On mass-independence of the minimal subtraction scheme in dimensional regularization II

A self-contained argument is given for the mass independence of the renormalization constants in the minimal subtraction scheme in dimensional regularization in a two mass theory (Yukawa theory). An extension to a theory containing more mass parameters seems straightforward.     

Nonlinear regression modeling using regularized local likelihood method

We introduce a nonlinear regression modeling strategy, using a regularized local likelihood method. The local likelihood method is effective for analyzing data with complex structure. It might be, however, pointed out that the stability of the local likelihood estimator is not necessarily guaranteed in the case that the structure of system is quite complex. In order to overcome this difficulty, we propose a regularized local likelihood method with a polynomial function which unites local likelihood and regularization. A crucial issue in constructing nonlinear regression models is the choice of a smoothing parameter, the degree of polynomial and a regularization parameter. In order to evaluate models estimated by the regularized local likelihood method, we derive a model selection criterion from an information-theoretic point of view. Real data analysis and Monte Carlo experiments are conducted to examine the performance of our modeling strategy.     

Investigating the anomaly puzzle in <Emphasis Type="Italic">N</Emphasis>=1 supersymmetric electrodynamics

Using Schwinger-Dyson equations and Ward identities in the N=1 supersymmetric electrodynamics regularized by higher derivatives, we find that we can calculate some contributions to the two-point Greens function of the gauge field and to the -function exactly in all orders of the perturbation theory. We use the results to investigate the anomaly puzzle in the considered theory.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 35–56, January, 2005.     

The determination of pair distance distributions by pulsed ESR using Tikhonov regularization

Pulsed ESR techniques with the aid of site-directed spin labeling have proven useful in providing unique structural information about proteins. The determination of distance distributions in electron spin pairs directly from the dipolar time evolution of the pulsed ESR signals by means of the Tikhonov regularization method is reported. The difficulties connected with numerically inverting this ill-posed mathematical problem are clearly illustrated. The Tikhonov regularization with the regularization parameter determined by the L-curve criterion is then described and tested to confirm its accuracy and reliability. The method is applied to recent experimental results on doubly labeled proteins that have been studied using two pulsed ESR techniques, double quantum coherence (DQC) ESR and double electron-electron resonance (DEER). The extracted distance distributions are able to provide valuable information about the conformational constraints in various partially folded states of proteins. This study supplies a mathematically reliable method for extracting pair distributions from pulsed ESR experimental data and has extended the use of pulsed ESR to provide results of greater value for structural biology.     

Edge-preserving restoration in 2-D fluorescence microscopy

Procedures for software image restoration can be useful for studying biological events. This is especially true in the case of low light-intensity fluorescence images, obtained with both wide-field and confocal microscopy. This review describes most of the algorithms for image restoration, with particular emphasis on edge-preserving procedures, and shows the results of their application to synthetic and fluorescence 2-D images.     

Two-Loop Anomalous Dimension of N = 1 Supersymmetric Quantum Electrodynamics Regularized Using Higher Covariant Derivatives

We calculate the two-loop anomalous dimension in the N=1 supersymmetric electrodynamics regularized through the higher covariant derivative method using the minimum subtraction scheme and show that the result is independent of the form of the regularizing term but does depend on the ratio between the masses M of the Pauli–Villars fields and the dimensional constant in the regularizing term. We propose a simple subtraction scheme in which the result is independent of the parameters of the regularization used.     

A Levenberg–Marquardt Scheme for Nonlinear Image Registration

This paper presents a Levenberg—Marquardt scheme to obtain a displacement vector field u(x)=(u ₁(x),u ₂(x)) ^t , which matches two images recorded with the same imaging machinery. The displacement vector should transform the image location x=(x ₁,x ₂) ^t of an image T, such that the grey level are equal to another image R. The so-called mono-modal image registration problem leads to minimize the nonlinear least squares functional D(u(x))=R(x)–T(x–u(x))².To apply the Levenberg—Marquardt method, we replace the nonlinear functional D by its linearization around a current approximation. The resulting quadratic minimization problem is ill-posed, due to the fact that determining the unknown components of the displacements merely from the images is an underdetermined problem. We use an auxiliary Lagrange term borrowed from linear elasticity theory, which incorporates smoothness constraints to the displacement field. Finally, numerical experiments demonstrate the robustness and effectiveness of the proposed approach.This revised version was published online in October 2005 with corrections to the Cover Date.     

Asymptotic analysis of certain classes of singularly perturbed problems on the semiaxis

We propose a new method for asymptotic integration of certain classes of singularly perturbed Cauchy problems on the semiaxis for nonhomogeneous systems of linear ordinary differential equations; this method is a further development of the ideas of the regularization method. This method enables us to prove the existence of a unique bounded (as ε→+0) solution of such problems and leads to a simpler and more constructive algorithm for obtaining the asymptotic expansion of the solution and singling out all of its singularities in closed analytic form (including the critical case in which the spectral points of the limit operator may touch the imaginary axis). The proposed method supplements and sharpens earlier results. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 111–117, July, 1997. Translated by N. K. Kulman     

Maximum entropy method for solving operator equations of the first kind

The maximum entropy method for linear ill-posed problems with modeling error and noisy data is considered and the stability and convergence results are obtained. When the maximum entropy solution satisfies the “source condition”, suitable rates of convergence can be derived. Considering the practical applications, ana posteriori choice for the regularization parameter is presented. As a byproduct, a characterization of the maximum entropy regularized solution is given.     

不适定问题的迭代Tikhonov正则化方法

Tikhonov正则化方法是研究不适定问题最重要的正则化方法之一,但由于这种方法的饱和效应,使得不可能随着解的光滑性假设的提高而提高收敛率,即不能使正则解与准确解的误差估计达到阶数最优．本文所讨论的迭代的Tikhonov正则化方法对此进行了改进,保证了误差估计总可以达到阶数最优．数值试验结果表明计算效果良好．