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Isatins are extensively researched compounds with diverse applications, particularly as synthetic precursors in pharmaceutical developments. However, their use as optical probes for enantioselective sensing of chiral amines has not been explored to date. Herein, we present a novel chiroptical assay with an optimized isatin that generates strong, red‐shifted circular dichroism (CD) signals at approximately 380 nm upon ketimine formation with chiral amines. The intensity of the induced CD signal increases linearly with the enantiomeric excess of the analyte and thus allows quantitative chirality analysis. The general usefulness of this approach is demonstrated with a broad range of aliphatic and aromatic chiral amines, and by accurate determination of the enantiomeric composition of 10 samples. 

We ask how fiscal deficits are financed in environments with two key features: (i) nominal rigidity, and (ii) a violation of Ricardian equivalence due to finite lives or liquidity constraints. In such environments, deficits can contribute to their own financing through two channels: a boom in real economic activity, which expands the tax base; and a surge in inflation, which erodes the real value of nominal government debt. Our main theoretical result establishes that this mechanism becomes more potent as fiscal adjustment is delayed, leading to full self‐financing in the limit: if the monetary authority does not lean too heavily against the fiscal stimulus, then the government can run a deficit today, refrain from tax hikes or spending cuts in the future, and still see its debt converge back to its initial level. We further demonstrate that a significant degree of self‐financing is achievable when the theory is disciplined by empirical evidence on marginal propensities to consume, nominal rigidities, the monetary policy reaction, and the speed of fiscal adjustment. 

We present an introduction to the area of computability in dynamical systems. One of the central questions in this area is if relevant dynamical objects can be algorithmically presented by a Turing machine. After providing an overview of the relevant objects we discuss recent results concerning the computability of the entropy for symbolic systems and the computability of Julia sets as well as their Brolin–Lyubich measures. 

The analysis of the absolute configuration, enantiomeric composition, and concentration of chiral compounds are frequently encountered tasks across the chemical and health sciences. Chiroptical sensing methods can streamline this work and allow high-throughput screening with remarkable reduction of operational time and cost. During the last few years, significant methodological advances with innovative chirality sensing systems, the use of computer-generated calibration curves, machine learning assistance, and chemometric data processing, to name a few, have emerged and are now matched with commercially available multi-well plate CD readers. These developments have reframed the chirality sensing space and provide new opportunities that are of interest to a large group of chemists. This review will discuss chirality sensing strategies and applications with representative small-molecule CD sensors. Emphasis will be given to important milestones and recent advances that accelerate chiral compound analysis by outperforming traditional methods, conquer new directions, and pioneering efforts that lie at the forefront of chiroptical high-throughput screening developments. The goal is to provide the reader with a thorough understanding of the current state and a perspective of future directions of this rapidly emerging field. 

Abstract A reaction‐based optical relay sensing strategy that enables accurate determination of the concentration and enantiomeric ratio (er) of challenging chiral alcohols exhibiting stereocenters at the α‐, β‐, γ‐ or even δ‐position or hard‐to‐detect cryptochirality arising from H/D substitution is described. This unmatched application scope is achieved with a conceptually new sensing approach by which the alcohol moiety is replaced with an optimized achiral sulfonamide chromophore to minimize the distance between the covalently attached chiroptical reporter unit and the stereogenic center in the substrate. The result is a remarkably strong, red‐shifted CD induction that increases linearly with the sampleer. The CD sensing part of the tandem assay is seamlessly coupled to a redox reaction with a quinone molecule to generate a characteristic UV response that is independent of the enantiopurity of the alcohol and thus allows determination of the total analyte concentration. The robustness and utility of the CD/UV relay are further verified by chromatography‐free asymmetric reaction analysis with small aliquots of crude product mixtures, paving the way toward high‐throughput chiral compound screening workflows which is a highly sought‐after goal in the pharmaceutical industry. 

The analysis of mixtures of chiral compounds is a common task in academic and industrial laboratories typically achieved by laborious and time-consuming physical separation of the individual stereoisomers to allow interference-free quantification, for example using chiral chromatography coupled with UV detection. Current practice thus impedes high-throughput and slows down progress in countless chiral compound development projects. Here we describe a chemometric solution to this problem using a redox-responsive naphthoquinone that enables chromatography-free click chemistry sensing of challenging mixtures. The achiral probe covalently binds amino alcohols within a few minutes at room temperature and generates characteristic UVA and CDA spectra that are intentionally altered via sodium borohydride reduction to provide a second, strikingly different chiroptical data set (UVB and CDB). Chemometric partial least squares processing of the chiroptical outputs then enables spectral deconvolution and accurate determination of individual analyte concentrations. The success of this approach is demonstrated with 35 samples covering considerably varied total analyte amounts and stereoisomeric ratios. All chemicals and machine learning algorithms are readily available and can be immediately adapted by any laboratory. 

We show that, in a general family of linearized structural macroeconomic models, knowledge of the empirically estimable causal effects of contemporaneous and news shocks to the prevailing policy rule is sufficient to construct counterfactuals under alternative policy rules. If the researcher is willing to postulate a loss function, our results furthermore allow her to recover an optimal policy rule for that loss. Under our assumptions, the derived counterfactuals and optimal policies are robust to the Lucas critique. We then discuss strategies for applying these insights when only a limited amount of empirical causal evidence on policy shock transmission is available.