相关论文: Pre-processing the nuclear many-body problem: Impo…
Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning. Among various tensor models, low-Tucker-rank tensors are particularly attractive for capturing multi-mode subspace…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
In this paper, we investigate the use of multilinear algebra for reducing the order of multidimensional linear time-invariant (MLTI) systems. Our main tools are tensor rational Krylov subspace methods, which enable us to approximate the…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…
High-precision knowledge of electromagnetic form factors of nuclei is a subject of much current experimental and theoretical activity in nuclear and atomic physics. Such precision mandates that effects of the non-zero spatial extent of the…
Nuclear resonances provide a rich and versatile testbed for exploring fundamental aspects of physics, particularly within the domain of strongly correlated many-body systems. The overarching goal of the theory is to develop a consistent and…
The two-sided Bogoliubov inequality for classical and quantum many-body systems is a theorem that provides rigorous bounds on the free-energy cost of partitioning a given system into two or more independent subsystems. This theorem…
This paper discusses weighted tensor Golub-Kahan-type bidiagonalization processes using the t-product. This product was introduced in [M. E. Kilmer and C. D. Martin, Factorization strategies for third order tensors, Linear Algebra Appl.,…
Effective field theories have established themselves as key pillars of modern nuclear physics. They enable a quantitative understanding of the strong nuclear force, provided low-energy constants that parametrize short-distance physics can…
The operators of localized spins within a magnetic material commute at different sites of its lattice and anticommute on the same site, so they are neither fermionic nor bosonic operators. Thus, to construct diagrammatic many-body…
Tensor contraction operations in computational chemistry consume significant fractions of computing time on large-scale computing platforms. The widespread use of tensor contractions between large multi-dimensional tensors in describing…
We discuss modeling of nuclear structure beyond the 2-body interaction paradigm. Our first example is related to the need of three nucleon contact interaction terms suggested by chiral perturbation theory. The relationship of the two…
Tensor decomposition of convolutional and fully-connected layers is an effective way to reduce parameters and FLOP in neural networks. Due to memory and power consumption limitations of mobile or embedded devices, the quantization step is…
A method for solving the shell-model eigenproblem in a severely truncated space, spanned by properly selected correlated states obtained by partitioning the full configuration space, is proposed. The method describes in a practically exact…
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA),…
The Unitary Correlation Operator Method (UCOM) provides a means for nuclear structure calculations starting from realistic NN potentials. The dominant short-range central and tensor correlations are described explicitly by a unitary…
The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…
The confinement problem remains one of the most difficult problems in theoretical physics. An important step toward the solution of this problem is the Polyakov's work on abelian confinement. The Georgi-Glashow model is a natural testing…
The equations of state for symmetric nuclear matter and pure neutron matter are investigated with the tensor-optimized Fermi Sphere method (TOFS) up to the density $\rho=0.5$~fm$^{-3}$. This method is based on a linked-cluster expansion…