An interlaboratory capillary zone electrophoresis-UV study of various monoclonal antibodies,instruments, and ε-aminocaproic acid lots

Capillary zone electrophoresis ultraviolet (CZE-UV) has become increasingly popular for the charge heterogeneity determination of mAbs and vaccines. The ε-aminocaproic acid (eACA) CZE-UV method has been used as a rapid platform method. However, in the last years, several issues have been observed, for example, loss in electrophoretic resolution or baseline drifts. Evaluating the role of eACA on the reported issues, various laboratories were requested to provide their routinely used eACA CZE-UV methods, and background electrolyte compositions. Although every laboratory claimed to use the He et al. eACA CZE-UV method, most methods actually deviate from He's. Subsequently, a detailed interlaboratory study was designed wherein two commercially available mAbs (Waters’ Mass Check Standard mAb [pI 7] and NISTmAb [pI 9]) were provided to each laboratory, along with two detailed eACA CZE-UV protocols for a short-end, high-speed, and a long-end, high-resolution method. Ten laboratories participated each using their own instruments, and commodities, showing excellence method performance (relative standard deviations [RSDs] of percent time-corrected main peak areas from 0.2% to 1.9%, and RSDs of migration times from 0.7% to 1.8% [n = 50 per laboratory], analysis times in some cases as short as 2.5 min). This study clarified that eACA is not the main reason for the abovementioned variations.     

The Second Cohomology of Simple SL 3-Modules

Let G be the simple, simply connected algebraic group SL ₃ defined over an algebraically closed field K of characteristic p > 0. In this article, we find H ²(G, V) for any irreducible G-module V. When p > 7, we also find H ²(G(q), V) for any irreducible G(q)-module V for the finite Chevalley groups G(q) = SL(3, q) where q is a power of p.     

Model‐Based Inquiry and School Science: Creating Connections

Much has been made in recent years of inquiry approaches to science education and the promise of such instruction to alleviate some of the ills of science education, yet in some ways this construct is still unclear to many in the field. In this paper we explore one view of inquiry in science that is based on the development, use, assessment, and revision of models and related explanations. Because modeling plays a central role in scientific inquiry it should be a prominent feature of students’ science education. We present a framework based on this view that can serve as a guide to curriculum development and instructional decision‐making with the goal of creating classroom environments that mirror important aspects of scientific practice. Specifically, the framework allows us to emphasize that scientists: engage in inquiry other than controlled experiments, use existing models in their inquiries, engage in inquiry that leads to revised models, use models to construct explanations, use models to unify their understanding, and engage in argumentation. Here, we discuss how these practices can be incorporated into science classrooms and illustrate that discussion with examples from our research classrooms.     

Properties of a representation of a basis for the null space

Given a rectangular matrixA(x) that depends on the independent variablesx, many constrained optimization methods involve computations withZ(x), a matrix whose columns form a basis for the null space ofA ^T(x). WhenA is evaluated at a given point, it is well known that a suitableZ (satisfyingA ^T Z = 0) can be obtained from standard matrix factorizations. However, Coleman and Sorensen have recently shown that standard orthogonal factorization methods may produce orthogonal bases that do not vary continuously withx; they also suggest several techniques for adapting these schemes so as to ensure continuity ofZ in the neighborhood of a given point.This paper is an extension of an earlier note that defines the procedure for computingZ. Here, we first describe howZ can be obtained byupdating an explicit QR factorization with Householder transformations. The properties of this representation ofZ with respect to perturbations inA are discussed, including explicit bounds on the change inZ. We then introduceregularized Householder transformations, and show that their use implies continuity of the full matrixQ. The convergence ofZ andQ under appropriate assumptions is then proved. Finally, we indicate why the chosen form ofZ is convenient in certain methods for nonlinearly constrained optimization.The research of the Stanford authors was supported by the U.S. Department of Energy Contract DE-AM03-76SF00326, PA No. DE-AT03-76ER72018; the National Science Foundation Grants MCS-7926009 and ECS-8312142; the Office of Naval Research Contract N00014-75-C-0267; and the U.S. Army Research Office Contract DAAG29-84-K-0156.The research of G.W. Stewart was supported by the Air Force Office of Scientific Research Contract AFOSR-82-0078.     

Four algorithms for the the efficient computation of truncated pivoted QR approximations to a sparse matrix

Summary. In this paper we propose four algorithms to compute truncated pivoted QR approximations to a sparse matrix. Three are based on the Gram–Schmidt algorithm and the other on Householder triangularization. All four algorithms leave the original matrix unchanged, and the only additional storage requirements are arrays to contain the factorization itself. Thus, the algorithms are particularly suited to determining low-rank approximations to a sparse matrix. Received February 23, 1998 / Revised version received April 16, 1998     

Constructing integer programming models by the predicate calculus

A modelling language for Integer Programming (IP) based on the Predicate Calculus is described. This is particularly suitable for building models with logical conditions. Using this language a model is specified in terms of predicates. This is then converted automatically by a series of transformation rules into a normal form from which an IP model can be created. There is also some discussion of alternative IP formulations which can be incorporated into the system as options. Further practical considerations are discussed briefly concerning implementation language and incorporation into practical Mathematical Programming Systems.     

A global existence theorem for the general coagulation–fragmentation equation with unbounded kernels

In this article an existence theorem is proved for the coagulation–fragmentation equation with unbounded kernel rates. Solutions are shown to be in the space X⁺ = {c∈L¹: ∫ (1 + x)∣c(x)∣dx < ∞} whenever the kernels satisfy certain growth properties and the non-negative initial data belong to X⁺. The proof is based on weak L¹ compactness methods applied to suitably chosen approximating equations.     

K3 surfaces, rational curves, and rational points

We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981.     

A statistical process control approach to selecting a warm-up period for a discrete-event simulation

The selection of a warm-up period for a discrete-event simulation continues to be problematic. A variety of selection methods have been devised, and are briefly reviewed. It is apparent that no one method can be recommended above any other. A new approach, based upon the principles of statistical process control, is described (SPC method). Because simulation output data are often highly autocorrelated and potentially non-normal, the batch means method is employed in constructing the control chart. The SPC method is tested on seven data sets and encouraging results are obtained concerning its accuracy. The approach is also discussed with respect to its ease of implementation, simplicity, generality of use and requirements for parameter estimation.