| 1. |
- Asadzadeh, Mohammad, 1952, et al.
(author)
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A combined discontinuous Galerkin and finite volume scheme for multi-dimensional VPFP system
- 2011
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In: AIP Conference Proceedings. 27th International Symposium on Rarefied Gas Dynamics, RGD27; Pacific Grove, CA; United States; 10 July 2011 through 15 July 2011. - : AIP. - 0094-243X .- 1551-7616. - 9780735408890 ; 1333:Part 1, s. 57-62, s. 57-62
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Conference paper (peer-reviewed)abstract
- We construct a numerical scheme for the multi-dimensional Vlasov-Poisson-Fokker-Planck system based on a combined finite volume (FV) method for the Poisson equation in spatial domain and the streamline diffusion (SD) and discontinuous Galerkin (DG) finite element in time, phase-space variables for the Vlasov-Fokker-Planck equation.
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| 2. |
- Asadzadeh, Mohammad, 1952, et al.
(author)
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Convergence of Finite Volume Scheme for a Three-Dimensional Poisson Equation
- 2014
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In: Journal of Mathematical Sciences. - : Springer-Verlag New York. - 1072-3374 .- 1573-8795. ; 202:2, s. 130-153
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Journal article (peer-reviewed)abstract
- We construct and analyze a finite volume scheme for numerical solution of a three-dimensional Poisson equation. We derive optimal convergence rates in the discrete H1 norm and sub-optimal convergence in the maximum norm, where we use the maximal available regularity of the exact solution and minimal smoothness requirement on the source term. The theoretical results are justified through implementing some canonical examples in 3D.
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| 3. |
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| 4. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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A novel algorithm to reconstruct phylogenies using gene sequences and expression data
- 2014
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In: International Proceedings of Chemical, Biological & Environmental Engineering; Environment, Energy and Biotechnology III. ; , s. 8-12
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Conference paper (peer-reviewed)abstract
- Phylogenies based on single loci should be viewed with caution and the best approach for obtaining robust trees is to examine numerous loci across the genome. It often happens that for the same set of species trees derived from different genes are in conflict between each other. There are several methods that combine information from different genes in order to infer the species tree. One novel approach is to use informationfrom different -omics. Here we describe a phylogenetic method based on an Ornstein–Uhlenbeck process that combines sequence and gene expression data. We test our method on genes belonging to the histidine biosynthetic operon. We found that the method provides interesting insights into selection pressures and adaptive hypotheses concerning gene expression levels.
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| 5. |
- Bartoszek, Krzysztof, 1984, et al.
(author)
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A phylogenetic comparative method for studying multivariate adaptation
- 2012
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In: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 314, s. 204-215
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Journal article (peer-reviewed)abstract
- Phylogenetic comparative methods have been limited in the way they model adaptation. Although some progress has been made, there are still no methods that can fully account for coadaptation between traits. Based on Ornstein–Uhlenbeck (OU) models of adaptive evolution, we present a method, with R implementation, in which multiple traits evolve both in response to each other and, as in previous OU models, to fixed or randomly evolving predictor variables. We present the interpretation of the model parameters in terms of evolutionary and optimal regressions enabling the study of allometric and adaptive relationships between traits. To illustrate the method we reanalyze a data set of antler and body-size evolution in deer (Cervidae).
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| 6. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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Critical case stochastic phylogenetic tree model via the Laplace transform
- 2014
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In: Demonstratio Matematicae. - : De Gruyter. - 0420-1213 .- 2391-4661. ; 47:2, s. 474-481
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Journal article (peer-reviewed)abstract
- Birth-and-death models are now a common mathematical tool to describe branching patterns observed in real-world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth-and-death model that is compatible with phylogenetic trees of both in uenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the death rate. This is a non-trivial situation and to study its asymptotic behaviour we employed the Laplace transform. With this we correct the proof of Liggett and Schinazi (2009) in the critical case.
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| 7. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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Influenza differentiation and evolution
- 2010
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In: Acta Physica Polonica B Proceedings Supplement. ; 3:2, s. 417-452
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Conference paper (peer-reviewed)abstract
- The aim of the study is to do a very wide analysis of HA, NA and M influenza gene segments to find short nucleotide regions,which differentiate between strains (i.e. H1, H2, ... e.t.c.), hosts, geographic regions, time when sequence was found and combination of time and region using a simple methodology. Finding regions differentiating between strains has as its goal the construction of a Luminex microarray which will allow quick and efficient strain recognition. Discovery for the other splitting factors could shed lighton structures significant for host specificity and on the history of influenza evolution. A large number of places in the HA, NA and M gene segments were found that can differentiate between hosts, regions, time and combination of time and region. Also very good differentiation between different Hx strains can be seen.We link one of our findings to a proposed stochastic model of creation of viral phylogenetic trees.
