In this article, the behavior of the C(α)-manifold satisfying the conditions R(X,Y)W∗ = 0,W∗
(X,Y)R = 0,W∗
(X,Y)Z˜ =
0, W∗
(X,Y)S = 0 and W∗
(X,Y)C˜ = 0 on the M−projective curvature tensor is ...investigated. The C(α)−Manifold is characterized
according to these states of the curvature tensor. Here, W∗
,R,S,Z˜ and C˜ are M−projective, Riemann, Ricci, concircular and quasiconformal curvature tensors
In this article, the behavior of the C(α)-manifold satisfying the conditions R(X,Y)W∗ = 0,W∗
(X,Y)R = 0,W∗
(X,Y)Z˜ =
0, W∗
(X,Y)S = 0 and W∗
(X,Y)C˜ = 0 on the M−projective curvature tensor is investigated. The C(α)−Manifold is characterized
according to these states of the curvature tensor. Here, W∗
,R,S,Z˜ and C˜ are M−projective, Riemann, Ricci, concircular and quasiconformal curvature tensors
H-matrices (matrices whose comparison matrix is an M-matrix) are well studied in matrix theory and have numerous applications, e.g., linear complementarity problems and iterative methods for solving ...systems of linear equations. In this article we establish some properties of their tensor counterparts: strong H-tensors and (general) H-tensors.
The simplest α -attractor T model is given by the potential V = V0tanh2 (λϕ/Mpl) . However its generalization to the class of models of the type V = V0 tanhp (λϕ/Mpl) is difficult to interpret as a ...model of inflation for most values of p . Keeping the basic model, we propose a new generalization, where the final potential is of the form V = V0 (1 − sechp (λϕ/Mpl)), which does not present any of the problems that plague the original generalization, allowing a successful interpretation as a model of inflation for any value of p and, at the same time, providing the potential with a region where reheating can occur for any p (including odd and fractional values) without difficulty. In the cases p = 1 , 2, 4 we obtain the solutions r (ns, Nke) where r is the tensor-to-scalar ratio, ns the spectral index and Nke the number of e -folds during inflation. We also show how these solutions connect to the ϕ2 monomial.
Cyber-physical-social big data generated from ubiquitous devices and diverse spaces generally are multi-source, heterogeneous, and deeply intertwined. To efficiently analyze and handle the ubiquitous ...cyber-physical-social big data, tensor is considered as an effective tool, but the curse of dimensionality is still the main bottleneck of tensor-based big data analysis. Tensor networks can considerably alleviate or overcome it through the tensor approximate theory. Therefore, this paper focuses on developing an efficient big data processing framework based on tensor networks and providing an incremental tensor train decomposition approach for the streaming big data. Concretely, this paper first presents a hierarchical cyber-physical-social big data processing framework composed of three planes, namely, data representation and decomposition, data storage and processing, and data analysis and service, in which tensor train (TT) and quantized TT decompositions are particularly introduced to remarkably overcome the curse of dimensionality. Besides, to efficiently handle the continuous streaming big data and avoid the repeated decomposition for the history data, an incremental tensor train decomposition (ITTD) approach is proposed and the complexities are further analyzed in detail. Experimental results demonstrate that ITTD demonstrably outperforms the nonincremental TT decomposition in execution time on the precise of guaranteeing the nearly equal approximation error.
Gluon-gluon to photon-photon scattering gg→γγ offers to the LHC experiments a uniquely powerful probe of dimension-8 operators in the standard model effective field theory that are quadratic in both ...the electromagnetic and gluonic field-strength tensors, such as would appear in the Born-Infeld extension of the standard model. We use 13-TeV ATLAS data on the production of isolated photon pairs to set lower limits on the scales of dimension-8 operators M≳1 TeV and discuss the prospective sensitivities of possible future hadron colliders.
A H igh- D imensional and I ncomplete (HDI) tensor is frequently encountered in a big data-related application concerning the complex dynamic interactions among numerous entities. Traditional tensor ...factorization-based models cannot handle an HDI tensor efficiently, while existing latent factorization of tensors models are all linear models unable to model an HDI tensor's nonlinearity. Motivated by this critical discovery, this paper proposes a Neural Latent Factorization of Tensors model, which provides a novel approach to nonlinear Canonical Polyadic decomposition on an HDI tensor. It is implemented with three-fold interesting ideas: a) adopting the density-oriented modeling principle to build rank-one tensor series with high computational efficiency and affordable storage cost; b) treating each rank-one tensor as a hidden neuron to achieve an efficient neural network structure; and c) developing an a daptive b ackward p ropagation (ABP) learning scheme for efficient model training. Experimental results on six HDI tensors from a real system demonstrate that compared with state-of-the-art models, the proposed model achieves significant performance gain in both convergence rate and accuracy. Hence, it is of great significance in performing challenging HDI tensor analysis.
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