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Abstract Economic shocks provide both risks and opportunities for workplace training programs—the risk of program cancellation or interruption to skills development, and the opportunity to be at the vanguard of economic recovery. This paper analyzes the impact of Covid-19 and the resulting economic shock on training programs in the US using a survey amongst employers participating in training support networks, run from April-June 2021. We anticipate that programs expressly motivated by returns to investment and those that are higher quality and leading to stronger credentials will be most likely to survive the shock and have minimal disruption to skills acquisition. Results suggest that expressed motivations to train are generally not linked to training disruption or skills loss, while there is some evidence of paid programs and those offering better credentials being more likely to survive. Internships and programs that are more demographically diverse show a greater likelihood of disruption and skills loss.

Objective: Islets from the same pancreas show remarkable variability in glucose sensitivity. While mitochondrial respiration is essential for glucose-stimulated insulin secretion, little is known regarding heterogeneity in mitochondrial function at the individual islet level. This is due in part to a lack of high-throughput and non-invasive methods for detecting single islet function. Methods: We have developed a novel non-invasive, high-throughput methodology capable of assessing mitochondrial respiration in large-sized individual islets using the XF96 analyzer (Agilent Technologies). Results: By increasing measurement sensitivity, we have reduced the minimal size of mouse and human islets needed to assess mitochondrial respiration to single large islets of >35,000 μm2 area (∼210 μm diameter). In addition, we have measured heterogeneous glucose-stimulated mitochondrial respiration among individual human and mouse islets from the same pancreas, allowing population analyses of islet mitochondrial function for the first time. Conclusions: We have developed a novel methodology capable of analyzing mitochondrial function in large-sized individual islets. By highlighting islet functional heterogeneity, we hope this methodology can significantly advance islet research. Keywords: Islets, Mitochondria, Respirometry, Glucose

Technical and vocational education and training (TVET) programs are most successful at supporting youth labor markets when they combine education and employment. Education–employment linkage theory describes this combination in terms of power-sharing between actors from the education system and their counterparts in the employment system over key processes in the curriculum value chain of curriculum design, curriculum application (program delivery), and curriculum updating. The Education–Employment Linkage Index measures linkage for every function in a TVET program where actors from the two systems interact, aggregating those into processes and phases and eventually an index score. We apply this index to the largest upper-secondary TVET programs in Benin, Chile, Costa Rica, and Nepal. We find that Benin has relatively high education–employment linkage, while the other three countries score very low. Benin’s situation is unique because its TVET program is moving from employer-led to linked, rather than the typical employer integration into an education-based program. Other countries with large informal economies, low formal education and training rates, and existing non-formal employer-led training may be able to implement similar approaches.

Background: Survey-based research finds a sizeable unexplained wage gap between mothers and nonmothers in affluent countries. The source of this wage gap is unclear: It can stem either from the unobserved effects of motherhood on productivity or from employer discrimination against mothers. Objective: This paper opens the black box of the motherhood wage gap by directly measuring discrimination in Switzerland based on two complementary methods. Methods: We first use two longitudinal population surveys to establish the size of the wage residual for motherhood. We then run a factorial survey experiment among HR managers (N=714) whom we asked to assign a starting wage to the résumés of fictitious job candidates. Results: The population surveys show an unexplained wage penalty per child of 4Š to 8Š. The factorial survey experiment shows that recruiters assign wages to mothers that are 2Š to 3Š below those of nonmothers. The wage penalty is larger for younger mothers, 6Š for ages 40 and less, but disappears for older mothers or mothers in a blue-collar occupation. Conclusions: The motherhood wage gap found in panel studies cannot be reduced to unobserved dimensions of work productivity. The experimental evidence shows that recruiters discriminate against mothers. Contribution: Our paper's novelty is to uncover wage discrimination against mothers by combining two different methods. Our national panel surveys mirror the supply side of the labor market and provide us with strong external validity. The factorial survey experiment on recruiters informs on the demand side of the labor market and shows a causal effect.

Let $X_t$ be a one-dimensional diffusion with infinitesimal generator given by the operator $L = \frac12 (a(x) \frac{d}{dx})^2 + b(x) \frac{d}{dx}$ where $a(x)$ is a smooth, positive real-valued function and the ratio of $a(x)$ and $b(x)$ is a constant. Given a compact interval, we prove a Weierstrass-type theorem for the exit time moments of $X_t$ and their corresponding (naturally weighted) first derivatives, and we provide an algorithm that produces uniform approximations of arbitrary continuous functions by exit time moments. We investigate analogues of these results in higher-dimensional Euclidean spaces. We give expansions for several families of special functions in terms of exit time moments. [ABSTRACT FROM AUTHOR]

Given a pair of planar isospectral, nonisometric polygons constructed as a quotient of the plane by a finite group, we construct an associated pair of planar isospectral, nonisometric weighted graphs. Using the natural heat operators on the weighted graphs, we associate to each graph a heat content. We prove that the coefficients in the small time asymptotic expansion of the heat content distinguish our isospectral pairs. As a corollary, we prove that the sequence of exit time moments for the natural Markov chains associated to each graph, averaged over starting points in the interior of the graph, provides a collection of invariants that distinguish isospectral pairs in general. [ABSTRACT FROM AUTHOR]

We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. We associate to certain subgraphs (domains) a pair of sequences, each of which is invariant under the action of the automorphism group of the underlying graph. We prove that these invariants differ by an explicit combinatorial factor given by Stirling numbers of the first and second kind. We prove that for any domain with a natural weighting, these invariants determine the eigenvalues of the Laplace operator corresponding to eigenvectors with nonzero mean. As a specific example, we investigate the relationship between our invariants and heat content asymptotics, expressing both as special values of an analog of a spectral zeta function. [ABSTRACT FROM AUTHOR]

Let $D$ be a smoothly bounded domain in Euclidean space and let $X_{t}$ be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from $D$ of a particle driven by $X_{t},$ where the average is taken over all starting points in $D.$ [ABSTRACT FROM AUTHOR]

We examine solutions of two related boundary value problems for smooth domains in Euclidean space which arise from variational problems in probability. We show that the existence of solutions to each problem implies that the domain is a sphere. [ABSTRACT FROM AUTHOR]

Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points. [ABSTRACT FROM AUTHOR]

Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points. [ABSTRACT FROM AUTHOR]

We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguished by torsional rigidity. [ABSTRACT FROM AUTHOR]