The Citron homology domain of MAP4Ks improves outcomes of traumatic brain injury

The mitogen-activated protein kinase kinase kinase kinases(MAP4Ks)signaling pathway plays a pivotal role in axonal regrowth and neuronal degeneration following insults.Whether targeting this pathway is beneficial to brain injury remains unclear.In this study,we showed that adeno-associated virus-delivery of the Citron homology domain of MAP4Ks effectively reduces traumatic brain injury-induced reactive gliosis,tauopathy,lesion size,and behavioral deficits.Pharmacological inhibition of MAP4Ks replicated the ameliorative effects observed with expression of the Citron homology domain.Mechanistically,the Citron homology domain acted as a dominant-negative mutant,impeding MAP4K-mediated phosphorylation of the dishevelled proteins and thereby controlling the Wnt/β-catenin pathway.These findings implicate a therapeutic potential of targeting MAP4Ks to alleviate the detrimental effects of traumatic brain injury.

Interaction of major facilitator superfamily domain containing 2A with the blood-brain barrier

The functional and structural integrity of the blood-brain barrier is crucial in maintaining homeostasis in the brain microenvironment;however,the molecular mechanisms underlying the formation and function of the blood-brain barrier remain poorly understood.The major facilitator superfamily domain containing 2A has been identified as a key regulator of blood-brain barrier function.It plays a critical role in promoting and maintaining the formation and functional stability of the blood-brain barrier,in addition to the transport of lipids,such as docosahexaenoic acid,across the blood-brain barrier.Furthermore,an increasing number of studies have suggested that major facilitator superfamily domain containing 2A is involved in the molecular mechanisms of blood-brain barrier dysfunction in a variety of neurological diseases;however,little is known regarding the mechanisms by which major facilitator superfamily domain containing 2A affects the blood-brain barrier.This paper provides a comprehensive and systematic review of the close relationship between major facilitator superfamily domain containing 2A proteins and the blood-brain barrier,including their basic structures and functions,cross-linking between major facilitator superfamily domain containing 2A and the blood-brain barrier,and the in-depth studies on lipid transport and the regulation of blood-brain barrier permeability.This comprehensive systematic review contributes to an in-depth understanding of the important role of major facilitator superfamily domain containing 2A proteins in maintaining the structure and function of the blood-brain barrier and the research progress to date.This will not only help to elucidate the pathogenesis of neurological diseases,improve the accuracy of laboratory diagnosis,and optimize clinical treatment strategies,but it may also play an important role in prognostic monitoring.In addition,the effects of major facilitator superfamily domain containing 2A on blood-brain barrier leakage in various diseases and the research progress on cross-blood-brain barrier drug delivery are summarized.This review may contribute to the development of new approaches for the treatment of neurological diseases.

INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS

The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.

ATTRACTORS FOR THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained.

Random Attractors for Stochastic Reaction-Diffusion Equations with Distribution Derivatives on Unbounded Domains

In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.

NON-ISOTROPIC JACOBI SPECTRAL METHODS FOR UNBOUNDED DOMAINS

Some specific non-isotropic Jacobi approximations in multiple-dimensions are investigated, which are used for numerical solutions of differential equations on various unbounded domains. The convergence of proposed schemes are proved. Some efficient algorithms are provided. Numerical results are presented to illustrate the efficiency of this new approach.

THE EXISTENCE OF INFINITELY MANY SO UTIONS OF QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS IN UNBOUNDED DOMAINS

In this paper, we use the concentration-compactness principle together with the Mountain Pass Lemma to get the existence of nontrivial solutions and the existence of infinitely many solutions of the problem need not be compact operators from E to R~1.

