Toward Improved Accuracy in Quasi-Static Elastography Using Deep Learning

Elastography is a non-invasive medical imaging technique to map the spatial variation of elastic properties of soft tissues.The quality of reconstruction results in elastography is highly sensitive to the noise induced by imaging measurements and processing.To address this issue,we propose a deep learning(DL)model based on conditional Generative Adversarial Networks(cGANs)to improve the quality of nonhomogeneous shear modulus reconstruction.To train this model,we generated a synthetic displacement field with finite element simulation under known nonhomogeneous shear modulus distribution.Both the simulated and experimental displacement fields are used to validate the proposed method.The reconstructed results demonstrate that the DL model with synthetic training data is able to improve the quality of the reconstruction compared with the well-established optimization method.Moreover,we emphasize that our DL model is only trained on synthetic data.This might provide a way to alleviate the challenge of obtaining clinical or experimental data in elastography.Overall,this work addresses several fatal issues in applying the DL technique into elastography,and the proposed method has shown great potential in improving the accuracy of the disease diagnosis in clinical medicine.

Conditional Generative Adversarial Network Enabled Localized Stress Recovery of Periodic Composites

Structural damage in heterogeneousmaterials typically originates frommicrostructures where stress concentration occurs.Therefore,evaluating the magnitude and location of localized stress distributions within microstructures under external loading is crucial.Repeating unit cells(RUCs)are commonly used to represent microstructural details and homogenize the effective response of composites.This work develops a machine learning-based micromechanics tool to accurately predict the stress distributions of extracted RUCs.The locally exact homogenization theory efficiently generates the microstructural stresses of RUCs with a wide range of parameters,including volume fraction,fiber/matrix property ratio,fiber shapes,and loading direction.Subsequently,the conditional generative adversarial network(cGAN)is employed and constructed as a surrogate model to establish the statistical correlation between these parameters and the corresponding localized stresses.The stresses predicted by cGAN are validated against the remaining true data not used for training,showing good agreement.This work demonstrates that the cGAN-based micromechanics tool effectively captures the local responses of composite RUCs.It can be used for predicting potential crack initiations starting from microstructures and evaluating the effective behavior of periodic composites.

Enhancing Pneumonia Detection in Pediatric Chest X-Rays Using CGAN-Augmented Datasets and Lightweight Deep Transfer Learning Models

Pneumonia ranks as a leading cause of mortality, particularly in children aged five and under. Detecting this disease typically requires radiologists to examine chest X-rays and report their findings to physicians, a task susceptible to human error. The application of Deep Transfer Learning (DTL) for the identification of pneumonia through chest X-rays is hindered by a shortage of available images, which has led to less than optimal DTL performance and issues with overfitting. Overfitting is characterized by a model’s learning that is too closely fitted to the training data, reducing its effectiveness on unseen data. The problem of overfitting is especially prevalent in medical image processing due to the high costs and extensive time required for image annotation, as well as the challenge of collecting substantial datasets that also respect patient privacy concerning infectious diseases such as pneumonia. To mitigate these challenges, this paper introduces the use of conditional generative adversarial networks (CGAN) to enrich the pneumonia dataset with 2690 synthesized X-ray images of the minority class, aiming to even out the dataset distribution for improved diagnostic performance. Subsequently, we applied four modified lightweight deep transfer learning models such as Xception, MobileNetV2, MobileNet, and EfficientNetB0. These models have been fine-tuned and evaluated, demonstrating remarkable detection accuracies of 99.26%, 98.23%, 97.06%, and 94.55%, respectively, across fifty epochs. The experimental results validate that the models we have proposed achieve high detection accuracy rates, with the best model reaching up to 99.26% effectiveness, outperforming other models in the diagnosis of pneumonia from X-ray images.

A PRIORI ESTIMATES TO THE MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ANISOTROPIC GROWTH CONDITIONS

In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.

Application of generalized impedance boundary conditions to sommerfeld half-space problem

Generalized impedance boundary conditions are employed to simplify the solution of the Sommerfeld half-space problem. An analytical expression is derived for the Hertz potential of a vertical electric dipole over the earth’s surface, in which the earth is assumed to be a layered media or homogeneous dissipative half-space. A Sommerfeld type integral in the potential function is expressed as the sum of two parts: a zeroth order Hankel function and an absolutely convergent series of Bessel functions. In addition, two expressions in closed form are obtained as the far-field and near-field approximation of the present result.

Consistency Conditions and Constraints on Generalized f(R) Gravity with Arbitrary Geometry-Matter Coupling

We study the consistency conditions of the generalized f （ R） gravity by extending f （ R） gravity with non-minimal coupling to the generalized f（R） with arbitrary geometry-matter coupling. Specifically, we discuss the two particular models of generalized f（R） by means of consistency conditions. It is found that the second model is not physically viable so as to be ruled out. Moreover, we further constrain the first model using the Dolgov- Kawasaki stability criterion, and give the value ranges of the parameters in the first model It is worth stressing that our results include the ones in f（R） gravity with non-minimal coupling as the special case of Q（Lm） = Lm.

Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions

In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.

Energy Conditions and Constraints on the Generalized Non-Local Gravity Model

We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity obtained by adding a term m2n-2R□-nRto the Einstein-Hilbert action. Moreover, to obtain some insight on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the model parameter ε for different n. By analysis we give the constraints on the model parameters ε.

