified EBT method induces a bounded number of cohorts, independent of the number of time steps. This in turn, improve the numerical algorithm from polynomial to linear time. An EBT simulation of the Daphnia model is used as an illustration of these findings.
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| 2. |
- Aye, Tin Nwe, 1989-, et al.
(författare)
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Increasing Efficiency in the EBT Algorithm
- 2020
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Ingår i: Demography of Population Health, Aging and Health Expenditures. - Cham : Springer. - 9783030446956 - 9783030446956 ; , s. 289-317
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Bokkapitel (refereegranskat)abstract
- The Escalator Boxcar Train (EBT) is a commonly used method for solving physiologically structured population models. The main goal of this paper is to overcome computational disadvantages of the EBT method. We prove convergence, for a general class of EBT models in which we modify the original EBT formulation, allowing merging of cohorts. We show that this modified EBT method induces a bounded number of cohorts, independent of the number of time steps. This in turn, improves the numerical algorithm from polynomial to linear time. An EBT simulation of the Daphnia model is used as an illustration of these findings.
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| 3. |
- Aye, Tin Nwe, 1989-, et al.
(författare)
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Method development for emergent properties in stage-structured population models with stochastic resource growth.
- 2022
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Ingår i: <em>Springer Proceedings in Mathematics and Statistics</em>. - Cham : Springer International Publishing. ; , s. 33-58
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Konferensbidrag (refereegranskat)abstract
- Modelling population dynamics in ecological systems reveals properties that are difficult to find by empirical means, such as the probability that a population will go extinct when it is exposed to harvesting. In this article, we use an aquatic ecological system containing one fish species and an underlying resource as our model. In particular, we study a class of stage-structured population systems, in both the deterministic and the stochastic settings, including stochasticity in such a way such that we allow the underlying resource to have a random growth rate. In these models, we study how properties connected to the fish species depend on different harvesting rates. To investigate models in the stochastic setting, we use Monte Carlo simulations to capture several of the emergent properties of the population. These properties have previously been studied in the deterministic case. In the stochastic setting, we get estimates for the expected outcome of population properties in our model, but we also get measures of dispersion. There are properties that emerge when introducing randomness in the model that cannot be studied in the deterministic cases, such as the probability of extinction. In this paper, we develop a method to derive this property. We also construct a method to determine the recovery potential of a species by introducing it in a virgin environment.
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| 4. |
- Aye, Tin Nwe, 1989-, et al.
(författare)
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Numerical stability of the escalator boxcar train under reducing system of ordinary differential equations.
- 2017
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Konferensbidrag (refereegranskat)abstract
- The Escalator Boxcar Train (EBT) is one of the most popular numericalmethods used to study the dynamics of physiologically structured population models.The original EBT model accumulates an increasing system of ODEs to solve for eachtime step. In this project, we propose a merging procedure to overcome computationaldisadvantageous of the EBT method, the merging is done as an automatic feature.In particular we apply the model including merging to a colony of Daphnia Pulex.
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| 5. |
- Aye, Tin Nwe, 1989-, et al.
(författare)
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Pipe Model Theory for Prediction Tree Sapwood and Heartwood Profiles
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The classical pipe model theory introduced by Shinozaki, Yoda, Hozumi,and Kira (1964a,b) is used to estimate tree sapwood area. It rests on theconceptual idea that leaves are supported by pipes, serving as vascularpassages. The simple pipe model of plant form does not predict the heartwood area and is thus not suitable for stem diameter estimates below thetree crown. For this reason, Shinozaki, Yoda, Hozumi, and Kira (1964a)verbally described an extended pipe model theory of tree form that inprinciple accounts for the accumulation of disused pipes from discardedbranches and leaves. However, this pipe model theory of tree form is difficultto apply in practice as lost branches and leaves are rarely known. Here, we synthesize the pipe model theory of plant form with a recentlydeveloped theory of branch thinning that quantify discarded branches andleaves. This allows us to develop a new stem model of tree profiles frombreast height up to the top of the tree. We test the stem model performance on empirical data from four tree species across three continents.We find that the stem model accurately describes heartwood and sapwoodprofiles of all tested tree species (calibration; R2: 84-99 %). Furthermore,once calibrated to a tree species, the stem model predicts heartwood andsapwood profiles of conspecific trees in similar growing environments basedonly on the age and height of a tree (cross-validation / prediction; R2:62-98 %).
