Unified greedy approximability beyond submodular maximization

We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove that it encompasses several important subclasses, such as functions of bounded submodularity ratio, $\alpha$-augmentable functions, and weighted rank functions of an independence system of bounded rank quotient - as well as additional objective functions for which the greedy algorithm yields an approximation. For this general class of functions, we show a tight bound of $\frac{\alpha}{\gamma}\cdot\frac{\mathrm{e}^\alpha}{\mathrm{e}^\alpha-1}$ on the approximation ratio of the greedy algorithm that tightly interpolates between bounds from the literature for functions of bounded submodularity ratio and for $\alpha$-augmentable functions. In paritcular, as a by-product, we close a gap left in [Math.Prog., 2020] by obtaining a tight lower bound for $\alpha$-augmentable functions for all $\alpha\geq1$. For weighted rank functions of independence systems, our tight bound becomes $\frac{\alpha}{\gamma}$, which recovers the known bound of $1/q$ for independence systems of rank quotient at least $q$

Overproduction and characterization of a recombinant D -amino acid oxidase from Arthrobacter protophormiae

A screening of soil samples for d-amino acid oxidase (d-AAO) activity led to the isolation and identification of the gram-positive bacterium Arthrobacter protophormiae. After purification of the wild-type d-AAO, the gene sequence was determined and designated dao. An alignment of the deduced primary structure with eukaryotic d-AAOs and d-aspartate oxidases showed that the d-AAO from A. protophormiae contains five of six conserved regions; the C-terminal type 1 peroxisomal targeting signal that is typical for d-AAOs from eukaryotic origin is missing. The dao gene was cloned and expressed in Escherichia coli. The purified recombinant d-AAO had a specific activity of 180U mg protein−1 for d-methionine and was slightly inhibited in the presence of l-methionine. Mainly, basic and hydrophobic d-amino acids were oxidized by the strictly enantioselective enzyme. After a high cell density fermentation, 2.29 × 106U of d-AAO were obtained from 15l of fermentation brot

Incremental Maximization via Continuization

We consider the problem of finding an incremental solution to a cardinality-constrained maximization problem that not only captures the solution for a fixed cardinality, but also describes how to gradually grow the solution as the cardinality bound increases. The goal is to find an incremental solution that guarantees a good competitive ratio against the optimum solution for all cardinalities simultaneously. The central challenge is to characterize maximization problems where this is possible, and to determine the best-possible competitive ratio that can be attained. A lower bound of $2.18$ and an upper bound of $\varphi + 1 \approx 2.618$ are known on the competitive ratio for monotone and accountable objectives [Bernstein et al., Math. Prog., 2022], which capture a wide range of maximization problems. We introduce a continuization technique and identify an optimal incremental algorithm that provides strong evidence that $\varphi + 1$ is the best-possible competitive ratio. Using this continuization, we obtain an improved lower bound of $2.246$ by studying a particular recurrence relation whose characteristic polynomial has complex roots exactly beyond the lower bound. Based on the optimal continuous algorithm combined with a scaling approach, we also provide a $1.772$-competitive randomized algorithm. We complement this by a randomized lower bound of $1.447$ via Yao's principle

Maintained partial protection against Streptococcus pneumoniae despite B‐cell depletion in mice vaccinated with a pneumococcal glycoconjugate vaccine

Objectives: Anti-CD20 monoclonal antibody therapy rapidly depletes > 95% of CD20+ B cells from the circulation. B-cell depletion is an effective treatment for autoimmune disease and B-cell malignancies but also increases the risk of respiratory tract infections. This effect on adaptive immunity could be countered by vaccination. We have used mouse models to investigate the effects of B-cell depletion on pneumococcal vaccination, including protection against infection and timing of vaccination in relation to B-cell depletion. // Methods: C57BL/6 female mice were B-cell depleted using anti-CD20 antibody and immunized with two doses of Prevnar-13 vaccine either before or after anti-CD20 treatment. B-cell repertoire and Streptococcus pneumoniae–specific IgG levels were measured using whole-cell ELISA and flow cytometry antibody-binding assay. Protection induced by vaccination was assessed by challenging the mice using a S. pneumoniae pneumonia model. // Results: Antibody responses to S. pneumoniae were largely preserved in mice B-cell depleted after vaccination resulting in full protection against pneumococcal infections. In contrast, mice vaccinated with Prevnar-13 while B cells were depleted (with > 90% reduction in B-cell numbers) had decreased circulating anti–S. pneumoniae IgG and IgM levels (measured using ELISA and flow cytometry antibody binding assays). However, some antibody responses were maintained, and, although vaccine-induced protection against S. pneumoniae infection was impaired, septicaemia was still prevented in 50% of challenged mice. // Conclusions: This study showed that although vaccine efficacy during periods of profound B-cell depletion was impaired some protective efficacy was preserved, suggesting that vaccination remains beneficial

Potential sources of interference with the highly sensitive detection and quantification of alpha‐synuclein seeds by qRT‐QuIC

Parkinson’s disease (PD) is a progressive neurodegenerative disease which is histologically characterized by loss of dopaminergic neurons in the substantia nigra and deposition of aggregated alpha‐synuclein (aSyn) in the brain. The detection of aSyn in well accessible fluids has been one of the central approaches in the development of biomarkers for PD. Recently, real‐time quaking‐induced conversion (RT‐QuIC) has been successfully adapted for use with aSyn seeds. Here, we systematically analysed parameters potentially impacting the reliability of this assay by using quantitative real‐time quaking‐induced conversion (qRT‐QuIC) with in vitro‐formed aSyn seeds. Seeds diluted in cerebrospinal fluid (CSF) accelerated the seeding reaction and slightly increased the sensitivity without affecting specificity. Repeated freeze–thaw cycles decreased the apparent lag times of seeds diluted in ddH2O but did not alter the seeding activity of seeds diluted in CSF. High levels of artificial contamination with blood resulted in prolonged apparent lag times, while sensitivity and specificity were unaffected. Altogether, qRT‐QuIC with aSyn seems to be robust concerning sensitivity and specificity in our model system, but quantitative interpretation might be limited under certain conditions