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1.	Bartoszek, Krzysztof, 1984-, et al. (författare) A Noether theorem for stochastic operators on Schatten classes 2017 Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 452:2, s. 1395-1412 Tidskriftsartikel (refereegranskat)abstract We show that a stochastic (Markov) operator S acting on a Schatten class C-1 satisfies the Noether condition (i.e. S' (A) = A and S' (A(2)) = A(2), where A is an element of C-infinity is a Hermitian and bounded operator on a fixed separable and complex Hilbert space (H, <.,.>)), if and only if S(E-A(G)XEA(G)) = E-A (G)S(X)E-A (G) for any state X is an element of C-1 and all Borel sets G subset of R, where E-A (G) denotes the orthogonal projection coming from the spectral resolution A = integral(sigma(A)) zE(A)(dz). Similar results are obtained for stochastic one-parameter continuous semigroups.
2.	Bartoszek, Krzysztof, 1984-, et al. (författare) Fast mvSLOUCH: Model comparison for multivariate Ornstein--Uhlenbeck-based models of trait evolution on large phylogenies 2023 Annan publikationabstract These are the Supplementary Material, R scripts and numerical results accompanying Bartoszek, Fuentes Gonzalez, Mitov, Pienaar, Piwczyński, Puchałka, Spalik and Voje "Model Selection Performance in Phylogenetic Comparative Methods under multivariate Ornstein–Uhlenbeck Models of Trait Evolution".The four data files concern two datasets. Ungulates: measurements of muzzle width, unworn lower third molar crown height, unworn lower third molar crown width and feeding style and their phylogeny; Ferula: measurements of ratio of canals, periderm thickness, wing area, wing thickness, and fruit mass, and their phylogeny.MethodsUngulatesThe compiled ungulate dataset involves two key components: phenotypic data (Data.csv) and phylogenetic tree (Tree.tre), which consist on the following (full references for the citations presented below are provided in the paper linked to this repository, which also provides further details on the compiled dataset):The phenotypic data includes three continuous variables and one categorical variable. The continuous variables (MZW: muzzle width; HM3: unworn lower third molar crown height; WM3: unworn lower third molar crown width), measured in cm, come from Mendoza et al. (2002; J. Zool.). The categorical variable (FS, i.e. feeding style: B=browsers, G=grazers, M=mixed feeders) is based on Pérez–Barbería and Gordon (2001; Proc. R. Soc. B: Biol. Sci.). Taxonomic mismatches between these two sources were resolved based on Wilson and Reeder (2005; Johns Hopkins University Press). Only taxa with full entries for all these variables were included (i.e. no missing data allowed).The phylogenetic tree is pruned from the unsmoothed mammalian timetree of Hedges et al. (2015; MBE) to only include the 104 ungulate species for which there is complete phenotypic data available. Wilson and Reeder (2005; Johns Hopkins University Press) was used again to resolve taxonomic mismatches with the phenotypic data. The branch lengths of the tree are scaled to unit height and thus informative of relative time.Ferula1) The phenotypic data are divided into two data sets: first containing five continuous variables (no_ME) measured on mericarps (the dispersal unit of fruit in Apiaceae), whereas the second having the same variables together with measurement error (ME; see paper for computational details) for 75 species of Ferula and three species of Leutea. Three continuous variables were measured on anatomical cross sections (ratio_canals_ln – the proportion of oil ducts covering the space between median and lateral ribs [dimensionless], mean_gr_peri_ln_um – periderm (fruit wall) thickness [μm], thick_wings_ln_um – wing thickness [μm]); the remaining two on whole mericarps (Wings_area_ln_mm – wings area [mm2], Seed_mass_ln_mg – seed mass [mg])2) The phylogenetic tree was pruned from the tree obtained from the recent taxonomic revision of the genus (Panahi et al. 2018) to only include the 78 species for which the phenotypic data were generated. This tree and the associated alignment, composed of one nuclear and three plastid markers (Panahi et al. 2018), constituted an input to mcmctree software (Yang 2007) to obtain dated tree using a secondary calibration point for the root based on Banasiak et al.’s (2013) work. The branch lengths of the final tree (Ferula_fruits_tree.txt) were scaled to unit height and thus informative of relative time.The R setup for the manuscript was as follows:R version 3.6.1 (2019-09-12) Platform: x86_64-pc-linux-gnu (64-bit) Running under: openSUSE Leap 42.3The exact output can depend on the random seed. However, in the script we have the option of rerunning the analyses as it was in the manuscript, i.e.the random seeds that were used to generate the results are saved, included and can be read in.The code is divided into several directories with scripts, random seeds and result files.1) LikelihoodTestingDirectory contains the script test_rotation_invariance_mvSLOUCH.R that demonstrates that mvSLOUCH's likelihood calculations are rotation invariant. 