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We contend a better way to teach ethics to freshman engineering students would be to address engineering ethics not solely in the abstract of philosophy or moral development, but as situated in the everyday decisions of engineers. Since everyday decisions are not typically a part of university courses, our approach in large lecture classes is to simulate engineering decision-making situations using the role-playing mechanic and narrative structure of a fictional choose-your-own-adventure. Drawing on the contemporary learning theory of situated learning [1], [2], such playful learning may enable instructors to create assignments that induce students to break free of the typical student mindset of finding the “right” answer. Mars: An Ethical Expedition! is an interactive, 12 week, narrative game about the colonization of Mars by various engineering specialists. Students take on the role of a head engineer and are presented with situations that require high-stakes decision-making. Various game mechanics induce students to act as they would on-the-fly, within a real engineering project context, using personal reasoning and richly context-dependent justifications, rather than simply right/wrong answers. Each segment of the game is presented in audio and text that ends with a binary decision that determines what will happen next in the story. Historically, this game had been led by an instructor and played weekly, as a whole-class assignment, completed at the beginning of class. The class votes and the majority option is presented next. In addition to the central decision, there are also follow-up questions at the end of each week that provoke deeper analysis of the situation and reflection on the ethical principles involved. This prototype was initially developed within a learning management system, then supported by the TwineTM game engine, and studied in use in our 2021 NSF EETHICS grant. In 2022-23 the game was redesigned and extended using the GodotTM game engine. In addition to streamlining the gameplay loop and reducing the set-up and data management required by instructors, this redesign supported instructors with an option to allow the game to be student-paced and played by individual students or to keep the instructor-led 12 week whole-class playstyle. Our proposed driving research question is "In what ways does individual student play differ from whole class instructor-led play with regard to learning that ethical behavior is situated?" In the next phase of our ongoing investigation, we plan to further evaluate the use of playful assessment to estimate its validity and reliability in comparison to current best practices of engineering ethics assessment. 

We study the problem of representing all distances between n points in Rd, with arbitrarily small distortion, using as few bits as possible. We give asymptotically tight bounds for this problem, for Euclidean metrics, for ℓ1 (a.k.a.~Manhattan) metrics, and for general metrics. Our bounds for Euclidean metrics mark the first improvement over compression schemes based on discretizing the classical dimensionality reduction theorem of Johnson and Lindenstrauss (Contemp.~Math.~1984). Since it is known that no better dimension reduction is possible, our results establish that Euclidean metric compression is possible beyond dimension reduction. 

Data-driven algorithms can adapt their internal structure or parameters to inputs from unknown application-specific distributions, by learning from a training sample of inputs. Several recent works have applied this approach to problems in numerical linear algebra, obtaining significant empirical gains in performance. However, no theoretical explanation for their success was known. In this work we prove generalization bounds for those algorithms, within the PAC-learning framework for data-driven algorithm selection proposed by Gupta and Roughgarden (SICOMP 2017). Our main results are closely matching upper and lower bounds on the fat shattering dimension of the learning-based low rank approximation algorithm of Indyk et al.~(NeurIPS 2019). Our techniques are general, and provide generalization bounds for many other recently proposed data-driven algorithms in numerical linear algebra, covering both sketching-based and multigrid-based methods. This considerably broadens the class of data-driven algorithms for which a PAC-learning analysis is available. 

Histograms, i.e., piece-wise constant approximations, are a popular tool used to represent data distributions. Traditionally, the difference between the histogram and the underlying distribution (i.e., the approximation error) is measured using the Lp norm, which sums the differences between the two functions over all items in the domain. Although useful in many applications, the drawback of this error measure is that it treats approximation errors of all items in the same way, irrespective of whether the mass of an item is important for the downstream application that uses the approximation. As a result, even relatively simple distributions cannot be approximated by succinct histograms without incurring large error. In this paper, we address this issue by adapting the definition of approximation so that only the errors of the items that belong to the support of the distribution are considered. Under this definition, we develop efficient 1-pass and 2-pass streaming algorithms that compute near-optimal histograms in sub-linear space. We also present lower bounds on the space complexity of this problem. Surprisingly, under this notion of error, there is an exponential gap in the space complexity of 1-pass and 2-pass streaming algorithms. Finally, we demonstrate the utility of our algorithms on a collection of real and synthetic data sets. 

We study fast algorithms for computing basic properties of an n x n positive semidefinite kernel matrix K corresponding to n points x_1,...,x_n in R^d. In particular, we consider the estimating the sum of kernel matrix entries, along with its top eigenvalue and eigenvector. These are some of the most basic problems defined over kernel matrices. We show that the sum of matrix entries can be estimated up to a multiplicative factor of 1+epsilon in time sublinear in n and linear in d for many popular kernel functions, including the Gaussian, exponential, and rational quadratic kernels. For these kernels, we also show that the top eigenvalue (and a witnessing approximate eigenvector) can be approximated to a multiplicative factor of 1+epsilon in time sub-quadratic in n and linear in d. Our algorithms represent significant advances in the best known runtimes for these problems. They leverage the positive definiteness of the kernel matrix, along with a recent line of work on efficient kernel density estimation. 

Polar amplification is a widely discussed phenomenon, and a range of mechanisms have been proposed to contribute to it, many of which involve atmospheric and surface processes. However, substantial questions remain regarding the role of ocean heat transport. Previous studies have found that ocean heat transport into the Arctic increases under global warming, but the reasons behind this remain unresolved. Here, we investigate changes in oceanic heat fluxes and associated impacts on polar amplification using an idealized ocean‐sea ice‐climate model of the Northern Hemisphere. We show that beneath the sea ice, vertical temperature gradients across the halocline increase as the ocean warms, since the surface mixed layer temperatures in ice‐covered regions are fixed near the freezing point. These enhanced vertical temperature gradients drive enhanced horizontal heat transport into the polar region and can contribute substantially to polar amplification.