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The stable Auslander-Reiten components of certain monomorphism categories

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Science China Mathematics 2024年第3期67卷 505-526页

作者： Rasool Hafezi Yi Zhang School of Mathematics and statistics Nanjing University of Information Science and TechnologyNanjing 210044China

Let Λ be an Artin algebra and let Gprj-Λ denote the class of all the finitely generated Gorenstein projective Λ-modules. In this paper, we study the components of the stable Auslander-Reiten quiver of a certain subcategory of the monomorphism category S(Gprj-Λ) containing boundary vertices. We describe the shape of such components. It is shown that certain components are linked to the orbits of an auto-equivalence on the stable category Gprj. In particular, for the finite components, we show that under certain mild conditions,their cardinalities are divisible by 3. We see that this three-periodicity phenomenon reoccurs several times in the paper.

关键词： monomorphism category almost split sequence Auslander-Reiten quiver Gorenstein projective module

Data-Driven Earthquake Multi-impact Modeling: A Comparison of Models

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International Journal of Disaster Risk Science 2024年第3期15卷 421-433页

作者： Hamish Patten Max Anderson Loake David Steinsaltz information Management International Federation of Red Cross and Red Crescent Societies (IFRC) Department of statistics University of Oxford

In this study, a broad range of supervised machine learning and parametric statistical, geospatial, and non-geospatial models were applied to model both aggregated observed impact estimate data and satellite image-derived geolocated building damage data for earthquakes, via regression-and classification-based models, respectively. For the aggregated observational data, models were ranked via predictive performance of mortality, population displacement, building damage, and building destruction for 375 observations across 161 earthquakes in 61 countries. For the satellite image-derived data, models were ranked via classification performance(damaged/unaff ected) of 369,813 geolocated buildings for 26 earthquakes in 15 countries. Grouped k-fold, 3-repeat cross validation was used to ensure out-of-sample predictive performance. Feature importance of several variables used as proxies for vulnerability to disasters indicates covariate utility. The 2023 Türkiye–Syria earthquake event was used to explore model limitations for extreme events. However, applying the AdaBoost model on the 27,032 held-out buildings of the 2023 Türkiye–Syria earthquake event, predictions had an AUC of 0.93. Therefore, without any geospatial, building-specific, or direct satellite image information, this model accurately classified building damage,with significantly improved performance over satellite image trained models found in the literature.

关键词： Disaster risk modeling Earthquake impact models Machine learning Disaster statistics Satellite image-derived building damage

On Leray's problem in an infinitely long pipe with the Navier-slip boundary condition

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Science China Mathematics 2024年第4期67卷 819-854页

作者： Zijin Li Xinghong Pan Jiaqi Yang School of Mathematics and statistics Nanjing University of Information Science and TechnologyNanjing 210044China School of Mathematics and Key Laboratory of Ministry of Industry and information Technology Nanjing University of Aeronautics and AstronauticsNanjing 211106China School of Mathematics and statistics Northwestern Polytechnical UniversityXi'an 710129China

The original Leray’s problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe,which approach the Poiseuille flow subject to the no-slip boundary condition at spatial *** this paper,the same problem with the Navier-slip boundary condition instead of the no-slip boundary condition,is *** to the complexity of the boundary condition,some new ideas,presented as follows,are introduced to handle the extra difficulties caused by boundary ***,the Poiseuille flow in the semi-infinite straight pipe with the Navier-slip boundary condition will be introduced,which will serve as the asymptotic profile of the solution to the generalized Leray’s problem at spatial ***,a solenoidal vector function defined in the whole pipe,satisfying the Navierslip boundary condition,having the designated flux and equalling the Poiseuille flow at a large distance,will be carefully *** plays an important role in reformulating our ***,the energy estimates depend on a combined L2-estimate of the gradient and the stress tensor of the velocity.

关键词： stationary Navier-Stokes system Navier-slip boundary condition Leray's problem

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An integrable generalization of the Fokas–Lenells equation:Darboux transformation, reduction and explicit soliton solutions

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Chinese Physics B 2024年第7期33卷 117-124页

作者：魏姣耿献国王鑫 School of Mathematics and statistics Zhengzhou UniversityZhengzhou 450001China School of Mathematics and information Science Zhongyuan University of TechnologyZhengzhou 450007China

Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.

关键词： Darboux transformation soliton solutions generalized Fokas–Lenells equation

Curve Classification Based onMean-Variance Feature Weighting and Its Application

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Computers, Materials & Continua 2024年第5期79卷 2465-2480页

作者： Zewen Zhang Sheng Zhou Chunzheng Cao School of Mathematics and statistics Nanjing University of Information Science and TechnologyNanjing210044China Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and TechnologyNanjing210044China

The classification of functional data has drawn much attention in recent *** main challenge is representing infinite-dimensional functional data by finite-dimensional features while utilizing those features to achieve better classification *** this paper,we propose a mean-variance-based(MV)feature weighting method for classifying functional data or functional *** the feature extraction stage,each sample curve is approximated by B-splines to transfer features to the coefficients of the spline *** that,a feature weighting approach based on statistical principles is introduced by comprehensively considering the between-class differences and within-class variations of the *** also introduce a scaling parameter to adjust the gap between the weights of *** new feature weighting approach can adaptively enhance noteworthy local features while mitigating the impact of confusing *** algorithms for feature weighted K-nearest neighbor and support vector machine classifiers are both ***,the new approach can be well integrated into existing functional data classifiers,such as the generalized functional linear model and functional linear discriminant analysis,resulting in a more accurate *** performance of the mean-variance-based classifiers is evaluated by simulation studies and real *** results show that the newfeatureweighting approach significantly improves the classification accuracy for complex functional data.

