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Yajing Li

Publications and source records attributed to Yajing Li.

17 recordsLinked to original sources

Pilot selection in the era of Virtual reality: algorithms for accurate and interpretable machine learning models

With the rapid growth of the aviation industry, there is a need for a large number of flight crew. How to select the right pilots in a cost-efficient manner has become an important research question. In the current study, twenty-three pilots were recruited from China Eastern Airlines, and 23 novices were from the community of Tsinghua University. A novel approach incorporating machine learning and virtual reality technology was applied to distinguish features between these participants with different flight skills. Results indicate that SVM with the MIC feature selection method consistently achieved the highest prediction performance on all metrics with an Accuracy of 0.93, an AUC of 0.96, and an F1 of 0.93, which outperforms four other classifier algorithms and two other feature selection methods. From the perspective of feature selection methods, the MIC method can select features with a nonlinear relationship to sampling labels, instead of a simple filter-out. Our new implementation of the SVM + MIC algorithm outperforms all existing pilot selection algorithms and perhaps provides the first implementation based on eye tracking and flight dynamics data. This study's VR simulation platforms and algorithms can be used for pilot selection and training.

cs.LG

Two-person zero-sum stochastic linear quadratic control problems with Markov chains and fractional Brownian motion in infinite horizon

This paper addresses a class of two-person zero-sum stochastic differential equations, which encompass Markov chains and fractional Brownian motion, and satisfy some monotonicity conditions over an infinite time horizon. Within the framework of forward-backward stochastic differential equations (FBSDEs) that describe system evolution, we extend the classical It$\rm\hat{o}$'s formula to accommodate complex scenarios involving Brownian motion, fractional Brownian motion, and Markov chains simultaneously. By applying the Banach fixed-point theorem and approximation methods respectively, we theoretically guarantee the existence and uniqueness of solutions for FBSDEs in infinite horizon. Furthermore, we apply the method for the first time to the optimal control problem in a two-player zero-sum game, deriving the optimal control strategies for both players by solving the FBSDEs system. Finally, we conduct an analysis of the impact of the cross-term $S(\cdot)$ in the cost function on the solution, revealing its crucial role in the optimization process.

math.OC

Multifractal scaling analyses of the spatial diffusion pattern of COVID-19 pandemic in Chinese mainland

Revealing spatiotemporal evolution regularity in the spatial diffusion of epidemics is helpful for preventing and controlling the spread of epidemics. Based on the real-time COVID-19 datasets by prefecture-level cities, this paper is devoted to exploring the multifractal scaling in spatial diffusion pattern of COVID-19 pandemic and its evolution characteristics in Chinese mainland. The ArcGIS technology and box-counting method are employed to extract spatial data and the least square regression based on rescaling probability (miu-weight method) is used to calculate fractal parameters. The results show multifractal distribution of COVID-19 pandemic in China. The generalized correlation dimension spectrums are inverse S-shaped curves, but the fractal dimension values significantly exceed the Euclidean dimension of embedding space when moment order q<<0. The local singularity spectrums are asymmetric unimodal curves, which slant to right. The fractal dimension growth curves are shown as quasi S-shaped curves. From these spectrums and growth curves, the main conclusions can be drawn as follows: First, self-similar patterns developed in the process of COVID-19 pandemic, which seem be dominated by multifractal scaling law. Second, the spatial pattern of COVID-19 across China can be characterized by global clustering with local disordered diffusion. Third, the spatial diffusion process of COVID-19 in China experienced four stages, i.e., initial stage, the rapid diffusion stage, the hierarchical diffusion stage, and finally the contraction stage. This study suggests that multifractal theory can be utilized to characterize spatio-temporal diffusion of COVID-19 pandemic, and the case analyses may be instructive for further exploring natural laws of spatial diffusion.

physics.soc-ph

A statistical fat-tail test of predicting regulatory regions in the Drosophila genome

A statistical study of cis-regulatory modules (CRMs) is presented based on the estimation of similar-word set distribution. It is observed that CRMs tend to have a fat-tail distribution. A new statistical fat-tail test with two kurtosis-based fatness coefficients is proposed to distinguish CRMs from non-CRMs. As compared with the existing fluffy-tail test, the first fatness coefficient is designed to reduce computational time, making the novel fat-tail test very suitable for long sequences and large database analysis in the post-genome time and the second one to improve separation accuracy between CRMs and non-CRMs. These two fatness coefficients may be served as valuable filtering indexes to predict CRMs experimentally.

