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We present the design of a portable coronagraph, CATEcor, that incorporates a novel "shaded truss" style of external occultation and serves as a proof-of-concept for that family of coronagraphs. The shaded truss design style has the potential for broad application in various scientific settings. We conceived CATEcor itself as a simple instrument to observe the corona during the darker skies available during a partial solar eclipse, or for students or interested amateurs to detect the corona under ideal non-eclipsed conditions. CATEcor is therefore optimized for simplicity and accessibility to the public. It is implemented using an existing dioptric telescope and an adapter rig that mounts in front of the objective lens, restricting the telescope aperture and providing external occultation. The adapter rig, including occulter, is fabricated using fusion deposition modeling (FDM; colloquially "3D printing"), greatly reducing cost. The structure is designed to be integrated with moderate care and may be replicated in a university or amateur setting. While CATEcor is a simple demonstration unit, the design concept, process, and trades are useful for other more sophisticated coronagraphs in the same general family, which might operate under normal daytime skies outside the annular-eclipse conditions used for CATEcor., Comment: 27pp; 12 figures; accepted to Solar Physics

We present results of a dual eclipse expedition to observe the solar corona from two sites during the annular solar eclipse of 2023 October 14, using a novel coronagraph designed to be accessible for amateurs and students to build and deploy. The coronagraph "CATEcor" builds on the standardized eclipse observing equipment developed for the Citizen CATE 2024 experiment. The observing sites were selected for likelihood of clear observations, for historic relevance (near the Climax site in the Colorado Rocky Mountains), and for centrality to the annular eclipse path (atop Sandia Peak above Albuquerque, New Mexico). The novel portion of CATEcor is an external occulter assembly that slips over the front of a conventional dioptric telescope, forming a "shaded-truss" externally occulted coronagraph. CATEcor is specifically designed to be easily constructed in a garage or "makerspace" environment. We successfully observed some bright features in the solar corona to an altitude of approximately 2.25 R$_\odot$ during the annular phases of the eclipse. Future improvements to the design, in progress now, will reduce both stray light and image artifacts; our objective is to develop a design that can be operated successfully by amateur astronomers at sufficient altitude even without the darkened skies of a partial or annular eclipse., Comment: Accepted by Solar Physics

Alzheimer's disease is a progressive, debilitating neurodegenerative disease that affects 50 million people globally. Despite this substantial health burden, available treatments for the disease are limited and its fundamental causes remain poorly understood. Previous work has suggested the existence of clinically-meaningful sub-types, which it is suggested may correspond to distinct etiologies, disease courses, and ultimately appropriate treatments. Here, we use unsupervised learning techniques on electronic health records (EHRs) from a cohort of memory disorder patients to characterise heterogeneity in this disease population. Pre-trained embeddings for medical codes as well as transformer-derived Clinical BERT embeddings of free text are used to encode patient EHRs. We identify the existence of sub-populations on the basis of comorbidities and shared textual features, and discuss their clinical significance., Comment: 14 pages, 5 figures in main text

The broadband solar K-corona is linearly polarized due to Thomson scattering. Various strategies have been used to represent coronal polarization. Here, we present a new way to visualize the polarized corona, using observations from the 2023 April 20 total solar eclipse in Australia in support of the Citizen CATE 2024 project. We convert observations in the common four-polarizer orthogonal basis (0{\deg}, 45{\deg}, 90{\deg}, & 135{\deg}) to -60{\deg}, 0{\deg}, and +60{\deg} (MZP) polarization, which is homologous to R, G, B color channels. The unique image generated provides some sense of how humans might visualize polarization if we could perceive it in the same way we perceive color., Comment: 4 pages, 1 figure; accepted for publication in Research Notes of the American Astronomical Society (RNAAS)

Background: Proof Blocks is a software tool that enables students to construct proofs by assembling prewritten lines and gives them automated feedback. Prior work on learning gains from Proof Blocks has focused on comparing learning gains from Proof Blocks against other learning activities such as writing proofs or reading. Purpose: The study described in this paper aims to compare learning gains from different variations of Proof Blocks. Specifically, we attempt to quantify the difference in learning gains for students who complete Proof Blocks problems with and without distractors. Methods: We conducted a randomized controlled trial with three experimental groups: a control group that completed an off-topic Proof Blocks activity, one that completed a \tool{} activity without distractors, and one that completed a Proof Blocks activity with distractors. All three groups read a book chapter on proof by induction before completing their activity. Findings: The group that completed the Proof Blocks activity with distractors performed better on the posttest than the group that completed the Proof Blocks without distractors, who in turn performed better than the group that completed the off-topic Proof Blocks activity. However, none of these differences were statistically significant. While the results of this study are inconclusive, we hope that it can serve as a foundation for future work., Comment: arXiv admin note: text overlap with arXiv:2211.09609

