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We introduce a distance between kernels based on the Wasserstein distances between their values, study its properties, and prove that it is a metric on an appropriately defined space of kernels. We also relate it to various modes of convergence in the space of kernels. Then we consider the problem of approximating solutions to forward--backward systems, where the forward part is a Markov system described by a sequence of kernels, and the backward part calculates the values of a risk measure by operators that may be nonlinear with respect to the system's kernels. We propose recursively approximating the forward system with the use of the integrated transportation distance between kernels and we estimate the error of the risk evaluation by the errors of individual kernel approximations. We illustrate the results on stopping problems and several well-known risk measures. Then we develop a particle-based numerical procedure, in which the approximate kernels have finite support sets. Finally, we illustrate the efficacy of the approach on the financial problem of pricing an American basket option. 

Long-lived radiogenic isotopes of abyssal peridotites, residues of MORB extraction, show that the asthenosphere is intrinsically heterogeneous, which is inherited from ancient melting events and crustal recycling during Earth's history. Yet, Mid Ocean Ridge Basalts (MORB) have a rather uniform average composition, suggesting that the variability of their mantle source is concealed during their ascent. Here we document that mantle heterogeneity is exceptionally well preserved in high permeability mantle conduits from the Lanzo South mantle massif, Western Italian Alps. Nd-Hf-Os isotopes of decametre-scale replacive bodies provide evidence for the existence of two generations of mantle channels. The first generation consists of dunites concordant to the main foliation of host peridotites. The replacive dunites include clinopyroxene with MORB-like incompatible element signature and initial (160 Ma) ƐNd and ƐHf ranging from +4 to +7 and from +10 to +15, respectively. The second generation, made up of pyroxene-poor harzburgites discordant to the main foliation, is geochemically depleted in incompatible elements and its clinopyroxene displays highly radiogenic Hf isotopes (initial ƐHf up to +202). The mantle channel heterogeneity is confirmed by Resingle bondOs isotopes and platinum-groups elements. The MORB-type dunites have high Pt, Pd and, locally, Re, and have 187Os/188Os ratios similar to the host peridotite (0.122–0.128). On the other hand, the depleted bodies have lower Pt, Pd and Re, and 187Os/188Os ratios ranging from those of host peridotites (0.124) to highly unradiogenic values (0.118) in the most refractory sample. The preserved heterogeneity in trace elements, PGE, and Nd-Hf-Os isotopes highlights infiltration of melts from a highly heterogeneous mantle, still partially preserved within these mantle bodies. If applied to present-day Mid Ocean Ridges, our model indicates that the isotopic variability of melts migrating through replacive mantle conduits is by far larger than magmas erupted on the seafloor, which implies that diverse mantle components are mainly delivered and homogenised above the crust-mantle boundary. 

Abstract The dynamics of levitated liquid droplets can be used to measure their thermophysical properties by correlating the frequencies at which normal modes of oscillation most strongly resonate when subject to an external oscillatory force. In two preliminary works, it was shown via electrostatic levitation and processing of various metals and alloys that (1) the resonance of the first principal mode of oscillation (moden = 2) can be used to accurately measure surface tension and (2) that so-called “higher-order resonance” ofn = 3 is observable at a predictable frequency. It was also shown, in the context of future space-based experimentation on the Electrostatic Levitation Furnace (ELF), a setup on the International Space Station (ISS) operated by Japan Aerospace Exploration Agency (JAXA), that while the shadow array method in which droplet behavior is visualized would be challenging to identify then = 3 resonance, the normal moden = 4 was predicted to be more easily identifiable. In this short communication, experimental evidence of the first three principal modes of oscillation is provided using molten samples of Tin and Indium and it is subsequently shown that, as predicted, an “image-less approach can be used to identify bothn = 2 andn = 4 resonances in levitated liquid droplets. This suggests that the shadow array method may be satisfactorily used to obtain a self-consistent benchmark of thermophysical properties by comparing results from two successive even-mode natural frequencies. 

