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- Vladimir Kazeev, Mustafa Khammash, Michael Nip, Christoph Schwab
- PLoS Computational Biology
- 2014

The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their… (More)

- Vladimir Kazeev, Christoph Schwab
- SIAM J. Matrix Analysis Applications
- 2015

We prove that the stationary distribution of a system of reacting species with a weaklyreversible reaction network of zero deficiency in the sense of Feinberg admits tensor-structured approximation of complexity which scales linearly with respect to the number of species and logarithmically in the maximum copy numbers as well as in the desired accuracy. Our… (More)

- Vladimir Kazeev, Ivan V. Oseledets, Maksim Rakhuba, Christoph Schwab
- Adv. Comput. Math.
- 2017

Tensor-compressed numerical solution of elliptic multiscale-diffusion and high frequency scattering problems is considered. For either problem class, solutions exhibit multiple length scales governed by the corresponding scale parameter: the scale of oscillations of the diffusion coefficient or smallest wavelength, respectively. As is well-known, this… (More)

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