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In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...
In this letter we consider mean field type control problems with multiple species that have different dynamics. We formulate the discretized problem using a new type of entropy-regularized multimarginal optimal transport problems where the cost is a decomp ...
2023
Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor ' in the tensor train fo ...
A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves connection tenso ...
Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...
Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to ...
A geometric method of lattice reduction based on cycles of directional and hyperplanar shears is presented. The deviation from cubicity at each step of the reduction is evaluated by a parameter called 'basis rhombicity' which is the sum of the absolute val ...
INT UNION CRYSTALLOGRAPHY2022
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We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method orig ...
We introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangenti ...
Body posture influences human and robots performance in manipulation tasks, as appropriate poses facilitate motion or force exertion along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze, control and design ...
