Linear Algebra and Its Applications, ISSN 0024-3795, 10/2013, Volume 439, Issue 8, pp. 2350 - 2366

We study a general product of two n-dimensional tensors A and B with orders m⩾2 and k⩾1. This product satisfies the associative law, and is a generalization of...

Hypergraph | Direct product | Nonnegative tensor | Tensor | Primitive tensor | Characteristic polynomial | Eigenvalue | Product | MATHEMATICS | MATHEMATICS, APPLIED | LARGEST EIGENVALUE | PERRON-FROBENIUS THEOREM

Hypergraph | Direct product | Nonnegative tensor | Tensor | Primitive tensor | Characteristic polynomial | Eigenvalue | Product | MATHEMATICS | MATHEMATICS, APPLIED | LARGEST EIGENVALUE | PERRON-FROBENIUS THEOREM

Journal Article

The Journal of Chemical Physics, ISSN 0021-9606, 07/2016, Volume 145, Issue 1, p. 014102

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the...

CHEMISTRY, PHYSICAL | WAVE-FUNCTIONS | CLUSTER | DMRG | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | Operators (mathematics) | Languages | Algorithms | Density | INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY | ab initio calculations | ground states | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | configuration interaction | tensor methods | renormalization | quantum entanglement | Hilbert space | singular values | wave functions | nonperturbative techniques

CHEMISTRY, PHYSICAL | WAVE-FUNCTIONS | CLUSTER | DMRG | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | Operators (mathematics) | Languages | Algorithms | Density | INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY | ab initio calculations | ground states | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | configuration interaction | tensor methods | renormalization | quantum entanglement | Hilbert space | singular values | wave functions | nonperturbative techniques

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/2019

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 17

To construct dual frames with good structure for a given frame is a fundamental problem in the theory of frames. The tensor product duals of tensor product...

47A80 | Dual frame | Frame | 41A58 | Analysis | Tensor product frame | Mathematics, general | Mathematics | Applications of Mathematics | 42C15 | MATHEMATICS | MATHEMATICS, APPLIED | Frames | Tensors | Hilbert space | Mathematical analysis

47A80 | Dual frame | Frame | 41A58 | Analysis | Tensor product frame | Mathematics, general | Mathematics | Applications of Mathematics | 42C15 | MATHEMATICS | MATHEMATICS, APPLIED | Frames | Tensors | Hilbert space | Mathematical analysis

Journal Article

PHYSICAL REVIEW LETTERS, ISSN 0031-9007, 09/2019, Volume 123, Issue 10, p. 100502

Charge and energy transfer in biological and synthetic organic materials are strongly influenced by the coupling of electronic states to a highly structured...

SYSTEM | ELECTRON-TRANSFER | TIME EVOLUTION | FLUORESCENCE | RESONANCE | PHYSICS, MULTIDISCIPLINARY | MATTHEWS-OLSON COMPLEX | VIBRATIONS | ENERGY-TRANSFER | QUANTUM COHERENCE | ULTRAFAST CHARGE-TRANSFER | Damping | Solar cells | Organic materials | Computer simulation | Entanglement | Factorization | Harmonic oscillators | Electron states | Tensors | Photovoltaic cells | Mathematical analysis | Energy dissipation | Representations | Charge transfer | Energy transfer | Coarsening | Physics - Quantum Physics

SYSTEM | ELECTRON-TRANSFER | TIME EVOLUTION | FLUORESCENCE | RESONANCE | PHYSICS, MULTIDISCIPLINARY | MATTHEWS-OLSON COMPLEX | VIBRATIONS | ENERGY-TRANSFER | QUANTUM COHERENCE | ULTRAFAST CHARGE-TRANSFER | Damping | Solar cells | Organic materials | Computer simulation | Entanglement | Factorization | Harmonic oscillators | Electron states | Tensors | Photovoltaic cells | Mathematical analysis | Energy dissipation | Representations | Charge transfer | Energy transfer | Coarsening | Physics - Quantum Physics

Journal Article

Annals of Physics, ISSN 0003-4916, 03/2017, Volume 378, pp. 183 - 233

Quantum tensor network states and more particularly projected entangled-pair states provide a natural framework for representing ground states of gapped,...

