Analysis of Single-Cell Data. ODE Constrained Mixture by Carolin Loos

By Carolin Loos

Carolin bogs introduces novel techniques for the research of single-cell facts. either techniques can be utilized to review mobile heterogeneity and hence improve a holistic realizing of organic methods. the 1st approach, ODE limited combination modeling, allows the id of subpopulation buildings and assets of variability in single-cell photograph facts. the second one process estimates parameters of single-cell time-lapse information utilizing approximate Bayesian computation and is ready to make the most the temporal cross-correlation of the knowledge in addition to lineage information. 

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2009) already showed for some processes that measurements at less time points are needed to obtain identifiable parameters if second order moments are measured besides the means. 1 conc. 1 conc. 1 ) 1 ME RRE true param. 8: Results for Scenario 1. (A) Fitted data of the optimal model MH2,1 using ODE-MMs with MEs. (B, C) Comparison of profile likelihoods for ODEMMs with RREs (red line) and MEs (dotted dark red line) for different numbers of measurements. (B) For the case of 7 time points, almost no difference can be detected between the profiles.

7) The entries of Γ are incorporated in the parameter vector. The moments of the measurand without measurement noise are denoted by my = (my,1 , . . , my,d ) and Cy and can be calculated from x. 2 Multivariate Mixture of Normal and Log-Normal Distributions In this thesis we focus on the mixture of d-dimensional multivariate normal distributions N (y|μ, Σ) = 1 1 1 d (2π) 2 det (Σ) 2 e− 2 (y−μ) T Σ−1 (y−μ) , and multivariate log-normal distributions logN (y|μ, Σ) = 1 d 2 (2π) det (Σ) with mixture parameters ϕ = (μ, Σ).

Wsmax As 0 ≤ eqs −qsmax ≤ 1 the reformulation gives better numerical properties than the direct computation of log(p), which gets unstable for p close to 0. 4 Simultaneous Analysis of Multivariate Measurements with Hs such that ps H s = dws dps dws ps = ps + ws . 8) This is again unstable for p close to 0 and needs to be reformulated. Using ps ns j=1 wj pj ps psmax ns pj j=1 wj psmax = eqs −qsmax = ns qj −qsmax j=1 wj e , we obtain d log(p) = dθ ns 1 ns qj −qsmax j=1 wj e s=1 Example (Normal Distribution).

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