| 1. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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A Noether theorem for stochastic operators on Schatten classes
- 2017
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 452:2, s. 1395-1412
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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.
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| 2. |
- Antonelli, Alexandre, 1978, et al.
(författare)
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Embracing heterogeneity: Coalescing the tree of life and the future of phylogenomics
- 2019
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Ingår i: PeerJ. - : PeerJ. - 2167-8359. ; 2019:2
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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.
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| 3. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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A consistent estimator of the evolutionary rate
- 2015
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Ingår i: Journal of Theoretical Biology. - 0022-5193 .- 1095-8541. ; 371, s. 69-78
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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.
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| 4. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
- 2015
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Ingår i: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 114, s. 26-39
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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.
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| 5. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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Phylogenetic confidence intervals for the optimal trait value
- 2015
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 52:4, s. 1115-1132
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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.
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| 6. |
- Bartoszek, Krzysztof, 1984-
(författare)
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Phylogenetic effective sample size
- 2016
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Ingår i: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 407, s. 371-386
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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.
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| 7. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1
- 2018
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Ingår i: Bulletin of the Malaysian Mathematical Sciences Society. - : Springer Science and Business Media LLC. - 0126-6705 .- 2180-4206. ; 41:1, s. 159-173
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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.
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| 8. |
- Bartoszek, Krzysztof, 1984-
(författare)
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Simulating an infinite mean waiting time
- 2019
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Ingår i: Mathematica Applicanda. - Warsaw, Poland : Polskie Towarzystwo Matematyczne. - 1730-2668 .- 2299-4009. ; 47:1, s. 93-102
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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.
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| 9. |
- Bartoszek, Krzysztof, 1984-
(författare)
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Trait evolution with jumps: illusionary normality
- 2017
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Ingår i: Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine. ; , s. 23-28
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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.
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| 10. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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Using the Ornstein-Uhlenbeck process to model the evolution of interacting populations
- 2017
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Ingår i: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 429, s. 35-45
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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.
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| 11. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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Weak Stability of Centred Quadratic Stochastic Operators
- 2019
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Ingår i: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY. - : MALAYSIAN MATHEMATICAL SCIENCES SOC. - 0126-6705 .- 2180-4206. ; 42:4, s. 1813-1830
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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.
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| 12. |
- Woniacki, Piotr, et al.
(författare)
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The impact of the Polish mass breast cancer screening program on prognosis in the Pomeranian Province
- 2017
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Ingår i: Archives of Medical Science. - : TERMEDIA PUBLISHING HOUSE LTD. - 1734-1922 .- 1896-9151. ; 13:2, s. 441-447
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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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