We present an extension of the Coronal Reconstruction Onto B-Aligned Regions (CROBAR) method to Linear Force Free Field (LFFF) extrapolations, and apply it to the reconstruction of a set of AIA, MDI, and STEREO EUVI data. The results demonstrate that CROBAR can not only reconstruct coronal emission structures, but also that it can help constrain the coronal field extrapolations via the LFFF's helicity $\alpha$ parameter. They also provide a real-world example of how CROBAR can easily incorporate information from multiple perspectives to improve its reconstructions, and we also use the additional perspectives to help validate the reconstructions. We furthermore touch on the use of real-world emission passbands rather than idealized power-law type ones using DEMs. We conclude with a comparison of CROBAR generated emission to observed emission and those produced with idealized DEM based power-laws. These results further illustrate the promise of CROBAR for real-world applications, and we make available a preliminary release of the software available for download., Comment: 18 Pages, 14 Figures, to be submitted to ApJ

We report on the closest view of a coronal mass ejection observed by the Parker Solar Probe (PSP)/Wide-field Imager for {Parker} Solar PRobe (WISPR) instrument on September 05, 2022, when PSP was traversing from a distance of 15.3~to~13.5~R$_\odot$ from the Sun. The CME leading edge and an arc-shaped {\emph{concave-up} structure near the core} was tracked in WISPR~field of view using the polar coordinate system, for the first time. Using the impact distance on Thomson surface, we measured average speeds of CME leading edge and concave-up structure as $\approx$2500~$\pm$~270\,km\,s$^{-1}$ and $\approx$400~$\pm$~70\,km\,s$^{-1}$ with a deceleration of $\approx$20~m~s$^{-2}$ for the later. {The use of the plane-of-sky approach yielded an unrealistic speed of more than three times of this estimate.} We also used single viewpoint STEREO/COR-2A images to fit the Graduated Cylindrical Shell (GCS) model to the CME while incorporating the source region location from EUI of Solar Orbiter and estimated a 3D speed of $\approx$2700\,km\,s$^{-1}$. We conclude that this CME exhibits the highest speed during the ascending phase of solar cycle 25. This places it in the category of extreme speed CMEs, which account for only 0.15\% of all CMEs listed in the CDAW CME catalog., Comment: 13 Pages, 6 Figures; Accepted in The Astrophysical Journal Letters

Cloud droplets containing ice-nucleating particles (INPs) may freeze at temperatures above than the homogeneous freezing threshold. This process, referred to as immersion freezing, is one of the major modulator of aerosol-cloud interactions in the Earth's atmosphere that impacts cloud radiative properties, and thus, climate. In modeling studies, immersion freezing is often implemented using either so-called ``singular'' or ``time-dependent'' parameterizations. In this paper, we juxtapose both approaches and discuss them in the context of probabilistic particle-based cloud microphysics modeling, referred to as the super-particle or super-droplet techniques. These techniques work by populating the particle-attribute phase space with large numbers of computational particles and tracking the evolution of particle attributes. We outline the congruence of the singular and time-dependent approaches with Poissonian process description and point to limitations pertinent to the singular approach. Simulations with both box and two-dimensional kinematic models focus on the following aspects of immersion freezing modeling. First, we contrast how both parameterizations respond to different idealized ambient cooling rate profiles. Second, we quantify how the polydispersity of the immersed surface spectrum impacts macroscopic features of the system. Third, we illustrate the implications of applying the singular model in simulations with flow regimes relevant to ambient cloud conditions rather than to the cloud-chamber experiments on which these parameterizations are built upon. We discuss the critical role of the attribute-space sampling strategy for particle-based model simulations in modeling heterogeneous ice nucleation which is contingent on the presence of relatively sparse immersed INPs.

PyPartMC is a Pythonic interface to PartMC, a stochastic, particle-resolved aerosol model implemented in Fortran. Both PyPartMC and PartMC are free, libre, and open-source. PyPartMC reduces the number of steps and mitigates the effort necessary to install and utilize the resources of PartMC. Without PyPartMC, setting up PartMC requires: working with UNIX shell, providing Fortran and C libraries, and performing standard Fortran and C source code configuration, compilation and linking. This can be challenging for those less experienced with computational research or those intending to use PartMC in environments where provision of UNIX tools is less straightforward (e.g., on Windows). PyPartMC offers a single-step installation/upgrade process of PartMC and all dependencies through the pip Python package manager on Linux, macOS, and Windows. This allows streamlined access to the unmodified and versioned Fortran internals of the PartMC codebase from both Python and other interoperable environments (e.g., Julia through PyCall). Consequently, users of PyPartMC can setup, run, process and visualize output of PartMC simulations using a single general-purpose programming language.

