Determination of molecular weight distribution by applying a modified regularization technique

The Newsletter is a key element in further enhancing the value of the journal to the inverse problems community. So why not be a part of this exciting forum by sending to our Bristol office material suitable for inclusion under any of the categories mentioned above. Your contributions will be very welcome. Book review Introduction to Inverse Problems in Imaging M Bertero and P Boccacci 1998 Bristol: Institute of Physics 362 pp ISBN 0-7503-0435-9 (pbk) £25.00, $49.00 This book shows that several problems in imaging are in fact linear inverse problems. In general inverse problems are ill-posed in the sense that small perturbations in the (measured) data have a significant influence on the output. Consequently, numerical methods developed in a general setting of inverse problems which cure the ill-posedness (such methods are called regularization methods) can be applied to solve problems in imaging. This is an excellent textbook on the principle of linear inverse problems, methods of their numerical solution and practical applications in imaging. It introduces basic ideas and methods for the solution of inverse and ill-posed problems while avoiding the mathematics of functional treatment of operator equations. This goal is achieved by a bottom-up presentation: the authors focus on the two problems of image deconvolution and tomography (bottom) and develop regularization theory specifically for these two problems. Most other books which are concerned with the numerical solution of inverse problems present a top-down approach. That is, a general regularization theory (top) is developed which is then applied to particular problems. The distinguished presentation makes the book very useful to students in applied mathematics, practitioners in engineering science and image processing. This book has the best prerequisites to establish a close link between the mathematical fields of imaging and inverse problems. Mainly the book focuses on two topics: image deconvolution and linear imaging systems. 1. In image deconvolution the goal is to restore a space invariant blurred image. This part of the book contains mathematical tools in image deconvolution, examples of space invariant imaging systems, a comparison of image deconvolution techniques and low-pass filtering techniques, the analysis of the ill-posedness of the deconvolution problem, regularization methods for deconvolution such as constrained least squares regularization, Tikhonov regularization, iterative regularization and statistical methods. Since the authors focus on particular problems they are able to analyse various methods for deconvolution on a very concrete level. As an example I would like to mention that the authors analyse Fourier methods for deconvolution. Thus they provide an optimal starting point to the theory of inverse problems for people working in the area of signal and image processing. 2. The second part of the book considers linear imaging systems that are not of a convolution type such as tomography problems, diffraction problems and inverse scattering problems. Efficient numerical methods for the solution of this class of problems such as singular value decomposition, Tikhonov regularization methods and Fourier-based methods are presented. O Scherzer Universität Linz

Calf-thymus (CT-DNA) is widely used as a binding agent. The commercial samples are known to be "highly polymerized DNA" samples. CT-DNA is known to be fragile in particular upon ultrasonic wave irradiation. Degradation products could have dramatic consequences on its bio-sensing activity, and an accurate determination of the molecular weight distribution and stability of commercial samples is highly demanded. We investigated the sensitivity of charge detection mass spectrometry (CDMS), a single-molecule MS method, both with single-pass and ion trap CDMS ("Benner" trap) modes to the determination of the composition and stability (under multiphoton IR irradiation) of calf-thymus DNAs. We also investigated the changes in molecular weight distributions in the course of sonication by irradiating ultrasonic waves to CT-DNA. We report, for the first time, the direct molecular weight (MW) distribution of DNA sodium salt from calf-thymus revealing two populations at high (~10MDa) and low (~3MDa) molecular weights. We evidence a transition between the high-MW to the low-MW distribution, confirming that the low-MW distribution results from degradation of CT-DNA. Finally, we report also IRMPD experiments carried out on trapped single-stranded linear DNAs from calf-thymus allowing extraction of their activation energy for unimolecular dissociation. We show that single-pass CDMS is a direct, efficient and accurate MS-based approach to determine the composition of calf-thymus DNAs. Furthermore, ion trap CDMS allows us to evaluate the stability (both under multiphoton IR irradiation and in the course of sonication by irradiating ultrasonic wave) of calf-thymus DNAs.

This paper is about a regularization method applied to a chemical process considered as a nonlinear system. The Volterra model is used to represent such a nonlinear system. Volterra kernels are expanded on generalized orthonormal function bases in order to provide a quite flexible and accurate model. Tikhonov's regularization method, optimized on a sliding window, is then applied to the Volterra model in order to restore an unknown quantity from measurements of another quantity. Such an inverse method is then applied to a simulated pollutant oxidation process

Comparisons between direct and inverse approaches in problems of recovering the true profile of a spectral line

A convenient method that enables determination of molecular weight distributions of diblock copolymers with conventional size exclusion chromatography (SEC) without referring to any kind of calibration curve or molar mass-sensitive detecting devices is described. It is based on the well-established procedure to calculate the number-average molecular weight of copolymers from their chemical composition and the molar mass of the first block segment (precursor), applied on an ensemble of monodisperse copolymer fractions. The chemical composition of SEC fractions is calculated from their UV and RI detector traces, and the number-average molecular weight of the precursor, which is to be known from independent measurements, is taken as the molar mass of the first block segment. The molecular weight distributions and averages obtained by this method for selected copolymer samples were found to be in reasonably good agreement with the ones determined by NMR and SEC with on-line viscosity or multiangle laser light scattering detection.