Background:Engineering's introduction into K–12 classrooms has been purported to support meaningful and inclusive learning environments. However, teachers must contend with dominant discourses embedded in US schooling that justify inequitable distributions of resources. Purpose:Drawing on Gee's notion of discourses, we examine how teachers incorporate language legitimizing socially and culturally constructed values and beliefs. In particular, we focus on the discourse of ability hierarchy—reflecting dominant values of sorting and ranking students based on perceived academic abilities—and the discourse of individual blame—reflecting dominant framings of educational problems as solely the responsibility of individual students or families. We aim to understand how these discourses surface in teachers' reasoning about teaching engineering. Method:We interviewed 15 teachers enrolled in an online graduate program in engineering education. Utilizing critical discourse analysis, we analyzed how teachers drew on discourses of blame and ability hierarchy when reasoning about problems of practice in engineering. Results:Teachers drew on engineering education concepts to reinforce dominant discourses (echoing specific language and preserving given roles) as well as to disrupt (utilizing different language or roles that [implicitly] challenge) dominant discourses. Importantly, teachers could also retool discourses of ability hierarchy (arguing for a more equitable distribution of resources but problematically preserving the values of ranking and sorting students). Conclusions:K–12 schooling's sociohistorical context can shape how teachers make sense of engineering in ways that implicate race, gender, disability, and language, suggesting a need to grapple with how discourses from schooling—and engineering culture—maintain marginalizing environments for students. 

We experimentally explore single-shot state identification using long alphabets of states and employing different modulation schemes. We use time-resolved quantum measurement and Bayesian inference to identify the input state and demonstrate the advantage of this single-shot measurement over classical state identification. For each single-shot measurement, we estimate the confidence of state identification based on the quantum measurement and demonstrate the physical significance of confidence estimates. Particularly, we show that a set of confidence values correctly represents the probabilities of successful state identification for a given experimental outcome. We investigate the alphabets of coherent states with different modulations and show that confidence estimates yield the reliability of each act of measurement independently of the modulation used. 

Abstract Partial differential equation (PDE)-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes required to accurately compute the PDE solution introduce an enormous number of parameters and require large-scale computing resources such as more processors and more memory to solve such systems in a reasonable time. For inverse problems constrained by time-dependent PDEs, the adjoint method often employed to compute gradients and higher order derivatives efficiently requires solving a time-reversed, so-called adjoint PDE that depends on the forward PDE solution at each timestep. This necessitates the storage of a high-dimensional forward solution vector at every timestep. Such a procedure quickly exhausts the available memory resources. Several approaches that trade additional computation for reduced memory footprint have been proposed to mitigate the memory bottleneck, including checkpointing and compression strategies. In this work, we propose a close-to-ideal scalable compression approach using autoencoders to eliminate the need for checkpointing and substantial memory storage, thereby reducing the time-to-solution and memory requirements. We compare our approach with checkpointing and an off-the-shelf compression approach on an earth-scale ill-posed seismic inverse problem. The results verify the expected close-to-ideal speedup for the gradient and Hessian-vector product using the proposed autoencoder compression approach. To highlight the usefulness of the proposed approach, we combine the autoencoder compression with the data-informed active subspace (DIAS) prior showing how the DIAS method can be affordably extended to large-scale problems without the need for checkpointing and large memory. 

