Recurrent neural network decoding of rotated surface codes based on distributed strategy

Quantum error correction is a crucial technology for realizing quantum computers.These computers achieve faulttolerant quantum computing by detecting and correcting errors using decoding algorithms.Quantum error correction using neural network-based machine learning methods is a promising approach that is adapted to physical systems without the need to build noise models.In this paper,we use a distributed decoding strategy,which effectively alleviates the problem of exponential growth of the training set required for neural networks as the code distance of quantum error-correcting codes increases.Our decoding algorithm is based on renormalization group decoding and recurrent neural network decoder.The recurrent neural network is trained through the ResNet architecture to improve its decoding accuracy.Then we test the decoding performance of our distributed strategy decoder,recurrent neural network decoder,and the classic minimum weight perfect matching(MWPM)decoder for rotated surface codes with different code distances under the circuit noise model,the thresholds of these three decoders are about 0.0052,0.0051,and 0.0049,respectively.Our results demonstrate that the distributed strategy decoder outperforms the other two decoders,achieving approximately a 5%improvement in decoding efficiency compared to the MWPM decoder and approximately a 2%improvement compared to the recurrent neural network decoder.

Variable-order rotated staggered-grid method for elastic-wave forward modeling

Numerical simulations of a seismic wavefield are important to analyze seismic wave propagation. Elastic-wave equations are used in data simulation for modeling migration and imaging. In elastic wavefield numerical modeling, the rotated staggered-grid method （RSM） is a modification of the standard staggered-grid method （SSM）. The variable-order method is based on the method of variable-length spatial operators and wavefield propagation, and it calculates the real dispersion error by adapting different finite-difference orders to different velocities. In this study, the variable-order rotated staggered-grid method （VRSM） is developed after applying the variable-order method to RSM to solve the numerical dispersion problem of RSM in low-velocity regions and reduce the computation cost. Moreover, based on theoretical dispersion and the real dispersion error of wave propagation calculated with the wave separation method, the application of the original method is extended from acoustic to shear waves, and the calculation is modified from theoretical to time-varying values. A layered model and an overthrust model are used to demonstrate the applicability of VRSM. We also evaluate the order distribution, wave propagation, and computation time. The results suggest that the VRSM order distribution is reasonable and VRSM produces high-precision results with a minimal computation cost.

Irregular surface seismic forward modeling by a body-fitted rotated–staggered-grid finite-difference method

Finite-difference(FD) methods are widely used in seismic forward modeling owing to their computational efficiency but are not readily applicable to irregular topographies. Thus, several FD methods based on the transformation to curvilinear coordinates using body-fitted grids have been proposed, e.g., stand staggered grid(SSG) with interpolation, nonstaggered grid, rotated staggered grid(RSG), and fully staggered. The FD based on the RSG is somewhat superior to others because it satisfies the spatial distribution of the wave equation without additional memory and computational requirements; furthermore, it is simpler to implement. We use the RSG FD method to transform the firstorder stress–velocity equation in the curvilinear coordinates system and introduce the highprecision adaptive, unilateral mimetic finite-difference(UMFD) method to process the freeboundary conditions of an irregular surface. The numerical results suggest that the precision of the solution is higher than that of the vacuum formalism. When the minimum wavelength is low, UMFD avoids the surface wave dispersion. We compare FD methods based on RSG, SEM, and nonstaggered grid and infer that all simulation results are consistent but the computational efficiency of the RSG FD method is higher than the rest.

Numerical simulation of seismic wavefields in TTI media using the rotated staggered-grid compact finite-difference scheme

Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme（RSG） is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme（CSG） is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme（RSGC）. The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.

Improvement of visual acuity in children with anisometropic amblyopia treated with rotated prisms combined with near activity