2) CarnivoransDirectory contains files connected to the Carnivrons' vignette in mvSLOUCH. 2.1) Carnivora_mvSLOUCH_objects_Full.RDataFull output of running the R code in the vignette.With mvSLOUCH is a very bare-minimum subset of this file that allows for the creation of the vignette. 2.2) Carnivora_mvSLOUCH_objects.RData Reduced objects from Carnivora_mvSLOUCH_objects_Full.RData that are included with mvSLOUCH's vignette. 2.3) Carnivora_mvSLOUCH_objects_remove_script.R R script to reduce Carnivora_mvSLOUCH_objects_Full.RData to Carnivora_mvSLOUCH_objects.RData. 2.4) mvSLOUCH_Carnivorans.Rmd The vignette itself. 2.5) refs_mvSLOUCH.bib Bib file for the vignette. 2.6) ScaledTree.png, ScaledTree2.png, ScaledTree3.png, ScaledTree4.png Plots of phylogenetic trees for vignette.3) SimulationStudyDirectory contains all the output of the simulation study presented in the manuscript and scripts that allow for replication (the random number generator seeds are also provided) or running ones own simulation study, and scripts to generate graphs, and model comparison summary. This study was done using version 2.6.2 of mvSLOUCH. If one reruns using mvSLOUCH >= 2.7, then one will obtain different (corrected) values of R2 and an additional R2 version. 4) UngulatesDirectory contains files connected to the "Feeding styles and oral morphology in ungulates" analyses performed for the manuscript. 4.1) Data.csv The phenotypic data includes three continuous variables and one categorical variable. Continuous variables (MZW: muzzle width; HM3: unworn lower third molar crown height; WM3: unworn lower third molar crown width) from Mendoza et al. (2002), measured in cm. Categorical variable (FS, i.e. feeding style: B=browsers, G=grazers, M=mixed feeders) based on Pérez–Barbería and Gordon (2001). Phylogeny pruned from Hedges et al. (2015).Taxonomic mismatches among these sources were resolved based on Wilson and Reeder (2005). Hedges, S. B., J. Marin, M. Suleski, M. Paymer, and S. Kumar. 2015. Tree of life reveals clock-like speciation and diversification. Molecular Biology and Evolution 32:835-845. Mendoza, M., C. M. Janis, and P. Palmqvist. 2002. Characterizing complex craniodental patterns related to feeding behaviour in ungulates:a multivariate approach. Journal of Zoology 258:223-246 Pérez–Barbería, F. J., and I. J. Gordon. 2001. Relationships between oral morphology and feeding style in the Ungulata: a phylogenetically controlled evaluation. Proceedings of the Royal Society of London. Series B: Biological Sciences 268:1023-1032. Wilson, D. E., and D. M. Reeder. 2005. Mammal species of the world: A taxonomic and geographic reference. Johns Hopkins University Press, Baltimore, Maryland. 4.2) Tree.tre Ungulates' phylogeny, extracted from the mammalian phylogeny of Hedges, S. B., J. Marin, M. Suleski, M. Paymer, and S. Kumar. 2015. Tree of life reveals clock–like speciation and diversification. Mol. Biol. Evol. 32:835–845. 4.3) OUB.R, OUF.R, OUG.R R scripts for the analyses performed in the manuscript. Different files correspond to different regime setups of the feeding style variable. 4.4) OU1.txt, OUB.txt, OUF.txt, OUG.txt Outputs of the model comparison conducted under the R scripts presented above (4.3). Different files correspond to different regime setups of the feeding style variable. 5) Ferula analysesIn the models_ME directory there are input and output files from the mvSLOUCH analyzes of Ferula data with measurement error included, while in the models_no_ME directory the analyzes of data without measurement error. In each directory, one can find the following files:- input files: Data_ME.csv (with mesurment error) or Data_no_ME.csv (without measurement error) and tree file in Newick format (Ferula_fruits_tree.txt); the trait names in data files are abbreviated as follows: ration_canals – the proportion of oil ducts covering the space between median and lateral ribs, mean_gr_peri – periderm thickness, wings_area – wing area, thick_wings – wing thickness and seed_mass – seed mass,- the results for 8 analyzed models (see Fig. 2 in the main text), each in separate directory named model1, model2 and so on,- each model directory comprises the following files: two R scripts (for analyzes with diagonal and with upper triangular matrix Σyy; each model was run 1000 times), two csv files included information such as number of repetition (i), seed for preliminary analyzes generating starting point (seed_start_point), seed for the main analyses (seed) and AIC, AICc, SIC, BIC, R2 and loglik for each model run (these csv files are sorted according to AICc values), two directories containing results for 1000 analyzes, and two files extracted from these directories showing parameter estimation for the best models (with UpperTri and Diagonal matrix Σyy)
