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We analyze a decentralized process in a basic labor market where finitely many heterogeneous firms and workers meet directly and randomly in pursuit of higher payoffs over time and agents may behave myopically. We find a general random decentralized market process that almost surely converges in finite time to a competitive equilibrium of the market. A key proposition en route to this result exhibits a finite sequence of successive bilateral trades from an arbitrary initial market state to a stable matching between firms and workers with a scheme of competitive salary offers.

Nitrile hydration provides access to amides that are indispensable to researchers in chemical and pharmaceutical industries. Prohibiting the use of this venerable reaction, however, are 1) the dearth of biphasic catalysts that can effectively hydrate nitriles at ambient temperatures with high turnover numbers, and 2) the unsolved challenge of hydrating cyanohydrins. Herein, we report the design of new "donor-acceptor"-type platinum catalysts by precisely arranging electron-rich and electron-deficient ligands trans to one other, thereby enhancing both the nucleophilicity of the hydroxyl group and the electrophilicity of the nitrile group. Leveraging a high-throughput, automated workflow and evaluating a library of bidentate ligands, we have discovered that commercially available, inexpensive DPPF [1,1'-ferrocenendiyl-bis(diphenylphosphine)] provides superior reactivity. The corresponding "donor-acceptor"-type catalyst 2a is readily prepared from (DPPF)PtCl 2 , PMe 2 OH and AgOTf. The enhanced activity of 2a permits the hydration of a wide range of nitriles and cyanohydrins to proceed at 40 °C with excellent turnover numbers. Rational reevaluation of the ligand structure has led to the discovery of modified catalyst 2c, harboring the more electron-rich 1,1'-bis[bis(5methyl-2-furanyl) phosphino] ferrocene ligand, which demonstrates the highest activity towards hydration of nitriles and cyanohydrins at room temperature. Finally, the correlation between the electron-donating ability of the phosphine ligands with catalyst efficiencies of 2a, 2c, 2d and 2e in the hydration of nitrile 7 are examined, and the results support the "donor-acceptor" hypothesis.

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Background: Clinical examination alone is neither sensitive nor specific for predicting flap necrosis, so several technologies, including indocyanine green angiography, thermal imaging (using the FLIR ONE), and near-infrared spectroscopy, have been developed to supplement perfusion assessment. This study aims to compare the accuracy of these three methods for intraoperatively predicting clinical flap necrosis in a rat perforator flap model. The authors hypothesized that near-infrared spectroscopy, assessing oxygenation rather than direct perfusion, would yield significantly different predictions. Methods: A 10 × 3-cm epigastric perforator flap was elevated in 14 adult male rats weighing 250 ± 50 g. Flap perfusion was assessed immediately after flap elevation using thermal imaging, near-infrared spectroscopy, and indocyanine green angiography. Measurements were correlated to the clinical endpoint and gold standard of flap necrosis on postoperative day 7. Results: All three technologies detected significant differences in perfusion along flap length (all p < 0.001), and were associated with significant differences in the odds of developing flap necrosis (all p < 0.001). The areas under the receiver operating characteristic curves were 0.948 for indocyanine green angiography as an absolute value, 0.873 for relative changes with thermal imaging, and 0.792 for tissue oxygenation. The sensitivity, specificity, and accuracy for indocyanine green angiography measured as an absolute value were the highest at 97.8, 87.5, and 92 percent, respectively. Conclusions: Indocyanine green angiography most accurately predicted flap necrosis in this study; however, tissue oximetry and thermal imaging were also capable of predicting necrosis and represented potentially less expensive or more readily available alternatives for objective perfusion assessment. Additional research can further delineate their roles and cost-efficacy in clinical practice.