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.

Data-driven human and bot recognition from web activity logs based on hybrid learning techniques

Distinguishing between web traffic generated by bots and humans is an important task in the evaluation of online marketing campaigns.One of the main challenges is related to only partial availability of the performance metrics:although some users can be unambiguously classified as bots,the correct label is uncertain in many cases.This calls for the use of classifiers capable of explaining their decisions.This paper demonstrates two such mechanisms based on features carefully engineered from web logs.The first is a man-made rule-based system.The second is a hierarchical model that first performs clustering and next classification using human-centred,interpretable methods.The stability of the proposed methods is analyzed and a minimal set of features that convey the classdiscriminating information is selected.The proposed data processing and analysis methodology are successfully applied to real-world data sets from online publishers.

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.

BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED K-HOLOMORPHIC FUNCTIONS IN C^(2)

In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.

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.

An integrable generalization of the Fokas–Lenells equation:Darboux transformation, reduction and explicit soliton solutions

Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.

GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY

We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations,with the initial data(u0,B0)being located in the critical Besov space■and the initial densityρ0 being close to a positive constant.By using weighted global estimates,maximal regularity estimates in the Lorentz space for the Stokes system,and the Lagrangian approach,we show that the 2-D MHD equations have a unique global solution.

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.

Local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity

In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems.

Spectral Fittings of Warm Coronal Radiation with High Seed Photon Temperature:Apparent Low-temperature and Flat Soft Excess in AGNs

A warm corona has been widely proposed to explain the soft excess(SE)in X-ray above the 2-10 ke V power law extrapolation in Active Galactic Nuclei(AGNs).In actual spectral fittings,the warm coronal seed photon temperature(T_s)is usually assumed to be far away from the soft X-ray,but kT_scan reach close to 0.1 ke V in the standard accretion disk model.In this study,we used Monte Carlo simulations to obtain radiation spectra from a slab-like warm corona and fitted the spectra using the spherical-geometry-based routine THCOMP or a thermal component.Our findings reveal tha high T_scan influence the fitting results.A moderately high kT_s(around 0.03 ke V)can result in an apparent low-temperature and flat SE,while an extremely high kT_s(around 0.07 ke V)can even produce an unobserved blackbody-like SE.Our conclusions indicate that,for spectral fittings of the warm coronal radiation(SE in AGNs),kT_sshould be treated as a free parameter with an upper limit,and an accurate coronal geometry is necessary when kT_s>0.01 ke V.

Local existence and uniqueness of the incompressible Navier-Stokes-Landau-Lifshitz equations with the Dzyaloshinskii-Moriya interaction and V-flow term

In this paper,we prove that there exists a unique local solution for the Cauchy problem of a system of the incompressible Navier-Stokes-Landau-Lifshitz equations with the Dzyaloshinskii-Moriya interaction and V-flow term inR^(2) and R^(3).Our methods rely upon approximating the system with a perturbed parabolic system and parallel transport.

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.

GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY

A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.