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Bartoszek, KrzysztofORCID iD iconorcid.org/0000-0002-5816-4345
Publications (10 of 32) Show all publications
Bartoszek, K., Domsta, J. & Pulka, M. (2019). Weak Stability of Centred Quadratic Stochastic Operators. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 42(4), 1813-1830
Open this publication in new window or tab >>Weak Stability of Centred Quadratic Stochastic Operators
2019 (English)In: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, Vol. 42, no 4, p. 1813-1830Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
MALAYSIAN MATHEMATICAL SCIENCES SOC, 2019
Keywords
Asymptotic stability, Dyadic stability, Infinite divisible distributions, Quadratic stochastic operators, Weak convergence
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-390084 (URN)10.1007/s40840-017-0575-8 (DOI)000471896200032 ()
Funder
Knut and Alice Wallenberg FoundationSwedish Institute, 11142/2013Swedish Institute, 19826/2014Swedish Institute, 00507/2012
Available from: 2019-08-06 Created: 2019-08-06 Last updated: 2019-08-06Bibliographically approved
Bartoszek, K. & Pułka, M. (2018). Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1. Bulletin of the Malaysian Mathematical Sciences Society, 41(1), 159-173
Open this publication in new window or tab >>Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1
2018 (English)In: Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, Vol. 41, no 1, p. 159-173Article in journal (Refereed) Published
Abstract [en]

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.

Keywords
Quadratic stochastic operators, Nonhomogeneous Markov operators, Baire category, Mixing nonlinear Markov process
National Category
Probability Theory and Statistics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-283630 (URN)10.1007/s40840-015-0245-7 (DOI)000419716700010 ()
Funder
Swedish Institute, 00507/2012, 11142/2013, 19826/2014
Available from: 2016-04-13 Created: 2016-04-13 Last updated: 2018-02-26Bibliographically approved
Bartoszek, K. & Bartoszek, W. (2017). A Noether theorem for stochastic operators on Schatten classes. Journal of Mathematical Analysis and Applications, 452(2), 1395-1412
Open this publication in new window or tab >>A Noether theorem for stochastic operators on Schatten classes
2017 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 452, no 2, p. 1395-1412Article in journal (Refereed) Published
Abstract [en]

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.

Keywords
Schatten classes, Markov operator, Noether property
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:uu:diva-322500 (URN)10.1016/j.jmaa.2017.03.068 (DOI)000400224400039 ()
Funder
Swedish Institute, 00507/2012Swedish Institute, 11142/2013Swedish Institute, 19826/2014
Available from: 2017-05-30 Created: 2017-05-30 Last updated: 2017-05-30Bibliographically approved
Woniacki, P., Skokowskil, J., Bartoszek, K., Kosowskal, A., Kalinowski, L. & JaSkiewicz, J. (2017). The impact of the Polish mass breast cancer screening program on prognosis in the Pomeranian Province. Archives of Medical Science, 13(2), 441-447
Open this publication in new window or tab >>The impact of the Polish mass breast cancer screening program on prognosis in the Pomeranian Province
Show others...
2017 (English)In: Archives of Medical Science, ISSN 1734-1922, E-ISSN 1896-9151, Vol. 13, no 2, p. 441-447Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
TERMEDIA PUBLISHING HOUSE LTD, 2017
Keywords
breast cancer, screening, mass screening, prognostic factors, MCC staging, prognosis
National Category
Cancer and Oncology
Identifiers
urn:nbn:se:uu:diva-320343 (URN)10.5114/aoms.2016.60387 (DOI)000395365500022 ()28261300 (PubMedID)
Available from: 2017-04-19 Created: 2017-04-19 Last updated: 2017-04-19Bibliographically approved
Bartoszek, K., Glemin, S., Kaj, I. & Lascoux, M. (2017). Using the Ornstein-Uhlenbeck process to model the evolution of interacting populations. Journal of Theoretical Biology, 429, 35-45
Open this publication in new window or tab >>Using the Ornstein-Uhlenbeck process to model the evolution of interacting populations
2017 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 429, p. 35-45Article in journal (Refereed) Published
Abstract [en]

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.

Keywords
Migration, Ornstein-Uhlenbeck process, Phylogenetic comparative methods, Species interactions, Trait evolution
National Category
Biological Sciences
Identifiers
urn:nbn:se:uu:diva-333740 (URN)10.1016/j.jtbi.2017.06.011 (DOI)000407873100003 ()28619246 (PubMedID)
Available from: 2017-11-16 Created: 2017-11-16 Last updated: 2018-05-31Bibliographically approved
Bartoszek, K. (2016). Phylogenetic effective sample size. Journal of Theoretical Biology, 407, 371-386
Open this publication in new window or tab >>Phylogenetic effective sample size
2016 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 407, p. 371-386Article in journal (Refereed) Published
Abstract [en]

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.