3.	Bartoszek, Krzysztof, 1984-, et al. (författare) Model Selection Performance in Phylogenetic Comparative Methods Under Multivariate Ornstein–Uhlenbeck Models of Trait Evolution 2023 Ingår i: Systematic Biology. - : OXFORD UNIV PRESS. - 1063-5157 .- 1076-836X. ; 72:2, s. 275-293 Tidskriftsartikel (refereegranskat)abstract The advent of fast computational algorithms for phylogenetic comparative methods allows for considering multiple hypotheses concerning the co-adaptation of traits and also for studying if it is possible to distinguish between such models based on contemporary species measurements. Here we demonstrate how one can perform a study with multiple competing hypotheses using mvSLOUCH by analyzing two data sets, one concerning feeding styles and oral morphology in ungulates, and the other concerning fruit evolution in Ferula (Apiaceae). We also perform simulations to determine if it is possible to distinguish between various adaptive hypotheses. We find that Akaikes information criterion corrected for small sample size has the ability to distinguish between most pairs of considered models. However, in some cases there seems to be bias towards Brownian motion or simpler Ornstein-Uhlenbeck models. We also find that measurement error and forcing the sign of the diagonal of the drift matrix for an Ornstein-Uhlenbeck process influences identifiability capabilities. It is a cliche that some models, despite being imperfect, are more useful than others. Nonetheless, having a much larger repertoire of models will surely lead to a better understanding of the natural world, as it will allow for dissecting in what ways they are wrong. [Adaptation; AICc; model selection; multivariate Ornstein-Uhlenbeck process; multivariate phylogenetic comparative methods; mvSLOUCH.]
4.	Bartoszek, Krzysztof, 1984-, et al. (författare) On the Time Behaviour of Okazaki Fragments 2006 Ingår i: Journal of Applied Probability. - Cambridge : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 43, s. 500-509 Tidskriftsartikel (refereegranskat)abstract We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.
5.	Antonelli, Alexandre, 1978, et al. (författare) Embracing heterogeneity: Coalescing the tree of life and the future of phylogenomics 2019 Ingår i: PeerJ. - : PeerJ. - 2167-8359. ; 2019:2 Tidskriftsartikel (refereegranskat)abstract Building the Tree of Life (ToL) is a major challenge of modern biology, requiring advances in cyberinfrastructure, data collection, theory, and more. Here, we argue that phylogenomics stands to benefit by embracing the many heterogeneous genomic signals emerging from the first decade of large-scale phylogenetic analysis spawned by high-throughput sequencing (HTS). Such signals include those most commonly encountered in phylogenomic datasets, such as incomplete lineage sorting, but also those reticulate processes emerging with greater frequency, such as recombination and introgression. Here we focus specifically on how phylogenetic methods can accommodate the heterogeneity incurred by such population genetic processes; we do not discuss phylogenetic methods that ignore such processes, such as concatenation or supermatrix approaches or supertrees. We suggest that methods of data acquisition and the types of markers used in phylogenomics will remain restricted until a posteriori methods of marker choice are made possible with routine whole-genome sequencing of taxa of interest. We discuss limitations and potential extensions of a model supporting innovation in phylogenomics today, the multispecies coalescent model (MSC). Macroevolutionary models that use phylogenies, such as character mapping, often ignore the heterogeneity on which building phylogenies increasingly rely and suggest that assimilating such heterogeneity is an important goal moving forward. Finally, we argue that an integrative cyberinfrastructure linking all steps of the process of building the ToL, from specimen acquisition in the field to publication and tracking of phylogenomic data, as well as a culture that values contributors at each step, are essential for progress.
6.	Asadzadeh, Mohammad, 1952, et al. (författare) A combined discontinuous Galerkin and finite volume scheme for multi-dimensional VPFP system 2011 Ingår i: 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 Konferensbidrag (refereegranskat)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.
7.	Asadzadeh, Mohammad, 1952, et al. (författare) Convergence of Finite Volume Scheme for a Three-Dimensional Poisson Equation 2014 Ingår i: Journal of Mathematical Sciences. - : Springer-Verlag New York. - 1072-3374 .- 1573-8795. ; 202:2, s. 130-153 Tidskriftsartikel (refereegranskat)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.
