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Weighted Probability Density Estimator with Updated Bandwidths

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Journal of Systems science & Complexity 2024年第2期37卷 886-906页

作者： WU Yi YU Wei WANG Xuejun PRAKASA RAO B L S school of big data and Artificial Intelligence Chizhou UniversityChizhou 247000China school of big data and Statistics Anhui UniversityHefei 230601China CR Rao Advanced Institute of mathematics Statistics and Computer ScienceHyderabad 500046India

In this paper,the authors study a class of weighted version of probability density *** is shown that the weighted estimator contains some existing estimators of probability density,no matter they are recursive or *** statistical results including weak consistency,strong consistency,rate of strong consistency,and asymptotic normality are established under some mild ***,the random weighted estimator is also *** numerical simulations and a real data analysis are presented to study the numerical performances of the estimators.

关键词： Asymptotic normality consistency numerical simulation probability density real data analysis updated bandwidths weighted estimator

On the convergence of tracking differentiator with multiple stochastic disturbances

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science China(Information sciences) 2024年第2期67卷 157-169页

作者： Zehao WU Huacheng ZHOU Baozhu GUO Feiqi DENG school of mathematics and big data Foshan University school of mathematics and Statistics Central South University Academy of mathematics and Systems science Chinese Academy of Sciences Systems Engineering Institute South China University of Technology

This paper investigates the convergence, noise-tolerance, and filtering performance of a tracking differentiator in the presence of multiple stochastic disturbances for the first time. We consider a general case wherein the input signal is corrupted by additive colored noise, and the tracking differentiator is disturbed by additive colored noise and white noise. The tracking differentiator is shown to track the input signal and its generalized derivatives in the mean square sense. Further, the almost sure convergence can be achieved when the stochastic noise affecting the input signal is vanishing. Herein, numerical simulations are performed to validate the theoretical results.

关键词： tracking differentiator convergence noise-tolerance filtering performance multiple stochastic disturbances

Computing Persistent Homology by Spanning Trees and Critical Simplices

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Research 2024年第2期2023卷 519-527页

作者： Dinghua Shi Zhifeng Chen Chuang Ma Guanrong Chen Department of mathematics Cllege of ScienceShanghai UniversityShanghaiChina school of big data Fuzhou University of International Studies and TradeFuzhouChina Department of data science and big data Technology School of InternetAnhui UniversityHefeiChina Department of Electrical Engineering City University of Hong KongHong KongChina

Topological data analysis can extract effective information from higher-dimensional *** mathematical basis is persistent *** persistent homology can calculate topological features at different spatiotemporal scales of the dataset,that is,establishing the integrated taxonomic relation among points,lines,and ***,the simplicial network composed of all-order simplices in a simplicial complex is *** the sequence of nested simplicial subnetworks can be regarded as a discrete Morse function from the simplicial network to real values,a method based on the concept of critical simplices can be developed by searching all-order spanning *** this new method,not only the Morse function values with the theoretical minimum number of critical simplices can be obtained,but also the Betti numbers and composition of all-order cavities in the simplicial network can be calculated ***,this method is used to analyze some examples and compared with other methods,showing its effectiveness and feasibility.

关键词： Morse establishing topological

L_(1)-Smooth SVM with Distributed Adaptive Proximal Stochastic Gradient Descent with Momentum for Fast Brain Tumor Detection

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Computers, Materials & Continua 2024年第5期79卷 1975-1994页

作者： Chuandong Qin Yu Cao Liqun Meng school of mathematics and Information science North Minzu UniversityYinchuan750021China Ningxia Key Laboratory of Intelligent Information and big data Processing Yinchuan750021China

Brain tumors come in various types,each with distinct characteristics and treatment approaches,making manual detection a time-consuming and potentially ambiguous *** tumor detection is a valuable tool for gaining a deeper understanding of tumors and improving treatment *** learning models have become key players in automating brain tumor *** descent methods are the mainstream algorithms for solving machine learning *** this paper,we propose a novel distributed proximal stochastic gradient descent approach to solve the L_(1)-Smooth Support Vector Machine(SVM)classifier for brain tumor ***,the smooth hinge loss is introduced to be used as the loss function of *** avoids the issue of nondifferentiability at the zero point encountered by the traditional hinge loss function during gradient descent ***,the L_(1) regularization method is employed to sparsify features and enhance the robustness of the ***,adaptive proximal stochastic gradient descent(PGD)with momentum,and distributed adaptive PGDwithmomentum(DPGD)are proposed and applied to the L_(1)-Smooth *** computing is crucial in large-scale data analysis,with its value manifested in extending algorithms to distributed clusters,thus enabling more efficient processing ofmassive amounts of *** DPGD algorithm leverages Spark,enabling full utilization of the computer’s multi-core *** to its sparsity induced by L_(1) regularization on parameters,it exhibits significantly accelerated convergence *** the perspective of loss reduction,DPGD converges faster than *** experimental results show that adaptive PGD withmomentumand its variants have achieved cutting-edge accuracy and efficiency in brain tumor ***-trained models,both the PGD andDPGD outperform other models,boasting an accuracy of 95.21%.