Keywords
Biodiversity;Effective sample size;Measurement error;Ornstein-Uhlenbeck process;Phylogenetic comparative methods; Quantitative trait evolution
National Category
Probability Theory and Statistics Bioinformatics and Systems Biology Evolutionary Biology
Research subject
Applied Mathematics and Statistics; Bioinformatics
Identifiers
urn:nbn:se:uu:diva-300893 (URN)10.1016/j.jtbi.2016.06.026 (DOI)000383111800030 ()27343033 (PubMedID)
Funder
Knut and Alice Wallenberg Foundation
Available from: 2016-08-15 Created: 2016-08-15 Last updated: 2017-11-28Bibliographically approved
Bartoszek, K. & Sagitov, S. (2015). A consistent estimator of the evolutionary rate. Journal of Theoretical Biology, 371, 69-78
Open this publication in new window or tab >>A consistent estimator of the evolutionary rate
2015 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 371, p. 69-78Article in journal (Refereed) Published
Abstract [en]

We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate 2, 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 sigma(2). 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 4 of the evolutionary rate rho(2) - sigma(2)/lambda. The estimator R-n(2) is proportional to the sample variance S-n(2) computed from n trait values. We find an approximate formula for the standard error of R-n(2), based on a neat asymptotic relation for the variance of S-n(2). (C) 2015 Elsevier Ltd. All rights reserved.

Keywords
Branching Brownian motion, Conditioned branching process, Tree-free phylogenetic comparative method, Quantitative trait evolution, Yule process
National Category
Evolutionary Biology Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-252680 (URN)10.1016/j.jtbi.2015.01.019 (DOI)000353011200006 ()25636492 (PubMedID)
Funder
Swedish Research Council, 621-2010-5623The Royal Swedish Academy of Sciences
Available from: 2015-05-26 Created: 2015-05-11 Last updated: 2017-12-04Bibliographically approved
Bartoszek, K. & Sagitov, S. (2015). A consistent estimator of the evolutionary rate. Journal of Theoretical Biology, 371, 69-78
Open this publication in new window or tab >>A consistent estimator of the evolutionary rate
2015 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 371, p. 69-78Article in journal (Refereed) Published
Abstract [en]

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 ρ22/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.

Keywords
Branching Brownian motion; Conditioned branching process; Tree-free phylogenetic comparative method; Quantitative trait evolution; Yule process
National Category
Probability Theory and Statistics Evolutionary Biology
Research subject
Statistics; Mathematical Statistics; Biology
Identifiers
urn:nbn:se:uu:diva-246249 (URN)
Available from: 2015-03-04 Created: 2015-03-04 Last updated: 2017-12-04
Bartoszek, K. & Pulka, M. (2015). Asymptotic properties of quadratic stochastic operators acting on the L1 space. Nonlinear Analysis, 114, 26-39
Open this publication in new window or tab >>Asymptotic properties of quadratic stochastic operators acting on the L1 space
2015 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 114, p. 26-39Article in journal (Refereed) Published
Abstract [en]

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.

Keywords
Quadratic stochastic operators, Nonhomogeneous Markov operators, Mixing nonlinear Markov process
National Category
Mathematical Analysis Probability Theory and Statistics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-241868 (URN)10.1016/j.na.2014.10.032 (DOI)000348041700004 ()
Funder
Swedish Institute
Note

Svenska institutet supported this work through their Östersjösamarbetet scholarship program.

Available from: 2015-01-19 Created: 2015-01-19 Last updated: 2017-12-05Bibliographically approved
Bartoszek, K. & Sagitov, S. (2015). Phylogenetic confidence intervals for the optimal trait value. Journal of Applied Probability, 52(4), 1115-1132
Open this publication in new window or tab >>Phylogenetic confidence intervals for the optimal trait value
2015 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 4, p. 1115-1132Article in journal (Refereed) Published
Abstract [en]

We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree ismodelled 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 samplemean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean isapproximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

Keywords
Central limit theorem; conditioned Yule process; macroevolution; martingales; Ornstein–Uhlenbeck process; phylogenetics
National Category
Probability Theory and Statistics Evolutionary Biology
Research subject
Mathematical Statistics; Statistics
Identifiers
urn:nbn:se:uu:diva-241872 (URN)10.1239/jap/1450802756 (DOI)000368467600014 ()
Funder
Swedish Research Council, 621-2010-5623The Foundation for Baltic and East European StudiesKnut and Alice Wallenberg FoundationThe Royal Swedish Academy of Sciences
Available from: 2015-01-19 Created: 2015-01-19 Last updated: 2017-12-05Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-5816-4345

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