A Beta-splitting model for evolutionary trees

In this article, we construct a generalization of the Blum-Fran\c{c}ois Beta-splitting model for evolutionary trees, which was itself inspired by Aldous' Beta-splitting model on cladograms. The novelty of our approach allows for asymmetric shares of diversification rates (or diversification `potential') between two sister species in an evolutionarily interpretable manner, as well as the addition of extinction to the model in a natural way. We describe the incremental evolutionary construction of a tree with n leaves by splitting or freezing extant lineages through the Generating, Organizing and Deleting processes. We then give the probability of any (binary rooted) tree under this model with no extinction, at several resolutions: ranked planar trees giving asymmetric roles to the first and second offspring species of a given species and keeping track of the order of the speciation events occurring during the creation of the tree, unranked planar trees, ranked non-planar trees and finally (unranked non-planar) trees. We also describe a continuous-time equivalent of the Generating, Organizing and Deleting processes where tree topology and branch-lengths are jointly modeled and provide code in SageMath/python for these algorithms.Comment: 23 pages, 3 figures, 1 tabl

Rescaling limits of the spatial Lambda-Fleming-Viot process with selection

We consider the spatial Lambda-Fleming-Viot process model for frequencies of genetic types in a population living in R^d, with two types of individuals (0 and 1) and natural selection favouring individuals of type 1. We first prove that the model is well-defined and provide a measure-valued dual process encoding the locations of the `potential ancestors' of a sample taken from such a population. We then consider two cases, one in which the dynamics of the process are driven by events of bounded radii and one incorporating large-scale events whose radii have a polynomial tail distribution. In both cases, we consider a sequence of spatial Lambda-Fleming-Viot processes indexed by n, and we assume that the fraction of individuals replaced during a reproduction event and the relative frequency of events during which natural selection acts tend to 0 as n tends to infinity. We choose the decay of these parameters in such a way that when reproduction is only local, the measure-valued process describing the local frequencies of the less favoured type converges in distribution to a (measure-valued) solution to the stochastic Fisher-KPP equation in one dimension, and to a (measure-valued) solution to the deterministic Fisher-KPP equation in more than one dimension. When large-scale extinction-recolonisation events occur, the sequence of processes converges instead to the solution to the analogous equation in which the Laplacian is replaced by a fractional Laplacian. We also consider the process of `potential ancestors' of a sample of individuals taken from these populations, which we see as a system of branching and coalescing symmetric jump processes. We show their convergence in distribution towards a system of Brownian or stable motions which branch at some finite rate. In one dimension, in the limit, pairs of particles also coalesce at a rate proportional to their collision local time.Comment: 97 page

A new model for evolution in a spatial continuum

We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large scale extinction-recolonisation events. The lineages ancestral to a sample from a population evolving according to this model can be described in terms of a spatial version of the Lambda-coalescent. Using a technique of Evans(1997), we prove existence and uniqueness in law for the model. We then investigate the asymptotic behaviour of the genealogy of a finite number of individuals sampled uniformly at random (or more generally `far enough apart') from a two-dimensional torus of side L as L tends to infinity. Under appropriate conditions (and on a suitable timescale), we can obtain as limiting genealogical processes a Kingman coalescent, a more general Lambda-coalescent or a system of coalescing Brownian motions (with a non-local coalescence mechanism).Comment: 63 pages, version accepted to Electron. J. Proba

An Analysis of the Company Norgren CZ Using Time Series

Předmětem bakalářské práce je analýza vybraných ukazatelů společnosti Norgren CZ pomocí statistických metod, která zachycuje souvislosti mezi přesuny výroby z podniků v západní Evropě do České republiky a vývojem jednotlivých ukazatelů. Obsahuje doporučení, která po zavedení do praxe přispějí ke zlepšení firemních procesů a snížení stavu zásob i teoretická východiska nezbytná k pochopení všech prostředků, které byly v práci využity.The financial analysis of chosen indicators of Norgren CZ Company based on statistical methods, which captures links between production transfer from the Western European companies into the Czech Republic and development of particular indicators, is the object of presented thesis. The thesis contains recommendations, which after putting themselves into practice contribute to the betterment of business process and to the stock reduction, and theoretical background needed for full understanding of all measures used in the thesis as well.

Confirmation Bias: Misinformation in Society, Refutation as a Pedagogical Solution, and the Turn of the Screw

This thesis explores the societal implications of confirmation bias through the analysis of the characters and criticism of Henry James’ The Turn of the Screw, and the application of modern psychological and pedagogical studies to demonstrate a similar misunderstanding of truth in society. The aim of this study is to provide an approach to teach students that the plausibility of a belief based on selective evidence is insufficient justification for validation. Such flawed logic insidiously erodes one’s trust in objective truths, instead promoting subjective truths that are misinformed by media forms like fake news, biased claims, and unfiltered online content. The findings of this thesis suggest that students show an overwhelming difficulty in discerning opinion from fact and evaluating arguments and that a refutational approach to new information, as outlined in this thesis, is a skill that democracy hinges upon as it requires an educated populace that effectively evaluates information

Cloud service purchasedecision process

This article analyzes questions arising from a choice of available cloud computing services. Precisely what type of services should an organization choose? The article aims to introduce decision-making process according to the best practices. In order to describe this decision-making process we divide organizations into classes and for each class we recommend one or more available types of suitable cloud computing services. Moreover, there are introduced interesting cloud computing provider practices and service aspects including service operation, service parameters and service costs There are also introduced steps for customers how to deal with mentioned aspects