关键词： Functional data analysis classification feature weighting B-splines

A Fast Algorithm for Computing the Deficiency Number of a Mahjong Hand

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Chinese Journal of Electronics 2024年

作者： Xueqing YAN Yongming LI Sanjiang LI School of Computer Science Shaanxi Normal University School of Mathematics and statistics Shaanxi Normal University centre for Quantum Software and information Faculty of Engineering and Information Technology University of Technology Sydney

The tile-based multiplayer game Mahjong is widely played in Asia and has also become increasingly popular worldwide. Face-to-face or online, each player begins with a hand of 13 tiles and players draw and discard tiles in turn until they complete a winning hand. An important notion in Mahjong is the deficiency number(*** number in Japanese Mahjong) of a hand, which estimates how many tile changes are necessary to complete the hand into a winning hand. The deficiency number plays an essential role in major decision-making tasks such as selecting a tile to discard. This paper proposes a fast algorithm for computing the deficiency number of a Mahjong hand. Compared with the baseline algorithm, the new algorithm is usually 100 times faster and, more importantly,respects the agent's knowledge about available tiles. The algorithm can be used as a basic procedure in all Mahjong variants by both rule-based and machine learning-based Mahjong AI.

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A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

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Journal of Computational Mathematics 2024年第3期42卷 784-813页

作者： Bo Zhang Yuelin Gao Xia Liu Xiaoli Huang School of Civil and Hydraulic Engineering School of Mathematics and StatisticsNingxia UniversityYinchuan 750021China School of Mathematics and information Science North Minzu UniversityYinchuan 750021China Ningxia Province Key Laboratory of Intelligent information and Data Processing Yinchuan 750021China School of Mathematics and statistics Ningxia UniversityYinchuan 750021China

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network ***,most of the solutions to such problems are often designed for their unique *** paper puts forward a new global optimization algorithm for solving the problem *** first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer ***,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative *** that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is ***,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

关键词： Global optimization Branch and bound Quadratic fractional programming Mixed integer programming

MSADCN:Multi-Scale Attentional Densely Connected Network for Automated Bone Age Assessment

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Computers, Materials & Continua 2024年第2期78卷 2225-2243页

作者： Yanjun Yu Lei Yu Huiqi Wang Haodong Zheng Yi Deng College of Computer and information Science Chongqing Normal UniversityChongqing401331China College of Mathematics and statistics Chongqing UniversityChongqing401331China

Bone age assessment(BAA)helps doctors determine how a child’s bones grow and develop in clinical *** BAA methods rely on clinician expertise,leading to time-consuming predictions and inaccurate *** deep learning-based BAA methods feed the extracted critical points of images into the network by providing additional *** operation is costly and *** address these problems,we propose a multi-scale attentional densely connected network(MSADCN)in this *** constructs a multi-scale dense connectivity mechanism,which can avoid overfitting,obtain the local features effectively and prevent gradient vanishing even in limited training ***,MSADCN designs multi-scale structures in the densely connected network to extract fine-grained features at different ***,coordinate attention is embedded to focus on critical features and automatically locate the regions of interest(ROI)without additional *** addition,to improve the model’s generalization,transfer learning is applied to train the proposed MSADCN on the public dataset IMDB-WIKI,and the obtained pre-trained weights are loaded onto the Radiological Society of North America(RSNA)***,label distribution learning(LDL)and expectation regression techniques are introduced into our model to exploit the correlation between hand bone images of different ages,which can obtain stable age *** experiments confirm that our model can converge more efficiently and obtain a mean absolute error(MAE)of 4.64 months,outperforming some state-of-the-art BAA methods.

关键词： Bone age assessment deep learning attentional densely connected network muti-scale

THE LONG TIME BEHAVIOR OF THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS WITH LINEAR SELF-REPELLING DRIFT

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Acta Mathematica Scientia 2024年第2期44卷 671-685页

作者：夏晓宇闫理坦杨晴 College of information Science and Technology Donghua UniversityShanghai201620China Department of statistics College of ScienceDonghua UniversityShanghai201620China

Let B^(H) be a fractional Brownian motion with Hurst index 1/2≤H<*** this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dX_(t)^(H)=dB_(t)^(H)+σ X_(t)^(H)dt+vdt-θ(∫_(0)^(t)(X_(t)^(H)-X_(s)^(H))ds)dt,whereθ<0,σ,v∈ℝ.The process is an analogue of self-attracting diffusion(Cranston,Le *** Ann,1995,303:87–93).Our main aim is to study the large time behaviors of the *** show that the solution X^(H)diverges to infinity as t tends to infinity,and obtain the speed at which the process X^(H)diverges to infinity.

关键词： fractional Brownian motion stochastic difference equations rate of convergence asymptotic