Remaining Useful Life Prediction of Rail Based on Improved Pulse Separable Convolution Enhanced Transformer Encoder

In order to prevent possible casualties and economic loss, it is critical to accurate prediction of the Remaining Useful Life (RUL) in rail prognostics health management. However, the traditional neural networks is difficult to capture the long-term dependency relationship of the time series in the modeling of the long time series of rail damage, due to the coupling relationship of multi-channel data from multiple sensors. Here, in this paper, a novel RUL prediction model with an enhanced pulse separable convolution is used to solve this issue. Firstly, a coding module based on the improved pulse separable convolutional network is established to effectively model the relationship between the data. To enhance the network, an alternate gradient back propagation method is implemented. And an efficient channel attention (ECA) mechanism is developed for better emphasizing the useful pulse characteristics. Secondly, an optimized Transformer encoder was designed to serve as the backbone of the model. It has the ability to efficiently understand relationship between the data itself and each other at each time step of long time series with a full life cycle. More importantly, the Transformer encoder is improved by integrating pulse maximum pooling to retain more pulse timing characteristics. Finally, based on the characteristics of the front layer, the final predicted RUL value was provided and served as the end-to-end solution. The empirical findings validate the efficacy of the suggested approach in forecasting the rail RUL, surpassing various existing data-driven prognostication techniques. Meanwhile, the proposed method also shows good generalization performance on PHM2012 bearing data set.

Separable Symmetric Tensors and Separable Anti-symmetric Tensors

In this paper,we first initialize the S-product of tensors to unify the outer product,contractive product,and the inner product of tensors.Then,we introduce the separable symmetry tensors and separable anti-symmetry tensors,which are defined,respectively,as the sum and the algebraic sum of rank-one tensors generated by the tensor product of some vectors.We offer a class of tensors to achieve the upper bound for rank(A)≤6 for all tensors of size 3×3×3.We also show that each 3×3×3 anti-symmetric tensor is separable.

MSSTNet:Multi-scale facial videos pulse extraction network based on separable spatiotemporal convolution and dimension separable attention

Background The use of remote photoplethysmography(rPPG)to estimate blood volume pulse in a noncontact manner has been an active research topic in recent years.Existing methods are primarily based on a singlescale region of interest(ROI).However,some noise signals that are not easily separated in a single-scale space can be easily separated in a multi-scale space.Also,existing spatiotemporal networks mainly focus on local spatiotemporal information and do not emphasize temporal information,which is crucial in pulse extraction problems,resulting in insufficient spatiotemporal feature modelling.Methods Here,we propose a multi-scale facial video pulse extraction network based on separable spatiotemporal convolution(SSTC)and dimension separable attention(DSAT).First,to solve the problem of a single-scale ROI,we constructed a multi-scale feature space for initial signal separation.Second,SSTC and DSAT were designed for efficient spatiotemporal correlation modeling,which increased the information interaction between the long-span time and space dimensions;this placed more emphasis on temporal features.Results The signal-to-noise ratio(SNR)of the proposed network reached 9.58dB on the PURE dataset and 6.77dB on the UBFC-rPPG dataset,outperforming state-of-the-art algorithms.Conclusions The results showed that fusing multi-scale signals yielded better results than methods based on only single-scale signals.The proposed SSTC and dimension-separable attention mechanism will contribute to more accurate pulse signal extraction.

SepFE:Separable Fusion Enhanced Network for Retinal Vessel Segmentation

The accurate and automatic segmentation of retinal vessels fromfundus images is critical for the early diagnosis and prevention ofmany eye diseases,such as diabetic retinopathy(DR).Existing retinal vessel segmentation approaches based on convolutional neural networks(CNNs)have achieved remarkable effectiveness.Here,we extend a retinal vessel segmentation model with low complexity and high performance based on U-Net,which is one of the most popular architectures.In view of the excellent work of depth-wise separable convolution,we introduce it to replace the standard convolutional layer.The complexity of the proposed model is reduced by decreasing the number of parameters and calculations required for themodel.To ensure performance while lowering redundant parameters,we integrate the pre-trained MobileNet V2 into the encoder.Then,a feature fusion residual module(FFRM)is designed to facilitate complementary strengths by enhancing the effective fusion between adjacent levels,which alleviates extraneous clutter introduced by direct fusion.Finally,we provide detailed comparisons between the proposed SepFE and U-Net in three retinal image mainstream datasets(DRIVE,STARE,and CHASEDB1).The results show that the number of SepFE parameters is only 3%of U-Net,the Flops are only 8%of U-Net,and better segmentation performance is obtained.The superiority of SepFE is further demonstrated through comparisons with other advanced methods.

