A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.

INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM

In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.

MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.

Identification of an immune-related gene signature for predicting prognosis and immunotherapy efficacy in liver cancer via cell-cell communication

BACKGROUND Liver cancer is one of the deadliest malignant tumors worldwide.Immunotherapy has provided hope to patients with advanced liver cancer,but only a small fraction of patients benefit from this treatment due to individual differences.Identifying immune-related gene signatures in liver cancer patients not only aids physicians in cancer diagnosis but also offers personalized treatment strategies,thereby improving patient survival rates.Although several methods have been developed to predict the prognosis and immunotherapeutic efficacy in patients with liver cancer,the impact of cell-cell interactions in the tumor microenvir-onment has not been adequately considered.AIM To identify immune-related gene signals for predicting liver cancer prognosis and immunotherapy efficacy.METHODS Cell grouping and cell-cell communication analysis were performed on single-cell RNA-sequencing data to identify highly active cell groups in immune-related pathways.Highly active immune cells were identified by intersecting the highly active cell groups with B cells and T cells.The significantly differentially expressed genes between highly active immune cells and other cells were subsequently selected as features,and a least absolute shrinkage and selection operator(LASSO)regression model was constructed to screen for diagnostic-related features.Fourteen genes that were selected more than 5 times in 10 LASSO regression experiments were included in a multivariable Cox regression model.Finally,3 genes(stathmin 1,cofilin 1,and C-C chemokine ligand 5)significantly associated with survival were identified and used to construct an immune-related gene signature.RESULTS The immune-related gene signature composed of stathmin 1,cofilin 1,and C-C chemokine ligand 5 was identified through cell-cell communication.The effectiveness of the identified gene signature was validated based on experi-mental results of predictive immunotherapy response,tumor mutation burden analysis,immune cell infiltration analysis,survival analysis,and expression analysis.CONCLUSION The findings suggest that the identified gene signature may contribute to a deeper understanding of the activity patterns of immune cells in the liver tumor microenvironment,providing insights for personalized treatment strategies.

Fuzzing:Progress,Challenges,and Perspectives

As one of the most effective techniques for finding software vulnerabilities,fuzzing has become a hot topic in software security.It feeds potentially syntactically or semantically malformed test data to a target program to mine vulnerabilities and crash the system.In recent years,considerable efforts have been dedicated by researchers and practitioners towards improving fuzzing,so there aremore and more methods and forms,whichmake it difficult to have a comprehensive understanding of the technique.This paper conducts a thorough survey of fuzzing,focusing on its general process,classification,common application scenarios,and some state-of-the-art techniques that have been introduced to improve its performance.Finally,this paper puts forward key research challenges and proposes possible future research directions that may provide new insights for researchers.

GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM

The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.

THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

Breather and its interaction with rogue wave of the coupled modified nonlinear Schrodinger equation

We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localized wave solution,the N-fold generalized Darboux transformation is given.Under the condition that the characteristic equation admits a double-root,we present the expression of the first-order interactional solution.Then we graphically analyze the dynamics of the breather and rogue wave.Due to the simultaneous existence of nonlinear and self-steepening terms in the equation,different profiles in two components for the breathers are presented.

DT-Net:Joint Dual-Input Transformer and CNN for Retinal Vessel Segmentation

Retinal vessel segmentation in fundus images plays an essential role in the screening,diagnosis,and treatment of many diseases.The acquired fundus images generally have the following problems:uneven illumination,high noise,and complex structure.It makes vessel segmentation very challenging.Previous methods of retinal vascular segmentation mainly use convolutional neural networks on U Network(U-Net)models,and they have many limitations and shortcomings,such as the loss of microvascular details at the end of the vessels.We address the limitations of convolution by introducing the transformer into retinal vessel segmentation.Therefore,we propose a hybrid method for retinal vessel segmentation based on modulated deformable convolution and the transformer,named DT-Net.Firstly,multi-scale image features are extracted by deformable convolution and multi-head selfattention(MHSA).Secondly,image information is recovered,and vessel morphology is refined by the proposed transformer decoder block.Finally,the local prediction results are obtained by the side output layer.The accuracy of the vessel segmentation is improved by the hybrid loss function.Experimental results show that our method obtains good segmentation performance on Specificity(SP),Sensitivity(SE),Accuracy(ACC),Curve(AUC),and F1-score on three publicly available fundus datasets such as DRIVE,STARE,and CHASE_DB1.

