Meta-Auto-Decoder:a Meta-Learning-Based Reduced Order Model for Solving Parametric Partial Differential Equations

Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.

Remote sensing of air pollution incorporating integrated-path differential-absorption and coherent-Doppler lidar

An innovative complex lidar system deployed on an airborne rotorcraft platform for remote sensing of atmospheric pollution is proposed and demonstrated.The system incorporates integrated-path differential absorption lidar(DIAL) and coherent-doppler lidar(CDL) techniques using a dual tunable TEA CO_(2)laser in the 9—11 μm band and a 1.55 μm fiber laser.By combining the principles of differential absorption detection and pulsed coherent detection,the system enables agile and remote sensing of atmospheric pollution.Extensive static tests validate the system’s real-time detection capabilities,including the measurement of concentration-path-length product(CL),front distance,and path wind speed of air pollution plumes over long distances exceeding 4 km.Flight experiments is conducted with the helicopter.Scanning of the pollutant concentration and the wind field is carried out in an approximately 1 km slant range over scanning angle ranges from 45°to 65°,with a radial resolution of 30 m and10 s.The test results demonstrate the system’s ability to spatially map atmospheric pollution plumes and predict their motion and dispersion patterns,thereby ensuring the protection of public safety.

REDUCTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATION AND EXACT SOLUTIONS

Nonlinear partial differetial equation(NLPDE) is converted into ordinary differential equation(ODE) via a new ansatz.Using undetermined function method,the ODE obtained above is replaced by a set of algebraic equations which are solved out with the aid of Mathematica.The exact solutions and solitary solutions of NLPDE are obtained.

Differential diagnosis of Crohn’s disease and intestinal tuberculosis based on ATR-FTIR spectroscopy combined with machine learning

BACKGROUND Crohn’s disease(CD)is often misdiagnosed as intestinal tuberculosis(ITB).However,the treatment and prognosis of these two diseases are dramatically different.Therefore,it is important to develop a method to identify CD and ITB with high accuracy,specificity,and speed.AIM To develop a method to identify CD and ITB with high accuracy,specificity,and speed.METHODS A total of 72 paraffin wax-embedded tissue sections were pathologically and clinically diagnosed as CD or ITB.Paraffin wax-embedded tissue sections were attached to a metal coating and measured using attenuated total reflectance fourier transform infrared spectroscopy at mid-infrared wavelengths combined with XGBoost for differential diagnosis.RESULTS The results showed that the paraffin wax-embedded specimens of CD and ITB were significantly different in their spectral signals at 1074 cm^(-1) and 1234 cm^(-1) bands,and the differential diagnosis model based on spectral characteristics combined with machine learning showed accuracy,specificity,and sensitivity of 91.84%,92.59%,and 90.90%,respectively,for the differential diagnosis of CD and ITB.CONCLUSION Information on the mid-infrared region can reveal the different histological components of CD and ITB at the molecular level,and spectral analysis combined with machine learning to establish a diagnostic model is expected to become a new method for the differential diagnosis of CD and ITB.

Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.

Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.

A Comparison between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations

In this work, approximate analytical solutions to the lid-driven square cavity flow problem, which satisfied two-dimensional unsteady incompressible Navier-Stokes equations, are presented using the kinetically reduced local Navier-Stokes equations. Reduced differential transform method and perturbation-iteration algorithm are applied to solve this problem. The convergence analysis was discussed for both methods. The numerical results of both methods are given at some Reynolds numbers and low Mach numbers, and compared with results of earlier studies in the review of the literatures. These two methods are easy and fast to implement, and the results are close to each other and other numerical results, so it can be said that these methods are useful in finding approximate analytical solutions to the unsteady incompressible flow problems at low Mach numbers.

Syntheses and properties of associative acrylamide copolymers containing short hydrophobic chains used in a friction reducer for slick-water fracturing

Two allyldimethylalkyl quaternary ammonium salt(AQAS)monomers,N,N-dimethylallylphenylpropylammonium bromide(AQAS1)and N,N-dimethylallylnonylammonium bromide(AQAS2),were synthesized and used to prepare modified polyacrylamide materials.Two new drag reducers were synthesized from acrylamide(AM),sodium acrylate(Na AA)and a cationic modified monomer(AQAS1 or AQAS2)via aqueous solution polymerization,and the copolymers were named P(AM/Na AA/AQAS1)and P(AM/Na AA/AQAS2),respectively.The structures of the drag reduction agents were confirmed by IR and1H NMR spectroscopies.The molecular weight(Mw)of P(AM/Na AA/AQAS1)was 1.79×10^(6)g/mol.When the copolymer concentration was 1000 mg/L and the flow rate was 45 L/min,in fresh water the highest drag reduction rate was 75.8%,in 10,000 mg/L Na Cl solution the drag reduction rate decreased to 72.9%.The molecular weight of P(AM/Na AA/AQAS2)was 3.17×10^(6)g/mol.When the copolymer concentration was500 mg/L and the flow rate was 45 L/min,the drag reduction rate reached 75.2%,and in 10,000 mg/L Na Cl solution the drag reduction rate was 73.3%,decreased by approximately 1.9%.The drag reduction rate for partially hydrolyzed polyacrylamide(HPAM)was also investigated,and the results showed that the drag reduction rates for 500 and 1000 mg/L HPAM solutions were merely 43.2%and 49.0%in brine,respectively.Compared with HPAM,both of the above copolymers presented better drag reduction capacities.

