A Geometric Characterization of the Power of Finite Adaptability in Multistage Stochastic and Adaptive Optimization

In this paper, we show a significant role that geometric properties of uncertainty sets, such as symmetry, play in determining the power of robust and finitely adaptable solutions in multistage stochastic and adaptive optimization problems. We consider a fairly general class of multistage mixed integer stochastic and adaptive optimization problems and propose a good approximate solution policy with performance guarantees that depend on the geometric properties of the uncertainty sets. In particular, we show that a class of finitely adaptable solutions is a good approximation for both the multistage stochastic and the adaptive optimization problem. A finitely adaptable solution generalizes the notion of a static robust solution and specifies a small set of solutions for each stage; the solution policy implements the best solution from the given set, depending on the realization of the uncertain parameters in past stages. Therefore, it is a tractable approximation to a fully adaptable solution for the multistage problems. To the best of our knowledge, these are the first approximation results for the multistage problem in such generality. Moreover, the results and the proof techniques are quite general and also extend to include important constraints such as integrality and linear conic constraints.National Science Foundation (U.S.) (Grant EFRI-0735905

An inter-laboratory comparison demonstrates that [1H]-NMR metabolite fingerprinting is a robust technique for collaborative plant metabolomic data collection

In any metabolomics experiment, robustness and reproducibility of data collection is of vital importance. These become more important in collaborative studies where data is to be collected on multiple instruments. With minimisation of variance in sample preparation and instrument performance it is possible to elucidate even subtle differences in metabolite fingerprints due to genotype or biological treatment. In this paper we report on an inter laboratory comparison of plant derived samples by [1H]-NMR spectroscopy across five different sites and within those sites utilising instruments with different probes and magnetic field strengths of 9.4 T (400 MHz), 11.7 T (500 MHz) and 14.1 T (600 MHz). Whilst the focus of the study is on consistent data collection across laboratories, aspects of sample stability and the requirement for sample rotation within the NMR magnet are also discussed. Comparability of the datasets from participating laboratories was exceptionally good and the data were amenable to comparative analysis by multivariate statistics. Field strength differences can be adjusted for in the data pre-processing and multivariate analysis demonstrating that [1H]-NMR fingerprinting is the ideal technique for large scale plant metabolomics data collection requiring the participation of multiple laboratories

Successful sample preparation for serial crystallography experiments

Serial crystallography, at both synchrotron and X-ray free-electron laser light sources, is becoming increasingly popular. However, the tools in the majority of crystallization laboratories are focused on producing large single crystals by vapour diffusion that fit the cryo-cooled paradigm of modern synchrotron crystallography. This paper presents several case studies and some ideas and strategies on how to perform the conversion from a single crystal grown by vapour diffusion to the many thousands of micro-crystals required for modern serial crystallography grown by batch crystallization. These case studies aim to show (i) how vapour diffusion conditions can be converted into batch by optimizing the length of time crystals take to appear; (ii) how an understanding of the crystallization phase diagram can act as a guide when designing batch crystallization protocols; and (iii) an accessible methodology when attempting to scale batch conditions to larger volumes. These methods are needed to minimize the sample preparation gap between standard rotation crystallography and dedicated serial laboratories, ultimately making serial crystallography more accessible to all crystallographers

Gene conversion in human rearranged immunoglobulin genes

Over the past 20 years, many DNA sequences have been published suggesting that all or part of the V<sub>H</sub> segment of a rearranged immunoglobulin gene may be replaced in vivo. Two different mechanisms appear to be operating. One of these is very similar to primary V(D)J recombination, involving the RAG proteins acting upon recombination signal sequences, and this has recently been proven to occur. Other sequences, many of which show partial V<sub>H</sub> replacements with no addition of untemplated nucleotides at the V<sub>H</sub>–V<sub>H</sub> joint, have been proposed to occur by an unusual RAG-mediated recombination with the formation of hybrid (coding-to-signal) joints. These appear to occur in cells already undergoing somatic hypermutation in which, some authors are convinced, RAG genes are silenced. We recently proposed that the latter type of V<sub>H</sub> replacement might occur by homologous recombination initiated by the activity of AID (activation-induced cytidine deaminase), which is essential for somatic hypermutation and gene conversion. The latter has been observed in other species, but not in human Ig genes, so far. In this paper, we present a new analysis of sequences published as examples of the second type of rearrangement. This not only shows that AID recognition motifs occur in recombination regions but also that some sequences show replacement of central sections by a sequence from another gene, similar to gene conversion in the immunoglobulin genes of other species. These observations support the proposal that this type of rearrangement is likely to be AID-mediated rather than RAG-mediated and is consistent with gene conversion