关键词： Support vector machine proximal stochastic gradient descent brain tumor detection distributed computing

Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

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Applied mathematics(A Journal of Chinese Universities) 2024年第1期39卷 98-113页

作者： LIU Zai-ming GENG Bing-zhen WANG Shi-jie school of mathematics and Statistics Central South UniversityChangsha 410083China school of big data and Statistics Anhui UniversityHefei 230601China

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily *** some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite *** we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

关键词： bidimensional risk model asymptotic formula subexponential distribution consistently varying tail ruin probability

Cohomology groups of a new class of Kadison-Singer algebras

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science China mathematics 2024年第3期67卷 593-606页

作者： Guangyu An Xing Cheng Jun Sheng school of mathematics and data science Shaanxi University of Science and TechnologyXi’an 710021China

Let N be a maximal discrete nest on an infinite-dimensional separable Hilbert space H,ξ=∑^(∞)_(n=1)en/2n be a separating vector for the commutant N',E_(ξ)be the projection from H onto the subspace[Cξ]spanned by the vectorξ,and Q be the projection from K=H⊕H⊕H onto the closed subspace{(η,η,η)^(T):η∈H}.Suppose that L is the projection lattice generated by the projections(E_(ξ) 0 0 0 0 0 0 0 0),{(E 0 0 0 0 0 0 0 0):E∈N},(I 0 0 0 I 0 0 0 0) and *** show that L is a Kadison-Singer lattice with the trivial ***,we prove that every n-th bounded cohomology group H~n(AlgL,B(K))with coefficients in B(K)is trivial for n≥1.

关键词： Kadison-Singer algebra Kadison-Singer lattice derivation cohomology group

Perpendicular-Cutdepth:Perpendicular Direction Depth Cutting data Augmentation Method

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Computers, Materials & Continua 2024年第4期79卷 927-941页

作者： Le Zou Linsong Hu Yifan Wang Zhize Wu Xiaofeng Wang Anhui Provincial Engineering Laboratory of big data Technology Application forUrban Infrastructure School ofArtificial Intelligence and Big DataHefei UniversityHefei230601China Institute of Applied Optimization School of Artificial Intelligence and Big DataHefei UniversityHefei230601China

Depth estimation is an important task in computer *** data at scale for monocular depth estimation is challenging,as this task requires simultaneously capturing RGB images and depth ***,data augmentation is crucial for this *** data augmentationmethods often employ pixel-wise transformations,whichmay inadvertently disrupt edge *** this paper,we propose a data augmentationmethod formonocular depth estimation,which we refer to as the Perpendicular-Cutdepth *** method involves cutting realworld depth maps along perpendicular directions and pasting them onto input images,thereby diversifying the data without compromising edge *** validate the effectiveness of the algorithm,we compared it with existing convolutional neural network(CNN)against the current mainstream data augmentation ***,to verify the algorithm’s applicability to Transformer networks,we designed an encoder-decoder network structure based on Transformer to assess the generalization of our proposed *** results demonstrate that,in the field of monocular depth estimation,our proposed method,Perpendicular-Cutdepth,outperforms traditional data *** the indoor dataset NYU,our method increases accuracy from0.900 to 0.907 and reduces the error rate from0.357 to *** the outdoor dataset KITTI,our method improves accuracy from 0.9638 to 0.9642 and decreases the error rate from 0.060 to 0.0598.

关键词： Perpendicular depth estimation data augmentation

Temporal Second-order Scheme for a Hidden-memory Variable Order Time Fractional Diffusion Equation with an Initial Singularity

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Acta Mathematicae Applicatae Sinica 2024年

作者： Rui-lian DU Zhi-zhong SUN school of big data Changzhou University school of mathematics Southeast University

In this work, a novel time-stepping L1 scheme is developed for recovering an initial singularity of a time fractional diffusion model with a hidden-memory variable-order Caputo’s fractional derivative. We derive an L1 formula to approximate the variable-order Caputo’s derivative, which can obtain second-order *** error estimate is analyzed strictly. For completeness, a full discrete scheme is established combined with the standard second-order central difference quotient for the spatial discretization. Numerical experiments are provided to support our theoretical results.

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Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1127-1142页

作者： Yi WU Xue Jun WANG school of big data and Artificial Intelligence Chizhou UniversityChizhou 247000P.R.China school of big data and Statistics Anhui UniversityHefei 230601P.R.China

Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real *** this paper,the Marcinkiewicz-Zygmund type weak law of large numb... 详细信息

关键词： Martingale difference random vectors weighted sums Marcinkiewicz–Zygmund type weak law of large numbers complete convergence strong law of large numbers multivariate simple linear regression model