Optimization of parameters for semiempirical methods. III Extension of PM3 to Be,Mg, Zn,Ga, Ge,As, Se,Cd, In,Sn, Sb,Te, Hg,Tl, Pb,and Bi

Using a recently developed procedure for optimizing parameters for semiempirical methods,¹ PM3 has been extended to a total of 28 elements. Average ΔH_f errors for the newly parameterized elements are Be: 8.6, Mg: 8.4, Zn: 5.8, Ga: 14.9, Ge: 11.4, As: 8.5, Se: 11.1, Cd: 2.6, In: 11.3, Sn: 9.0, Sb: 13.7, Te: 11.3, Hg: 6.8, Tl: 6.5, Pb: 7.4, and Bi: 10.9 kcal/mol. For some elements the paucity of data has resulted in a method, which, while highly accurate, is likely to be only poorly predictive.     

Hyperpolarized 13C Magnetic Resonance Imaging of Fumarate Metabolism by Parahydrogen-induced Polarization: A Proof-of-Concept in vivo Study

Hyperpolarized [1-¹³C]fumarate is a promising magnetic resonance imaging (MRI) biomarker for cellular necrosis, which plays an important role in various disease and cancerous pathological processes. To demonstrate the feasibility of MRI of [1-¹³C]fumarate metabolism using parahydrogen-induced polarization (PHIP), a low-cost alternative to dissolution dynamic nuclear polarization (dDNP), a cost-effective and high-yield synthetic pathway of hydrogenation precursor [1-¹³C]acetylenedicarboxylate (ADC) was developed. The trans-selectivity of the hydrogenation reaction of ADC using a ruthenium-based catalyst was elucidated employing density functional theory (DFT) simulations. A simple PHIP set-up was used to generate hyperpolarized [1-¹³C]fumarate at sufficient ¹³C polarization for ex vivo detection of hyperpolarized ¹³C malate metabolized from fumarate in murine liver tissue homogenates, and in vivo ¹³C MR spectroscopy and imaging in a murine model of acetaminophen-induced hepatitis.     

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.     

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.     

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.     

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.     

Deformation of bilayer lipid membranes in bio-inspired materials and systems

Planar bilayer lipid membranes (BLMs) are currently employed to construct many bio-inspired material systems and structures. In order to characterize the pressure effects on the equilibrium configurations of these biological membranes, a novel continuum model is proposed. The BLM is assumed to be a two-layer Smectic A liquid crystal. The mean orientation of the amphiphilic molecules comprising the membrane is postulated to be perpendicular to the layers and each layer is idealized as a two dimensional liquid. Moreover, the BLM is modeled as a simply supported plate undergoing small deformations. It is subjected to a pressure load that acts perpendicularly to the layers. The equilibrium equations and boundary conditions are derived from the bulk elastic energy for Smectic A liquid crystals as described by de Gennes and Prost (1993) by using variational methods. The resulting fourth-order linear partial differential equation is solved by employing cylindrical functions and the series solution is proved to be convergent. The solution is numerically computed for values of the model parameters that are reported in the literature. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution of the normal state of a strongly interacting Fermi gas from a pseudogap phase to a molecular Bose gas

Wave-vector resolved radio frequency spectroscopy data for an ultracold trapped Fermi gas are reported for several couplings at T(c), and extensively analyzed in terms of a pairing-fluctuation theory. We map the evolution of a strongly interacting Fermi gas from the pseudogap phase into a fully gapped molecular Bose gas as a function of the interaction strength, which is marked by a rapid disappearance of a remnant Fermi surface in the single-particle dispersion. We also show that our theory of a pseudogap phase is consistent with a recent experimental observation as well as with quantum Monte Carlo data of thermodynamic quantities of a unitary Fermi gas above T(c).