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  1. Graphs are ubiquitous in various domains, such as social networks and biological systems. Despite the great successes of graph neural networks (GNNs) in modeling and analyzing complex graph data, the inductive bias of locality assumption, which involves exchanging information only within neighboring connected nodes, restricts GNNs in capturing long-range dependencies and global patterns in graphs. Inspired by the classic Brachistochrone problem, we seek how to devise a new inductive bias for cutting-edge graph application and present a general framework through the lens of variational analysis. The backbone of our framework is a two-way mapping between the discrete GNN model and continuous diffusion functional, which allows us to design application-specific objective function in the continuous domain and engineer discrete deep model with mathematical guarantees. First, we address over-smoothing in current GNNs. Specifically, our inference reveals that the existing layer-by-layer models of graph embedding learning are equivalent to a ℓ 2 -norm integral functional of graph gradients, which is the underlying cause of the over-smoothing problem. Similar to edge-preserving filters in image denoising, we introduce the total variation (TV) to promote alignment of the graph diffusion pattern with the global information present in community topologies. On top of this, we devise a new selective mechanism for inductive bias that can be easily integrated into existing GNNs and effectively address the trade-off between model depth and over-smoothing. Second, we devise a novel generative adversarial network (GAN) to predict the spreading flows in the graph through a neural transport equation. To avoid the potential issue of vanishing flows, we tailor the objective function to minimize the transportation within each community while maximizing the inter-community flows. Our new GNN models achieve state-of-the-art (SOTA) performance on graph learning benchmarks such as Cora, Citeseer, and Pubmed. 
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    Free, publicly-accessible full text available September 21, 2024
  2. Free, publicly-accessible full text available September 28, 2024
  3. Cook, S. ; Katz, B. ; Moore-Russo, D. (Ed.)
    Postsecondary instructors interested in inquiry-oriented instruction of Linear Algebra participated in a sequence of eight one-hour online work group meetings with other experienced inquiry-oriented linear algebra facilitators and teachers. Recordings from three meetings were analyzed for how two participants referenced goals of instruction in preparation for teaching a new instructional unit on subspaces. We identified four goals of instruction of teaching subspaces. We discuss the intersections of several goals of instruction and possible implications for those who want to transition to inquiry oriented instructional approaches. 
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  4. Cook, S. ; Katz, B. ; Moore-Russo, D. (Ed.)
    Postsecondary instructors interested in inquiry-oriented instruction of Linear Algebra participated in a sequence of eight one-hour online work group meetings with other experienced inquiry-oriented linear algebra facilitators and teachers. Recordings from three meetings were analyzed for how participants referenced goals of instruction in preparation for teaching a new instructional unit on subspaces. We identified four goals of instruction of teaching subspaces. We discuss the intersections of several goals of instruction and possible implications for those who want to transition to inquiry oriented instructional approaches. 
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  5. S. Cook ; B. Katz ; and D. Moore-Russo (Ed.)
    Post-secondary instructors interested in inquiry-oriented instruction of Linear Algebra participated in a sequence of eight one-hour online work group meetings with other experienced inquiry-oriented linear algebra facilitators and teachers. Recordings from three meetings were analyzed for how participants referenced goals of instruction in preparation for teaching a new instructional unit on subspaces. We identified four goals of instruction of teaching subspaces. We discuss the intersections of several goals of instruction and possible implications for those who want to transition to inquiry oriented instructional approaches. 
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  6. Abstract

    Environmental DNA (eDNA) data make it possible to measure and monitor biodiversity at unprecedented resolution and scale. As use‐cases multiply and scientific consensus grows regarding the value of eDNA analysis, public agencies have an opportunity to decide how and where eDNA data fit into their mandates. Within the United States, many federal and state agencies are individually using eDNA data in various applications and developing relevant scientific expertise. A national strategy for eDNA implementation would capitalize on recent scientific developments, providing a common set of next‐generation tools for natural resource management and public health protection. Such a strategy would avoid patchwork and possibly inconsistent guidelines in different agencies, smoothing the way for efficient uptake of eDNA data in management. Because eDNA analysis is already in widespread use in both ocean and freshwater settings, we focus here on applications in these environments. However, we foresee the broad adoption of eDNA analysis to meet many resource management issues across the nation because the same tools have immediate terrestrial and aerial applications.

     
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    Free, publicly-accessible full text available January 1, 2025
  7. We investigate the tropical Pacific annual cycle and the El Niño/Southern Oscillation (ENSO) in four mid‐Holocene simulations. Our results show that both ENSO variability and the amplitude of the annual cycle of the tropical Pacific cold tongue are reduced under mid‐Holocene forcing, along with a modified annual cycle in ENSO variance. The weakened annual cycle of the cold tongue is attributed to an ocean dynamical response to westerly wind anomalies in the western equatorial Pacific in boreal spring in addition to a thermodynamic response to local insolation changes in the eastern Pacific. The anomalous westerly winds in boreal spring excite an annual downwelling Kelvin wave that deepens the thermocline and propagates eastward along the equator, reaching the central and eastern equatorial Pacific during the development season of ENSO in boreal summer. Upon reaching the eastern Pacific, the downwelling Kelvin wave deepens the near‐surface thermocline, warming the surface ocean and weakening the local ocean‐atmosphere coupling critical to the growth of ENSO events. The westerly wind anomaly is associated with a shift in convection in the western Pacific driven by greater cooling of the Maritime Continent than western Pacific Ocean during the first half of the year (January to June) under tropical insolation forcing. By elucidating a common set of mechanisms responsible for a reduced cold tongue annual cycle and ENSO variability in a diverse range of mid‐Holocene simulations, this work yields important insight into the linkages between the tropical Pacific annual cycle and ENSO that are critical for understanding tropical Pacific climate variability. 
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