| 1. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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A Noether theorem for stochastic operators on Schatten classes
- 2017
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In: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 452:2, s. 1395-1412
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Journal article (peer-reviewed)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.
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| 2. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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Fast mvSLOUCH: Model comparison for multivariate Ornstein--Uhlenbeck-based models of trait evolution on large phylogenies
- 2023
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Other publicationabstract
- 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)
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| 3. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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Model Selection Performance in Phylogenetic Comparative Methods Under Multivariate Ornstein–Uhlenbeck Models of Trait Evolution
- 2023
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In: Systematic Biology. - : OXFORD UNIV PRESS. - 1063-5157 .- 1076-836X. ; 72:2, s. 275-293
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Journal article (peer-reviewed)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.]
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| 4. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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On the Time Behaviour of Okazaki Fragments
- 2006
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In: Journal of Applied Probability. - Cambridge : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 43, s. 500-509
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Journal article (peer-reviewed)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.
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| 5. |
- Antonelli, Alexandre, 1978, et al.
(author)
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Embracing heterogeneity: Coalescing the tree of life and the future of phylogenomics
- 2019
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In: PeerJ. - : PeerJ. - 2167-8359. ; 2019:2
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Journal article (peer-reviewed)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.
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| 6. |
- 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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| 7. |
- 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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| 8. |
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| 9. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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A consistent estimator of the evolutionary rate
- 2015
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In: Journal of Theoretical Biology. - 0022-5193 .- 1095-8541. ; 371, s. 69-78
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Journal article (peer-reviewed)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.
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| 10. |
- Bartoszek, Krzysztof, 1984-
(author)
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A Graph – String Model of Gene Assembly in Ciliates
- 2006
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In: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej. ; , s. 521-534
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Conference paper (peer-reviewed)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.
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