Tensor field visualization aims at the depiction of the full information contained in the underlying data set or the extraction and display of specific features. Here, we focus on the first task and evaluate various methods with regard to their power of providing an intuitive visual representation. Tensor fields are reviewed in a differential geometric context and we provide a coordinate-free d...

It is known that the second dominant eigenvalue of a matrix determines the convergence rate of the power method. Though ineffective for general eigenvalue computation, the power method has been of practical usage for computing the stationary distribution of a stochastic matrix. For a Markov chain with memory m, the transition “matrix" becomes an order-m tensor. Under suitable assumptions, the s...

We characterize the variational power of quantum circuit tensor networks in representation physical many-body ground-states. Such are formed by replacing dense block unitaries and isometries standard local circuits. explore both matrix product states multi-scale entanglement renormalization ansatz, introduce an adaptive method to optimize resulting circuits high fidelity with more than $10^4$ p...

In this paper, we calculate the relativistic bulk tensor and shear tensor of the relativistic accretion ows in the Kerr metric, overall and without any approximation. We obtain the relations of all components of the relativistic bulk and shear tensor in terms of components of four-velocity and its derivatives, Christoffel symbols and metric components in the BLF. Then, these components are deri...

In this paper, we study the tensor commutativity degree of pair of finite groups. Erdos introduced the relative commutativity degree and studied its properties. Then, Mr. Niroomand introduced the tensor relative commutativity degree, calculated tensor relative degree for some groups, and studied its properties. Also, he explained its relation with relative commutativity degree. In this paper, w...