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We model the production of complex goods in a large supply network. Each firm sources several essential inputs through relationships with other firms. Individual supply relationships are at risk of idiosyncratic failure, which threatens to disrupt production. To protect against this, firms multisource inputs and strategically invest to make relationships stronger, trading off the cost of investment against the benefits of increased robustness. A supply network is called fragile if aggregate output is very sensitive to small aggregate shocks. We show that supply networks of intermediate productivity are fragile in equilibrium, even though this is always inefficient. The endogenous configuration of supply networks provides a new channel for the powerful amplification of shocks.

Steady two-dimensional Rayleigh–Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios ${\\rm \\pi} /5\\leqslant \\varGamma \\leqslant 4{\\rm \\pi}$, where $\\varGamma$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, $10^3\\leqslant Ra\\leqslant 10^{11}$, and four orders of magnitude in the Prandtl number, $10^{-2}\\leqslant Pr\\leqslant 10^2$. At large $Ra$ where steady rolls are dynamically unstable, the computed rolls display $Ra \\rightarrow \\infty$ asymptotic scaling. In this regime, the Nusselt number $Nu$ that measures heat transport scales as $Ra^{1/3}$ uniformly in $Pr$. The prefactor of this scaling depends on $\\varGamma$ and is largest at $\\varGamma \\approx 1.9$. The Reynolds number $Re$ for large-$Ra$ rolls scales as $Pr^{-1} Ra^{2/3}$ with a prefactor that is largest at $\\varGamma \\approx 4.5$. All of these large-$Ra$ features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini & Cox (Phys. Fluids, vol. 21, 2009, 083603). Convergence of $Nu$ and $Re$ to their asymptotic scalings occurs more slowly when $Pr$ is larger and when $\\varGamma$ is smaller.

The efficacy of positive end-expiratory pressure (PEEP) in treating intraoperative hypoxemia during one-lung ventilation (OLV) remains in question given conflicting results of prior studies. This study aims to (1) evaluate the efficacy of PEEP during OLV, (2) assess the utility of preoperative predictors of response to PEEP, and (3) explore optimal intraoperative settings that would maximize the effects of PEEP on oxygenation. Forty-one thoracic surgery patients from a single tertiary care university center were prospectively enrolled in this observational study. After induction of general anesthesia, a double-lumen endotracheal tube was fiberoptically positioned and OLV initiated. Intraoperatively, PEEP = 5 and 10 cmH 2 O were sequentially applied to the ventilated lung during OLV. Arterial oxygenation, cardiovascular performance parameters, and proposed perioperative variables that could predict or enhance response to PEEP were analysed. T-test and c2 tests were utilized for continuous and categorical variables, respectively. Multivariate analyses were carried out using a classification tree model of binary recursive partitioning. PEEP improved arterial oxygenation by >20% in 29% of patients (n = 12) and failed to do so in 71% (n = 29); however, no cardiovascular impact was noted. Among the proposed clinical predictors, only intraoperative tidal volume per kilogram differed significantly between responders to PEEP and non-responders (mean 6.6 vs. 5.7 ml/kg, P = 0.013); no preoperative variable predicted response to PEEP. A multivariate analysis did not yield a clinically significant model for predicting PEEP responsiveness. PEEP improved oxygenation in a subset of patients; larger, although still protective tidal volumes favored a positive response to PEEP. No preoperative variables, however, could be identified as reliable predictors for PEEP responders.

Successive governments must decide whether to implement an affirmative action policy aimed at improving the performance distribution of the next generation of a targeted group. Workers receive wages corresponding to their expected performance, suffer a feeling of injustice when getting less than their performance, and employers do not (perfectly) observe whether workers benefited from affirmative action. We find that welfare-maximizing governments choose to implement affirmative action perpetually, despite the resulting feeling of injustice that eventually dominates the purported beneficial effect on the performance of the targeted group. This is in contrast with the first-best that requires affirmative action to be temporary.

We model the production of complex goods in a large supply network. Each firm sources several essential inputs through relationships with other firms. Individual supply relationships are at risk of idiosyncratic failure, which threatens to disrupt production. To protect against this, firms multisource inputs and strategically invest to make relationships stronger, trading off the cost of investment against the benefits of increased robustness. A supply network is called fragile if aggregate output is very sensitive to small aggregate shocks. We show that supply networks of intermediate productivity are fragile in equilibrium, even though this is always inefficient. The endogenous configuration of supply networks provides a new channel for the powerful amplification of shocks.

We model the production of complex goods in a large supply network. Each firm sources several essential inputs through relationships with other firms. Individual supply relationships are at risk of idiosyncratic failure, which threatens to disrupt production. To protect against this, firms multisource inputs and strategically invest to make relationships stronger, trading off the cost of investment against the benefits of increased robustness. We find that equilibrium aggregate production is robust to idiosyncratic disruptions. Nevertheless, there is a regime in which arbitrarily small systemic shocks cause arbitrarily steep drops in output, so that the the supply network is fragile. The endogenous configuration of supply networks provides a new channel for the powerful amplification of shocks.

Steady two-dimensional Rayleigh--Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios \\(\\pi/5\\le\\Gamma\\le4\\pi\\), where \\(\\Gamma\\) is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, \\(10^3\\le Ra\\le10^{11}\\), and four orders of magnitude in the Prandtl number, \\(10^{-2}\\le Pr\\le10^2\\). At large \\(Ra\\) where steady rolls are dynamically unstable, the computed rolls display \\(Ra \\rightarrow \\infty\\) asymptotic scaling. In this regime, the Nusselt number \\(Nu\\) that measures heat transport scales as \\(Ra^{1/3}\\) uniformly in \\(Pr\\). The prefactor of this scaling depends on \\(\\Gamma\\) and is largest at \\(\\Gamma \\approx 1.9\\). The Reynolds number \\(Re\\) for large-\\(Ra\\) rolls scales as \\(Pr^{-1} Ra^{2/3}\\) with a prefactor that is largest at \\(\\Gamma \\approx 4.5\\). All of these large-\\(Ra\\) features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini \\& Cox (2009). Convergence of \\(Nu\\) and \\(Re\\) to their asymptotic scalings occurs more slowly when \\(Pr\\) is larger and when \\(\\Gamma\\) is smaller.

We model the production of complex goods in a large supply network. Each firm sources several essential inputs through relationships with other firms. Individual supply relationships are at risk of idiosyncratic failure, which threatens to disrupt production. To protect against this, firms multisource inputs and strategically invest to make relationships stronger, trading off the cost of investment against the benefits of increased robustness. We find that equilibrium aggregate production is robust to idiosyncratic disruptions. Nevertheless, there is a regime in which arbitrarily small systemic shocks cause arbitrarily steep drops in output, so that the the supply network is fragile. The endogenous configuration of supply networks provides a new channel for the powerful amplification of shocks.

According to his attestation he had blue eyes, fair hair, and a fair complexion while standing approximately five feet nine inches tall. According to his active service record, John arrived Nov. 18, 1917, in France just as the Battle of Passchendaele was coming to a close and likely motivated to be at the front where his brother, William, had been killed a few months earlier. According to his circumstances of death record, he was transported to the #1 London Field Ambulance May 5, 1918 where medical treatment could not save his life.