A NON-OVERLAPPING DOMAIN DECOMPOSITION ALGORITHM BASED ON THE NATURAL BOUNDARY REDUCTION FOR WAVE EQUATIONS IN AN UNBOUNDED DOMAIN

In this paper, a new domain decomposition method based on the natural boundary reduction, which solves wave problems over an unbounded domain, is suggestted. An circular artifcial boundary is introduced. The original unbounded domain is divided into two subdomains, an internal bounded region and external unbounded region outside the artificial boundary. A Dirichlet-Neumann(D-N) alternating iteration algorithm is constructed. We prove that the algorithm is equavilent to preconditional Richardson iteration method. Numerical studies are performed by finite element method. The numerical results show that the convergence rate of the discrete D-N iteration is independent of the fnite element mesh size.

EXISTENCE AND STABILITY OF PERIODIC AND ALMOST PERIODIC SOLUTIONS TO THE BOUSSINESQ SYSTEM IN UNBOUNDED DOMAINS

In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of R^(n) in the framework of interpolation spaces.For the linear Boussinesq system we combine the L^(p)—L^(q)-smoothing estimates and interpolation functors to prove the existence of bounded mild solutions.Then,we prove the existence of periodic solutions by invoking Massera’s principle.We also prove the existence of almost periodic solutions.Then we use the results of the linear Boussinesq system to establish the existence,uniqueness and stability of the small periodic and almost periodic solutions to the Boussinesq system using fixed point arguments and interpolation spaces.Our results cover and extend the previous ones obtained in[13,34,38].

ON NONLINEAR HYPERBOLIC EQUATION IN UNBOUNDED DOMAIN

The following nonlinear hyperbolic equation is discussed in this paper:where A= -? + Iandx∈Rn. The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local solution of the above equation as M depends on x.

THE EXPONENTIAL PROPERTY OF SOLUTIONS BOUNDED FROM BELOW TO DEGENERATE EQUATIONS IN UNBOUNDED DOMAINS

This paper is focused on studying the structure of solutions bounded from below to degenerate elliptic equations with Neumann and Dirichlet boundary conditions in unbounded domains.After establishing the weak maximum principles,the global boundary Holder estimates and the boundary Harnack inequalities of the equations,we show that all solutions bounded from below are linear combinations of two special solutions(exponential growth at one end and exponential decay at the other)with a bounded solution to the degenerate equations.

Asymptotic Behavior for A Class of Non-autonomous Nonclassical Parabolic Equations with Delay on Unbounded Domain

In this article,we investigate the longtime behavior for the following nonautonomous nonclassical parabolic equations on unbounded domain ut−∆ut−∆u+λu=f(x,u(x,t−ρ(t)))+g(x,t).Under some suitable conditions on the delay term f and the non-autonomous forcing term g,we prove the existence of uniform attractors in Banach space CH1(RN)for the multivalued process generated by non-autonomous nonclassical parabolic equations with delays in unbounded domain.

NON-EXISTENCE FOR QUASILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS

Since [1] established the Pohozaev identity in bounded domains, this identity has been the principal tool to deal with the non-existence of the equation

Approximate Method of Riemann-Hilbert Problem for Elliptic Complex Equations of First Order in Multiply Connected Unbounded Domains

In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.

PoincaréProblem for Nonlinear Elliptic Equations of Second Order in Unbounded Domains

In [1], I. N. Vekua propose the Poincaré problem for some second order elliptic equations, but it can not be solved. In [2], the authors discussed the boundary value problem for nonlinear elliptic equations of second order in some bounded domains. In this article, the Poincaré boundary value problem for general nonlinear elliptic equations of second order in unbounded multiply connected domains have been completely investigated. We first provide the formulation of the above boundary value problem and corresponding modified well posed-ness. Next we obtain the representation theorem and a priori estimates of solutions for the modified problem. Finally by the above estimates of solutions and the Schauder fixed-point theorem, the solvability results of the above Poincaré problem for the nonlinear elliptic equations of second order can be obtained. The above problem possesses many applications in mechanics and physics and so on.