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| 8. |
- Bartoszek, Krzysztof, 1984
(author)
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Multivariate Aspects of Phylogenetic Comparative Methods
- 2011
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Licentiate thesis (other academic/artistic)abstract
- his thesis concerns multivariate phylogenetic comparative methods. We investigate two aspects of them. The first is the bias caused by measurement error in regression studies of comparative data. We calculate the formula for the bias and show how to correct for it. We also study whether it is always advantageous to correct for the bias as correction can increase the mean square error of the estimate. We propose a criterion, which depends on the observed data, that indicates whether it is beneficial to correct or not. Accompanying the results is an R program that offers the bias correction tool. The second topic is a multivariate model for trait evolution which is based on an Ornstein-Uhlenbeck type stochastic process, often used for studying trait adaptation, co--evolution, allometry or trade--offs. Alongside the description of the model and presentation of its most important features we present an R program estimating the model's parameters. To the best of our knowledge our program is the first program that allows for nearly all combinations of key model parameters providing the biologist with a flexible tool for studying multiple interacting traits in the Ornstein-Uhlenbeck framework. There are numerous packages available that include the Ornstein-Uhlenbeck process but their multivariate capabilities seem limited.
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| 9. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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Performance of pseudo-likelihood estimator in modelling cells' proliferation with noisy measurements
- 2010
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In: Conference materials XII International Workshop for Young Mathematicians. ; , s. 21-42, s. 21-42
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Conference paper (other academic/artistic)abstract
- Branching processes are widely used to describe cell development and proliferation. Currently parameter estimation is studied in mathematical models describing the dynamics of cell cultures where we can get very accurate measurements of cell counts. In vivo samples we will not have this accuracy, here the noise levels can be very significant. We will study a newly proposed pseudo-likelihood estimator of a multitype Bellman-Harris process modelling cell development and see how it performs under noisy measurements of cell counts.
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| 10. |
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| 11. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait
- 2013
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In: Proceedings of the XIX National Conference on Applications of Mathematics in Biology and Medicine. - 8360253862 ; , s. 19-24
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Conference paper (peer-reviewed)abstract
- Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introducedand studied recently. In the present work we discuss biological interpretations that can be attributedto them. We also propose a computer simulation method to illustrate the behaviour of iterates of quadratic stochastic operators.
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| 12. |
- Bartoszek, Krzysztof, 1984
(author)
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Stochastic Models in Phylogenetic Comparative Methods: Analytical Properties and Parameter Estimation
- 2013
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Doctoral thesis (other academic/artistic)abstract
- Phylogenetic comparative methods are well established tools for using inter-species variation to analyse phenotypic evolution and adaptation. They are generally hampered, however, by predominantly univariate approaches and failure to include uncertainty and measurement error in the phylogeny as well as the measured traits. This thesis addresses all these three issues. First, by investigating the effects of correlated measurement errors on a phylogenetic regression. Second, by developing a multivariate Ornstein-Uhlenbeck model combined with a maximum-likelihood estimation package in R. This model allows, uniquely, a direct way of testing adaptive coevolution. Third, accounting for the often substantial phylogenetic uncertainty in comparative studies requires an explicit model for the tree. Based on recently developed conditioned branching processes, with Brownian and Ornstein-Uhlenbeck evolution on top, expected species similarities are derived, together with phylogenetic confidence intervals for the optimal trait value. Finally, inspired by these developments, the phylogenetic framework is illustrated by an exploration of questions concerning “time since hybridization”, the distribution of which proves to be asymptotically exponential.
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| 13. |
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| 14. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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Survival time prognosis under a Markov model of cancer development
- 2010
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In: Proceedings of the XVI National Conference on Applications of Mathematics in Biology and Medicine. ; , s. 6-11
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Conference paper (peer-reviewed)abstract
- In this study we look at a breast cancer data set of women from the Pomerania region collected in the year 1987- 1992 in the Medical University of Gdansk.We analyze the clinical risk factors in conjunction with a Markov model of cancer development. We evaluate Artificial Neural Network (ANN) survival time prediction (which was done on this data set in a previous study) via a simulation study.
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| 15. |
- Bartoszek, Krzysztof, 1984-
(author)
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The Laplace Motion in Phylogenetic Comparative Methods
- 2012
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In: Proceedings of the Eightteenth National Conference on Applications of Mathematics in Biology and Medicine. - 9788373484344 ; , s. 25-30
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Conference paper (peer-reviewed)abstract
- The majority of current phylogenetic comparative methods assume that the stochastic evolutionary process is homogeneous over the phylogeny or offer relaxations of this in rather limited and usually parameter expensive ways. Here we make a preliminary investigation, by means of a numerical experiment, whether the Laplace motion process can offer an alternative approach.
