Brain Functional Network Generation Using Distribution-Regularized Adversarial Graph Autoencoder with Transformer for Dementia Diagnosis

The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlation between abnormal connectivities and dementia disorders.However,it is challenging to access considerable amounts of brain functional network data,which hinders the widespread application of data-driven models in dementia diagnosis.In this study,a novel distribution-regularized adversarial graph auto-Encoder(DAGAE)with transformer is proposed to generate new fake brain functional networks to augment the brain functional network dataset,improving the dementia diagnosis accuracy of data-driven models.Specifically,the label distribution is estimated to regularize the latent space learned by the graph encoder,which canmake the learning process stable and the learned representation robust.Also,the transformer generator is devised to map the node representations into node-to-node connections by exploring the long-term dependence of highly-correlated distant brain regions.The typical topological properties and discriminative features can be preserved entirely.Furthermore,the generated brain functional networks improve the prediction performance using different classifiers,which can be applied to analyze other cognitive diseases.Attempts on the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset demonstrate that the proposed model can generate good brain functional networks.The classification results show adding generated data can achieve the best accuracy value of 85.33%,sensitivity value of 84.00%,specificity value of 86.67%.The proposed model also achieves superior performance compared with other related augmentedmodels.Overall,the proposedmodel effectively improves cognitive disease diagnosis by generating diverse brain functional networks.

Pressure-Controlled Inverse Ratio Ventilation during General Anesthesia for Open Abdominal Surgery Improves Postoperative Pulmonary Function

Background: Studies have shown that pressure-controlled ventilation improves alveolar gas distribution. And inverse ratio ventilation has advantages of improving oxygenation in acute respiratory distress syndrome (ARDS) patients. However, the effects that pressure-controlled inverse ration ventilation in patients undergoes endotracheal intubation general anesthesia have not been assessed. Objective: To investigate whether pressure-controlled inverse ratio ventilation (PIV) would improve ventilatory and oxygenation parameters as well as lung function compared to conventional ventilation in patients undergoing open abdominal surgery. Interventions: In the conventional ventilation (CV) group, the ventilation strategy involved zero end-expiratory pressure and volume-controlled ventilation. In the pressure-controlled inverse ratio ventilation (PIV) group, the strategy involved P high starting at 7 cm H2O, P low starting at 4 cm H2O, T high at 4 s, T low at 2 s, and an inspiratory-to-expiratory time ratio of 2:1. The ΔP value was adjusted according to VT. Pressure levels were increased by 2 cm H2O until a maximal VT was observed. Inspired oxygen fraction (FIO2) was 1.0 and tidal volume (VT) was 6 mL/kg in both groups. Main Outcome Measures: The primary outcome is pulmonary function tests. Hemodynamic, ventilatory and oxygenation parameters were measured;visual analog scale (VAS) scores, and nausea and vomiting scores were also measured. Results: The PIV group tolerated pressure-controlled inverse ratio ventilation without significant hemodynamic instability. Mean airway pressure and static compliance were significantly higher in the PIV group than those in CV group (P P 2 h was well tolerated and improved respiratory compliance and lung function on the first postoperative day.

Degeneracy Cases of Generalized Inverse Function-Valued Padé Approximation

A new generalized inverse function-valued Padé approximation (GIFPA) was defined. Existence condition of GIFPA was given and its uniqueness theorem was proved. All possible degeneracy cases of GIFPA were discussed and constructed. An example was given to illustrate its application.

The Fourier Transform of a Sort of Generalized Function

The Fourier transforms of functions X ln e are given. where λ is a complex constant (λ≠-1,-2. …), a is a complex number. m=0. 1. 2,…,and

结合Transformer与生成对抗网络的水下图像增强算法

由于水下环境的多样性和光在水中受到的散射及选择性吸收作用,采集到的水下图像通常会产生严重的质量退化问题,如颜色偏差、清晰度低和亮度低等,为解决以上问题,本文提出了一种基于Transformer和生成对抗网络的水下图像增强算法。以生成对抗网络为基础架构,结合编码解码结构、基于空间自注意力机制的全局特征建模Transformer模块和通道级多尺度特征融合Transformer模块构建了TGAN(generative adversarial network with transformer)网络增强模型,重点关注水下图像衰减更严重的颜色通道和空间区域,有效增强了图像细节并解决了颜色偏差问题。此外,设计了一种结合RGB和LAB颜色空间的多项损失函数,约束网络增强模型的对抗训练。实验结果表明,与CLAHE(contrast limited adaptive histogram equalization)、UDCP(underwater dark channel prior)、UWCNN(underwater based on convolutional neural network)、FUnIE-GAN(fast underwater image enhancement for improved visual perception)等典型水下图像增强算法相比,所提算法增强后的水下图像在清晰度、细节纹理和色彩表现等方面都有所提升,客观评价指标如峰值信噪比、结构相似性和水下图像质量度量的平均值分别提升了5.8%、1.8%和3.6%,有效地提升了水下图像的视觉感知效果。

Generalized Inverses of Matrices over Rings

Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.