Matrix product operators | Topological order | Anyons | Entanglement | Tensor networks | Fusion category | PHASES | PARTICLES | PHYSICS, MULTIDISCIPLINARY | STATISTICS | QUANTUM | SUBFACTORS | CLASSIFICATION | ENTANGLED PAIR STATES | TRANSFORMATIONS | RENORMALIZATION | Algebra

Matrix product operators | Topological order | Anyons | Entanglement | Tensor networks | Fusion category | PHASES | PARTICLES | PHYSICS, MULTIDISCIPLINARY | STATISTICS | QUANTUM | SUBFACTORS | CLASSIFICATION | ENTANGLED PAIR STATES | TRANSFORMATIONS | RENORMALIZATION | Algebra

Journal Article

Annals of Physics, ISSN 0003-4916, 10/2014, Volume 349, pp. 117 - 158

This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the...

MPS | Entanglement | Tensor networks | PEPS | RENORMALIZATION-GROUP | PHYSICS, MULTIDISCIPLINARY | FLOW-EQUATIONS | QUANTUM | ALGORITHM | CHAIN | GAUGE-THEORY | SYSTEMS | LATTICE | Quantum physics | Numerical analysis | Networks | Tensors | Mathematical analysis | Lattices | Mathematical models | Lectures | TENSORS | QUANTUM ENTANGLEMENT | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | PAIRING INTERACTIONS

MPS | Entanglement | Tensor networks | PEPS | RENORMALIZATION-GROUP | PHYSICS, MULTIDISCIPLINARY | FLOW-EQUATIONS | QUANTUM | ALGORITHM | CHAIN | GAUGE-THEORY | SYSTEMS | LATTICE | Quantum physics | Numerical analysis | Networks | Tensors | Mathematical analysis | Lattices | Mathematical models | Lectures | TENSORS | QUANTUM ENTANGLEMENT | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | PAIRING INTERACTIONS

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2000, Volume 123, Issue 1, pp. 85 - 100

The Kronecker product has a rich and very pleasing algebra that supports a wide range of fast, elegant, and practical algorithms. Several trends in scientific...

HIGHER-ORDER STATISTICS | MATHEMATICS, APPLIED | MATRIX EIGENVALUE PROBLEMS | LEAST-SQUARES PROBLEMS | IMAGES | TENSOR PRODUCT | TRANSFORM | ALGORITHMS | EQUATION | VOLTERRA FILTERS

HIGHER-ORDER STATISTICS | MATHEMATICS, APPLIED | MATRIX EIGENVALUE PROBLEMS | LEAST-SQUARES PROBLEMS | IMAGES | TENSOR PRODUCT | TRANSFORM | ALGORITHMS | EQUATION | VOLTERRA FILTERS

Journal Article

Physical Review D - Particles, Fields, Gravitation and Cosmology, ISSN 1550-7998, 11/2012, Volume 86, Issue 10

We clarify questions related to the convergence of the operator product expansion and conformal block decomposition in unitary conformal field theories (for...

INVARIANCE | VACUUM | TENSOR | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS

INVARIANCE | VACUUM | TENSOR | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS

Journal Article

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 01/2013, Volume 35, Issue 1, pp. 28 - 38

In many applications, we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise...

Manifolds | Context | Image segmentation | Tensile stress | Shape | affinity learning | Noise | Diffusion processes | Diffusion process | image retrieval | tensor product graph | image segmentation | SCALE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Models, Theoretical | Algorithms | Information Storage and Retrieval - methods | Artificial Intelligence | Computer Simulation | Diffusion | Pattern Recognition, Automated - methods | Measurement | Finite sets | Usage | Image processing | Innovations | Graph theory | Pixels | Simulation methods | Studies | Analogies | Data points | Tensors | Mathematical analysis | Images | Affinity | Graphs

Manifolds | Context | Image segmentation | Tensile stress | Shape | affinity learning | Noise | Diffusion processes | Diffusion process | image retrieval | tensor product graph | image segmentation | SCALE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Models, Theoretical | Algorithms | Information Storage and Retrieval - methods | Artificial Intelligence | Computer Simulation | Diffusion | Pattern Recognition, Automated - methods | Measurement | Finite sets | Usage | Image processing | Innovations | Graph theory | Pixels | Simulation methods | Studies | Analogies | Data points | Tensors | Mathematical analysis | Images | Affinity | Graphs

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2019, Volume 371, Issue 4, pp. 2963 - 2985

We show that the configuration spaces of a product of parallelizable manifolds may be recovered from those of the factors as the Boardman-Vogt tensor product...

OPERADS | MATHEMATICS | TENSOR PRODUCT | HOMOLOGY

OPERADS | MATHEMATICS | TENSOR PRODUCT | HOMOLOGY

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 10/2016, Volume 10, Issue 7, pp. 1411 - 1426

In Advances in Mathematical Physics (2011) we showed that the weighted shift $$z^{p}\frac{d^{p+1}}{dz^{p+1}} (p=0, 1, 2,\ldots )$$ z p d p + 1 d z p + 1 ( p =...