8.	Asadzadeh, Mohammad, 1952, et al. (författare) Convergence of finite volume scheme for three dimensional Poisson's equation 2014 Annan publikation (övrigt vetenskapligt/konstnärligt)
9.	Bartoszek, Krzysztof, 1984-, et al. (författare) A consistent estimator of the evolutionary rate 2015 Ingår i: Journal of Theoretical Biology. - 0022-5193 .- 1095-8541. ; 371, s. 69-78 Tidskriftsartikel (refereegranskat)abstract We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate λ, conditioned on the observed number of particles to be equal to n. Particles are assumed to move independently on the real line according to the Brownian motion with the local variance σ2. In this paper we treat n particles as a sample of related species. The spatial Brownian motion of a particle describes the development of a trait value of interest (e.g. log-body-size). We propose an unbiased estimator Rn2 of the evolutionary rate ρ2=σ2/λ. The estimator Rn2 is proportional to the sample variance Sn2 computed from n trait values. We find an approximate formula for the standard error of Rn2 based on a neat asymptotic relation for the variance of Sn2.
10.	Bartoszek, Krzysztof, 1984- (författare) A Graph – String Model of Gene Assembly in Ciliates 2006 Ingår i: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej. ; , s. 521-534 Konferensbidrag (refereegranskat)abstract The ciliates are a family of unicellular organisms that characterize themselves by having two types of nuclei, micro - and macronuclei. During cell mating the genetic material must change from the micronuclei to the macronuclei form. The paper summarises a formal model for this change. The model, which is described in recent works, is based on strings and graphs. It shows that inside the cell complex computational operations have to take place.
11.	Bartoszek, Krzysztof, 1984- (författare) A Graph – String Model of Gene Assembly in Ciliates [Grafowo-tekstowy model rekombinacji DNA u orzęsek] 2006 Ingår i: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej. ; , s. 521-534 Konferensbidrag (refereegranskat)abstract The ciliates are a family of unicellular organisms that characterize themselves by having two types of nuclei, micro - and macronuclei. During cell mating the genetic material must change from the micronuclei to the macronuclei form. The paper summarises a formal model for this change. The model, which is described in recent works, is based on strings and graphs. It shows that inside the cell complex computational operations have to take place.
12.	Bartoszek, Krzysztof, 1984-, et al. (författare) A novel algorithm to reconstruct phylogenies using gene sequences and expression data 2014 Ingår i: International Proceedings of Chemical, Biological & Environmental Engineering; Environment, Energy and Biotechnology III. ; , s. 8-12 Konferensbidrag (refereegranskat)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.
13.	Bartoszek, Krzysztof, 1984, et al. (författare) A phylogenetic comparative method for studying multivariate adaptation 2012 Ingår i: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 314, s. 204-215 Tidskriftsartikel (refereegranskat)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).
14.	Bartoszek, Krzysztof, 1984-, et al. (författare) Asymptotic properties of quadratic stochastic operators acting on the L1 space 2015 Ingår i: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 114, s. 26-39 Tidskriftsartikel (refereegranskat)abstract Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours andthese have been introduced and studied recently in the l1 space. It turns out that inprinciple most of the results can be carried over to the L1 space. However, due to topologicalproperties of this space one has to restrict in some situations to kernel quadratic stochasticoperators. In this article we study the uniform and strong asymptotic stability of quadratic stochastic operators acting on the L1 space in terms of convergence of the associated (linear)nonhomogeneous Markov chains.
15.	Bartoszek, Krzysztof, 1984- (författare) Closed and asymptotic formulæ for harmonic and quadratic harmonic sums Annan publikation (övrigt vetenskapligt/konstnärligt)abstract We present here a large collection of harmonic and quadratic harmonic sums, that can be useful in applied questions, e.g., probabilistic ones. We find closed-form formulae, that we were not able to locate in the literature.
16.	Bartoszek, Krzysztof, 1984-, et al. (författare) Critical case stochastic phylogenetic tree model via the Laplace transform 2014 Ingår i: Demonstratio Matematicae. - : De Gruyter. - 0420-1213 .- 2391-4661. ; 47:2, s. 474-481 Tidskriftsartikel (refereegranskat)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.
17.	Bartoszek, Krzysztof, 1984-, et al. (författare) Identifying clusters in Czekanowski's diagram 2023 Ingår i: Mathematica Applicanda. - Warsaw, Poland : Polskie Towarzystwo Matematyczne. - 1730-2668 .- 2299-4009. ; 51:2, s. 183-198 Tidskriftsartikel (refereegranskat)abstract Visualizing data through Czekanowski’s diagram has as its aim the illus-tration of the relationships between objects. Often, obvious clusters of observationsare directly visible. However, it is not straightforward to precisely delineate theseclusters. This paper presents the development of the package RMaCzek, which nowincludes features for cluster identification in Czekanowski diagrams.
18.	Bartoszek, Krzysztof, 1984-, et al. (författare) Influenza differentiation and evolution 2010 Ingår i: Acta Physica Polonica B Proceedings Supplement. ; 3:2, s. 417-452 Konferensbidrag (refereegranskat)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.