BRIDGES is a software framework for creating engaging assignments for required courses such as data structures and algorithms. It provides students with a simplified API that populates their own data structure implementations with live and real-world data, and provides the ability for students to easily visualize the data structures they create as part of routine classroom exercises. The objective is to use the infrastructure to promote a better understanding of the data structure and its underlying algorithms. This report describes the BRIDGES infrastructure and provides evaluation data col- lected over the first five years of the project. In the first 2 years, as we were developing the BRIDGES projects, our focus was on gathering data to assess whether the addi- tion of the BRIDGES exercises had an effect on student retention of core concepts in data structures; and throughout the 5-year duration of the project, student interest and faculty feedback were collected online and anonymously. A mixed method design was used to evaluate the project impact. A quasiexperimental design compared stu- dent cohorts who were enrolled in comparable course sections that used BRIDGES with those that did not. Qualitative and quantitative measures were developed and used together with course grades and grade point averages. Interest and relevance in BRIDGES programming assignments was assessed with additional survey data from students and instructors. Results showed that students involved in BRIDGES projects demonstrated larger gains in knowledge of data structures compared to stu- dents enrolled in comparable course sections, as well as long-term benefits in their performance in four follow-on required courses. Survey responses indicated that some investment of time was needed to use BRIDGES, but the extra efforts were associated with several notable outcomes. Students and instructors had positive perceptions of the value of engaging in BRIDGES projects. BRIDGES can become a tool to get students more engaged in critical foundational courses, demonstrating relevance and context to today’s computational challenges. 

Teachers can play critical roles in challenging or reinscribing dominant narratives about what counts as STEM, who is seen within STEM disciplines, and how these disciplines should be taught. However, teachers have often experienced STEM in limited ways in their own education and are thereby provided with few resources for re-imagining these disciplines. While teacher educators have designed learning environments that engage teachers in new forms of disciplinary activities, there have been few accounts that describe how teachers make connections between these experiences and dominant narratives that impact their own and their students’ learning. In this study, I report on the experiences of Alma, a white, working-class, female elementary teacher in an online graduate certificate program for K-12 engineering educators. Through her engagement in engineering design in the program, Alma appropriated—transformed and made her own—discourse of the engineering design process in ways that trouble some of the narratives that restrict her, her family, and her students in STEM and in school. Alma’s experiences emphasize the need to consider not just what teachers learn about disciplinary tools and discourses, but how they transform these for their own purposes and contexts. 

Molecular phylogenetic analyses were conducted to infer relationships between the eastern and western Nearctic Androprosopa Mik and amongst the considerably more diverse western Nearctic species. Fresh, molecular-grade material was obtained for all Nearctic Androprosopa species except two Mexican species, An. sonorensis (Arnaud & Boussy) and An. zempoala Sinclair & Huerta, that eluded capture. Molecular sequences from two nuclear proteincoding genes, big zinc finger (BZF) and molybdenum cofactor sulfurase (MCS), were sampled from representatives of several outgroup and ingroup taxa and analyzed phylogenetically using maximum likelihood criteria to confirm identifications of females and immatures using a barcoding approach, test species boundaries among morphologically similar species, and infer relationships among more morphologically disparate groups. Resulting phylogenies suggest the following with significant node (bootstrap) support: (1) the eastern Nearctic Androprosopa species form the sister group to the lineage comprised of all sampled Palearctic thaumaleids, i.e., An. larvata (Mik), An. striata (Okada), and Thaumalea testacea Ruthe; (2) the aforementioned lineage is the sister group to the clade comprised of western Nearctic Androprosopa species; (3) the western Nearctic Androprosopa species form three multispecies lineages, two of which can be further divided into three or more well founded species groups. Our results suggest that Androprosopa as currently defined is paraphyletic. Additionally, we propose several new species groups within the western Nearctic Androprosopa based on molecular and morphological data. 

Because noise is inherent to all measurements, optical communication requires error identification and correction to protect and recover user data. Yet, error correction, routinely used in classical receivers, has not been applied to receivers that take advantage of quantum measurement. Here, we show how information uniquely available in a quantum measurement can be employed for efficient error correction. Our quantum-enabled forward error correction protocol operates on quadrature phase shift keying (QPSK) and achieves more than 80 dB error suppression compared to the raw symbol error rate and approximately 40 dB improvement of symbol error rates beyond the QPSK classical limit. With a symbol error rate below 10−9 for just 11 photons per bit, this approach enables reliable use of quantum receivers for ultra-low power optical communications. Limiting optical power improves the information capacity of optical links and enables scalable networks with coexisting quantum and classical channels in the same optical fiber.