相关论文: The lowest modes around Gaussian solutions of tens…
Tensor models can be regarded as theories of dynamical fuzzy spaces, and provide background independent theories of space. Their classical solutions correspond to classical background spaces, and the small fluctuations around them can be…
Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary…
This paper gives a summary of the author's works concerning the emergent general relativity in a particular class of tensor models, which possess Gaussian classical solutions. In general, a classical solution in a tensor model may be…
Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the…
The tensor model can be regarded as theory of dynamical fuzzy spaces, and gives a way to formulate gravity on fuzzy spaces. It has recently been shown that the low-lying fluctuations around the Gaussian background solutions in the tensor…
Accretion flows with pressure gradients permit the existence of standing waves which may be responsible for observed quasi-periodic oscillations (QPO's) in X-ray binaries. We present a comprehensive treatment of the linear modes of a…
Recovery of sparse vectors and low-rank matrices from a small number of linear measurements is well-known to be possible under various model assumptions on the measurements. The key requirement on the measurement matrices is typically the…
Rank-three tensor model may be regarded as theory of dynamical fuzzy spaces, because a fuzzy space is defined by a three-index coefficient of the product between functions on it, f_a*f_b=C_ab^cf_c. In this paper, this previous proposal is…
We give a proof of the convergence of an algorithm for the construction of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. The existence of such invariant tori is proved by leading the Hamiltonian to a suitable…
We discuss the consistency of a recently proposed class of theories described by an arbitrary function of the Ricci scalar, the trace of the energy-momentum tensor and the contraction of the Ricci tensor with the energy-momentum tensor. We…
This paper investigates the low-rank tensor completion problem, which is about recovering a tensor from partially observed entries. We consider this problem in the tensor train format and extend the preconditioned metric from the matrix…
We generalize and simplify an earlier approach. In three dimensions we present the most general averaging formula in lowest order which respects the requirements of covariance. It involves a bitensor, made up of a basis of six tensors, and…
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…
We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…
Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
Dimensionality reduction for high-order tensors is a challenging problem. In conventional approaches, higher order tensors are `vectorized` via Tucker decomposition to obtain lower order tensors. This will destroy the inherent high-order…
Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly…