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Tensors arise naturally in high-dimensional problems in chemistry, financial mathematics and many others. The numerical treatment of such kind of problems is difficult due to the curse of dimensionality: the number of unknowns and computational complexity grows exponentially with the dimension of the problem. To break the curse of dimensionality,(More)
We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high–dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of dimensionality and make storage and computational cost feasible. Applying a block version of the TT format to several vectors(More)
We propose algorithms for the solution of high-dimensional symmetrical positive definite (SPD) linear systems with the matrix and the right-hand side given and the solution sought in a low-rank format. Similarly to density matrix renormalization group (DMRG) algorithms, our methods optimize the components of the tensor product format subsequently. To(More)
We propose Fourier transform algorithms using QTT format for data-sparse approximate representation of one– and multi-dimensional vectors (m–tensors). Although the Fourier matrix itself does not have a low-rank QTT representation, it can be efficiently applied to a vector in the QTT format exploiting the multilevel structure of the Cooley-Tukey algorithm.(More)
The effect of selective agents on the efficiency of Agrobacterium-mediated transformation of pear was shown. The transformation frequency of the pear stock PS no. 217 by a binary vector carrying the nptII gene conferring kanamycin resistance was 0.4 or 3.1%, while the hpt gene for hygromycin resistance used as a selective marker increased transformation(More)
The sequencing of the moss Physcomitrella patens genome has facilitated studies of the plant proteome. To develop a proteome reference map based on the genome sequence, we conducted 2D electrophoreses of proteins extracted from moss protoplasts, protonemata, and gametophores grown under standard conditions on Petri dishes. On silver-stained gels, depending(More)
In this paper we accomplish the development of the fast rank–adaptive solver for tensor–structured symmetric positive definite linear systems in higher dimensions. In [9] this problem is approached by alternating minimization of the energy function, which we combine with steps of the basis expansion in accordance with the steepest descent algorithm. In this(More)
We study the application of the novel tensor formats (TT, QTT, QTT-Tucker) to the solution of d-dimensional chemical master equations, applied mostly to gene regulating networks (signaling cascades, toggle switches, phage-λ). For some important cases, e.g. signaling cascade models, we prove good separability properties of the system operator. The time is(More)