Search

Every m by n matrix A with rank r has exactly r independent rows and r independent columns. The fact has become the most fundamental theorem in linear algebra such that we may favor it in an unconscious way. The sole aim of this paper is to give a self-contained introduction to concepts and mathematical tools for the rank of a matrix in order to seamlessly introduce how it works in applied linear algebra. However, we clearly realize our inability to cover all the useful and interesting results concerning this topic and given the paucity of scope to present this discussion, e.g., a proof via the injective linear map. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields., Comment: arXiv admin note: substantial text overlap with arXiv:2107.02579, arXiv:2105.04240

We construct a relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading order in covariant baryon chiral perturbation theory. We show that a good description of the $np$ phase shifts up to $T_\mathrm{lab}=200$ MeV and even higher can be achieved with a $\tilde{\chi}^2/\mathrm{d.o.f.}$ less than 1. Both the next-to-leading order results and the next-to-next-to-leading order results describe the phase shifts equally well up to $T_\mathrm{lab}=200$ MeV, but for higher energies, the latter behaves better, showing satisfactory convergence. The relativistic chiral potential provides the most essential inputs for relativistic ab initio studies of nuclear structure and reactions, which has been in need for almost two decades., Comment: Accepted for publication in PRL. Uncertainty estimates updated and comparison with the Granada PWA added

Entanglement routing establishes remote entanglement connection between two arbitrary nodes, which is one of the most important functions in quantum networks. The existing routing mechanisms mainly improve the robustness and throughput facing the failure of entanglement generations, which, however, rarely include the considerations on the most important metric to evaluate the quality of connection, entanglement fidelity. To solve this problem, we propose purification-enabled entanglement routing designs to provide fidelity guarantee for multiple Source-Destination (SD) pairs in quantum networks. In our proposal, we first consider the single S-D pair scenario and design an iterative routing algorithm, Q-PATH, to find the optimal purification decisions along the routing path with minimum entangled pair cost. Further, a low-complexity routing algorithm using an extended Dijkstra algorithm, Q-LEAP, is designed to reduce the computational complexity by using a simple but effective purification decision method. Then we consider the common scenario with multiple S-D pairs and design a greedy-based algorithm considering resource allocation and rerouting process for multiple routing requests. To verify the effectiveness and superiority of the proposed algorithms, extensive simulations are conducted, and the simulation results show that the proposed algorithms not only can provide fidelity-guarantee routing solutions, but also has superior performance in terms of throughput, fidelity of end-to-end entanglement connection, and resource utilization ratio, compared with the existing routing scheme.

The vortex phases in type-II superconductors are very important since they determine many magnetic and electric properties of the parent compound. However, a universal tool to characterize the vortex phases is still lacking. We demonstrate in a type-II superconductors YBa2Cu3O7-x polycrystal sample that its vortex phases and phase boundaries can be comprehensively studied by a magnetoelectric technique. In this method, a thin piezoelectric material 0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3(PMN-PT) is mechanically bonded with YBa2Cu3O7-x to form a laminate structure and act as a strain gauge. The phase diagram of the YBa2Cu3O7-x polycrystalline was explored by this method. Surprisingly, it can accurately estimate the Hc1, irreversible line, Hc2 and distinguish among vortex glass, vortex liquid, non-vortex states. Moreover, it can probe the dynamic response under different frequencies and observe the threshold phenomena of vortex liquid phase. It can even account for the density of vortices in the vortex solid phase. Our technique is readily extended to investigate the vortex phases in other type-II superconductors., Comment: 23 pages, 6 figures

We calculate the nonperturbative two-pion exchange (TPE) contributions to the $NN$ interaction in covariant baryon chiral perturbation theory. We study how the nonperturbative resummation affects the $NN$ phase shifts for partial waves with $J \geq 3$ and $L \leq 6$. No significant differences are observed between the nonperturbative phase shifts and perturbative ones for most partial waves except for $^3D_3$, for which the nonperturbative resummation greatly improves the description of the phase shifts. However, a significant cutoff dependence is found for this partial wave and a reasonable description of the phase shifts can only be obtained with a particular cutoff. Furthermore, we compare the so-obtained nonperturbative phase shifts with those obtained in the heavy baryon chiral perturbation theory. We show that the contributions from relativistic nonperturbative TPE are more moderate than those from the nonrelativistic TPE obtained in the dimensional regularization scheme. A proper convergence pattern is observed for most of the partial waves studied except for $^3F_3$, $^3F_4$, and $^3H_6$, for which the subleading TPE contributions are a bit strong. We find that for $H$ and $I$ partial waves, the OPE alone can already describe the phase shifts reasonably well., Comment: 17 pages, 11 figures, to appear in Physical Review C

Charge radius is one of the most fundamental properties of a nucleus. However, a precise description of the evolution of charge radii along an isotopic chain is highly nontrivial, as reinforced by recent experimental measurements. In this paper, we propose a novel approach which combines a three-parameter formula and a Bayesian neural network. We find that the novel approach can describe the charge radii of all $A\ge40$ and $Z\ge20$ nuclei with a root-mean-square deviation about 0.015 fm. In particular, the charge radii of the calcium isotopic chain are reproduced very well, including the parabolic behavior and strong odd-even staggerings. We further test the approach for the potassium isotopes and show that it can describe well the experimental data within uncertainties., Comment: 13 pages, 4 figures, to appear in Physical Review C

We consider using the system's optical imaging process with convolutional neural networks (CNNs) to solve the snapshot hyperspectral imaging reconstruction problem, which uses a dual-camera system to capture the three-dimensional hyperspectral images (HSIs) in a compressed way. Various methods using CNNs have been developed in recent years to reconstruct HSIs, but most of the supervised deep learning methods aimed to fit a brute-force mapping relationship between the captured compressed image and standard HSIs. Thus, the learned mapping would be invalid when the observation data deviate from the training data. Especially, we usually don't have ground truth in real-life scenarios. In this paper, we present a self-supervised dual-camera equipment with an untrained physics-informed CNNs framework. Extensive simulation and experimental results show that our method without training can be adapted to a wide imaging environment with good performance. Furthermore, compared with the training-based methods, our system can be constantly fine-tuned and self-improved in real-life scenarios.