BOUNDARY VALUE PROBLEMS FOR FULLY NONLINEAR UNIFORMLY ELLIPTIC EQUATIONS OF SECOND IN UNBOUNDED DOMAINS

We consider fully nonlinear equations of the formF（z,u,Du,D2u） = F（x,y,u,uz,uy,uzz,uzy,uyy） = 0 （1）in unbounded open subset G = R2\Ωof the plane R2,where F is a real continuous function on U = G×R×R2×R3 and Ω= Ωi,Ωi is a simply connected region （i=1,2,"",N） . We assume the function F hascontinuous partial der ivatives Fuzz, Fuzy, Fuyy. on U.For a real function r C（ G） a real function u（x,y） is called a solution of （1） satisfyingu = r on G,（2）if there exists a constant P0】2 such that u C1 （ ） W2.pLoc0 （G） satisfies （1） almost everywhere and （2）in the common sense.The method for treating the above exterior Dirichlet problem in a given unbounded region is as fol-

NUMERICAL SOLUTIONS OF AN EIGENVALUE PROBLEM IN UNBOUNDED DOMAINS

A coupling method of finite element and infinite large element is proposed for the numerical solution of an eigenvalue problem in unbounded domains in this paper. With some conditions satisfied, the considered problem is proved to have discrete spectra. Several numerical experiments are presented. The results demonstrate the feasibility of the proposed method.

<i>L_p</i>-Estimations of Vector Fields in Unbounded Domains

Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier results for bounded domains. Estimations for scalar products make it possible to investigate wide classes of mathematical physics problems in physically inhomogeneous domains. Such estimations allow studying issues of correctness for problems with non-smooth coefficients. The paper analyses solvability of stationary set of Maxwell equations in inhomogeneous unbounded domains based on the proved Lp-estimations.

Diabetic retinopathy identification based on multi-sourcefree domain adaptation

AIM:To address the challenges of data labeling difficulties,data privacy,and necessary large amount of labeled data for deep learning methods in diabetic retinopathy(DR)identification,the aim of this study is to develop a source-free domain adaptation(SFDA)method for efficient and effective DR identification from unlabeled data.METHODS:A multi-SFDA method was proposed for DR identification.This method integrates multiple source models,which are trained from the same source domain,to generate synthetic pseudo labels for the unlabeled target domain.Besides,a softmax-consistence minimization term is utilized to minimize the intra-class distances between the source and target domains and maximize the inter-class distances.Validation is performed using three color fundus photograph datasets(APTOS2019,DDR,and EyePACS).RESULTS:The proposed model was evaluated and provided promising results with respectively 0.8917 and 0.9795 F1-scores on referable and normal/abnormal DR identification tasks.It demonstrated effective DR identification through minimizing intra-class distances and maximizing inter-class distances between source and target domains.CONCLUSION:The multi-SFDA method provides an effective approach to overcome the challenges in DR identification.The method not only addresses difficulties in data labeling and privacy issues,but also reduces the need for large amounts of labeled data required by deep learning methods,making it a practical tool for early detection and preservation of vision in diabetic patients.

Estimation-free spatial-domain image reconstruction of structured illumination microscopy

Structured illumination microscopy(SIM)achieves super-resolution(SR)by modulating the high-frequency information of the sample into the passband of the optical system and subsequent image reconstruction.The traditional Wiener-filtering-based reconstruction algorithm operates in the Fourier domain,it requires prior knowledge of the sinusoidal illumination patterns which makes the time-consuming procedure of parameter estimation to raw datasets necessary,besides,the parameter estimation is sensitive to noise or aberration-induced pattern distortion which leads to reconstruction artifacts.Here,we propose a spatial-domain image reconstruction method that does not require parameter estimation but calculates patterns from raw datasets,and a reconstructed image can be obtained just by calculating the spatial covariance of differential calculated patterns and differential filtered datasets(the notch filtering operation is performed to the raw datasets for attenuating and compensating the optical transfer function(OTF)).Experiments on reconstructing raw datasets including nonbiological,biological,and simulated samples demonstrate that our method has SR capability,high reconstruction speed,and high robustness to aberration and noise.