Co-ordinated expression of amino acid metabolism in response to N and S deficiency during wheat grain filling

Increasing demands for productivity together with environmental concerns about fertilizer use dictate that the future sustainability of agricultural systems will depend on improving fertilizer use efficiency. Characterization of the biological processes responsible for efficient fertilizer use will provide tools for crop improvement under reduced inputs. Transcriptomic and metabolomic approaches were used to study the impact of nitrogen (N) and sulphur (S) deficiency on N and S remobilization from senescing canopy tissues during grain filling in winter wheat (Triticum aestivum). Canopy tissue N was remobilized effectively to the grain after anthesis. S was less readily remobilized. Nuclear magnetic resonance (NMR) metabolite profiling revealed significant effects of suboptimal N or S supply in leaves but not in developing grain. Analysis of amino acid pools in the grain and leaves revealed a strategy whereby amino acid biosynthesis switches to the production of glutamine during grain filling. Glutamine accumulated in the first 7 d of grain development, prior to conversion to other amino acids and protein in the subsequent 21 d. Transcriptome analysis indicated that a down-regulation of the terminal steps in many amino acid biosynthetic pathways occurs to control pools of amino acids during leaf senescence. Grain N and S contents increased in parallel after anthesis and were not significantly affected by S deficiency, despite a suboptimal N:S ratio at final harvest. N deficiency resulted in much slower accumulation of grain N and S and lower final concentrations, indicating that vegetative tissue N has a greater control of the timing and extent of nutrient remobilization than S

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Identifying SARS-CoV-2 antiviral compounds by screening for small molecule inhibitors of Nsp14 RNA cap methyltransferase

The COVID-19 pandemic has presented itself as one of the most critical public health challenges of the century, with SARS-CoV-2 being the third member of the Coronaviridae family to cause a fatal disease in humans. There is currently only one antiviral compound, remdesivir, that can be used for the treatment of COVID-19. To identify additional potential therapeutics, we investigated the enzymatic proteins encoded in the SARS-CoV-2 genome. In this study, we focussed on the viral RNA cap methyltransferases, which play key roles in enabling viral protein translation and facilitating viral escape from the immune system. We expressed and purified both the guanine-N7 methyltransferase nsp14, and the nsp16 2′-O-methyltransferase with its activating cofactor, nsp10. We performed an in vitro high-throughput screen for inhibitors of nsp14 using a custom compound library of over 5000 pharmaceutical compounds that have previously been characterised in either clinical or basic research. We identified four compounds as potential inhibitors of nsp14, all of which also showed antiviral capacity in a cell-based model of SARS-CoV-2 infection. Three of the four compounds also exhibited synergistic effects on viral replication with remdesivir

Casein Kinase 1 Underlies Temperature Compensation of Circadian Rhythms in Human Red Blood Cells

Temperature compensation and period determination by casein kinase 1 (CK1) are conserved features of eukaryotic circadian rhythms, whereas the clock gene transcription factors that facilitate daily gene expression rhythms differ between phylogenetic kingdoms. Human red blood cells (RBCs) exhibit temperature-compensated circadian rhythms, which, because RBCs lack nuclei, must occur in the absence of a circadian transcription-translation feedback loop. We tested whether period determination and temperature compensation are dependent on CKs in RBCs. As with nucleated cell types, broad-spectrum kinase inhibition with staurosporine lengthened the period of the RBC clock at 37°C, with more specific inhibition of CK1 and CK2 also eliciting robust changes in circadian period. Strikingly, inhibition of CK1 abolished temperature compensation and increased the Q10 for the period of oscillation in RBCs, similar to observations in nucleated cells. This indicates that CK1 activity is essential for circadian rhythms irrespective of the presence or absence of clock gene expression cycles