19.	Bartoszek, Krzysztof, 1984- (författare) Limit distribution of the quartet balance index for Aldous’s $(\beta \ge 0)$-model 2020 Ingår i: Applicationes Mathematicae. - : Institute of Mathematics, Polish Academy of Science. - 1233-7234 .- 1730-6280. ; 6, s. 29-44 Tidskriftsartikel (refereegranskat)abstract This paper builds on T. Martínez-Coronado, A. Mir, F. Rosselló and G. Valiente’s 2018 work, introducing a new balance index for trees. We show that this balance index, in the case of Aldous’s $(\beta \ge 0)$-model, converges weakly to a distribution that can be characterized as the fixed point of a contraction operator on a class of distributions.
20.	Bartoszek, Krzysztof, 1984-, et al. (författare) Moments of the Distribution of Okazaki Fragments 2006 Ingår i: Rose–Hulman Undergraduate Mathematics Journal. - : Department of Mathematics, Rose-Hulman Institute of Technology, Poland. ; 7:2 Tidskriftsartikel (refereegranskat)abstract This paper is a continuation of Bartoszek & Bartoszek (2006) who provide formulae for the probability distributions of the number of Okazaki fragments at time t during the process of DNA replication. Given the expressions for the moments of the probability distribution of the number of Okazaki fragments at time t in the recursive form, we evaluated formulae for the third and fourth moments, using Mathematica, and obtained results in explicit form. Having done this, we calculated the distribution’s skewness and kurtosis.
21.	Bartoszek, Krzysztof, 1984 (författare) Multivariate Aspects of Phylogenetic Comparative Methods 2011 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)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.
22.	Bartoszek, Krzysztof, 1984-, et al. (författare) Neural Network Breast Cancer Relapse Time Prognosis 2006 Ingår i: ASO Summer School 2006 Abstract Book. ; , s. 8-10, s. 8-10 Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract This paper is a result of a project at the Faculty of Electronics, Telecommunication and Computer Science (Technical University of Gdansk). The aim of the project was to create a neural network to predict the relapsetime of breast cancer. The neural network was to be trained on data collected over the past 20 years by dr. Jarosław Skokowski. The data includes 439 patient records described by about 40 parameters. For our neuralnetwork we only considered 6 medically most significant parameters the number of nodes showing evidence of cancer, size of tumour (in mm.), age, bloom score, estrogen receptors and proestrogen receptors and the relapsetime as the outcome. Our neural network was created in the MATLAB environment.
23.	Bartoszek, Krzysztof, 1984-, et al. (författare) “Old Techniques for New Times”: the RMaCzek package for producing Czekanowski’s diagrams 2020 Ingår i: Biometrical Letters. - : Polskie Towarzystwo Biometryczne. - 1896-3811. ; 57:2, s. 89-118 Tidskriftsartikel (refereegranskat)abstract Inspired by the MaCzek Visual Basic program we provide an R package, RMaCzek, that produces Czekanowski’s diagrams. Our package permits any seriation and distance method the user provides. In this paper we focus on the "OLO" and "QAP_2SUM" methods from the seriation package. We illustrate the possibilities of our package with three anthropological studies, one socioeconomic study and a phylogenetically motivated simulation study.
24.	Bartoszek, Krzysztof, 1984-, et al. (författare) Performance of pseudo-likelihood estimator in modelling cells' proliferation with noisy measurements 2010 Ingår i: Conference materials XII International Workshop for Young Mathematicians. ; , s. 21-42, s. 21-42 Konferensbidrag (övrigt vetenskapligt/konstnärligt)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.
25.	Bartoszek, Krzysztof, 1984, et al. (författare) Performance of pseudo–likelihood estimator in modelling cells’ proliferation with noisy measurement s 2010 Ingår i: onference proceedings from the 12th International Workshop for Young Mathematicians "Probability and Statistics", Krakow, Poland, 20th till 26th September 2009. ; , s. 21-42 Konferensbidrag (övrigt vetenskapligt/konstnärligt)
26.	Bartoszek, Krzysztof, 1984-, et al. (författare) Phylogenetic confidence intervals for the optimal trait value 2015 Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 52:4, s. 1115-1132 Tidskriftsartikel (refereegranskat)abstract We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein-Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the sample mean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean is approximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.
27.	Bartoszek, Krzysztof, 1984- (författare) Phylogenetic effective sample size 2016 Ingår i: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 407, s. 371-386 Tidskriftsartikel (refereegranskat)abstract In this paper I address the question—how large is a phylogenetic sample? I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein-Uhlenbeck processes-the regression effective sample size. I discuss how mutual information can be used to define an effective sample size in the non-normal process case and compare these two definitions to an already present concept of effective sample size (the mean effective sample size). Through a simulation study I find that the AICc is robust if one corrects for the number of species or effective number of species. Lastly I discuss how the concept of the phylogenetic effective sample size can be useful for biodiversity quantification, identification of interesting clades and deciding on the importance of phylogenetic correlations.
