Automatic differentiation for gradient-based optimization of radiatively heated microelectronics manufacturing equipment

Automatic differentiation is applied to the optimal design of microelectronic manufacturing equipment. The performance of nonlinear, least-squares optimization methods is compared between numerical and analytical gradient approaches. The optimization calculations are performed by running large finite-element codes in an object-oriented optimization environment. The Adifor automatic differentiation tool is used to generate analytic derivatives for the finite-element codes. The performance results support previous observations that automatic differentiation becomes beneficial as the number of optimization parameters increases. The increase in speed, relative to numerical differences, has a limited value and results are reported for two different analysis codes

Site-Specific Bioconjugation of a Murine Dihydrofolate Reductase Enzyme by Copper(I)-Catalyzed Azide-Alkyne Cycloaddition with Retained Activity

Cu(I)-catalyzed azide-alkyne cycloaddition (CuAAC) is an efficient reaction linking an azido and an alkynyl group in the presence of copper catalyst. Incorporation of a non-natural amino acid (NAA) containing either an azido or an alkynyl group into a protein allows site-specific bioconjugation in mild conditions via CuAAC. Despite its great potential, bioconjugation of an enzyme has been hampered by several issues including low yield, poor solubility of a ligand, and protein structural/functional perturbation by CuAAC components. In the present study, we incorporated an alkyne-bearing NAA into an enzyme, murine dihydrofolate reductase (mDHFR), in high cell density cultivation of Escherichia coli, and performed CuAAC conjugation with fluorescent azide dyes to evaluate enzyme compatibility of various CuAAC conditions comprising combination of commercially available Cu(I)-chelating ligands and reductants. The condensed culture improves the protein yield 19-fold based on the same amount of non-natural amino acid, and the enzyme incubation under the optimized reaction condition did not lead to any activity loss but allowed a fast and high-yield bioconjugation. Using the established conditions, a biotin-azide spacer was efficiently conjugated to mDHFR with retained activity leading to the site-specific immobilization of the biotin-conjugated mDHFR on a streptavidin-coated plate. These results demonstrate that the combination of reactive non-natural amino acid incorporation and the optimized CuAAC can be used to bioconjugate enzymes with retained enzymatic activityope

Jacobian Code Generated by Source Transformation and Vertex Elimination can be as Efficient as Hand-Coding

This article presents the first extended set of results from ELIAD, a source- transformation implementation of the vertex-elimination Automatic Differentiation approach to calculating the Jacobians of functions defined by Fortran code (Griewank and Reese, Automatic Differentiation of Algorithms: Theory, Implementation, and Application, 1991, pp. 126-135). We introduce the necessary theory in terms of well known algorithms of numerical linear algebra applied to the linear, extended Jacobian system that prescribes the relationship between the derivatives of all variables in the function code. Using an example, we highlight the potential for numerical instability in vertex-elimination. We describe the source transformation implementation of our tool ELIAD and present results from five test cases, four of which are taken from the MINPACK- 2 collection (Averick et al, Report ANL/MCS-TM-150, 1692) and for which hand- coded Jacobian codes are available. On five computer/compiler platforms, we show that the Jacobian code obtained by ELIAD is as efficient as hand-coded Jacobian code. It is also between 2 to 20 times more efficient than that produced by current, state of the art, Automatic Differentiation tools even when such tools make use of sophisticated techniques such as sparse Jacobian compression. We demonstrate the effectiveness of reverse-ordered pre-elimination from the (successively updated) extended Jacobian system of all intermediate variables used once. Thereafter, the monotonic forward/reverse ordered eliminations of all other intermediates is shown to be very efficient. On only one test case were orderings determined by the Markowitz or related VLR heuristics found superior. A re-ordering of the statements of the Jacobian code, with the aim of reducing reads and writes of data from cache to registers, was found to have mixed effects but could be very beneficial

Application Of Automatic Differentiation To Groundwater Transport Models

This paper describes the application of automatic differentiation to obtain codes that evaluate derivatives of complex computer models efficiently, exactly, and with a minimum of human effort. Automatic differentiation is a method that produces a derivative code, given the model code and a list of parameters that are considered dependent and independent with respect to differentiation. The method produces a code that will evaluate derivatives exactly (up to machine precision), usually in much less time than the approximate finite-differences method. There are no inherent limits on program size or complexity. We applied the automatic differentiation tool ADIFOR (Automatic Differentiation in Fortran) to a two-dimensional and a three-dimensional groundwater flow and contaminant transport finite-element model to demonstrate the method. The CPU times for automatic differentiation were much faster than for the divided-differences method for both models, and somewhat slower than handwritten optimized analytic derivative code (written b

Synthesis of Amphiphilic Poly(<i>N</i>-vinylpyrrolidone)-<i>b</i>-poly(vinyl acetate) Molecular Bottlebrushes

Well-defined molecular bottlebrushes with poly­(<i>N</i>-vinylpyrrolidone) and poly­(<i>N</i>-vinylpyrrolidone)-<i>b</i>-poly­(vinyl acetate) (PNVP-<i>b</i>-PVOAc) side chains were prepared via a combination of atom transfer radical polymerization (ATRP) and reversible addition–fragmentation chain transfer (RAFT). A macro chain transfer agent poly­(2-((2-ethylxanthatepropanoyl)­oxy)­ethyl methacrylate) (PXPEM) was prepared by attaching xanthate chain transfer agents onto each monomeric unit of poly­(2-hydroxyethyl methacrylate). Subsequently, a RAFT polymerization procedure was used to synthesize molecular bottlebrushes with PNVP side chains with controlled molecular weight and low polydispersity by grafting from the PXPEM backbone. The side chains were then chain extended with PVOAc, yielding a bottlebrush macromolecule with PNVP-<i>b</i>-PVOAc side chains. The comb-like shape of the chain extended bottlebrushes was confirmed by atomic force microscopy (AFM)