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Using multitype branching models to analyze bacterial pathogenicity

100%

Tahir D., Kaj I., Bartoszek K., Majchrzak M., Parniewski P., Sakowski S.

Mathematica Applicanda

2020

tom 48

We apply multitype, continuous time, Markov branching models to study pathogenicity in E. coli, a bacterium belonging to the genus Escherichia. First, we examine briefly, the properties of multitype branching processes and we also survey some fundamental limit theorems regarding the behavior of such models under various conditions. These theorems are then applied to discrete, state dependent models, in order to analyze pathogenicity in a published clinical data set consisting of 251 strains of E. coli. We use well established methods, incorporating maximum likelihood techniques, to estimate speciation rates as well as the rates of transition between different states of the models. From the analysis, we not only derive new results, but we also verify some preexisting notions about virulent behavior in bacterial strains.

Limit theorems in free probability theory II

100%

Chistyakov G., Götze F.

Open Mathematics

2008

tom 6

nr 1

87-117

Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line ℝ+ and on the unit circle $$ \mathbb{T} $$ we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.

Ograniczanie wyników

1 Mathematica Applicanda

1 Open Mathematics

1 Bartoszek K.

1 Chistyakov G.

1 Götze F.

1 Kaj I.

1 Majchrzak M.

1 Parniewski P.

1 Sakowski S.

1 Tahir D.

1 2020

1 2008

Wyniki wyszukiwania

Using multitype branching models to analyze bacterial pathogenicity

Limit theorems in free probability theory II