Colorimetric assay for the determination of molecular weight distribution and branching characteristics of starch hydrolysates

This paper presents a stable method for the identification of sources located on the separation interface of two homogeneous media (where one of them is contained by the other one), from measurement yielded by those sources on the exterior boundary of the media. This is an ill-posed problem because numerical instability is presented, i.e., minimal errors in the measurement can result in significant changes in the solution. To obtain the proposed stable method the identification problem is categorized into three subproblems, two of which present numerical instability and regularization methods must be applied to obtain their solution in a stable form. To manage the numerical instability due to the ill-posedness of these subproblems, the Tikhonov regularization and sequential smoothing methods are used. We illustrate this methodology in a circular and irregular region to demonstrate the feasibility of the proposed method, which yields convergent and stable solutions for input data with and without noise.

To obtain a unique and stable solution to the gravity inverse problem, a priori information reflecting geological attributes of the gravity source must be used. Mathematical conditions to obtain stable solutions are established in Tikhonov's regularization method, where the a priori information is introduced via a stabilizing functional, which may be suitably designed to incorporate some relevant geological information. However, there is no unifying approach establishing general uniqueness conditions for a gravity inverse problem. Rather, there are many theorems, usually establishing just abstract mathematical conditions and making it difficult to devise the type of geological information needed to guarantee a unique solution. In Part I of these companion papers, we show that translating the mathematical uniqueness conditions into geological constraints is an important step not only in establishing the type of geological setting where a particular method may be applied but also in designing new gravity inversion methods. As an example, we analyze three uniqueness theorems in gravimetry restricted to the class of homogeneous bodies with known density and show that the uniqueness conditions established by them are more probably met if the solution is constrained to be a compact body without curled protrusions at their borders. These conditions, together with stabilizing conditions (assuming a simple shape for the source), form a guideline to construct sound gravity inversion methods. A historical review of the gravity interpretation methods shows that several methods implicitly follow this guideline. In Part II we use synthetic examples to illustrate the theoretical results derived in Part I. We also illustrate that the presented guideline is not the only way to design sound inversion methods for the class of homogeneous bodies. We present an alternative approach which produces good results but whose design requires a good dose of the interpreter's art.

Determination of Molecular Weight Distribution of Polymeric Substances by Thin-Layer Chromatography

Determination of molecular weight distribution of polymers from the data of analytical summative fractionation or turbidimetric titration

Comparative investigation of unfolding methods

The potentiality of passive thermoacoustic tomography (PTT) is considered theoretically. The problem is formulated to reconstruct the distribution of the thermodynamic temperature at a depth from the acoustic radiation generated by thermal noise and measured by a set of piezotransducers on the body surface. The 2-D inverse problem has been studied. Three mathematical methods of reconstruction were investigated: (1) the least squares method; (2) Tikhonov's regularization method; and (3) the method of elimination of non-physical solutions. The reconstruction in square as well as in rectangular areas was studied. If one uses the least squares method the square area can be separated into 5 5 subareas, the typical dimension of every one is 0.5-2 cm for measurements conducted in the frequency range 2-0.5 MHz. The precision deltaT in temperature reconstruction in different layers is about 0.1-0.2 K for smooth distributions of the thermodynamic temperature and 0.1-0.4 K for abrupt distributions, if the number of different scans is about 102 and the time of data collecting is about 1 min.

The generalized discrepancy principle in regularization is investigated from the optimization point of view. Tikhonov's regularization method can be considered as a Lagrange multiplier method. This approach allows formulating a search algorithm for choosing the regularization parameter. Moreover, the developed relations may force the introduction of negative regularization parameters for realizing the generalized discrepancy principle.

Controlling nonstationary vibrations of a plate by means of additional loads

We consider the estimation of the particle size distribution (PSD) of concentrated particle systems with low contrast between particles and solvent from light scattering (LS) measurements. We follow Pedersen's monodisperse approximation, in which an effective particle volume fraction is used to take into account interference between particles. This parameter must be determined simultaneously with the PSD to characterize the system. To solve the inverse problem, we first assumed that the PSD is described by a log-normal function. We applied the Levenberg–Marquardt algorithm for the non-linear parameter estimation. We also approached the free-form case following a scheme by which Tikhonov's regularization method is used to estimate the PSD, simultaneously with a non-linear least-squares optimization used to estimate the effective parameter. The solutions obtained from the analysis of simulated measurements showed that a priori knowledge of the distribution form improves the quality of the estimation, but the problem can be solved properly when actual PSD form is not known.