The effect of deterministic noise in subgradient methods

In this paper, we study the influence of noise on subgradient methods for convex constrained optimization. The noise may be due to various sources, and is manifested in inexact computation of the subgradients and function values. Assuming that the noise is deterministic and bounded, we discuss the convergence properties for two cases: the case where the constraint set is compact, and the case where this set need not be compact but the objective function has a sharp set of minima (for example the function is polyhedral). In both cases, using several different stepsize rules, we prove convergence to the optimal value within some tolerance that is given explicitly in terms of the errors. In the first case, the tolerance is nonzero, but in the second case, the optimal value can be obtained exactly, provided the size of the error in the subgradient computation is below some threshold. We then extend these results to objective functions that are the sum of a large number of convex functions, in which case an incremental subgradient method can be used.     

An algorithm for stochastic programs with first-order dominance constraints induced by linear recourse

We derive a cutting plane decomposition method for stochastic programs with first-order dominance constraints induced by linear recourse models with continuous variables in the second stage.     

Tyrosine Conjugation Methods for Protein Labelling

Over the last two decades, the development of chemical biology and the need for more defined protein conjugates have fostered active research on new bioconjugation techniques. In particular, a wide range of biorthogonal labelling strategies have been reported to functionalise the phenol side chain of tyrosines (Tyr). Tyr occur at medium frequency and are partially buried at the protein surface, offering interesting opportunities for site-selective labelling of the most reactive residues. Tyr-targeting has proved effective for designing a wide range of important biomolecules including antibody–drug conjugates, fluorescent or radioactive protein probes, glycovaccines, protein aggregates, and PEG conjugates. Innovative methods have also been reported for site-specific labelling with ligand-directed anchors and for the specific affinity capture of proteins. This review will present and discuss these promising alternatives to the conventional labelling of the nucleophilic lysine and cysteine residues.     

Addendum to: Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem, NoDEA. Nonlinear Differential Equations Appl. 11 (2004), no. 3, 379-391, and a comment on the generalized Ambrosetti-Rabinowitz condition

We show the incompleteness of a usually used version of the generalized Ambrosetti?CRabinowitz condition in superlinear problems, also used in the paper cited in the title, and we propose a complete one.     

Regular 4-polytopes from the Livingstone graph of Janko’s first group

The Janko group J ₁ has, up to duality, exactly two regular rank four polytopes, of respective Schl?fli types {5,3,5} and {5,6,5}. The aim of this paper is to give geometric constructions of these two polytopes, starting from the Livingstone graph.     

An Aromatic Dyad Motif in Dye Decolourising Peroxidases Has Implications for Free Radical Formation and Catalysis

Dye decolouring peroxidases (DyPs) are the most recent class of heme peroxidase to be discovered. On reacting with H₂O₂, DyPs form a high-valent iron(IV)-oxo species and a porphyrin radical (Compound I) followed by stepwise oxidation of an organic substrate. In the absence of substrate, the ferryl species decays to form transient protein-bound radicals on redox active amino acids. Identification of radical sites in DyPs has implications for their oxidative mechanism with substrate. Using a DyP from Streptomyces lividans, referred to as DtpA, which displays low reactivity towards synthetic dyes, activation with H₂O₂ was explored. A Compound I EPR spectrum was detected, which in the absence of substrate decays to a protein-bound radical EPR signal. Using a newly developed version of the Tyrosyl Radical Spectra Simulation Algorithm, the radical EPR signal was shown to arise from a pristine tyrosyl radical and not a mixed Trp/Tyr radical that has been widely reported in DyP members exhibiting high activity with synthetic dyes. The radical site was identified as Tyr374, with kinetic studies inferring that although Tyr374 is not on the electron-transfer pathway from the dye RB19, its replacement with a Phe does severely compromise activity with other organic substrates. These findings hint at the possibility that alternative electron-transfer pathways for substrate oxidation are operative within the DyP family. In this context, a role for a highly conserved aromatic dyad motif is discussed.     

Intrinsic nonlinearity from LAOStrain—experiments on various strain- and stress-controlled rheometers: a quantitative comparison

Strain-controlled large amplitude oscillatory shear (LAOStrain) experiments on a polyisoprene melt and a polyisobutylene solution were conducted on four different rheometers. The results are compared using nonlinear quantities such as the normalized intensity of the third harmonic (I _3/1) and the intrinsic nonlinearity in order to assess the reproducibility of the experiments. Two of the investigated instruments were strain-controlled rheometers, another two, were advanced stress-controlled rheometers. Since the stress-controlled rheometers are able to conduct strain-controlled tests when employing an active deformation control loop, the two different rheometer types could be compared. Experimental details like the gain of the deformation control loop, and the method of temperature control have been shown to play crucial roles in achieving reasonable reproducibility across the different instruments. Furthermore, deviations from the quadratic scaling of I _3/1 with the strain amplitude and the influence of instrument inertia on nonlinear quantities were observed for one of the stress-controlled instruments. The standard deviation of the intrinsic nonlinearity Q ₀(ω ₀) at a specific angular frequency as determined by measurements on the same instrument was found to be 8 % or lower. The relative deviations of Q ₀ across different instruments were instead up to 12 % in the investigated frequency range with an exception for a specific instrument and one of the samples, where the deviation was considerably larger.