·AIM: To evaluate the efficacy of a new modality for improving visual acuity (VA) in pediatric patients with anisometropic amblyopia. · METHODS: Retrospective and interventional case series. Medical records of 360 children with anisometropic amblyopia treated with a modality that included rotated prisms, lenses, and near activities from January 2008 to January 2012 were analyzed. Characteristics such as improvement of VA and contrast sensitivity in amblyopic eyes and resolution of amblyopia (VA ≤ 0.1logMAR or a difference of ≤ 2 lines in logMAR between the eyes) were assessed. ·RESULTS: Among the patients, the mean VA of the amblyopic eyes improved from 0.48logMAR (SD=0.16) to 0.12logMAR (SD =0.16) and the mean VA improvement was 0.36logMAR (SD =0.10, P【0.001). Resolution of amblyopia was achieved in 233 of 360 patients (64.72%). The mean time for resolution of amblyopia was 8.05 weeks (SD=4.83) or 14.14 sessions (SD=8.76). Among the study group, refraction error did not change significantly after treatment (P=0.437). We found that better baseline VA may be related to success and shorten the time to amblyopic resolution. ·CONCLUSION: VA and contrast sensitivity improved with rotated prisms, correcting lenses, and near activities in children with anisometropic amblyopia. The VA improvement by this modality was comparable to other methods. However, the time to resolution of amblyopia was shorter with this method than with other modalities. Rotated prisms combined with near acuity could provide an alternative treatment in children with anisometropic amblyopia who can’t tolerant traditional therapy method like patching.

Geochemistry and Geochronology of Circumferential Dykes of the Franklin LIP: A Rotated Perspective on Plate Reconstruction

In addition to an extrusive volcanic component and associated sills,the Neoproterozoic Franklin Large Igneous Province(LIP)comprises a giant radiating dyke swarm spanning an arc of ca.110?,as well as a less-

Diffraction Pattern of a Rotated Grating

Diffraction patterns of a rotated grating are investigated from both theoretical and experimental points of view. It is shown that as the grating rotates, the angle of deviation of each diffracted line relative to the incident light goes through a minimum, and that the angle between any two successive diffracted lines goes through a minimum value which is the same for all adjacent diffracted lines. It is also shown that the angle between diffraction lines with n=1 and n=-1 is not sensitive to small variations of the grating from being normal to the incident light. Finally, a method is suggested for determining the line distance of a diffraction grating with high accuracy.

Compact Interlaced Dual Circularly Polarized Sequentially Rotated Dielectric-Resonator Antenna Array

In this study,a compact 2×2 interlaced sequentially rotated dual-polarized dielectric-resonator antenna array is proposed for 5.8 GHz applications.The array is composed of a novel unit elements that are made of rectangular dielectric resonator(RDR)coupled to an eye slot for generating the orthogonal modes,TEδx 21 and TE1yδ1 to acquire circular polarization(CP)radiation.For the purpose of miniaturization and achieving dual polarized resonance,the array is fed by two interlaced ports and each port excites two radiating elements.The first port feeds horizontal elements to obtain left hand circular polarization(LHCP).The second port feeds vertical elements to obtain right hand circular polarization(RHCP).A quarter-wave length transformer is employed to reduce the attenuation and consequently increase the array gain performance.The 35×35 mm2(0.676λ0×0.676λ0)gains were 8.4 and 8.2 dBi for port 1 and port 2,respectively,with port isolations of−33.51 dB.The design achieves a voltage standing-wave ratio(VSWR)<−10 dB and an axial ratio(AR)<−3 dB bandwidth of 2.48%(5.766 to 5.911 GHz)for LHCP at port 1 and a VSWR<−10 dB and AR<−3 dB bandwidth of 2.28%(5.788 to 5.922 GHz)for RHCP at port 2.The findings of the proposed design validate its use for ISM band applications.

Cooperative DVB-SH Satellite Broadcasting Systems with Rotated Signal Constellations

In this paper,we study the advantages of cooperation in broadcasting systems from a geosynchronous earth orbit(GEO)satellite to mobile terminals(MTs),achieved through a terrestrial complementary ground station(CGS) with fixed installment,which acts as a relay.Moreover and in the context of the digital video broadcasting-satellite-to-handheld(DVB-SH) standard,the performance improvements offered by the rotated constellations method are investigated,where prior transmission,a phase rotation of the transmitted symbols by a fixed angle is applied followed by a random component interleaver.Turbo codes with soft decision decoding and appropriate random channel interleavers are also considered.We present analytical expressions for the bit log-likelihood ratios(LLRs)that are needed for soft decision decoding at the MT turbo decoder,while the code combining technique is adapted to improve the end-to-end(E2E) performance.Then,we obtain through extensive computer simulations the average bit error probability(ABEP) of quadrature phase-shift keying(QPSK) signals received over pure land-mobile satellite(LMS)and pure CGS links for coding rates 1/3 and6/7.Moreover,the optimal rotation angles are obtained for both links.E2 E ABEP results are then presented assuming cooperation between GEO and CGS,while the power allocation issue is investigated under fixed total transmission power.Our performance evaluation results show that by using the constellation rotation technique,a performance gain can be achieved for high coding rates.