q-bio.QM

Hypercomplex cross-correlation of DNA sequences

A hypercomplex representation of DNA is proposed to facilitate comparison of DNA sequences with fuzzy composition. Using hypercomplex number representation, conventional sequence analysis method, such as, dot matrix analysis, dynamic programming, and cross-correlation method are extended and improved to align the DNA sequences with fuzzy composition. The hypercomplex dot matrix analysis can provide more control over the degree of alignment desired. A new scoring system has been proposed to accommodate the hypercomplex number representation of DNA and integrated with dynamic programming alignment method. By using hypercomplex cross-correlation, matching and mismatching alignment information between two aligned DNA sequences are stored in the resultant real part and imaginary parts, respectively. Mismatching alignment information is particularly useful for refining consensus sequence-based motif scanning.

q-bio.QM

Low-Rank Tensor Completion Based on Bivariate Equivalent Minimax-Concave Penalty

Low-rank tensor completion (LRTC) is an important problem in computer vision and machine learning. The minimax-concave penalty (MCP) function as a non-convex relaxation has achieved good results in the LRTC problem. To makes all the constant parameters of the MCP function as variables so that futherly improving the adaptability to the change of singular values in the LRTC problem, we propose the bivariate equivalent minimax-concave penalty (BEMCP) theorem. Applying the BEMCP theorem to tensor singular values leads to the bivariate equivalent weighted tensor $Γ$-norm (BEWTGN) theorem, and we analyze and discuss its corresponding properties. Besides, to facilitate the solution of the LRTC problem, we give the proximal operators of the BEMCP theorem and BEWTGN. Meanwhile, we propose a BEMCP model for the LRTC problem, which is optimally solved based on alternating direction multiplier (ADMM). Finally, the proposed method is applied to the data restorations of multispectral image (MSI), magnetic resonance imaging (MRI) and color video (CV) in real-world, and the experimental results demonstrate that it outperforms the state-of-arts methods.

cs.CV

Two New Low Rank Tensor Completion Methods Based on Sum Nuclear Norm

The low rank tensor completion (LRTC) problem has attracted great attention in computer vision and signal processing. How to acquire high quality image recovery effect is still an urgent task to be solved at present. This paper proposes a new tensor $L_{2,1}$ norm minimization model (TLNM) that integrates sum nuclear norm (SNN) method, differing from the classical tensor nuclear norm (TNN)-based tensor completion method, with $L_{2,1}$ norm and Qatar Riyal decomposition for solving the LRTC problem. To improve the utilization rate of the local prior information of the image, a total variation (TV) regularization term is introduced, resulting in a new class of tensor $L_{2,1}$ norm minimization with total variation model (TLNMTV). Both proposed models are convex and therefore have global optimal solutions. Moreover, we adopt the Alternating Direction Multiplier Method (ADMM) to obtain the closed-form solution of each variable, thus ensuring the feasibility of the algorithm. Numerical experiments show that the two proposed algorithms are convergent and outperform compared methods. In particular, our method significantly outperforms the contrastive methods when the sampling rate of hyperspectral images is 2.5\%.

math.NA

Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recovery

Tensor sparse modeling as a promising approach, in the whole of science and engineering has been a huge success. As is known to all, various data in practical application are often generated by multiple factors, so the use of tensors to represent the data containing the internal structure of multiple factors came into being. However, different from the matrix case, constructing reasonable sparse measure of tensor is a relatively difficult and very important task. Therefore, in this paper, we propose a new tensor sparsity measure called Tensor Full Feature Measure (FFM). It can simultaneously describe the feature information of each dimension of the tensor and the related features between two dimensions, and connect the Tucker rank with the tensor tube rank. This measurement method can describe the sparse features of the tensor more comprehensively. On this basis, we establish its non-convex relaxation, and apply FFM to low rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA). LRTC and TRPCA models based on FFM are proposed, and two efficient Alternating Direction Multiplier Method (ADMM) algorithms are developed to solve the proposed model. A variety of real numerical experiments substantiate the superiority of the proposed methods beyond state-of-the-arts.