Entropy Bayesian Analysis for the Generalized Inverse Exponential Distribution Based on URRSS

This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results.

GENERALIZED WAVELETS AND INVERSION OF THE RADON TRANSFORM ON THE LAGUERRE HYPERGROUP

Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.

The Dual Functionals for the Generalized Ball Basis of Wang-Said Type and Basis Transformation Formulas

The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual functionals for the generalized Ball basis of Wang-Said type. The relevant basis transformation formulae are also worked out.

SEMI-INVERSE METHOD AND GENERALIZED VARIATIONAL PRINCIPLES WITH MULTI-VARIABLES IN ELASTICITY

Semi-inverse method, which is an integration and an extension of Hu's try-and-error method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational principles with multi-variables without arty variational crisis phenomenon. The method is to construct an energy trial-functional with an unknown function F, which can be readily identified by making the trial-functional stationary and using known constraint equations. As a result generalized variational principles with two kinds of independent variables (such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle) and generalized variational principles with three kinds of independent variables (such as Chien's generalized variational principles) in elasticity have been deduced without using Lagrange multiplier method. By semi-inverse method, the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables, stress-strain relations are still its constraints.

Certain Integral Transforms of Generalized k-Bessel Function

The objective of this note is to provide some(potentially useful) integral transforms(for example, Euler, Laplace, Whittaker etc.) associated with the generalized k-Bessel function defined by Saiful and Nisar [3]. We have also discussed some other transforms as special cases of our main results.

Inversion of receiver function by wavelet transformation

A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low to high scale, with the inversion result for low order receiver function as the initial model for high order. A neighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on the initial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal and upper mantle velocity with high resolution.

GENERALIZED RAY APPROXIMATE METHOD TO INVERSE MEDIUM PARAMETERS

In this paper, the inverse problem of the medium parameters in an inhomogeneous medium is studied and a generalized ray approximate form of the total wave field is described. First, the acoustic wave equation derived from the elastic wave equation is studied, the referential variables and perturbational variables are introduced, and the integral equation of the medium perturbational parameters is obtained. Then from the point of view of the local principles of the wave function in an inhomogeneous medium, a generalized ray approximate form of the total wave field in an inhomogeneous medium is described, and attention is focused on the Fredholm integral equation of the first kind. Finally, the medium parameters in half-plane are inversed. Numerical examples show when the perturbations of the medium parameters are about 0.5, this method can effectively inverse its variation. Apparently, this method is better than the conventional Born weak scattering approximation.

STUDY ON STREAM CIPHERS USING GENERATING FUNCTIONS

Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.

Application of the Regularization Method to the Numberical Inversion of a Class of Generalized Radon Transform

In the research of bistatic tomography imaging of translating object, we get a class of generalized Radon transformation. In this paper, first we prove the existence and uniguenness of its solution in theory and point out this problem is ill-posed with an especial example.Secondly by means of multiplicative interpolation functions to approximate models, we constracted regularizing functional. Finally we simplify calculation by Fourier transformation,get regularizing solutions that converge to accurate solution.

Bayesian and Non-Bayesian Estimation of the Inverse Weibull Model Based on Generalized Order Statistics

The concept of generalized order statistics has been introduced as a unified approach to a variety of models of ordered random variables with different interpretations. In this paper, we develop methodology for constructing inference based on n selected generalized order statistics (GOS) from inverse Weibull distribution (IWD), Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameters and reliability function. We have examined Bayes estimates under various losses such as the balanced squared error (balanced SEL) and balanced LINEX loss functions are considered. We show that Bayes estimate under balanced SEL and balanced LINEX loss functions are more general, which include the symmetric and asymmetric losses as special cases. This was done under assumption of discrete-continuous mixture prior for the unknown model parameters. The parametric bootstrap method has been used to construct confidence interval for the parameters and reliability function. Progressively type-II censored and k-record values as a special case of GOS are considered. Finally a practical example using real data set was used for illustration.

Investigation of Probability Generating Function in an Interdependent <i>M/M/</i>1:(∞;GD) Queueing Model with Controllable Arrival Rates Using Rouche’s Theorem

Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.

The Similarity Transformation of Regularizing Functionals and Simularity Property of Their Fourier Transformations

Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.

Generalized canonical transformation for second-order Birkhoffian systems on time scales

The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.

On the generalized Cauchy function and new Conjecture on its exterior singularities

This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.