Learning power Gaussian modeling loss for dense rotated object detection in remote sensing images

Object detection in Remote Sensing(RS)has achieved tremendous advances in recent years,but it remains challenging for rotated object detection due to cluttered backgrounds,dense object arrangements and the wide range of size variations among objects.To tackle this problem,Dense Context Feature Pyramid Network(DCFPN)and a powerα-Gaussian loss are designed for rotated object detection in this paper.The proposed DCFPN can extract multi-scale information densely and accurately by leveraging a dense multi-path dilation layer to cover all sizes of objects in remote sensing scenarios.For more accurate detection while avoiding bottlenecks such as boundary discontinuity in rotated bounding box regression,a-Gaussian loss,a unified power generalization of existing Gaussian modeling losses is proposed.Furthermore,the properties ofα-Gaussian loss are analyzed comprehensively for a wider range of applications.Experimental results on four datasets(UCAS-AOD,HRSC2016,DIOR-R,and DOTA)show the effectiveness of the proposed method using different detectors,and are superior to the existing methods in both feature extraction and bounding box regression。

RB-SLAM:visual SLAM based on rotated BEBLID feature point description

The extraction and description of image features are very important for visual simultaneous localization and mapping(V-SLAM).A rotated boosted efficient binary local image descriptor(BEBLID)SLAM(RB-SLAM)algorithm based on improved oriented fast and rotated brief(ORB)feature description is proposed in this paper,which can solve the problems of low localization accuracy and time efficiency of the current ORB-SLAM3 algorithm.Firstly,it uses the BEBLID to replace the feature point description algorithm of the original ORB to enhance the expressiveness and description efficiency of the image.Secondly,it adds rotational invariance to the BEBLID using the orientation information of the feature points.It also selects the rotationally stable bits in the BEBLID to further enhance the rotational invariance of the BEBLID.Finally,it retrains the binary visual dictionary based on the BEBLID to reduce the cumulative error of V-SLAM and improve the loading speed of the visual dictionary.Experiments show that the dictionary loading efficiency is improved by more than 10 times.The RB-SLAM algorithm improves the trajectory accuracy by 24.75%on the TUM dataset and 26.25%on the EuRoC dataset compared to the ORB-SLAM3 algorithm.

Modulation of High-Order Harmonic Generation from a Monolayer ZnO by Co-rotating Two-Color Circularly Polarized Laser Fields

By numerically solving the two-dimensional semiconductor Bloch equation,we study the high-order harmonic emission of a monolayer ZnO under the driving of co-rotating two-color circularly polarized laser pulses.By changing the relative phase between the fundamental frequency field and the second one,it is found that the harmonic intensity in the platform region can be significantly modulated.In the higher order,the harmonic intensity can be increased by about one order of magnitude.Through time-frequency analysis,it is demonstrated that the emission trajectory of monolayer ZnO can be controlled by the relative phase,and the harmonic enhancement is caused by the second quantum trajectory with the higher emission probability.In addition,near-circularly polarized harmonics can be generated in the co-rotating two-color circularly polarized fields.With the change of the relative phase,the harmonics in the platform region can be altered from left-handed near-circularly polarization to right-handed one.Our results can obtain high-intensity harmonic radiation with an adjustable ellipticity,which provides an opportunity for syntheses of circularly polarized attosecond pulses.

CONSTRAINED QUADRILATERAL NONCONFORMING ROTATED Q1 ELEMENT

In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated Q1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigate the consistency, approximation, superclose property, discrete Green＇s function and superconvergence of this element. Moreover, we propose a new postprocessing technique and apply it to this element. It is proved that the postprocessed discrete solution is superconvergent under a mild assumption on the mesh.

Label Recovery and Trajectory Designable Network for Transfer Fault Diagnosis of Machines With Incorrect Annotation

The success of deep transfer learning in fault diagnosis is attributed to the collection of high-quality labeled data from the source domain.However,in engineering scenarios,achieving such high-quality label annotation is difficult and expensive.The incorrect label annotation produces two negative effects:1)the complex decision boundary of diagnosis models lowers the generalization performance on the target domain,and2)the distribution of target domain samples becomes misaligned with the false-labeled samples.To overcome these negative effects,this article proposes a solution called the label recovery and trajectory designable network(LRTDN).LRTDN consists of three parts.First,a residual network with dual classifiers is to learn features from cross-domain samples.Second,an annotation check module is constructed to generate a label anomaly indicator that could modify the abnormal labels of false-labeled samples in the source domain.With the training of relabeled samples,the complexity of diagnosis model is reduced via semi-supervised learning.Third,the adaptation trajectories are designed for sample distributions across domains.This ensures that the target domain samples are only adapted with the pure-labeled samples.The LRTDN is verified by two case studies,in which the diagnosis knowledge of bearings is transferred across different working conditions as well as different yet related machines.The results show that LRTDN offers a high diagnosis accuracy even in the presence of incorrect annotation.