THE EXISTENCE AND STABILITY OF NORMALIZED SOLUTIONS FOR A BI-HARMONIC NONLINEAR SCHR?DINGER EQUATION WITH MIXED DISPERSION

In this paper,we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrodinger equation with aμ-Laplacian term(BNLS).Such BNLS models the propagation of intense laser beams in a bulk medium with a second-order dispersion term.Denoting by Qpthe ground state for the BNLS withμ=0,we prove that in the mass-subcritical regime p∈(1,1+8/d),there exist orbit ally stable ground state solutions for the BNLS when p∈(-λ0,∞)for someλ0=λ0(p,d,‖Qp‖L2)>0.Moreover,in the mass-critical case p=1+8/d,we prove the orbital stability on a certain mass level below‖Q*‖L2,provided thatμ∈(-λ1,0),where■and Q*=Q1+8/d.The proofs are mainly based on the profile decomposition and a sharp Gagliardo-Nirenberg type inequality.Our treatment allows us to fill the gap concerning the existence of the ground states for the BNLS when p is negative and p∈(1,1+8/d].

Multi-Stage Improvement of Marine Predators Algorithm and Its Application

The metaheuristic algorithms are widely used in solving the parameters of the optimization problem.The marine predators algorithm(MPA)is a novel population-based intelligent algorithm.Although MPA has shown a talented foraging strategy,it still needs a balance of exploration and exploitation.Therefore,a multi-stage improvement of marine predators algorithm(MSMPA)is proposed in this paper.The algorithm retains the advantage of multistage search and introduces a linear flight strategy in the middle stage to enhance the interaction between predators.Predators further away from the historical optimum are required to move,increasing the exploration capability of the algorithm.In the middle and late stages,the searchmechanism of particle swarmoptimization(PSO)is inserted,which enhances the exploitation capability of the algorithm.This means that the stochasticity is decreased,that is the optimal region where predators jumping out is effectively stifled.At the same time,self-adjusting weight is used to regulate the convergence speed of the algorithm,which can balance the exploration and exploitation capability of the algorithm.The algorithm is applied to different types of CEC2017 benchmark test functions and threemultidimensional nonlinear structure design optimization problems,compared with other recent algorithms.The results show that the convergence speed and accuracy of MSMPA are significantly better than that of the comparison algorithms.

Solitons and Bifurcations for the Generalized Tzitzéica Type Equation in Nonlinear Fiber Optics

Solitons and bifurcations for the generalized Tzitzéica type equation are studied by using the theory of dynamical systems and Hamilton function. With the help of Maple and bifurcation theory of differential equations, the bifurcation parameter conditions and all the bifurcation phase portraits are obtained. Because the same energy value of the Hamiltonian function is corresponding to the same orbit, thus the periodic wave solutions, bright soliton and dark soliton solutions are defined.

Recent Advances on Deep Learning for Sign Language Recognition

Sign language,a visual-gestural language used by the deaf and hard-of-hearing community,plays a crucial role in facilitating communication and promoting inclusivity.Sign language recognition(SLR),the process of automatically recognizing and interpreting sign language gestures,has gained significant attention in recent years due to its potential to bridge the communication gap between the hearing impaired and the hearing world.The emergence and continuous development of deep learning techniques have provided inspiration and momentum for advancing SLR.This paper presents a comprehensive and up-to-date analysis of the advancements,challenges,and opportunities in deep learning-based sign language recognition,focusing on the past five years of research.We explore various aspects of SLR,including sign data acquisition technologies,sign language datasets,evaluation methods,and different types of neural networks.Convolutional Neural Networks(CNN)and Recurrent Neural Networks(RNN)have shown promising results in fingerspelling and isolated sign recognition.However,the continuous nature of sign language poses challenges,leading to the exploration of advanced neural network models such as the Transformer model for continuous sign language recognition(CSLR).Despite significant advancements,several challenges remain in the field of SLR.These challenges include expanding sign language datasets,achieving user independence in recognition systems,exploring different input modalities,effectively fusing features,modeling co-articulation,and improving semantic and syntactic understanding.Additionally,developing lightweight network architectures for mobile applications is crucial for practical implementation.By addressing these challenges,we can further advance the field of deep learning for sign language recognition and improve communication for the hearing-impaired community.

