Testing for polytomies in phylogenetic species trees using quartet frequencies

Phylogenetic species trees typically represent the speciation history as a bifurcating tree. Speciation events that simultaneously create more than two descendants, thereby creating polytomies in the phylogeny, are possible. Moreover, the inability to resolve relationships is often shown as a (soft) polytomy. Both types of polytomies have been traditionally studied in the context of gene tree reconstruction from sequence data. However, polytomies in the species tree cannot be detected or ruled out without considering gene tree discordance. In this paper, we describe a statistical test based on properties of the multi-species coalescent model to test the null hypothesis that a branch in an estimated species tree should be replaced by a polytomy. On both simulated and biological datasets, we show that the null hypothesis is rejected for all but the shortest branches, and in most cases, it is retained for true polytomies. The test, available as part of the ASTRAL package, can help systematists decide whether their datasets are sufficient to resolve specific relationships of interest

Entropy of continuous maps on quasi-metric spaces

The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are associated to a given quasi-metric space are introduced and the entropy of a map of a given quasi-metric space and the maps of its associated metric spaces are compared. It is shown that the entropy of a map when symmetric properties is included is grater or equal to the entropy in the case that the symmetric property of the space is not considered

PROPOSING A MODEL FOR AN IDEAL RELATIONSHIP BETWEEN WEALTHY CITIZENS AND STATE-OWNED BANKS USING GROUNDED THEORY

Abstract. Early investigations on the banking industry indicate that a considerable part of bank’s resources is provided through a limited number of valuable customers. However, many domestic banks in general and state-owned banks in particular, do not provide a clear definition on valuable customers, leading to the lack of an understanding of the subjective expectations of the customers regarding the nature of an effective relationship. This study aims to explain the size and components of the ideal relationship between the customers and banks according to the customers’ comments. Codes extracted from interviews with fourteen privileged customers of banks are analyzed using the grounded theory as a qualitative research approach. Accordingly, dimensions of the paradigmatic model and elements of a good relationship with the privileged customers are explained. After the analysis of the proposed model, some suggestions are presented for future bank managers and researchers in this field.Key words: privileged customers, customer relationship management, Grounded Theory, State-owned Ban

Distal Fuzzy Dynamical Systems

In this paper the t-distal notion is extended for fuzzy dynamical systems on fuzzy metric spaces. A method for constructing fuzzy metric spaces is studied. The product of t-distal fuzzy dynamical systems is considered. It is proved that: a product of fuzzy dynamical systems is t- distal if and only if its components are t-distal. The persistence of the t-distal property up to a fuzzy factor map is proved