cs.CV

Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Function

Non-convex relaxation methods have been widely used in tensor recovery problems, and compared with convex relaxation methods, can achieve better recovery results. In this paper, a new non-convex function, Minimax Logarithmic Concave Penalty (MLCP) function, is proposed, and some of its intrinsic properties are analyzed, among which it is interesting to find that the Logarithmic function is an upper bound of the MLCP function. The proposed function is generalized to tensor cases, yielding tensor MLCP and weighted tensor $Lγ$-norm. Consider that its explicit solution cannot be obtained when applying it directly to the tensor recovery problem. Therefore, the corresponding equivalence theorems to solve such problem are given, namely, tensor equivalent MLCP theorem and equivalent weighted tensor $Lγ$-norm theorem. In addition, we propose two EMLCP-based models for classic tensor recovery problems, namely low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA), and design proximal alternate linearization minimization (PALM) algorithms to solve them individually. Furthermore, based on the Kurdyka-Łojasiwicz property, it is proved that the solution sequence of the proposed algorithm has finite length and converges to the critical point globally. Finally, Extensive experiments show that proposed algorithm achieve good results, and it is confirmed that the MLCP function is indeed better than the Logarithmic function in the minimization problem, which is consistent with the analysis of theoretical properties.

eess.IV

Deep neural network methods for solving forward and inverse problems of time fractional diffusion equations with conformable derivative

Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the supervise learning task, we design a new spatio-temporal function approximator with high data efficiency. L-BFGS algorithm is used to optimize our loss function, and back propagation algorithm is used to update our parameters to give our numerical solutions. For the forward problem, we can take IC/BCs as the data, and use PINN to solve the corresponding partial differential equation. Three numerical examples are are carried out to demonstrate the effectiveness of our methods. In particular, when the order of the conformable fractional derivative $α$ tends to $1$, a class of weighted PINNs is introduced to overcome the accuracy degradation caused by the singularity of solutions. For the inverse problem, we use the data obtained to train the neural network, and the estimation of parameter $λ$ in the equation is elaborated. Similarly, we give three numerical examples to show that our method can accurately identify the parameters, even if the training data is corrupted with 1\% uncorrelated noise.

math.NA

Gravitational and Autoregressive Analysis Spatial Diffusion of COVID-19 in Hubei Province, China

The spatial diffusion of epidemic disease follows distance decay law in geography, but different diffusion processes may be modeled by different mathematical functions under different spatio-temporal conditions. This paper is devoted to modeling spatial diffusion patterns of COVID-19 stemming from Wuhan city to Hubei province. The methods include gravity and spatial auto-regression analyses. The local gravity model is derived from allometric scaling and global gravity model, and then the parameters of the local gravity model are estimated by observational data and linear regression. The main results are as below. The local gravity model based on power law decay can effectively describe the diffusion patterns and process of COVID-19 in Hubei Province, and the goodness of fit of the gravity model based on negative exponential decay to the observation data is not satisfactory. Further, the goodness of fit of the model to data entirely became better and better over time, the size elasticity coefficient increases first and then decreases, and the distance attenuation exponent decreases first and then increases. Moreover, the significance of spatial autoregressive coefficient in the model is low, and the confidence level is less than 80%. The conclusions can be reached as follows. (1) The spatial diffusion of COVID-19 of Hubei bears long range effect, and the size of a city and the distance of the city to Wuhan affect the total number of confirmed cases. (2) Wuhan direct transmission is the main process in the spatial diffusion of COVID-19 in Hubei at the early stage, and the horizontal transmission between regions is not significant. (3) The effect of spatial isolation measures taken by Chinese government against the transmission of COVID-19 is obvious. This study suggests that the role of gravity should be taken into account to prevent and control epidemic disease.

physics.soc-ph

Galerkin finite element approximation for semilinear stochastic time-tempered fractional wave equations with multiplicative white noise and fractional Gaussian noise

To model wave propagation in inhomogeneous media with frequency-dependent power-law attenuation, it is needed to use the fractional powers of symmetric coercive elliptic operators in space and the Caputo tempered fractional derivative in time. The model studied in this paper is semilinear stochastic space-time fractional wave equations driven by infinite dimensional multiplicative white noise and fractional Gaussian noise, because of the potential fluctuations of the external sources. The purpose of this work is to discuss the Galerkin finite element approximation for the semilinear stochastic fractional wave equation. We first provide a complete solution theory, e.g., existence, uniqueness, and regularity. Then the space-time multiplicative white noise and fractional Gaussian noise are discretized, which results in a regularized stochastic fractional wave equation while introducing a modeling error in the mean-square sense. We further present a complete regularity theory for the regularized equation. A standard finite element approximation is used for the spatial operator, and the mean-square priori estimates for the modeling error and for the approximation error to the solution of the regularized problem are established.