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| 16. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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Time to a single hybridization event in a group of species with unknown ancestral history
- 2013
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In: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 322, s. 1-6
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Journal article (peer-reviewed)abstract
- We consider a stochastic process for the generation of species which combines a Yule process with a simple model for hybridization between pairs of co-existent species. We assume that the origin of the process, when there was one species, occurred at an unknown time in the past, and we condition the process on producing n species via the Yule process and a single hybridization event. We prove results about the distribution of the time of the hybridization event. In particular we calculate a formula for all moments, and show that under various conditions, the distribution tends to an exponential with rate twice that of the birth rate for the Yule process.
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| 17. |
- Hansen, T. F., et al.
(author)
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Interpreting the Evolutionary Regression: The Interplay Between Observational and Biological Errors in Phylogenetic Comparative Studies
- 2012
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In: Systematic Biology. - Oxford : Oxford University Press (OUP). - 1063-5157 .- 1076-836X. ; 61:3, s. 413-425
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Journal article (peer-reviewed)abstract
- Regressions of biological variables across species are rarely perfect. Usually, there are residual deviations from the estimated model relationship, and such deviations commonly show a pattern of phylogenetic correlations indicating that they have biological causes. We discuss the origins and effects of phylogenetically correlated biological variation in regression studies. In particular, we discuss the interplay of biological deviations with deviations due to observational or measurement errors, which are also important in comparative studies based on estimated species means. We show how bias in estimated evolutionary regressions can arise from several sources, including phylogenetic inertia and either observational or biological error in the predictor variables. We show how all these biases can be estimated and corrected for in the presence of phylogenetic correlations. We present general formulas for incorporating measurement error in linear models with correlated data. We also show how alternative regression models, such as major axis and reduced major axis regression, which are often recommended when there is error in predictor variables, are strongly biased when there is biological variation in any part of the model. We argue that such methods should never be used to estimate evolutionary or allometric regression slopes.
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| 18. |
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| 19. |
- Sagitov, Serik, 1956, et al.
(author)
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Interspecies correlation for neutrally evolving traits
- 2012
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In: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 309, s. 11-19
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Journal article (peer-reviewed)abstract
- A simple way to model phenotypic evolution is to assume that after splitting, the trait values of the sister species diverge as independent Brownian motions. Relying only on a prior distribution for the underlying species tree (conditioned on the number, n, of extant species) we study the random vector (X-1, ... , X-n) of the observed trait values. In this paper we derive compact formulae for the variance of the sample mean and the mean of the sample variance for the vector (X-1, ... , X-n). The key ingredient of these formulae is the correlation coefficient between two trait values randomly chosen from (X-1,X- ... , X-n). This interspecies correlation coefficient takes into account not only variation due to the random sampling of two species out of n and the stochastic nature of Brownian motion but also the uncertainty in the phylogenetic tree. The latter is modeled by a (supercritical or critical) conditioned branching process. In the critical case we modify the Aldous-Popovic model by assuming a proper prior for the time of origin.
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| 20. |
- Steinhoff, Franciska S., et al.
(author)
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Phlorotannin Production and Lipid Oxidation as a Potential Protective Function Against High Photosynthetically Active and UV Radiation in Gametophytes of Alaria esculenta (Alariales, Phaeophyceae)
- 2012
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In: Photochemistry and Photobiology. - : Wiley. - 1751-1097 .- 0031-8655. ; 88:1, s. 46-57
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Journal article (peer-reviewed)abstract
- Radiation damage can inter alia result in lipid peroxidation of macroalgal cell membranes. To prevent photo-oxidation within the cells, photoprotective substances such as phlorotannins are synthesized. In the present study, changes in total fatty acids (FA), FA composition and intra/extracellular phlorotannin contents were determined by gas chromatography and the Folin-Ciocalteu method to investigate the photoprotective potential of phlorotannins to prevent lipid peroxidation. Alaria esculenta juveniles (Phaeophyceae) were exposed over 20 days to high/low photosynthetically active radiation (PAR) in combination with UV radiation (UVR) in the treatments: PAB (low/high PAR + UV-B + UV-A), PA (low/high PAR + UV-A) or low/high PAR only. While extracellular phlorotannins increased after 10 days, intracellular phlorotannins increased with exposure time and PA and decreased under PAB. Interactive effects of time:radiation wavebands, time:PAR dose as well as radiation wavebands:PAR dose were observed. Low FA contents were detected in the PA and PAB treatments; interactive effects were observed between time:high PAR and PAB:high PAR. Total FA contents were correlated to extra/intracellular phlorotannin contents. Our results suggest that phlorotannins might play a role in intra/extracellular protection by absorption and oxidation processes. Changes in FA content/composition upon UVR and high PAR might be considered as an adaptive mechanism of the A. esculenta juveniles subjected to variations in solar irradiance.
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