Tensor Transfer Learning for Intelligence Fault Diagnosis of Bearing with Semisupervised Partial Label Learning

A new tensor transfer approach is proposed for rotating machinery intelligent fault diagnosis with semisupervised partial label learning in this paper. Firstly, the vibration signals are constructed as a three-way tensor via trial, condition, and channel. Secondly, for adapting the source and target domains tensor representations directly, without vectorization, the domain adaptation (DA) approach named tensor-aligned invariant subspace learning (TAISL) is first proposed for tensor representation when testing and training data are drawn from different distribution. Then, semisupervised partial label learning (SSPLL) is first introduced for tackling a problem that it is hard to label a large number of instances and there exists much data left to be unlabeled. Ultimately, the proposed method is used to identify faults. The effectiveness and feasibility of the proposed method has been thoroughly validated by transfer fault experiments. The experimental results show that the presented technique can achieve better performance.

Thick branes in the scalar–tensor representation of f(R, T) gravity

Braneworld scenarios consider our observable universe as a brane embedded in a five-dimensional bulk. In this work, we consider thick braneworld systems in the recently proposed dynamically equivalent scalar–tensor representation of f(R, T) gravity, where R is the Ricci scalar and T the trace of the stress–energy tensor. In the general $$f\left( R,T\right) $$ f R , T case we consider two different models: a brane model without matter fields where the geometry is supported solely by the gravitational fields, and a second model where matter is described by a scalar field with a potential. The particular cases for which the function $$f\left( R,T\right) $$ f R , T is separable in the forms $$F\left( R\right) +T$$ F R + T and $$R+G\left( T\right) $$ R + G T , which give rise to scalar–tensor representations with a single auxiliary scalar field, are studied separately. The stability of the gravitational sector is investigated and the models are shown to be stable against small perturbations of the metric. Furthermore, we show that in the $$f\left( R,T\right) $$ f R , T model in the presence of an extra matter field, the shape of the graviton zero-mode develops internal structure under appropriate choices of the parameters of the model.

Tensor-tensor algebra for optimal representation and compression of multiway data

With the advent of machine learning and its overarching pervasiveness it is imperative to devise ways to represent large datasets efficiently while distilling intrinsic features necessary for subsequent analysis. The primary workhorse used in data dimensionality reduction and feature extraction has been the matrix singular value decomposition (SVD), which presupposes that data have been arranged in matrix format. A primary goal in this study is to show that high-dimensional datasets are more compressible when treated as tensors (i.e., multiway arrays) and compressed via tensor-SVDs under the tensor-tensor product constructs and its generalizations. We begin by proving Eckart–Young optimality results for families of tensor-SVDs under two different truncation strategies. Since such optimality properties can be proven in both matrix and tensor-based algebras, a fundamental question arises: Does the tensor construct subsume the matrix construct in terms of representation efficiency? The answer is positive, as proven by showing that a tensor-tensor representation of an equal dimensional spanning space can be superior to its matrix counterpart. We then use these optimality results to investigate how the compressed representation provided by the truncated tensor SVD is related both theoretically and empirically to its two closest tensor-based analogs, the truncated high-order SVD and the truncated tensor-train SVD.

Invariant quantities of scalar–tensor theories for stellar structure

We present the relativistic hydrostatic equilibrium equations for a wide class of gravitational theories possessing a scalar–tensor representation. It turns out that the stellar structure equations can be written with respect to the scalar–tensor invariants, allowing to interpret their physical role.

Multilinear Discriminative Spatial Patterns for Movement-Related Cortical Potential Based on EEG Classification with Tensor Representation

The discriminative spatial patterns (DSP) algorithm is a classical and effective feature extraction technique for decoding of voluntary finger premovements from electroencephalography (EEG). As a purely data-driven subspace learning algorithm, DSP essentially is a spatial-domain filter and does not make full use of the information in frequency domain. The paper presents multilinear discriminative spatial patterns (MDSP) to derive multiple interrelated lower dimensional discriminative subspaces of low frequency movement-related cortical potential (MRCP). Experimental results on two finger movement tasks’ EEG datasets demonstrate the effectiveness of the proposed MDSP method.

Dynamic wormhole geometries in hybrid metric-Palatini gravity

In this work, we analyse the evolution of time-dependent traversable wormhole geometries in a Friedmann–Lemaître–Robertson–Walker background in the context of the scalar–tensor representation of hybrid metric-Palatini gravity. We deduce the energy–momentum profile of the matter threading the wormhole spacetime in terms of the background quantities, the scalar field, the scale factor and the shape function, and find specific wormhole solutions by considering a barotropic equation of state for the background matter. We find that particular cases satisfy the null and weak energy conditions for all times. In addition to the barotropic equation of state, we also explore a specific evolving wormhole spacetime, by imposing a traceless energy–momentum tensor for the matter threading the wormhole and find that this geometry also satisfies the null and weak energy conditions at all times.

Weighted Low-Rank Tensor Representation for Multi-View Subspace Clustering

Multi-view clustering has been deeply explored since the compatible and complementary information among views can be well captured. Recently, the low-rank tensor representation-based methods have effectively improved the clustering performance by exploring high-order correlations between multiple views. However, most of them often express the low-rank structure of the self-representative tensor by the sum of unfolded matrix nuclear norms, which may cause the loss of information in the tensor structure. In addition, the amount of effective information in all views is not consistent, and it is unreasonable to treat their contribution to clustering equally. To address the above issues, we propose a novel weighted low-rank tensor representation (WLRTR) method for multi-view subspace clustering, which encodes the low-rank structure of the representation tensor through Tucker decomposition and weights the core tensor to retain the main information of the views. Under the augmented Lagrangian method framework, an iterative algorithm is designed to solve the WLRTR method. Numerical studies on four real databases have proved that WLRTR is superior to eight state-of-the-art clustering methods.

Thick brane structures in generalized hybrid metric-Palatini gravity

In this work, we study 5-dimensional braneworld scenarios in the scalar-tensor representation of the generalized hybrid metric-Palatini gravitational theory. We start by considering a model for a brane supported purely by the gravitational scalar fields of the theory and then consider other distinct cases where the models are also supported by an additional matter scalar field. We investigate the stability of the gravity sector and show that the models are all robust against small fluctuations of the metric. In particular, in the presence of the additional scalar field, we find that the profile of the gravitational zero mode may be controlled by the parameters of the model, being also capable of developing internal structure.