28.	Bartoszek, Krzysztof, 1984-, et al. (författare) Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1 2018 Ingår i: Bulletin of the Malaysian Mathematical Sciences Society. - : Springer Science and Business Media LLC. - 0126-6705 .- 2180-4206. ; 41:1, s. 159-173 Tidskriftsartikel (refereegranskat)abstract This paper is devoted to the study of the problem of prevalence in the classof quadratic stochastic operators acting on the L1 space for the uniform topology.We obtain that the set of norm quasi-mixing quadratic stochastic operators is a denseand open set in the topology induced by a very natural metric. This shows the typicallong-term behaviour of iterates of quadratic stochastic operators.
29.	Bartoszek, Krzysztof, 1984-, et al. (författare) Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait 2013 Ingår i: Proceedings of the XIX National Conference on Applications of Mathematics in Biology and Medicine. - 8360253862 ; , s. 19-24 Konferensbidrag (refereegranskat)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.
30.	Bartoszek, Krzysztof, 1984- (författare) Revisiting the Nowosiółka skull with RMaCzek 2023 Ingår i: Mathematica Applicanda. - : Polish Mathematical Society. - 1730-2668 .- 2299-4009. ; 50:2, s. 255-266 Tidskriftsartikel (refereegranskat)abstract One of the first fully quantitative distance matrix visualization methods was proposed by Jan Czekanowski at the beginning of the previous century. Recently, a software package, RMaCzek, was made available that allows for producing such diagrams in R. Here we reanalyze the original data that Czekanowski used for introducing his method, and in the accompanying code show how the user can specify their own custom distance functions in the package.
31.	Bartoszek, Krzysztof, 1984- (författare) Simulating an infinite mean waiting time 2019 Ingår i: Mathematica Applicanda. - Warsaw, Poland : Polskie Towarzystwo Matematyczne. - 1730-2668 .- 2299-4009. ; 47:1, s. 93-102 Tidskriftsartikel (refereegranskat)abstract We consider a hybrid method to simulate the return time to the initial state in a critical-case birth-death process. The expected value of this return time is infinite, but its distribution asymptotically follows a power-law. Hence, the simulation approach is to directly simulate the process, unless the simulated time exceeds some threshold and if it does, draw the return time from the tail of the power law.
32.	Bartoszek, Krzysztof, 1984 (författare) Stochastic Models in Phylogenetic Comparative Methods: Analytical Properties and Parameter Estimation 2013 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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.
33.	Bartoszek, Krzysztof, 1984, et al. (författare) Survival time prognosis under a Markov model of cancer development 2010 Ingår i: Proceedings of the XVI National Conference Applications of Mathematics to Biology and Medicine, Krynica, Poland, September 14–18, 2010. - 9788374643344 ; , s. 6-11 Konferensbidrag (refereegranskat)
34.	Bartoszek, Krzysztof, 1984-, et al. (författare) Survival time prognosis under a Markov model of cancer development 2010 Ingår i: Proceedings of the XVI National Conference on Applications of Mathematics in Biology and Medicine. ; , s. 6-11 Konferensbidrag (refereegranskat)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.
35.	Bartoszek, Krzysztof, 1984- (författare) The Bootstrap and Other Methods of Testing Phylogenetic Trees 2007 Ingår i: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej. ; , s. 103-108 Konferensbidrag (refereegranskat)abstract The final step of a phylogenetic analysis is the test of the generated tree. This is not a easy task for which there is an obvious methodology because we do not know the full probabilistic model of evolution. A number of methods have been proposed but there is a wide debate concerning the interpretations of the results they produce.
36.	Bartoszek, Krzysztof, 1984-, et al. (författare) The Fundamental Group, Covering Spaces and Topology in Biology 2006 Ingår i: Conference materials IX International Workshop for Young Mathematicians. ; , s. 19-29, s. 19-29 Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract Abstract. We give a short introduction to homotopy theory. We pass to the concepts of a pointed space (X, x0), the fundamental group of X, a simply connected space (with the example of the space contractible to a point), introduce basic concepts of covering spaces (e.g. covering map/space, fiber over x, Path lifting Theorem). With the use of the exponential map and the idea of the index of a loop, we show that the fundamental group of the circle S1 is isomorphic to the integers Z with addition. We mention some other interesting fundamental groups (e.g. the fundamental group of a torus or of thefigure eight). We also present some very interesting applications of topological concepts in Molecular Biology.
37.	Bartoszek, Krzysztof, 1984- (författare) The Laplace Motion in Phylogenetic Comparative Methods 2012 Ingår i: Proceedings of the Eightteenth National Conference on Applications of Mathematics in Biology and Medicine. - 9788373484344 ; , s. 25-30 Konferensbidrag (refereegranskat)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.
