The Inverse Fundamental Operator Marching Method for Cauchy Problems in Range-Dependent Stratified Waveguides

The inverse fundamental operator marching method (IFOMM) is suggested to solve Cauchy problems associated with the Helmholtz equation in stratified waveguides. It is observed that the method for large-scale Cauchy problems is computationally efficient, highly accurate, and stable with respect to the noise in the data for the propagating part of a starting field. In further, the application scope of the IFOMM is discussed through providing an error estimation for the method. The estimation indicates that the IFOMM particularly suits to compute wave propagation in long-range and slowly varying stratified waveguides

Mean-square stability of linear systems over channels with random transmission delays

This work studies the mean-square stability and stabilization problem for networked feedback systems. Data transmission delays in the network channels of the systems are considered. It is assumed that these delays are i.i.d. processes with given probability mass functions (PMFs). A necessary and sufficient condition of mean-square (input-output) stability is studied for the networked feedback systems in terms of the input-output model and state-space model. Furthermore, according to this condition, mean-square stabilization via output feedback is studied for the networked feedback systems.Comment: arXiv admin note: text overlap with arXiv:2108.1279

Marching schemes for inverse scattering problems in waveguides with curved boundaries

A marching scheme is developed for inverse scattering problems of the Helmholtz equation in waveguides with curved boundaries. We implement a local orthogonal transform to transform the irregular waveguide in physical plane into a regular rectangle in computing plane. Then the modified Helmholtz system in computational domain is piecewise solved through a second order numerical marching scheme, and we propose a spectral projector based on the truncated local propagating eigenfunction expansion to regularize the marching scheme. In the end, the marching scheme is verified by extensive numerical experiments, and it is shown that the scheme is efficient, stable and accurate in rapidly varying waveguides with curved boundaries, even when the number of propagating modes in the main propagation direction is variable

A Class of PDEs with Nonlinear Superposition Principles

Through assuming that nonlinear superposition principles (NLSPs) are embedded in a Lie group, a class of 3rd-order PDEs is derived from a general determining equation that determine the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the governing PDE is proved C-integrable. In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation

Histone demethylase PHF8 promotes epithelial to mesenchymal transition and breast tumorigenesis

Histone demethylase PHF8 is upregulated and plays oncogenic roles in various cancers; however, the mechanisms underlying its dysregulation and functions in carcinogenesis remain obscure. Here, we report the novel functions of PHF8 in EMT (epithelial to mesenchymal transition) and breast cancer development. Genome-wide gene expression analysis revealed that PHF8 overexpression induces an EMT-like process, including the upregulation of SNAI1 and ZEB1. PHF8 demethylates H3K9me1, H3K9me2 and sustains H3K4me3 to prime the transcriptional activation of SNAI1 by TGF-β signaling. We show that PHF8 is upregulated and positively correlated with MYC at protein levels in breast cancer. MYC post-transcriptionally regulates the expression of PHF8 via the repression of microRNAs. Specifically, miR-22 directly targets and inhibits PHF8 expression, and mediates the regulation of PHF8 by MYC and TGF-β signaling. This novel MYC/microRNAs/PHF8 regulatory axis thus places PHF8 as an important downstream effector of MYC. Indeed, PHF8 contributes to MYC-induced cell proliferation and the expression of EMT-related genes. We also report that PHF8 plays important roles in breast cancer cell migration and tumor growth. These oncogenic functions of PHF8 in breast cancer confer its candidacy as a promising therapeutic target for this disease

Effects of fiber orientation on tool wear evolution and wear mechanism when cutting carbon fiber reinforced plastics

The aim of the present paper is to reveal the influence of different fiber orientations on the tool wear evolution and wear mechanism. Side-milling experiments with large-diameter milling tools are conducted. A finite element (FE) cutting model of carbon fiber reinforced plastics (CFRP) is established to get insight into the cutting stress status at different wear stages. The results show that different fiber orientations bring about distinct differences in the extent, profile and mechanism of tool wear. Severer wear occurs when cutting 45° and 90° plies, followed by 0°, correspondingly, the least wear is obtained when θ = 135° (θ represents the orientation of fibers). Moreover, the worn profiles of cutting tools when θ = 0° and 45° are waterfall edge, while round edge occurs when θ = 135° and a combined shape of waterfall and round edge is obtained when θ = 90°. The wear mechanisms under different fiber orientations are strongly dependent on the cutting stress distributions. The evolution of tool wear profile is basically consistent with the stress distribution on the tool surface at different wear stages, and the extent of tool wear is determined by the magnitude of stress on the tool surface. Besides, the worn edges produce an actual negative clearance angle, which decreases the actual cutting thickness and leads to compressing and bending failure of fibers beneath the cutting region as well as low surface qualities

Deep quantum neural networks equipped with backpropagation on a superconducting processor

Deep learning and quantum computing have achieved dramatic progresses in recent years. The interplay between these two fast-growing fields gives rise to a new research frontier of quantum machine learning. In this work, we report the first experimental demonstration of training deep quantum neural networks via the backpropagation algorithm with a six-qubit programmable superconducting processor. In particular, we show that three-layer deep quantum neural networks can be trained efficiently to learn two-qubit quantum channels with a mean fidelity up to 96.0% and the ground state energy of molecular hydrogen with an accuracy up to 93.3% compared to the theoretical value. In addition, six-layer deep quantum neural networks can be trained in a similar fashion to achieve a mean fidelity up to 94.8% for learning single-qubit quantum channels. Our experimental results explicitly showcase the advantages of deep quantum neural networks, including quantum analogue of the backpropagation algorithm and less stringent coherence-time requirement for their constituting physical qubits, thus providing a valuable guide for quantum machine learning applications with both near-term and future quantum devices.Comment: 7 pages (main text) + 11 pages (Supplementary Information), 10 figure