相关论文: Fractal decompositions and tensor network represen…

We study mass-deformed N=2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly,…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered approximation tool combines a tensorization of functions in $L^p([0,1))$, which allows to identify a univariate function with…

For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to…

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite dimensional quantum group modules is clarified. We find a curious…

Partition functions of quantum critical systems, expressed as conformal thermal tensor networks, are defined on various manifolds which can give rise to universal entropy corrections. Through high-precision tensor network simulations of…

In this work, we investigate the entanglement structure in a $\textrm{T}\bar{\textrm{T}}$-deformed holographic CFT$_2$ with a conserved angular momentum. We utilize conformal perturbation theory to compute the leading order correction to…

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…

We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite…

Tensor networks have been an important concept and technique in many research areas, such as quantum computation and machine learning. We study the exponential complexity of contracting tensor networks on two special graph structures:…

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…

Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of…

Projected wave functions offer a means for incorporating local correlation effects in gapless electronic phases of matter like metals. Although such wave functions can be readily specified formally, it is challenging to compute their…

The exact Bethe eigenfunctions for the heptagonal ring within the isotropic XXX model exhibit a doubly degenerated energy level in the three-deviation sector at the centre of the Brillouin zone. We demonstrate an explicit construction of…

A systematic method of calculating the dynamical conductivity tensor in a general multiband electronic model with strong boson-mediated electron-electron interactions is described. The theory is based on the exact semiclassical expression…

The multifractal structure underlying a self-similar measure stems directly from the weighted self-similar system (or weighted iterated function system) which is used to construct the measure. This follows much in the way that the dimension…

Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…

Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical…

Entanglement related properties work as nice fingerprint of the quantum many-body wave function. However, those of fermionic models are hard to evaluate in standard numerical methods because they suffer from finite size effects. We show…