Weighted shift unbounded operators | Chaotic operators | Operator Theory | Fock–Bargmann spaces | Tensor product operators | 47B36 | 47B37 | Analysis | Mathematics, general | Mathematics | MATHEMATICS | CHAOS | MATHEMATICS, APPLIED | HYPERCYCLIC OPERATORS | Fock-Bargmann spaces | Bisphenol-A

Weighted shift unbounded operators | Chaotic operators | Operator Theory | Fock–Bargmann spaces | Tensor product operators | 47B36 | 47B37 | Analysis | Mathematics, general | Mathematics | MATHEMATICS | CHAOS | MATHEMATICS, APPLIED | HYPERCYCLIC OPERATORS | Fock-Bargmann spaces | Bisphenol-A

Journal Article

Image and Vision Computing, ISSN 0262-8856, 11/2018, Volume 79, pp. 1 - 10

As the object retrieval problem cannot be well solved by pairwise distances, many algorithms have been developed for visual re-ranking as the post-processing...

Diffusion process | Hybrid fitting constraint | Mean first-passage time | Contextual dissimilarity | Tensor product graph | COMPUTER SCIENCE, SOFTWARE ENGINEERING | DIFFUSION | COMPUTER SCIENCE, THEORY & METHODS | OPTICS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC

Diffusion process | Hybrid fitting constraint | Mean first-passage time | Contextual dissimilarity | Tensor product graph | COMPUTER SCIENCE, SOFTWARE ENGINEERING | DIFFUSION | COMPUTER SCIENCE, THEORY & METHODS | OPTICS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

NEURAL COMPUTATION, ISSN 1530-888X, 07/2019, Volume 31, Issue 7, pp. 1499 - 1517

Interest in quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled...

REFERENCE EVAPOTRANSPIRATION | NEUROSCIENCES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Classifiers | Computer simulation | Quantum computers | Quantum phenomena | Quantum computing | Tensors | Mathematical analysis | Coding | Data sets | Classification | Machine learning | Evapotranspiration | Performance measurement

REFERENCE EVAPOTRANSPIRATION | NEUROSCIENCES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Classifiers | Computer simulation | Quantum computers | Quantum phenomena | Quantum computing | Tensors | Mathematical analysis | Coding | Data sets | Classification | Machine learning | Evapotranspiration | Performance measurement

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 14

In this paper, we construct a bivariate tensor product generalization of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of ( p , q )...

( p , q ) $(p, q)$ -integers | bivariate tensor product | 41A25 | 41A36 | Analysis | Bernstein-Stancu-Schurer operators | 41A10 | Lipschitz continuous functions | Mathematics, general | Mathematics | Applications of Mathematics | modulus of continuity | (p, q) -integers | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | (p, q)-integers | Integers | Operators (mathematics) | Bivariate analysis | Mathematical analysis | Continuity (mathematics) | Convergence

( p , q ) $(p, q)$ -integers | bivariate tensor product | 41A25 | 41A36 | Analysis | Bernstein-Stancu-Schurer operators | 41A10 | Lipschitz continuous functions | Mathematics, general | Mathematics | Applications of Mathematics | modulus of continuity | (p, q) -integers | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | (p, q)-integers | Integers | Operators (mathematics) | Bivariate analysis | Mathematical analysis | Continuity (mathematics) | Convergence

Journal Article

International Journal of Quantum Chemistry, ISSN 0020-7608, 10/2015, Volume 115, Issue 19, pp. 1342 - 1391

The treatment of high‐dimensional problems such as the Schrödinger equation can be approached by concepts of tensor product approximation. We present general...

tensor networks | quantum infromation | DMRG | tensor product approximation | entanglement | DENSITY-MATRIX | STATES | QUANTUM SCIENCE & TECHNOLOGY | SPIN | INFORMATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | ELECTRONIC SCHRODINGER-EQUATION | GROUP ALGORITHM | MATRIX RENORMALIZATION-GROUP | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPTICAL-EXCITATIONS | ISING-MODEL | QC-DMRG

tensor networks | quantum infromation | DMRG | tensor product approximation | entanglement | DENSITY-MATRIX | STATES | QUANTUM SCIENCE & TECHNOLOGY | SPIN | INFORMATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | ELECTRONIC SCHRODINGER-EQUATION | GROUP ALGORITHM | MATRIX RENORMALIZATION-GROUP | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPTICAL-EXCITATIONS | ISING-MODEL | QC-DMRG

Journal Article