38.	Bartoszek, Krzysztof, 1984-, et al. (författare) Time to a single hybridization event in a group of species with unknown ancestral history 2013 Ingår i: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 322, s. 1-6 Tidskriftsartikel (refereegranskat)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.
39.	Bartoszek, Krzysztof, 1984- (författare) Trait evolution with jumps: illusionary normality 2017 Ingår i: Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine. ; , s. 23-28 Konferensbidrag (refereegranskat)abstract Phylogenetic comparative methods for real-valued traits usually make use of stochastic process whose trajectories are continuous.This is despite biological intuition that evolution is rather punctuated thangradual. On the other hand, there has been a number of recent proposals of evolutionarymodels with jump components. However, as we are only beginning to understandthe behaviour of branching Ornstein-Uhlenbeck (OU) processes the asymptoticsof branching OU processes with jumps is an even greater unknown. In thiswork we build up on a previous study concerning OU with jumps evolution on a pure birth tree.We introduce an extinction component and explore via simulations, its effects on the weak convergence of such a process.We furthermore, also use this work to illustrate the simulation and graphic generation possibilitiesof the mvSLOUCH package.
40.	Bartoszek, Krzysztof, 1984-, et al. (författare) Using the Ornstein-Uhlenbeck process to model the evolution of interacting populations 2017 Ingår i: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 429, s. 35-45 Tidskriftsartikel (refereegranskat)abstract The Ornstein-Uhlenbeck (OU) process plays a major role in the analysis of the evolution of phenotypic traits along phylogenies. The standard OU process includes random perturbations and stabilizing selection and assumes that species evolve independently. However, evolving species may interact through various ecological process and also exchange genes especially in plants. This is particularly true if we want to study phenotypic evolution among diverging populations within species. In this work we present a straightforward statistical approach with analytical solutions that allows for the inclusion of adaptation and migration in a common phylogenetic framework, which can also be useful for studying local adaptation among populations within the same species. We furthermore present a detailed simulation study that clearly indicates the adverse effects of ignoring migration. Similarity between species due to migration could be misinterpreted as very strong convergent evolution without proper correction for these additional dependencies. Finally, we show that our model can be interpreted in terms of ecological interactions between species, providing a general framework for the evolution of traits between "interacting" species or populations.
41.	Bartoszek, Krzysztof, 1984-, et al. (författare) Weak Stability of Centred Quadratic Stochastic Operators 2019 Ingår i: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY. - : MALAYSIAN MATHEMATICAL SCIENCES SOC. - 0126-6705 .- 2180-4206. ; 42:4, s. 1813-1830 Tidskriftsartikel (refereegranskat)abstract We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring's trait is equal to an additively perturbed arithmetic mean of the parents' traits. It is shown that for the existence of a weak limit, it is sufficient that the distributions of the trait and the perturbation have a finite variance or have tails controlled by a suitable power function. In particular, probability distributions from the domain of attraction of stable distributions have found an application, although in general the limit is not stable.
42.	Hansen, T. F., et al. (författare) Interpreting the Evolutionary Regression: The Interplay Between Observational and Biological Errors in Phylogenetic Comparative Studies 2012 Ingår i: Systematic Biology. - Oxford : Oxford University Press (OUP). - 1063-5157 .- 1076-836X. ; 61:3, s. 413-425 Tidskriftsartikel (refereegranskat)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.
43.	Kiang, Hao Chi, 1993-, et al. (författare) Data and Materials : Summarizing Global SARS-CoV-2 Geographical Spread by Phylogenetic Multitype Branching Models 2022 Annan publikationabstract Raw numerical results, phylogeny, and related data for the conference proceeding article "Summarizing Global SARS-CoV-2 Geographical Spread by Phylogenetic Multitype Branching Models".
44.	Kiang, Woodrow Hao Chi, 1993- (författare) Uncertainty Estimation in Models of Multivariate Trait Evolution on Given Phylogenies 2024 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract Phylogenetic comparative methods are a set of statistical methods that model the evolutionary history of species, especially in the context where one has data on certain traits of related extant species that have evolved over a phylogenetic tree in accordance to an underlying stochastic process. This thesis presents a Hessian-based closed-form asymptotic confidence region that covers a wide family of Gaussian continuous-trait evolution models; the result has been implemented in an R package. Also, some analyses have been done on the simpler Brownian Motion and Ornstein-Uhlenbeck process cases; and this leads to novel exact confidence regions for the Brownian Motion’s parameters and a closed-form ’partial’ unbiased estimator for the Ornstein-Uhlenbeck process’ varaince-covariance matrix when other parameters are given. The thesis contains two papers. Paper I is an applied work that uses discrete-trait speciation and extinction model to investigate early spread of COVID-19; it shows that it is possible to detect statistical signals of inter-continental spread of the virus from a very noisy world-wide phylogeny. Paper II is a more mathematical work that derived the closed-form formulae for the Hessian matrix of a wide family of Gaussian-process-based multivariate continuous-trait PCM models; accompanying with the Paper I have developed an R package called glinvci, publicly available on The Comprehensive R Archive Network (CRAN), that can compute Hessian-based confidence regions for these models while at the same time allowing users to have missing data and multiple evolutionary regimes.
