A Multi-Baseline PolInSAR Forest Height Inversion Method Taking into Account the Model Ill-posed Problem

Affected by the insufficient information of single baseline observation data,the three-stage method assumes the Ground-to-Volume Ratio(GVR)to be zero so as to invert the vegetation height.However,this assumption introduces much biases into the parameter estimates which greatly limits the accuracy of the vegetation height inversion.Multi-baseline observation can provide redundant information and is helpful for the inversion of GVR.Nevertheless,the similar model parameter values in a multi-baseline model often lead to ill-posed problems and reduce the inversion accuracy of conventional algorithm.To this end,we propose a new step-by-step inversion method applied to the multi-baseline observations.Firstly,an adjustment inversion model is constructed by using multi-baseline volume scattering dominant polarization data,and the regularized estimates of model parameters are obtained by regularization method.Then,the reliable estimates of GVR are determined by the MSE(mean square error)analysis of each regularized parameter estimation.Secondly,the estimated GVR is used to extracts the pure volume coherence,and then the vegetation height parameter is inverted from the pure volume coherence by least squares estimation.The experimental results show that the new method can improve the vegetation height inversion result effectively.The inversion accuracy is improved by 26%with respect to the three-stage method and the conventional solution of multi-baseline.All of these have demonstrated the feasibility and effectiveness of the new method.

Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).

Neurocircuit regeneration by extracellular matrix reprogramming

The brain's extracellular matrix(ECM),which is comprised of protein and glycosaminoglycan(GAG)scaffolds,constitutes 20%-40% of the human brain and is considered one of the largest influencers on brain cell functioning(Soles et al.,2023).Synthesized by neural and glial cells,the brain's ECM regulates a myriad of homeostatic cellular processes,including neuronal plasticity and firing(Miyata et al.,2012),cation buffering(Moraws ki et al.,2015),and glia-neuron interactions(Anderson et al.,2016).Considering the diversity of functions,dynamic remodeling of the brain's ECM indicates that this understudied medium is an active participant in both normal physiology and neurological diseases.

Stiffness-tunable biomaterials provide a good extracellular matrix environment for axon growth and regeneration

Neuronal growth, extension, branching, and formation of neural networks are markedly influenced by the extracellular matrix—a complex network composed of proteins and carbohydrates secreted by cells. In addition to providing physical support for cells, the extracellular matrix also conveys critical mechanical stiffness cues. During the development of the nervous system, extracellular matrix stiffness plays a central role in guiding neuronal growth, particularly in the context of axonal extension, which is crucial for the formation of neural networks. In neural tissue engineering, manipulation of biomaterial stiffness is a promising strategy to provide a permissive environment for the repair and regeneration of injured nervous tissue. Recent research has fine-tuned synthetic biomaterials to fabricate scaffolds that closely replicate the stiffness profiles observed in the nervous system. In this review, we highlight the molecular mechanisms by which extracellular matrix stiffness regulates axonal growth and regeneration. We highlight the progress made in the development of stiffness-tunable biomaterials to emulate in vivo extracellular matrix environments, with an emphasis on their application in neural repair and regeneration, along with a discussion of the current limitations and future prospects. The exploration and optimization of the stiffness-tunable biomaterials has the potential to markedly advance the development of neural tissue engineering.

A matrix metalloproteinase-responsive hydrogel system controls angiogenic peptide release for repair of cerebral ischemia/reperfusion injury

Vascular endothelial growth factor and its mimic peptide KLTWQELYQLKYKGI(QK)are widely used as the most potent angiogenic factors for the treatment of multiple ischemic diseases.However,conventional topical drug delivery often results in a burst release of the drug,leading to transient retention(inefficacy)and undesirable diffusion(toxicity)in vivo.Therefore,a drug delivery system that responds to changes in the microenvironment of tissue regeneration and controls vascular endothelial growth factor release is crucial to improve the treatment of ischemic stroke.Matrix metalloproteinase-2(MMP-2)is gradually upregulated after cerebral ischemia.Herein,vascular endothelial growth factor mimic peptide QK was self-assembled with MMP-2-cleaved peptide PLGLAG(TIMP)and customizable peptide amphiphilic(PA)molecules to construct nanofiber hydrogel PA-TIMP-QK.PA-TIMP-QK was found to control the delivery of QK by MMP-2 upregulation after cerebral ischemia/reperfusion and had a similar biological activity with vascular endothelial growth factor in vitro.The results indicated that PA-TIMP-QK promoted neuronal survival,restored local blood circulation,reduced blood-brain barrier permeability,and restored motor function.These findings suggest that the self-assembling nanofiber hydrogel PA-TIMP-QK may provide an intelligent drug delivery system that responds to the microenvironment and promotes regeneration and repair after cerebral ischemia/reperfusion injury.