Our current theoretical and observational understanding suggests that critical properties of the solar wind and Coronal Mass Ejections (CMEs) are imparted within 10 Rs, particularly below 4 Rs. This seemingly narrow spatial region encompasses the transition of coronal plasma processes through the entire range of physical regimes from fluid to kinetic, and from primarily closed to open magnetic field structures. From a physics perspective, therefore, it is more appropriate to refer to this region as the Critical Coronal Transition Region (CCTR) to emphasize its physical, rather than spatial, importance to key Heliophysics science. This white paper argues that the comprehensive exploration of the CCTR will answer two of the most central Heliophysics questions, "How and where does the solar wind form?" and "How do eruptions form?", by unifying hardware/software/modeling development and seemingly disparate research communities and frameworks. We describe the outlines of decadal-scale plan to achieve that by 2050., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033; 6 pages, 1 figure, 2 tables

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for training. As a result, accurate evaluation may be impractical, and we show that naive approximations at replacing these integrals with unbiased estimates lead to biased loss functions and solutions. To overcome this bias, we investigate three types of potential solutions: the deterministic sampling approaches, the double-sampling trick, and the delayed target method. We consider three classes of PDEs for benchmarking; one defining Poisson problems with singular charges and weak solutions of up to 10 dimensions, another involving weak solutions on electro-magnetic fields and a Maxwell equation, and a third one defining a Smoluchowski coagulation problem. Our numerical results confirm the existence of the aforementioned bias in practice and also show that our proposed delayed target approach can lead to accurate solutions with comparable quality to ones estimated with a large sample size integral. Our implementation is open-source and available at https://github.com/ehsansaleh/btspinn., Comment: Accepted in the main track of ICML 2024

The coronal magnetic field is the prime driver behind many as-yet unsolved mysteries: solar eruptions, coronal heating, and the solar wind, to name a few. It is, however, still poorly observed and understood. We highlight key questions related to magnetic energy storage, release, and transport in the solar corona, and their relationship to these important problems. We advocate for new and multi-point co-optimized measurements, sensitive to magnetic field and other plasma parameters, spanning from optical to $\gamma$-ray wavelengths, to bring closure to these long-standing and fundamental questions. We discuss how our approach can fully describe the 3D magnetic field, embedded plasma, particle energization, and their joint evolution to achieve these objectives., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033; 16 pages, 3 figures

Heliophysics image data largely relies on a forty-year-old ecosystem built on the venerable Flexible Image Transport System (FITS) data standard. While many in situ measurements use newer standards, they are difficult to integrate with multiple data streams required to develop global understanding. Additionally, most data users still engage with data in much the same way as they did decades ago. However, contemporary missions and models require much more complex support for 3D multi-parameter data, robust data assimilation strategies, and integration of multiple individual data streams required to derive complete physical characterizations of the Sun and Heliospheric plasma environment. In this white paper we highlight some of the 21$^\mathsf{st}$ century challenges for data frameworks in heliophysics, consider an illustrative case study, and make recommendations for important steps the field can take to modernize its data products and data usage models. Our specific recommendations include: (1) Investing in data assimilation capability to drive advanced data-constrained models, (2) Investing in new strategies for integrating data across multiple instruments to realize measurements that cannot be produced from single observations, (3) Rethinking old data use paradigms to improve user access, develop deep understanding, and decrease barrier to entry for new datasets, and (4) Investing in research on data formats better suited for multi-dimensional data and cloud-based computing., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033; 9 pages, 3 figures

COMPLETE is a flagship mission concept combining broadband spectroscopic imaging and comprehensive magnetography from multiple viewpoints around the Sun to enable tomographic reconstruction of 3D coronal magnetic fields and associated dynamic plasma properties, which provide direct diagnostics of energy release. COMPLETE re-imagines the paradigm for solar remote-sensing observations through purposefully co-optimized detectors distributed on multiple spacecraft that operate as a single observatory, linked by a comprehensive data/model assimilation strategy to unify individual observations into a single physical framework. We describe COMPLETE's science goals, instruments, and mission implementation. With targeted investment by NASA, COMPLETE is feasible for launch in 2032 to observe around the maximum of Solar Cycle 26., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033; 10 pages, 6 figures, 1 table