math.NA

Interplay of bias-driven charging and the vibrational Stark effect in molecular junctions

We observe large, reversible, bias driven changes in the vibrational energies of PCBM, based on simultaneous transport and surface-enhanced Raman spectroscopy (SERS) measurements on PCBM-gold junctions. A combination of linear and quadratic shifts in vibrational energies with voltage is analyzed and compared with similar measurements involving C60-gold junctions. A theoretical model based on density functional theory (DFT) calculations suggests that both a vibrational Stark effect and bias-induced charging of the junction contribute to the shifts in vibrational energies. In the PCBM case, a linear vibrational Stark effect is observed due to the permanent electric dipole moment of PCBM. The vibrational Stark shifts shown here for PCBM junctions are comparable to or larger than the charging effects that dominate in C60 junctions.

cond-mat.mes-hall

Galerkin Finite Element Approximations for Stochastic Space-Time Fractional Wave Equations

The traditional wave equation models wave propagation in an ideal conducting medium. For characterizing the wave propagation in inhomogeneous media with frequency dependent power-law attenuation, the space-time fractional wave equation appears; further incorporating the additive white Gaussian noise coming from many natural sources leads to the stochastic space-time fractional wave equation. This paper discusses the Galerkin finite element approximations for the stochastic space-time fractional wave equation forced by an additive space-time white noise. We firstly discretize the space-time additive noise, which introduces a modeling error and results in a regularized stochastic space-time fractional wave equation; then the regularity of the regularized equation is analyzed. For the discretization in space, the finite element approximation is used and the definition of the discrete fractional Laplacian is introduced. We derive the mean-squared $L^2$-norm priori estimates for the modeling error and for the approximation error to the solution of the regularized problem; and the numerical experiments are performed to confirm the estimates. For the time-stepping, we calculate the analytically obtained Mittag-Leffler type function.

math.NA

A statistical thin-tail test of predicting regulatory regions in the Drosophila genome

Background: The identification of transcription factor binding sites (TFBSs) and cis-regulatory modules (CRMs) is a crucial step in studying gene expression, but the computational method attempting to distinguish CRMs from NCNRs still remains a challenging problem due to the limited knowledge of specific interactions involved. Methods: The statistical properties of cis-regulatory modules (CRMs) are explored by estimating the similar-word set distribution with overrepresentation (Z-score). It is observed that CRMs tend to have a thin-tail Z-score distribution. A new statistical thin-tail test with two thinness coefficients is proposed to distinguish CRMs from non-coding non-regulatory regions (NCNRs). Results: As compared with the existing fluffy-tail test, the first thinness coefficient is designed to reduce computational time, making the novel thin-tail test very suitable for long sequences and large database analysis in the post-genome time and the second one to improve the separation accuracy between CRMs and NCNRs. These two thinness coefficients may serve as valuable filtering indexes to predict CRMs experimentally. Conclusions: The novel thin-tail test provides an efficient and effective means for distinguishing CRMs from NCNRs based on the specific statistical properties of CRMs and can guide future experiments aimed at finding new CRMs in the post-genome time.

q-bio.QM

Dark plasmons in hot spot generation and polarization in interelectrode nanoscale junctions

Nanoscale gaps between adjacent metallic nanostructures give rise to extraordinarily large field enhancements, known as "hot spots", upon illumination. Incident light with the electric field polarized across the gap (along the interparticle axis) is generally known to induce the strongest surface enhanced Raman spectroscopy (SERS) enhancements. However, here we show that for a nanogap located within a nanowire linking extended Au electrodes, the greatest enhancement and resulting SERS emission occurs when the electric field of the incident light is polarized along the gap (transverse to the interelectrode axis). This surprising and counterintuitive polarization dependence results from a strong dipolar plasmon mode that resonates transversely across the nanowire, coupling with dark multipolar modes arising from subtle intrinsic asymmetries in the nanogap. These modes give rise to highly reproducible SERS enhancements at least an order of magnitude larger than the longitudinal modes in these structures.

cond-mat.mes-hall