Immunohistochemical expression of matrix metalloproteinase-9 and 13 in oral squamous cell carcinoma and their role in predicting lymph node metastasis

BACKGROUND One of the main characteristics of oral squamous cell carcinoma(OSCC)is that it metastasizes to cervical lymph nodes frequently with a high degree of local invasiveness.A primary feature of malignant tumors is their penetration of neighboring tissues,such as lymphatic and blood arteries,due to the tumor cells'capacity to break down the extracellular matrix(ECM).Matrix metalloproteinases(MMPs)constitute a family of proteolytic enzymes that facilitate tissue remo-deling and the degradation of the ECM.MMP-9 and MMP-13 belong to the group of extracellular matrix degrading enzymes and their expression has been studied in OSCC because of their specific functions.MMP-13,a collagenase family member,is thought to play an essential role in the MMP activation cascade by breaking down the fibrillar collagens,whereas MMP-9 is thought to accelerate the growth of tumors.Elevated MMP-13 expression has been associated with tumor behavior and patient prognosis in a number of malignant cases.The authors wish to thank Jadhav KB for his valuable opinion during the preparation of the manuscript.

Arnoldi Projection Fractional Tikhonov for Large Scale Ill-Posed Problems

It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth for ill-posed problems,so fractional Tikhonov methods have been introduced to remedy this shortcoming.And Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining apartial Arnoldi decomposition of the given matrix.In this paper,we propose a new method to compute an approximate solution of large scale linear discrete ill-posed problems which applies projection fractional Tikhonov regularization in Krylov subspace via Arnoldi process.The projection fractional Tikhonov regularization combines the fractional matrices and orthogonal projection operators.A suitable value of the regularization parameter is determined by the discrepancy principle.Numerical examples with application to image restoration are carried out to examine that the performance of the method.

REGULARIZATION METHODS FOR NONLINEAR ILL-POSED PROBLEMS WITH ACCRETIVE OPERATORS

This article is devoted to the regularization of nonlinear ill-posed problems with accretive operators in Banach spaces. The data involved are assumed to be known approximately. The authors concentrate their discussion on the convergence rates of regular solutions.

ITERATIVE REGULARIZATION METHODS FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS WITH M-ACCRETIVE MAPPINGS IN BANACH SPACES

In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.

An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems

In order to improve the reconstruction performance for ill-posed emission tomographic problems with limited projections, a generalized interpolation method is proposed in this paper, in which the virtual lines of projection are fabricated from, but not linearly dependent on, the measured projections. The method is called the virtual projection（VP） method.Also, an iterative correction method for the integral lengths is proposed to reduce the error brought about by the virtual lines of projection. The combination of the two methods is called the iterative virtual projection（IVP） method. Based on a scheme of equilateral triangle plane meshes and a six asymmetrically arranged detection system, numerical simulations and experimental verification are conducted. Simulation results obtained by using a non-negative linear least squares method,without any other constraints or regularization, demonstrate that the VP method can gradually reduce the reconstruction error and converges to the desired one by fabricating additional effective projections. When the mean square deviation of normal error superimposed on the simulated measured projections is smaller than 0.03, i.e., the signal-to-noise ratio（SNR）for the measured projections is higher than 30.4, the IVP method can further reduce the reconstruction error reached by the VP method apparently. In addition, as the regularization matrix in the Tikhonov regularization method is updated by an iterative correction process similar to the IVP method presented in this paper, or the Tikhonov regularization method is used in the IVP method, good improvement is achieved.

Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

A mixed Newton-Tikhonov method for nonlinear ill-posed problems

Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems, which have attracted extensive attention. However, computational cost of Newton type methods is high because practical problems are complicated. We propose a mixed Newton-Tikhonov method, i.e., one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method. Convergence and stability of this method are proved under some conditions. Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs.

基于Doehlert Matrix的全贯流泵装置定转子进出流间隙优化设计

全贯流泵是一种新型的机电-水泵一体式贯流泵,然而其在运行时存在定转子间隙回流,扰乱了叶轮内的流场分布,导致泵装置产生能量损失、压力波动和噪声等问题,影响泵站的正常运行。通过数值模拟和模型试验研究全贯流泵装置定转子间隙流的水力特性,结合Doehlert Matrix设计-响应面优化法对其定转子进、出流间隙结构进行优化设计,揭示全贯流泵装置定转子进、出流间隙结构对泵装置性能的影响机理,并得到最终优化的折角式定转子进、出流间隙结构方案为:外侧延伸段长度t1为4.921r,外侧收缩段长度x1为0.624r,内侧延伸段长度t2为3.655r,内侧收缩段长度x2为1.6r(r为定转子间隙宽度),使得全贯流泵装置扬程和效率分别提升约10.3%和5.2%。

Numerical Experiments and Structural Transformation of Non-Linear Evolution in Ill-posed Systems

Numerical experiments on non-linear equations of the 1st-and 3rd-order derivatives have been carried out through structural analyses in the phase space according to the numerical instability of ill-posed systems,with changes of initial values and parameters,etc..The results show that the quantitative instability in an ill-posed system may reveal reversed transformation in system evolution by structural representation,and confirm A·Dauglas' theorem that "a non-linear equation does not satisfy the existence of the initial value in a linear well-posed system".

REGULARIZATION OF AN ILL-POSED HYPERBOLIC PROBLEM AND THE UNIQUENESS OF THE SOLUTION BY A WAVELET GALERKIN METHOD

We consider the problem K（x）Uxx = utt , 0 〈 x 〈 1, t 〉 0, with the boundary condition u（O,t） = g（t） E LZ（R） and ux（O,t） = 0, where K（x） is continuous and 0 〈α≤ K （x） 〈 ＋∞. This is an ill-posed problem in the sense that, if the solution exists, it does not depend continuously on g. Considering the existence of a solution u（x, .） E H2（R） and using a wavelet Galerkin method with Meyer multiresolution analysis, we regularize the ill-posedness of the problem. Furthermore we prove the uniqueness of the solution for this problem.

Nonlinear implicit iterative method for solving nonlinear ill-posed problems

In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.

WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS

This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.

A Newton-type method for nonlinear ill-posed problems with A-smooth regularization

In this paper we present a regularized Newton-type method for ill-posed problems, by using the A-smooth regularization to solve the linearized ill-posed equations. For noisy data a proper a posteriori stopping rule is used that yields convergence of the Newton iteration to a solution, as the noise level goes to zero, under certain smoothness conditions on the nonlinear operator. Some appropriate assumptions on the closedness and smoothness of the starting value and the solution are shown to lead to optimal convergence rates.

LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES

In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the imple- mentation of Lavrentiev regularization method. Using general HSlder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock （2005） for choosing the regularization parameter.

A New Regularized Solution to Ill-Posed Problem in Coordinate Transformation

Coordinates transformation is generally required in GPS applications. If the transformation parameters are solved with the known coordinates in a small area using the Bursa model, the precision of transformed coordinates is generally very poor. Since the translation parameters and rotation parameters are highly correlated in this case, a very large condition number of the coefficient matrix A exists in the linear system of equations. Regularization is required to reduce the effects caused by the intrinsic ill-conditioning of the problem and noises in the data, and to stabilize the solution. Based on advanced regularized methods, we propose a new regularized solution to the ill-posed coordinate transformation problem. Simulation numerical experiments of coordinate transformation are given to shed light on the relationship among different regularization approaches. The results indicate that the proposed new method can obtain a more reasonable resolution with higher precision and/or robustness.