
Analysis of tensor methods for stochastic models of gene regulatory networks
The tensorstructured parametric analysis (TPA) has been recently develo...
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Committor functions via tensor networks
We propose a novel approach for computing committor functions, which des...
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Approximation and inference methods for stochastic biochemical kinetics  a tutorial review
Stochastic fluctuations of molecule numbers are ubiquitous in biological...
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PostProcessing of HighDimensional Data
Scientific computations or measurements may result in huge volumes of da...
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Tensor Train Random Projection
This work proposes a novel tensor train random projection (TTRP) method ...
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Bayesian Additive Adaptive Basis Tensor Product Models for Modeling High Dimensional Surfaces: An application to highthroughput toxicity testing
Many modern data sets are sampled with error from complex highdimension...
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Reduced basis method for the nonlinear PoissonBoltzmann equation regularized by the rangeseparated canonical tensor format
The PoissonBoltzmann equation (PBE) is a fundamental implicit solvent c...
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Tensortrain approximation of the chemical master equation and its application for parameter inference
In this work, we perform Bayesian inference tasks for the chemical master equation in the tensortrain format. The tensortrain approximation has been proven to be very efficient in representing high dimensional data arising from the explicit representation of the chemical master equation solution. An additional advantage of representing the probability mass function in the tensor train format is that parametric dependency can be easily incorporated by introducing a tensor product basis expansion in the parameter space. Time is treated as an additional dimension of the tensor and a linear system is derived to solve the chemical master equation in time. We exemplify the tensortrain method by performing inference tasks such as smoothing and parameter inference using the tensortrain framework. A very high compression ratio is observed for storing the probability mass function of the solution. Since all linear algebra operations are performed in the tensortrain format, a significant reduction of the computational time is observed as well.
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