Hermite polynomial normal transformation for structural reliability analysis

PurposeNormal transformation is often required in structural reliability analysis to convert the non-normal random variables into independent standard normal variables. The existing normal transformation techniques, for example, Rosenblatt transformation and Nataf transformation, usually require the joint probability density function (PDF) and/or marginal PDFs of non-normal random variables. In practical problems, however, the joint PDF and marginal PDFs are often unknown due to the lack of data while the statistical information is much easier to be expressed in terms of statistical moments and correlation coefficients. This study aims to address this issue, by presenting an alternative normal transformation method that does not require PDFs of the input random variables.Design/methodology/approachThe new approach, namely, the Hermite polynomial normal transformation, expresses the normal transformation function in terms of Hermite polynomials and it works with both uncorrelated and correlated random variables. Its application in structural reliability analysis using different methods is thoroughly investigated via a number of carefully designed comparison studies.FindingsComprehensive comparisons are conducted to examine the performance of the proposed Hermite polynomial normal transformation scheme. The results show that the presented approach has comparable accuracy to previous methods and can be obtained in closed-form. Moreover, the new scheme only requires the first four statistical moments and/or the correlation coefficients between random variables, which greatly widen the applicability of normal transformations in practical problems.Originality/valueThis study interprets the classical polynomial normal transformation method in terms of Hermite polynomials, namely, Hermite polynomial normal transformation, to convert uncorrelated/correlated random variables into standard normal random variables. The new scheme only requires the first four statistical moments to operate, making it particularly suitable for problems that are constraint by limited data. Besides, the extension to correlated cases can easily be achieved with the introducing of the Hermite polynomials. Compared to existing methods, the new scheme is cheap to compute and delivers comparable accuracy

A Proposal to Reform Immigration Management Policy in China

Abstract China is facing the demographic challenge that a dangerously low birth rate would let the country “getting old before getting rich”. Immigrants can help China decrease the negative influence of demographic challenge, including lacking both professional and talented experts in high-ended industries and a cheaper labor force in manufactural industries. However, the legislation on managing and controlling immigrants in China lags current social development. This proposal reviews the immigration management history in China and briefly introduces the immigration management experience of other countries. The proposal recommends reforming the current visas classification method more detailed according to immigrate and non-immigrate and set a few policies to coordinate. This proposal analyzes the pros and cons of this reform in policy and political perspective to convince the reader to approve it

Lattice model constructions for gapless domain walls between topological phases

Domain walls between different topological phases are one of the most interesting phenomena that reveal the non-trivial bulk properties of topological phases. Very recently, gapped domain walls between different topological phases have been intensively studied. In this paper, we systematically construct a large class of lattice models for gapless domain walls between twisted and untwisted gauge theories with arbitrary finite group $G$. As simple examples, we numerically study several finite groups(including both Abelian and non-Abelian finite group such as $S_3$) in $2$D using the state-of-the-art loop optimization of tensor network renormalization algorithm. We also propose a physical mechanism for understanding the gapless nature of these particular domain wall models. Finally, by taking advantage of the classification and construction of twisted gauge theories using group cohomology theory, we generalize such constructions into arbitrary dimensions, which might provide us a systematical way to understand gapless domain walls and topological quantum phase transitions.Comment: Non-Abelian examples adde

Quantum approximate optimization algorithm with adaptive bias fields

The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wave function into one that encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which two unitary operators are alternately applied to the qubits. In this paper, the QAOA is modified by updating the operators themselves to include local fields, using information from the measured wave function at the end of one iteration step to improve the operators at later steps. It is shown by numerical simulation on MaxCut problems that, for a fixed accuracy, this procedure decreases the runtime of QAOA very substantially. This improvement appears to increase with the problem size. Our method requires essentially the same number of quantum gates per optimization step as the standard QAOA, and no additional measurements. This modified algorithm enhances the prospects for quantum advantage for certain optimization problems.journal articl

Q-SLAM: Quadric Representations for Monocular SLAM

Monocular SLAM has long grappled with the challenge of accurately modeling 3D geometries. Recent advances in Neural Radiance Fields (NeRF)-based monocular SLAM have shown promise, yet these methods typically focus on novel view synthesis rather than precise 3D geometry modeling. This focus results in a significant disconnect between NeRF applications, i.e., novel-view synthesis and the requirements of SLAM. We identify that the gap results from the volumetric representations used in NeRF, which are often dense and noisy. In this study, we propose a novel approach that reimagines volumetric representations through the lens of quadric forms. We posit that most scene components can be effectively represented as quadric planes. Leveraging this assumption, we reshape the volumetric representations with million of cubes by several quadric planes, which leads to more accurate and efficient modeling of 3D scenes in SLAM contexts. Our method involves two key steps: First, we use the quadric assumption to enhance coarse depth estimations obtained from tracking modules, e.g., Droid-SLAM. This step alone significantly improves depth estimation accuracy. Second, in the subsequent mapping phase, we diverge from previous NeRF-based SLAM methods that distribute sampling points across the entire volume space. Instead, we concentrate sampling points around quadric planes and aggregate them using a novel quadric-decomposed Transformer. Additionally, we introduce an end-to-end joint optimization strategy that synchronizes pose estimation with 3D reconstruction

Constructing Heterostructure through Bidentate Coordination toward Operationally Stable Inverted Perovskite Solar Cells

It has been reported that one of the influencing factors leading to stability issues in iodine-containing perovskite solar cells is the iodine loss from the perovskite layer. Herein, bidentate coordination is used with undercoordinated I− of the perovskite surface to construct the stable perovskite-based heterostructure. This strong halogen bonding effectively inhibits interfacial migration of I− into functional layers such as C60 and Ag. Moreover, passivation of the undercoordinated I− suppresses the release of I2 and further delays the formation of voids at the perovskite surface. The resulting inverted perovskite solar cell exhibits a power conversion efficiency of 22.59% and the unencapsulated device maintains 96.15% of its initial value after continuous operation for 500 h under illumination.journal articl