Adversarial Training-Aided Time-Varying Channel Prediction for TDD/FDD Systems

In this paper, a time-varying channel prediction method based on conditional generative adversarial network(CPcGAN) is proposed for time division duplexing/frequency division duplexing(TDD/FDD) systems. CPc GAN utilizes a discriminator to calculate the divergence between the predicted downlink channel state information(CSI) and the real sample distributions under a conditional constraint that is previous uplink CSI. The generator of CPcGAN learns the function relationship between the conditional constraint and the predicted downlink CSI and reduces the divergence between predicted CSI and real CSI.The capability of CPcGAN fitting data distribution can capture the time-varying and multipath characteristics of the channel well. Considering the propagation characteristics of real channel, we further develop a channel prediction error indicator to determine whether the generator reaches the best state. Simulations show that the CPcGAN can obtain higher prediction accuracy and lower system bit error rate than the existing methods under the same user speeds.

AUTOSIM:Automated Urban Traffic Operation Simulation via Meta-Learning

Online traffic simulation that feeds from online information to simulate vehicle movement in real-time has recently seen substantial advancement in the development of intelligent transportation systems and urban traffic management.It has been a challenging problem due to three aspects:1)The diversity of traffic patterns due to heterogeneous layouts of urban intersections;2)The nature of complex spatiotemporal correlations;3)The requirement of dynamically adjusting the parameters of traffic models in a real-time system.To cater to these challenges,this paper proposes an online traffic simulation framework called automated urban traffic operation simulation via meta-learning(AUTOSIM).In particular,simulation models with various intersection layouts are automatically generated using an open-source simulation tool based on static traffic geometry attributes.Through a meta-learning technique,AUTOSIM enables an automated learning process for dynamic model settings of traffic scenarios featured with different spatiotemporal correlations.Besides,AUTOSIM is capable of adapting traffic model parameters according to dynamic traffic information in real-time by using a meta-learner.Through computational experiments,we demonstrate the effectiveness of the meta-learningbased framework that is capable of providing reliable supports to real-time traffic simulation and dynamic traffic operations.

Poisson Theory of Generalized Birkhoff Systems

To study the Poisson theory of the generalized Birkhoff systems, the Lie algebra and the Poisson brackets were used to establish the Poisson theorem. The generalized Poisson condition for the first integral and the generalized Poisson theorem of the generalized Birkhoff systems are obtained. An example is given to illustrate the application of the result.

Sandstorms and desertification

Sandstorm is a frequently occurred disastrous weather in northern China. The increasing occurrence frequency recently, especially the much more frequently occurred sandstorms with high intensity in the spring of 2000 have caused great loss to national economy. The combination of strong wind, exposed sandy soil on ground surface and unstable air current constitutes the necessary conditions for the sandstorms. However, the accelerated desertification process resulting from irrational human economic activities is responsible for the accelerated sandstorms. The effective measures to mitigate sandstorm lie in strengthening desertification control and eco-environmental protection.

Time-varying confidence interval forecasting of travel time for urban arterials using ARIMA-GARCH model

To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity （ARIMA-GARCH） model. In which, the ARIMA model is used as the mean equation of the GARCH model to model the travel time levels and the GARCH model is used to model the conditional variances of travel time. The proposed method is validated and evaluated using actual traffic flow data collected from the traffic monitoring system of Kunshan city. The evaluation results show that, compared with the conventional ARIMA model, the proposed model cannot significantly improve the forecasting performance of travel time levels but has advantage in travel time volatility forecasting. The proposed model can well capture the travel time heteroskedasticity and forecast the time-varying confidence intervals of travel time which can better reflect the volatility of observed travel times than the fixed confidence interval provided by the ARIMA model.

THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE ONE-DIMENSIONAL CHAPLYGIN GAS EQUATIONS

In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.

Functional Variable Separation for Extended Nonlinear Elliptic Equations

This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions （FSSs） and construct some exact FSSs to the resulting equations.

The derivative-dependent functional variable separation for the evolution equations

This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.

Extension of Variable Separable Solutions for Nonlinear Evolution Equations

We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.

Approximate Generalized Conditional Symmetries for Perturbed Evolution Equations

The concept of approximate generalized conditional symmetry （AGCS） for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via their A GCSs is illustrated with examples.

Cauchy Problems for KdV-type Equations and Higher-Order Conditional Symmetries

We develop the generalized conditional symmetry （GCS） approach to solve the problem of dimensional reduction of Cauchy problems for the KdV-type equations. We characterize these equations that admit certain higherorder GCSs and show the main reduction procedure by some examples. The obtained reductions cannot be derived within the framework of the standard Lie approach.

Symmetry Reduction and Cauchy Problems for a Class of Fourth-Order Evolution Equations

We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations toCauchy problems for systems of ordinary differential equations (ODEs).We classify a class of fourth-order evolutionequations which admit certain higher-order generalized conditional symmetries (GCSs) and give some examples to showthe main reduction procedure.These reductions cannot be derived within the framework of the standard Lie approach,which hints that the technique presented here is something essential for the dimensional reduction of evolu tion equations.