45.	Sagitov, Serik, 1956, et al. (författare) A Consistent Estimator of the Evolutionary Rate 2014 Annan publikation (övrigt vetenskapligt/konstnärligt)
46.	Sagitov, Serik, 1956, et al. (författare) Interspecies correlation for neutrally evolving traits 2012 Ingår i: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 309, s. 11-19 Tidskriftsartikel (refereegranskat)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.
47.	Steinhoff, Franciska S., et al. (författare) 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 Ingår i: Photochemistry and Photobiology. - : Wiley. - 1751-1097 .- 0031-8655. ; 88:1, s. 46-57 Tidskriftsartikel (refereegranskat)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.
48.	Tahir, Daniah, 1988-, et al. (författare) Using multitype branching models to analyze bacterial pathogenicity Tidskriftsartikel (refereegranskat)abstract We apply multitype, continuous time Markov branching models to study pathogenicity in E. coli, a bacterium belonging to the genus Escherichia. First, we examine briefly the properties of multitype branching processes and we also survey some fundamental limit theorems regarding the behavior of such models under various conditions. These theorems are then applied to discrete, state dependent models in order to analyze pathogenicity in a published clinical data set consisting of 251 strains of E. coli. We use well established methods, incorporating maximum likelihood techniques, to estimate speciation rates as well as the rates of transition between different states of the models. From the analysis, we not only derive new results, we also verify some preexisting notions about virulent behavior in bacterial strains.
49.	Tahir, Daniah, et al. (författare) Using multitype branching models to analyze bacterial pathogenicity 2020 Ingår i: Mathematica Applicanda. - Warsaw, Poland : Polskie Towarzystwo Matematyczne. - 1730-2668 .- 2299-4009. ; 48:1, s. 59-86 Tidskriftsartikel (refereegranskat)abstract We apply multitype, continuous time, Markov branching models to study pathogenicity in E. coli, a bacterium belonging to the genus Escherichia. First, we examine briefly, the properties of multitype branching processes and we also survey some fundamental limit theorems regarding the behavior of such models under various conditions. These theorems are then applied to discrete, state dependent models, in order to analyze pathogenicity in a published clinical data set consisting of 251 strains of E. coli. We use well established methods, incorporating maximum likelihood techniques, to estimate speciation rates as well as the rates of transition between different states of the models. From the analysis, we not only derive new results, but we also verify some preexisting notions about virulent behavior in bacterial strains.
50.	Woniacki, Piotr, et al. (författare) The impact of the Polish mass breast cancer screening program on prognosis in the Pomeranian Province 2017 Ingår i: Archives of Medical Science. - : TERMEDIA PUBLISHING HOUSE LTD. - 1734-1922 .- 1896-9151. ; 13:2, s. 441-447 Tidskriftsartikel (refereegranskat)abstract Introduction: Mammographic screening results in diagnosis of less advanced breast cancer (BC). A meta-analysis of randomized clinical trials confirmed that BC screening reduces mortality. In 2007, the National Breast Cancer Screening Program (NBCSP) was established in Poland with the crucial aim of reducing mortality from BC. The purpose of this study was to assess the impact of participation in the NBCSP on prognosis. Material and methods: A single institution, non-randomized retrospective study was undertaken. The study population comprised 643 patients with BC treated in the Department of Surgical Oncology (DSO) at the Medical University of Gdansk over a 4-year period, from 01.01.2007 until 31.12.2010. Patients were divided into two groups: group A-patients who participated in the NBCSP (n = 238, 37.0%); and group B-patients who did not participate in the NBCSP (n = 405, 63.0%). Results: Statistical analysis revealed that group A displayed a less advanced MCC stage (more patients in AJCC stage I, p = 0.002), lower tumor diameter (more patients with pT1, p = 0.006, and pT < 15 mm, p = 0.008) and a lower incidence of metastases to axillary lymph nodes (more patients with pNO, p = 0.01). From 2009 to 2010 the NBCSP revealed a statistically significant benefit significantly more patients in stage 0 + I (60.7% vs. 48.8%, p = 0.018) and with tumors pT < 15 mm (48.8% vs. 35.1%, p = 0.011) were observed in group A. Conclusions: The study results revealed the beneficial impact of the NBCSP. Superior prognostic factors and favorable staging were observed in women who participated in the NBCSP.

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