Correction to:Theoretical analysis of the double-differential cross-sections of neutron,proton,deuteron,^(3)He,and α for the p+^(6)Li reaction

Correction to:Nuclear Science and Techniques(2024)35:61 https://doi.org/10.1007/s41365-024-01421-5 In this article,the figures were wrongly numbered.The Fig.7 and 8 should have been Fig.11 and 12.The Fig.9,10,11,and 12 should have been 7,8,9 and 10.The original article has been corrected.

Differential Collision Attack on Reduced FOX Block Cipher

This paper presents a method for differen- tial collision attack of reduced FOX block cipher based on 4-round distinguishing property. It can be used to attack 5, 6 and 7-round FOX64 and 5-round FOX128. Our attack has a precomputation phase, but it can be obtained before attack and computed once for all. This attack on the reduced to 4-round FOX64 requires only 7 chosen plaintexts, and performs 242.8 4-round FOX64 encryptions. It could be extended to 5 （6, 7）-round FOX64 by a key exhaustive search behind the fourth round.

Reduced Differential Transform Method for Solving Linear and Nonlinear Goursat Problem

In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.

A micro-crosslinked amphoteric hydrophobic association copolymer as high temperature-and salt-resistance fluid loss reducer for water-based drilling fluids

During ultradeep oil and gas drilling,fluid loss reducers are highly important for water-based drilling fluids,while preparing high temperature-and salt-resistance fluid loss reducers with excellent rheology and filtration performance remains a challenge.Herein,a micro-crosslinked amphoteric hydrophobic association copolymer(i.e.,DADC)was synthesized using N,N-dimethyl acrylamide,diallyl dimethyl ammonium chloride,2-acrylamido-2-methylpropane sulfonic acid,hydrophobic monomer,and pentaerythritol triallyl ether crosslinker.Due to the synergistic effects of hydrogen bonds,electrostatic interaction,hydrophobic association,and micro-crosslinking,the DADC copolymer exhibited outstanding temperature-and salt-resistance.The rheological experiments have shown that the DADC copolymer had excellent shear dilution performance and a certain degree of salt-responsive viscosity-increasing performance.The DADC copolymer could effectively adsorb on the surface of bentonite particles through electrostatic interaction and hydrogen bonds,which bring more negative charge to the bentonite,thus improving the hydration and dispersion of bentonite particles as well as the colloidal stability of the drilling fluids.Moreover,the drilling fluids constructed based on the DADC copolymer exhibited satisfactory rheological and filtration properties(FLHTHP=12 m L)after aging at high temperatures(up to200℃)and high salinity(saturated salt)environments.Therefore,this work provided new insights into designing and fabricating high-performance drilling fluid treatment agents,demonstrating good potential applications in deep and ultradeep drilling engineering.

A continuous and long-term in-situ stress measuring method based on fiber optic. Part I: Theory of inverse differential strain analysis

A method for in-situ stress measurement via fiber optics was proposed. The method utilizes the relationship between rock mass elastic parameters and in-situ stress. The approach offers the advantage of long-term stress measurements with high spatial resolution and frequency, significantly enhancing the ability to measure in-situ stress. The sensing casing, spirally wrapped with fiber optic, is cemented into the formation to establish a formation sensing nerve. Injecting fluid into the casing generates strain disturbance, establishing the relationship between rock mass properties and treatment pressure.Moreover, an optimization algorithm is established to invert the elastic parameters of formation via fiber optic strains. In the first part of this paper series, we established the theoretical basis for the inverse differential strain analysis method for in-situ stress measurement, which was subsequently verified using an analytical model. This paper is the fundamental basis for the inverse differential strain analysis method.

A Coupled Thermomechanical Crack Propagation Behavior of Brittle Materials by Peridynamic Differential Operator

This study proposes a comprehensive,coupled thermomechanical model that replaces local spatial derivatives in classical differential thermomechanical equations with nonlocal integral forms derived from the peridynamic differential operator(PDDO),eliminating the need for calibration procedures.The model employs a multi-rate explicit time integration scheme to handle varying time scales in multi-physics systems.Through simulations conducted on granite and ceramic materials,this model demonstrates its effectiveness.It successfully simulates thermal damage behavior in granite arising from incompatible mineral expansion and accurately calculates thermal crack propagation in ceramic slabs during quenching.To account for material heterogeneity,the model utilizes the Shuffle algorithm andWeibull distribution,yielding results that align with numerical simulations and experimental observations.This coupled thermomechanical model shows great promise for analyzing intricate thermomechanical phenomena in brittle materials.

ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

Decoding Retinoblastoma: Differential Gene Expression

Background: Retinoblastoma, the most common intraocular pediatric cancer, presents complexities in its genetic landscape that necessitate a deeper understanding for improved therapeutic interventions. This study leverages computational tools to dissect the differential gene expression profiles in retinoblastoma. Methods: Employing an in silico approach, we analyzed gene expression data from public repositories by applying rigorous statistical models, including limma and de seq 2, for identifying differentially expressed genes DEGs. Our findings were validated through cross-referencing with independent datasets and existing literature. We further employed functional annotation and pathway analysis to elucidate the biological significance of these DEGs. Results: Our computational analysis confirmed the dysregulation of key retinoblastoma-associated genes. In comparison to normal retinal tissue, RB1 exhibited a 2.5-fold increase in expression (adjusted p Conclusions: Our analysis reinforces the critical genetic alterations known in retinoblastoma and unveils new avenues for research into the disease’s molecular basis. The discovery of chemoresistance markers and immune-related genes opens potential pathways for personalized treatment strategies. The study’s outcomes emphasize the power of in silico analyses in unraveling complex cancer genomics.

Deep Structure Optimization for Incremental Hierarchical Fuzzy Systems Using Improved Differential Evolution Algorithm

The optimization of the rule base of a fuzzy logic system (FLS) based on evolutionary algorithm has achievednotable results. However, due to the diversity of the deep structure in the hierarchical fuzzy system (HFS) and thecorrelation of each sub fuzzy system, the uncertainty of the HFS’s deep structure increases. For the HFS, a largenumber of studies mainly use fixed structures, which cannot be selected automatically. To solve this problem, thispaper proposes a novel approach for constructing the incremental HFS. During system design, the deep structureand the rule base of the HFS are encoded separately. Subsequently, the deep structure is adaptively mutated basedon the fitness value, so as to realize the diversity of deep structures while ensuring reasonable competition amongthe structures. Finally, the differential evolution (DE) is used to optimize the deep structure of HFS and theparameters of antecedent and consequent simultaneously. The simulation results confirm the effectiveness of themodel. Specifically, the root mean square errors in the Laser dataset and Friedman dataset are 0.0395 and 0.0725,respectively with rule counts of rules is 8 and 12, respectively.When compared to alternative methods, the resultsindicate that the proposed method offers improvements in accuracy and rule counts.

Optimality of Group Testing with Differential Misclassification

Group testing is a method that can be used to estimate the prevalence of rare infectious diseases,which can effectively save time and reduce costs compared to the method of random sampling.However,previous literature only demonstrated the optimality of group testing strategy while estimating prevalence under some strong assumptions.This article weakens the assumption of misclassification rate in the previous literature,considers the misclassification rate of the infected samples as a differentiable function of the pool size,and explores some optimal properties of group testing for estimating prevalence in the presence of differential misclassification conforming to this assumption.This article theoretically demonstrates that the group testing strategy performs better than the sample by sample procedure in estimating disease prevalence when the total number of sample pools is given or the size of the test population is determined.Numerical simulation experiments were conducted to evaluate the performance of group tests in estimating prevalence in the presence of dilution effect.

A Differential Privacy Federated Learning Scheme Based on Adaptive Gaussian Noise

As a distributed machine learning method,federated learning(FL)has the advantage of naturally protecting data privacy.It keeps data locally and trains local models through local data to protect the privacy of local data.The federated learning method effectively solves the problem of artificial Smart data islands and privacy protection issues.However,existing research shows that attackersmay still steal user information by analyzing the parameters in the federated learning training process and the aggregation parameters on the server side.To solve this problem,differential privacy(DP)techniques are widely used for privacy protection in federated learning.However,adding Gaussian noise perturbations to the data degrades the model learning performance.To address these issues,this paper proposes a differential privacy federated learning scheme based on adaptive Gaussian noise(DPFL-AGN).To protect the data privacy and security of the federated learning training process,adaptive Gaussian noise is specifically added in the training process to hide the real parameters uploaded by the client.In addition,this paper proposes an adaptive noise reduction method.With the convergence of the model,the Gaussian noise in the later stage of the federated learning training process is reduced adaptively.This paper conducts a series of simulation experiments on realMNIST and CIFAR-10 datasets,and the results show that the DPFL-AGN algorithmperforms better compared to the other algorithms.

THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS

We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.