RepBoTNet-CESA:An Alzheimer’s Disease Computer Aided Diagnosis Method Using Structural Reparameterization BoTNet and Cubic Embedding Self Attention

Various deep learning models have been proposed for the accurate assisted diagnosis of early-stage Alzheimer’s disease(AD).Most studies predominantly employ Convolutional Neural Networks(CNNs),which focus solely on local features,thus encountering difficulties in handling global features.In contrast to natural images,Structural Magnetic Resonance Imaging(sMRI)images exhibit a higher number of channel dimensions.However,during the Position Embedding stage ofMulti Head Self Attention(MHSA),the coded information related to the channel dimension is disregarded.To tackle these issues,we propose theRepBoTNet-CESA network,an advanced AD-aided diagnostic model that is capable of learning local and global features simultaneously.It combines the advantages of CNN networks in capturing local information and Transformer networks in integrating global information,reducing computational costs while achieving excellent classification performance.Moreover,it uses the Cubic Embedding Self Attention(CESA)proposed in this paper to incorporate the channel code information,enhancing the classification performance within the Transformer structure.Finally,the RepBoTNet-CESA performs well in various AD-aided diagnosis tasks,with an accuracy of 96.58%,precision of 97.26%,and recall of 96.23%in the AD/NC task;an accuracy of 92.75%,precision of 92.84%,and recall of 93.18%in the EMCI/NC task;and an accuracy of 80.97%,precision of 83.86%,and recall of 80.91%in the AD/EMCI/LMCI/NC task.This demonstrates that RepBoTNet-CESA delivers outstanding outcomes in various AD-aided diagnostic tasks.Furthermore,our study has shown that MHSA exhibits superior performance compared to conventional attention mechanisms in enhancing ResNet performance.Besides,the Deeper RepBoTNet-CESA network fails to make further progress in AD-aided diagnostic tasks.

Generating Parametric G^n Blending Surface with Some Constraints

This paper presents a method of generating a parametric G^n blending surfacebased on reparameterizing the partial surface patches in the base surfaces on the basis of ErichHartmann method. This method is expressed as follows Firstly, the partial region near contact curvesin both base surfaces is reparameterized. The contact curves are used as the boundaries of thereparameterized partial region respectively. The reparameterized partial region in two base surfacesis called the reparameterized local base surfaces. Then the parametric G^n blending surface isgenerated by a linear combination of the reparameterized local base surface patches depending on oneof the common parameters. Therefore, generating a Parametric G^n Blending Surface between two basesurfaces is translated into generating a Parametric G^n Blending Surface between the tworeparameterized local base surfaces. This paper illustrates the method to generate the G^n blendingsurface with some constraints by generating a G^2 blending surface between the aerofoil and the bodyof a missile with the constraints of the forward and rear fringe curves. When the G^n blendingsurface with some constraints is generated, the partial region near contact curves in both basesurfaces is reparameterized, and the scale factors, offset, balance factor and thumb weight aredefined by meeting the constraints through using an optimization method. Then the parametric G^nblending surface is generated by the linear combination of the reparameterized local base surfacepatches. The shape of the blending surface can be adjusted by changing the size of thereparameterized local base surface patches.

Constrained multi-degree reduction of rational Bézier curves using reparameterization

Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduction for polynomial Bezier curves to the algorithms of constrained multi-degree reduction for rational Bezier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bezier curves, which are used to make uniform the weights of the rational Bezier curves as accordant as possible, and then do multi-degree reduction for each component in homogeneous coordinates. Compared with the two traditional algorithms of ＂cancelling the best linear common divisor＂ and ＂shifted Chebyshev polynomial＂, the two new algorithms presented here using reparameterization have advantages of simplicity and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction at one time, and have good approximating effect.

Judging or setting weight steady-state of rational Bézier curves and surfaces

Many works have investigated the problem of reparameterizing rational B^zier curves or surfaces via MSbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after MSbius transfor- mation. What＇s more the users of computer aided design softwares may require some guidelines for designing rational B6zier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway. The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational B6zier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal para- metric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational B6zier surfaces with compact derivative bounds.

G^0 and G^1 connection between two adjacent B-spline surfaces

In this paper, the smooth connection between two B-spline surfaces is discussed. First, a brief proof of some simple sufficient conditions of Go and G1 continuity is given. On this basis, a novel method for Go or G1 connection between two adjacent B-spline surfaces is presented. A reparameterization step is firstly taken for one of the surfaces such that they have the same parameterization in v direction, then, adjust their boundary control vertices to make them Go or Gl connected. The GI connection parameter is determined by an optimization problem. Compared with the existed methods, our method is simple and easy to be used in practice.

Reparameterization of Single Difference and Undifferenced Kinematic GPS Positioning Models

A series of advantages of single difference (SD) and undifferenced (ZD) models are given as compared with the double difference (DD) model. However, rank defects exist in SD and ZD models. The reparameterization method is provided to resolve this rank defect problem by estimating some combinations of the unknowns rather than the unknowns themselves. The reparameterization of SD and ZD functional models is discussed in detail with their stochastic models. The theoretical confirmation of the equivalence of undifferenced and differenced models is described in a straightforward way. The relationship between SD and ZD residuals is given and verified for some special purposes, e.g. research on the stochastical properties of GPS observations.

Extended Collapsibility of Association Measure

In this paper the amalgamation of (I+1)×J tables under consistent significance is considered and the sufficient condition is obtained. The sufficient and necessary conditions are given to avoid the famous paradoxes 'YAP' and 'YRP'. A practical algorithm is given to compute the critical value when pooling tables with odds ratio less than 1.

RepDDNet:a fast and accurate deforestation detection model with high-resolution remote sensing image

Forest is the largest carbon reservoir and carbon absorber on earth.Thus,mapping forest cover change accurately is of great significance to achieving the global carbon neutrality goal.Accurate forest change information could be acquired by deep learning methods using high-resolution remote sensing images.However,deforestation detection based on deep learning on a large-scale region with high-resolution images required huge computational resources.Therefore,there was an urgent need for a fast and accurate deforestation detection model.In this study,we proposed an interesting but effective re-parameterization deforestation detection model,named RepDDNet.Unlike other existing models designed for deforestation detection,the main feature of RepDDNet was its decoupling feature,which means that it allowed the multi-branch structure in the training stages to be converted into a plain structure in the inference stage,thus the computation efficiency can be significantly improved in the inference stage while maintaining the accuracy unchanged.A large-scale experiment was carried out in Ankang city with 2-meter high-resolution remote sensing images(the total area of it was over 20,000 square kilometers),and the result indicated that the model computation efficiency could be improved by nearly 30%compared with the model without re-parameterization.Additionally,compared with other lightweight models,RepDDNet also displayed a trade-off between accuracy and computation efficiency.

Measure-theoretic entropy for flows

New definitions of measure-theoretic entropy for flows are given and the invariant property of the entropy under conjugacy is discussed.