A uniform approach to gradient methods for linear operator equations

Let T be a bounded linear operator from one Hilbert space to another. A class of gradient methods for minimizing ∥Tx ? f ∥² is analyzed and characterized by the step-size used in the iteration $\text{x}{}_{\mathrm{n+1}}\text{= x}{}_{\mathrm{n}}\text{? s(x}{}_{\mathrm{n}}\text{) T}{}^1\text{(Tx}{}_{\mathrm{n}}\text{? f)}$. A general convergence theorem is proved under the simple assumption that the least-squares problem exhibits a solution. Specific convergence rates are established for operators with closed and nonclosed ranges.     

Edge effects in the membrane analogy

This paper explains the origin and magnitude of an edge effect which causes errors in stress analyses made with the use of the membrane analogy. Although Griffith and Taylor noted this effect in their classical paper on the use of soap films in solving torsion problems, it was not explained, nor were the magnitudes of the errors estimated there. The errors caused by the edge effect cannot be eliminated, but can be reduced by proper design, and compensated for once their origin and behavior are known.     

A modification of Armijo's step-size rule for negative curvature

Armijo's step-size procedure for function minimization is modified to include second derivative information. Accumulation points using this procedure are shown to be stationary points with positive semi-definite Hessian matrices.This research was supported by the United States Army Research Office.     

Alkylation of flavins using methyl fluorosulfonate

A method for N³ methylation of flavins is described using methyl fluorosulfonate. The reaction proceeds through O alkylation of the carbonyls followed by an O to N rearrangement.     

Strongly polynomial and fully combinatorial algorithms for bisubmodular function minimization

Bisubmodular functions are a natural “directed”, or “signed”, extension of submodular functions with several applications. Recently Fujishige and Iwata showed how to extend the Iwata, Fleischer, and Fujishige (IFF) algorithm for submodular function minimization (SFM) to bisubmodular function minimization (BSFM). However, they were able to extend only the weakly polynomial version of IFF to BSFM. Here we investigate the difficulty that prevented them from also extending the strongly polynomial version of IFF to BSFM, and we show a way around the difficulty. This new method gives a somewhat simpler strongly polynomial SFM algorithm, as well as the first combinatorial strongly polynomial algorithm for BSFM. This further leads to extending Iwata’s fully combinatorial version of IFF to BSFM. The research of S. T. McCormick was supported by an NSERC Operating Grant. The research of S. Fujishige was supported by a Grant-in-Aid of the Ministry of Education, Culture, Science and Technology of Japan.     

Max Flow and Min Cut with bounded-length paths: complexity, algorithms, and approximation

We consider the “flow on paths” versions of Max Flow and Min Cut when we restrict to paths having at most B arcs, and for versions where we allow fractional solutions or require integral solutions. We show that the continuous versions are polynomial even if B is part of the input, but that the integral versions are polynomial only when B ≤ 3. However, when B ≤ 3 we show how to solve the problems using ordinary Max Flow/Min Cut. We also give tight bounds on the integrality gaps between the integral and continuous objective values for both problems, and between the continuous objective values for the bounded-length paths version and the version allowing all paths. We give a primal–dual approximation algorithm for both problems whose approximation ratio attains the integrality gap, thereby showing that it is the best possible primal–dual approximation algorithm.     

High-performance liquid chromatography of biotin and analogues

Biotin, analogues, and chemical intermediates were separated by high-performance liquid chromatography (HPLC) using reversed-phase and anion-exchange chromatographic conditions. Reversed-phase separations provided a wide range of retention times and resolution of nearly all the biotin compounds from mixtures of the analogues. Anion-exchange separations gave generally shorter retention times as compared to reversed-phase separations and greater resolution between biotin l- and d-sulfoxide. However, fewer analogues were resolved from mixtures of the compounds with anion-exchange HPLC.     

Site‐Specific Encoding of Photoactivity in Antibodies Enables Light‐Mediated Antibody–Antigen Binding on Live Cells

Antibodies have found applications in several fields, including, medicine, diagnostics, and nanotechnology, yet methods to modulate antibody–antigen binding using an external agent remain limited. Here, we have developed photoactive antibody fragments by genetic site‐specific replacement of single tyrosine residues with photocaged tyrosine, in an antibody fragment, 7D12. A simple and robust assay is adopted to evaluate the light‐mediated binding of 7D12 mutants to its target, epidermal growth factor receptor (EGFR), on the surface of cancer cells. Presence of photocaged tyrosine reduces 7D12‐EGFR binding affinity by over 20‐fold in two out of three 7D12 mutants studied, and binding is restored upon exposure to 365 nm light. Molecular dynamics simulations explain the difference in effect of photocaging on 7D12‐EGFR interaction among the mutants. Finally, we demonstrate the application of photoactive antibodies in delivering fluorophores to EGFR‐positive live cancer cells in a light‐dependent manner.     

Quark-hadron duality in neutron (3He) spin structure

We present experimental results of the first high-precision test of quark-hadron duality in the spin-structure function g_{1} of the neutron and 3He using a polarized 3He target in the four-momentum-transfer-squared range from 0.7 to 4.0 (GeV/c);{2}. Global duality is observed for the spin-structure function g_{1} down to at least Q;{2}=1.8 (GeV/c);{2} in both targets. We have also formed the photon-nucleon asymmetry A1 in the resonance region for 3He and found no strong Q2 dependence above 2.2 (GeV/c);{2}.