Keywords: Multidimensional Time Model for Probability Cumulative Function, single-cell transcriptomics, plasmid DNA sequencing
The new method is based on changes of Cumulative Distribution Function in relation to time change in sampling patterns. Multidimensional Time Model for Probability Cumulative Function can be reduced to finite-dimensional time model, which can be characterized by Boolean algebra for operations over events and their probabilities and index set for reduction of infinite dimensional time model to finite number of dimensions of time model considering also the fractal-dimensional time arising from alike supersymmetrical properties of probability. It is based on the properties of composition of Brownian motion processes applied through application of Boolean prime ideal theorem and Stone duality. This model through Cumulant Analysis, Theory of Associated Random Variables., and Time Series analysis can be extended to uncertainty quantification of complex computational models in different areas of sciences that can require calculation of 5-fold integrals and the like. Along with chemical problems based on differences between single and multi cell analysis there are statistical problems related to noise models for single-cell transcriptomics and to challenging problems to distinguish genuine from technical stochastic allelic expression that is important in such questions as decomposition of tissues. The model can be applied to DNA and plasmid DNA sequencing in different vaccination trails.