Appearance Based Dynamic Hand Gesture Recognition Using 3D Separable Convolutional Neural Network

Appearance-based dynamic Hand Gesture Recognition(HGR)remains a prominent area of research in Human-Computer Interaction(HCI).Numerous environmental and computational constraints limit its real-time deployment.In addition,the performance of a model decreases as the subject’s distance from the camera increases.This study proposes a 3D separable Convolutional Neural Network(CNN),considering the model’s computa-tional complexity and recognition accuracy.The 20BN-Jester dataset was used to train the model for six gesture classes.After achieving the best offline recognition accuracy of 94.39%,the model was deployed in real-time while considering the subject’s attention,the instant of performing a gesture,and the subject’s distance from the camera.Despite being discussed in numerous research articles,the distance factor remains unresolved in real-time deployment,which leads to degraded recognition results.In the proposed approach,the distance calculation substantially improves the classification performance by reducing the impact of the subject’s distance from the camera.Additionally,the capability of feature extraction,degree of relevance,and statistical significance of the proposed model against other state-of-the-art models were validated using t-distributed Stochastic Neighbor Embedding(t-SNE),Mathew’s Correlation Coefficient(MCC),and the McNemar test,respectively.We observed that the proposed model exhibits state-of-the-art outcomes and a comparatively high significance level.

Accuracy analysis of the optimal separable approximation method of one-way wave migration

An approximation for the one-way wave operator takes the form of separated space and wave-number variables and makes it possible to use the FFT, which results in a great improvement in the computational efficiency. From the function approximation perspective, the OSA method shares the same separable approximation format to the one-way wave operator as other separable approximation methods but it is the only global function approximation among these methods. This leads to a difference in the phase error curve, impulse response, and migration result from other separable approximation methods. The difference is that the OSA method has higher accuracy, and the sensitivity to the velocity variation declines with increasing order.

Preparation and Photocatalytic Properties of Magnetically Separable TiO_2 Supported on Nickel Ferrite

A magnetically separable photocatalyst TiO2/SiO2/NiFe2O4 （TSN） with a typical ferromagnetic hysteresis was prepared by a liquid catalytic phase transfer method. When the intensity of applied magnetic field weakened to zero, the remnant magnetism of the prepared photocatalyst faded to zero. The photocatalytst can be separated from water when an external magnetic field is added and redispersed into aqueous solution after the external magnetic field is eliminated, that makes the photocatalysts promising for wastewater treatment. Transmission electron microscope （TEM） and X-ray diffractometer （XRD） were used to characterize the structure of the photocatalyst indicating that the magnetic SiOffNiFe204 （SN） particle was compactly enveloped by P-25 titania and Tit2 shell was formed. The magnetic composite showed high photocatalytic activity for the degradation of methyl orange in water. A thin SiO2 layer between NiFe2O4 and TiO2 shell prevented effectively the leakage of charges from TiO2 particles to NiFe2O4, which gave rise to the increase in photocatalytic activity. Moreover, the experiment on recycled use of TSN demonstrated a good repeatability of the photocatalytic activity.

基于FPGA的Separable Gabor滤波器设计

指纹图像滤波是指纹图像增强耗时最大的过程,为提高指纹滤波的实时性,提出了一种Separable Gabor滤波器,将二维的Gabor滤波器分别拆分为一维带通滤波器和一维低通滤波器.两种滤波器在互相垂直的方向上分别对指纹图像进行卷积.该算法用硬件描述语言在可编程逻辑门阵列(FPGA)上实现.为了节省存储空间,引入了坐标变换和方向变换.实验结果表明,对于同一幅指纹图像,Separable Gabor滤波器和Gabor滤波器的处理结果相似,且前者的处理速度是后者的1.9到4倍,存储空间的消耗仅为Gabor滤波器的16.4%,提高了滤波速度的同时极大的降低了硬件成本.

Variable Separation and Derivative-Dependent Functional Separable Solutions to Generalized Nonlinear Wave Equations

Using the generalized conditional symmetry approach, we obtain a number of new generalized (1+1)-dimensional nonlinear wave equations that admit derivative-dependent functional separable solutions.

Extension of Variable Separable Solutions for Nonlinear Evolution Equations

We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.

Classification and Functional Separable Solutions to Extended Nonlinear Wave Equations

The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed.