L_(1)-Smooth SVM with Distributed Adaptive Proximal Stochastic Gradient Descent with Momentum for Fast Brain Tumor Detection

Brain tumors come in various types,each with distinct characteristics and treatment approaches,making manual detection a time-consuming and potentially ambiguous process.Brain tumor detection is a valuable tool for gaining a deeper understanding of tumors and improving treatment outcomes.Machine learning models have become key players in automating brain tumor detection.Gradient descent methods are the mainstream algorithms for solving machine learning models.In this paper,we propose a novel distributed proximal stochastic gradient descent approach to solve the L_(1)-Smooth Support Vector Machine(SVM)classifier for brain tumor detection.Firstly,the smooth hinge loss is introduced to be used as the loss function of SVM.It avoids the issue of nondifferentiability at the zero point encountered by the traditional hinge loss function during gradient descent optimization.Secondly,the L_(1) regularization method is employed to sparsify features and enhance the robustness of the model.Finally,adaptive proximal stochastic gradient descent(PGD)with momentum,and distributed adaptive PGDwithmomentum(DPGD)are proposed and applied to the L_(1)-Smooth SVM.Distributed computing is crucial in large-scale data analysis,with its value manifested in extending algorithms to distributed clusters,thus enabling more efficient processing ofmassive amounts of data.The DPGD algorithm leverages Spark,enabling full utilization of the computer’s multi-core resources.Due to its sparsity induced by L_(1) regularization on parameters,it exhibits significantly accelerated convergence speed.From the perspective of loss reduction,DPGD converges faster than PGD.The experimental results show that adaptive PGD withmomentumand its variants have achieved cutting-edge accuracy and efficiency in brain tumor detection.Frompre-trained models,both the PGD andDPGD outperform other models,boasting an accuracy of 95.21%.

A Survey on Chinese Sign Language Recognition:From Traditional Methods to Artificial Intelligence

Research on Chinese Sign Language(CSL)provides convenience and support for individuals with hearing impairments to communicate and integrate into society.This article reviews the relevant literature on Chinese Sign Language Recognition(CSLR)in the past 20 years.Hidden Markov Models(HMM),Support Vector Machines(SVM),and Dynamic Time Warping(DTW)were found to be the most commonly employed technologies among traditional identificationmethods.Benefiting from the rapid development of computer vision and artificial intelligence technology,Convolutional Neural Networks(CNN),3D-CNN,YOLO,Capsule Network(CapsNet)and various deep neural networks have sprung up.Deep Neural Networks(DNNs)and their derived models are integral tomodern artificial intelligence recognitionmethods.In addition,technologies thatwerewidely used in the early days have also been integrated and applied to specific hybrid models and customized identification methods.Sign language data collection includes acquiring data from data gloves,data sensors(such as Kinect,LeapMotion,etc.),and high-definition photography.Meanwhile,facial expression recognition,complex background processing,and 3D sign language recognition have also attracted research interests among scholars.Due to the uniqueness and complexity of Chinese sign language,accuracy,robustness,real-time performance,and user independence are significant challenges for future sign language recognition research.Additionally,suitable datasets and evaluation criteria are also worth pursuing.

Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes

This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.

SOME NEW IDENTITIES OF ROGERS-RAMANUJAN TYPE

In this paper,we establish two transformation formulas for nonterminating basic hypergeometric series by using Carlitz's inversions formulas and Jackson s transformation formula.In terms of application,by specializing certain parameters in the two transformations,four Rogers-Ramanujan type identities associated with moduli 20 are obtained.

{(3,4),4}-富勒烯图的极大共振性

A {(3,4), 4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)~2,S_(12)~2,S_(12)~4,S_(12)~5,S_(14)~3,S_(14)~5,S_(16)~3,S_(18)~5,S_(24) as shown in Fig.1.As a corollary,it is shown that if a {(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.

规范场论中自对偶磁单极子解的存在唯一性

Magnetic monopoles stand for the static solution arising from a(1 + 3)–dimensional theory describing the interaction between a real scalar triplet and non–Abelian gauge field. In this paper, we obtain a two–point boundary value problem of a first–order ordinary differential equations from the self–dual monopole model. Then we establish the existence and uniqueness theorem for the problem by using a dynamical shooting method, we also obtain sharp asymptotic estimates for the solutions at infinity.

GLOBAL EXISTENCE AND BLOW-UP PHENOMENA OF CLASSICAL SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA

By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.