Granular behaviour under bi-directional shear with constant vertical stress and constant volume

This paper aims to investigate the role of bi-directional shear in the mechanical behaviour of granular materials and macro-micro relations by conducting experiments and discrete element method(DEM)modelling.The bi-directional shear consists of a static shear consolidation and subsequent shear under constant vertical stress and constant volume conditions.A side wall node loading method is used to exert bi-directional shear of various angles.The results show that bi-directional shear can significantly influence the mechanical behaviour of granular materials.However,the relationship between bidirectional shear and mechanical responses relies on loading conditions,i.e.constant vertical stress or constant volume conditions.The stress states induced by static shear consolidation are affected by loading angles,which are enlarged by subsequent shear,consistent with the relationship between bidirectional shear and principal stresses.It provides evidence for the dissipation of stresses accompanying static liquefaction of granular materials.The presence of bi-directional principal stress rotation(PSR)is demonstrated,which evidences why the bi-directional shear of loading angles with components in two directions results in faster dissipations of stresses with static liquefaction.Contant volume shearing leads to cross-anisotropic stress and fabric at micro-contacts,but constant vertical stress shearing leads to complete anisotropic stress and fabric at micro-contacts.It explains the differentiating relationship between stress-strain responses and fabric anisotropy under these two conditions.Micromechanical signatures such as the slip state of micro-contacts and coordination number are also examined,providing further insights into understanding granular behaviour under bi-directional shear.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term(up to 30 days)predictions of Earth Rotation Parameters(ERPs)such as Polar Motion(PM:PMX and PMY)play an essential role in real-time applications related to high-precision reference frame conversion.Currently,least squares(LS)+auto-regressive(AR)hybrid method is one of the main techniques of PM prediction.Besides,the weighted LS+AR hybrid method performs well for PM short-term prediction.However,the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model.In this study,we have derived a modified stochastic model for the LS+AR hybrid method,namely the weighted LS+weighted AR hybrid method.By using the PM data products of IERS EOP 14 C04,the numerical results indicate that for PM short-term forecasting,the proposed weighted LS+weighted AR hybrid method shows an advantage over both the LS+AR hybrid method and the weighted LS+AR hybrid method.Compared to the mean absolute errors(MAEs)of PMX/PMY sho rt-term prediction of the LS+AR hybrid method and the weighted LS+AR hybrid method,the weighted LS+weighted AR hybrid method shows average improvements of 6.61%/12.08%and 0.24%/11.65%,respectively.Besides,for the slopes of the linear regression lines fitted to the errors of each method,the growth of the prediction error of the proposed method is slower than that of the other two methods.

NONCONFORMING QUADRILATERAL ROTATED ELEMENT FOR REISSNER-MINDLIN PLATE

In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.

A V-CYCLE MUTIGRID FOR QUADRILATERAL ROTATED Q_1 ELEMENT WITH NUMERICAL INTEGRATION

In this paper, a V-cycle multigrid method is presented for quadrilateral rotated elements with numerical integration.

MATHEMATICAL ANALYSIS FOR QUADRILATERAL ROTATED Q_1 ELEMENT Ⅲ: THE EFFECT OF NUMERICAL INTEGRATION

This is the third part of the paper for the rotated Q1 nonconforming element on quadrilateral meshes for general second order elliptic problems. Some optimal numerical formulas are presented and analyzed. The novelty is that it includes a formula with only two sampling points which excludes even a Q1 unisolvent set. It is the optimal numerical integration formula over a quadrilateral mesh with least sampling points up to now.

ROTATED COMPLEX EMPIRICAL ORTHOGONAL FUNCTION(RCEOF)ANALYSIS:THEORY AND EXAMPLES—PART I

In this paper,a new diagnostic method,the rotated complex empirical orthogonal function (RCEOF)analysis is developed.The general principle and the mathematical foundation of RCEOF are discussed.