Novel Visible Light Driven Magnetically Separable Graphene/BiOBr Composite Photocatalysts with Enhanced Photocatalytic Activity

Novel visible light magnetically separable graphene-based BiOBr composite photocatalysts were prepared for the first time. The structures, morphologies and optical properties were characterized by field emission scanning electron microscopy, transmission electron microscopy, X-ray diffraction and ultravioletvisible spectroscopy, respectively. The photocatalytic activity of the resulting samples was evaluated by degradation of tetracycline under visible light irradiation. An appropriate amount of introduced graphene can significantly enhance the photocatalytic activities. The enhanced activities were mainly attributed to the enhanced light absorption and the interfacial transfer of electrons. The corresponding photocatalytic mechanism was proposed based on the results.

INVARIANT SUBSPACES AND GENERALIZED FUNCTIONAL SEPARABLE SOLUTIONS TO THE TWO-COMPONENT b-FAMILY SYSTEM

Invariant subspace method is exploited to obtain exact solutions of the two- component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Furthermore, blow up and behavior of those exact solutions are also investigated.

γ-Fe_2O_3:A magnetic separable catalyst for synthesis of 5-substituted 1H-tetrazoles from nitriles and sodium azide

An efficient route for the synthesis of 5-substituted 1H-tetrazole via[2＋3]cycloaddition of nitriles and sodium azide is reported usingγ-Fe2O3 nanoparticles as a magnetic separable catalyst.Under optimized conditions,the moderate to good yields（71-95%） can be obtained.The catalyst can be easily separated by a magnet and reused for several circles.

3D wavefield extrapolation with optimal separable approximation

An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on the optimal separable approximation presented in this paper, the mixed domain algorithm with forward and inverse Fourier transforms is used to construct the 3D one-way wavefield extrapolation operator. This operator separates variables in the wavenumber and spatial domains. The phase shift operation is implemented in the wavenumber domain while the time delay for lateral velocity variation is corrected in the spatial domain. The impulse responses of the one-way wave operator show that the numeric computation is consistent with the theoretical value for each velocity, revealing that the operator constructed with the optimal separable approximation can be applied to lateral velocity variations for the case of small steps. Imaging results of the SEG/EAGE model and field data indicate that the new method can be used to image complex structure.

SOME RESULTS RELATED TO THE SEPARABLE QUOTIENT PROBLEM

The problem whether every infinite dimensional Banach space has an infinite dimensional separable quotient space has remained unsolved for a long time. In this paper we prove: the Banach space X has an infinite dimensional separable quotient if and only if X has an infinite dimensional separable quasicomplemented subspace, also if and only if there exists a Banach space Y and a bounded linear operator T is an element of B(Y,X such that the range of T is nonclosed and dense in X. Besides, the other relevant questions for such spaces e.g. the question on operator ideals that on H.I.(hereditarily indecomposable) spaces, that on invariant subspaces of operators, etc, are also discussed.

Optical transfer function analysis of circular-pupil wavefront coding systems with separable phase masks

This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates. Based on the stationary phase method, the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function. Finally, a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.

Entanglement distribution using three-mode separable state with imperfect equipments

We show a scheme to distribute the entanglement by using three-mode separable Gaussian state prepared with imperfect equipments. The scheme achieves the aim that the entanglement is distributed between two distant parties with only Gaussian operations and linear optics elements. Moreover, we analyse the logarithmic negativity of the entanglement shared between the two parties when the systems are imperfect and arrive at the conclusion that the logarithmic negativity is asymptotically stable with fluctuations within a certain space range.

The Offset-Domain Prestack Depth Migration with Optimal Separable Approximation

The offset-domain prestack depth migration with optimal separable approximation, based on the double square root equation, is used to image complex media with large and rapid velocity variations. The method downward continues the source and the receiver wavefields simultaneously. The mixed domain algorithm with forward Fourier and inverse Fourier transform is used to construct the double square root equation wavefield extrapolation operator. This operator separates variables in the wave number domain and variables in the space domain. The phase operation is implemented in the wave number domain, whereas the time delay for lateral velocity variation is corrected in the space domain. The migration algorithm is efficient since the seismic data are not computed shot by shot. The data set test of the Marmousi model indicates that the offset-domain migration provides a satisfied seismic migration section on which complex geologic structures are imaged in media with large and rapid lateral velocity variations.

Note on maximal distance separable codes

In this paper, the maximal length of maximal distance separable (MDS) codes is studied, and a new upper bound formula of the maximal length of MDS codes is obtained. Especially, the exact values of the maximal length of MDS codes in some parameters are given.