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| 6. |
- Aye, Tin Nwe, 1989-
(författare)
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POPULATION DYNAMICS AND TREE GROWTH STRUCTURE IN MATHEMATICAL ECOLOGY
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is based on four papers related to mathematical biology, where three papers focus on population dynamics and one paper concerns tree growth and stem structure. The first two papers are mainly devoted to studying the dynamics of physiologically structured population models by using Escalator Boxcar Train (EBT) method. The third paper concerns a class of stage-structured population systems, in both deterministic and stochastic settings. The fourth paper explores how a branch thinning model can be utilized to describe the cross-sectional area of the stem of a tree, thus generalizing the classical pipe model.In Paper I, we present a merging procedure to reduce the increasing system of ordinary differential equations generated by the EBT method. In particular, we modify the EBT method to include merging of cohorts. The accuracy of this model is explored on a colony of Daphnia Pulex.In Paper II, we study the convergence rate of the modified EBT model, allowing a general class of non-linear merging procedures. We show that this modified EBT method induces a bounded number of cohorts, independent of the number of time steps. This in turn, improves the speed of the numerical algorithm for solving the population dynamics from polynomial time to linear time, that is, the time consumption to find the solution is proportional to the number of time steps.In Paper III, a class of non-linear two-stage structured population models is studied with different growth rates for the unstructured food resource under different harvesting rates in both deterministic and stochastic settings. In the stochastic setting, we develop methods to evaluate emergent properties equivalent to the properties investigated in the deterministic case. In addition, new emergent properties, e.g. probability of extinction, are also investigated.In Paper IV, we explore the stem model which is developed by combining the pipe model and the branch thinning model. The stem model provides estimates of the heartwood, sapwood and stem cross-sectional area at any height. We corroborate the accuracy of our model with empirical data and the cross validation of our results shows a very high goodness of fit for the stem model.
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| 7. |
- Aye, Tin Nwe, 1989-, et al.
(författare)
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Prediction of tree sapwood and heartwood profiles using pipe model and branch thinning theory
- 2022
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Ingår i: Tree Physiology. - : Oxford University Press. - 0829-318X .- 1758-4469. ; 42:11, s. 2174-2185
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Tidskriftsartikel (refereegranskat)abstract
- Estimates of tree heartwood and sapwood profiles are important in the pulp industry and for dynamic vegetation models, in which they determine tree biomechanical stability and hydraulic conductivity. Several phenomenological models of stem profiles have been developed for this purpose, based on assumptions on how tree crown and foliage distributions change over time. Here, we derive estimates of tree profiles by synthesizing a simple pipe model theory of plant form with a recently developed theory of branch thinning that from simple assumptions quantifies discarded branches and leaves. This allows us to develop a new trunk model of tree profiles from breast height up to the top of the tree. We postulate that leaves that are currently on the tree are connected by sapwood pipes, while pipes that previously connected discarded leaves or branches form the heartwood. By assuming that a fixed fraction of all pipes remain on the trunk after a branching event, as the trunk is traversed from the root system to the tips, this allows us to quantify trunk heartwood and sapwood profiles. We test the trunk model performance on empirical data from five tree species across three continents. We find that the trunk model accurately describes heartwood and sapwood profiles of all tested tree species (calibration; R2: 84-99%). Furthermore, once calibrated to a tree species, the trunk model predicts heartwood and sapwood profiles of conspecific trees in similar growing environments based only on the age and height of a tree (cross-validation/prediction; R2: 68-98%). The fewer and often contrasting parameters needed for the trunk model make it a potentially useful complementary tool for biologists and foresters.
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| 8. |
- Aye, Tin Nwe, 1989-, et al.
(författare)
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Properties in Stage-Structured Population Models with Deterministic and Stochastic Resource Growth
- 2022
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Ingår i: Journal of Applied Mathematics. - : Hindawi Limited. - 1110-757X .- 1687-0042. ; 2022
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Tidskriftsartikel (refereegranskat)abstract
- Modelling population dynamics in ecological systems reveals properties that are difficult to find by empirical means, such as the probability that a population will go extinct when it is exposed to harvesting. To study these properties, we use an aquatic ecological system containing one fish species and an underlying resource as our models. In particular, we study a class of stage-structured population systems with and without starvation. In these models, we study the resilience, the recovery potential, and the probability of extinction and show how these properties are affected by different harvesting rates, both in a deterministic and stochastic setting. In the stochastic setting, we develop methods for deriving estimates of these properties. We estimate the expected outcome of emergent population properties in our models, as well as measures of dispersion. In particular, two different approaches for estimating the probability of extinction are developed. We also construct a method to determine the recovery potential of a species that is introduced in a virgin environment.
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| 9. |
- Backlund, Ulf, et al.
(författare)
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Semi-Bloch functions in several complex variables
- 2013
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Let $M$ be an $n$-dimensional complex manifold. A holomorphic function $f:M\to \mathbb C$ is said to be semi-Bloch if for every $\lambda\in \mathbb C$ the function $g_\lambda=\exp(\lambda f(z))$ is normal on $M$. We characterise Semi-Bloch functions on infinitesimally Kobayashi non-degenerate $M$ in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.
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| 10. |
- Brännström, Åke, 1975-, et al.
(författare)
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On the convergence of the Escalator Boxcar Train
- 2013
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 51:6, s. 3213-3231
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Tidskriftsartikel (refereegranskat)abstract
- The Escalator Boxcar Train (EBT) is a numerical method that is widely used in theoretical biology to investigate the dynamics of physiologically structured population models, i.e., models in which individuals differ by size or other physiological characteristics. The method was developed more than two decades ago, but has so far resisted attempts to give a formal proof of convergence. Using a modern framework of measure-valued solutions, we investigate the EBT method and show that the sequence of approximating solution measures generated by the EBT method converges weakly to the true solution measure under weak conditions on the growth rate, birth rate, and mortality rate. In rigorously establishing the convergence of the EBT method, our results pave the way for wider acceptance of the EBT method beyond theoretical biology and constitutes an important step towards integration with established numerical schemes.Read More: http://epubs.siam.org/doi/abs/10.1137/120893215
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