Cross-device user matching is a critical problem in numerous domains, including advertising, recommender systems, and cybersecurity. It involves identifying and linking different devices belonging to the same person, utilizing sequence logs. Previous data mining techniques have struggled to address the long-range dependencies and higher-order connections between the logs. Recently, researchers have modeled this problem as a graph problem and proposed a two-tier graph contextual embedding (TGCE) neural network architecture, which outperforms previous methods. In this paper, we propose a novel hierarchical graph neural network architecture (HGNN), which has a more computationally efficient second level design than TGCE. Furthermore, we introduce a cross-attention (Cross-Att) mechanism in our model, which improves performance by 5% compared to the state-of-the-art TGCE method.

We show that there exist pairs of non-isometric potentials for the 1D semiclassical Schr\"odinger operator whose spectra agree up to $O(h^\infty)$, yet their corresponding eigenvalues differ no less than exponentially. This result was conjectured by Guillemen and Hezari in [GH12], where they prove a very similar result, yet cannot remove the possibility of a subsequence $h_k\to 0$ where the ground state eigenvalues may agree., Comment: 11 pages, 3 figures. To be published

Clustering is a commonplace problem in many areas of data science, with applications in biology and bioinformatics, understanding chemical structure, image segmentation, building recommender systems, and many more fields. While there are many different clustering variants (based on given distance or graph structure, probability distributions, or data density), we consider here the problem of clustering nodes in a graph, motivated by the problem of aggregating discrete degrees of freedom in multigrid and domain decomposition methods for solving sparse linear systems. Specifically, we consider the challenge of forming balanced clusters in the graph of a sparse matrix for use in algebraic multigrid, although the algorithm has general applicability. Based on an extension of the Bellman-Ford algorithm, we generalize Lloyd's algorithm for partitioning subsets of Rn to balance the number of nodes in each cluster; this is accompanied by a rebalancing algorithm that reduces the overall energy in the system. The algorithm provides control over the number of clusters and leads to "well centered" partitions of the graph. Theoretical results are provided to establish linear complexity and numerical results in the context of algebraic multigrid highlight the benefits of improved clustering., Comment: 29 pages, 14 figures

We present the SWAP Filter: an azimuthally varying, radial normalizing filter specifically developed for EUV images of the solar corona, named for the Sun Watcher with Active Pixels and Image Processing (SWAP) instrument on the Project for On-Board Autonomy 2 spacecraft. We discuss the origins of our technique, its implementation and key user-configurable parameters, and highlight its effects on data via a series of examples. We discuss the filter's strengths in a data environment in which wide field-of-view observations that specifically target the low signal-to-noise middle corona are newly available and expected to grow in the coming years., Comment: Contact D. B. Seaton for animations referenced in figure captions

The "middle corona," defined by West et al. (2022) as the region between ~1.5-6 solar radii, is a critical transition region that connects the highly structured lower corona to the outer corona where the magnetic field becomes predominantly radial. At radio wavelengths, remote-sensing of the middle corona falls in the meter-decameter wavelength range where a critical transition of radio emission mechanisms occurs. In addition, plasma properties of the middle corona can be probed by trans-coronal radio propagation methods including radio scintillation and Faraday rotation techniques. Together they offer a wealth of diagnostic tools for the middle corona, complementing current and planned missions at other wavelengths. These diagnostics include unique means for detecting and measuring the magnetic field and energetic electrons associated with coronal mass ejections, mapping coronal shocks and electron beam trajectories, as well as constraining the plasma density, magnetic field, and turbulence of the "young" solar wind. Following a brief overview of pertinent radio diagnostic methods, this white paper will discuss the current state of radio studies on the middle corona, challenges to obtaining a more comprehensive picture, and recommend an outlook in the next decade. Our specific recommendations for advancing the middle coronal sciences from the radio perspective are: (1) Prioritizing solar-dedicated radio facilities in the ~0.1-1 GHz range with broadband, high-dynamic-range imaging spectropolarimetry capabilities. (2) Developing facilities and techniques to perform multi-perspective, multiple lines-of-sight trans-coronal radio Faraday Rotation measurements., Comment: Science white paper submitted to the 2024 Solar and Space Physics Decadal Survey. All submitted white papers (including this one) are available at https://www.nationalacademies.org/our-work/decadal-survey-for-solar-and-space-physics-heliophysics-2024-2033. arXiv admin note: text overlap with arXiv:2208.04485

Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters, prescribing overlap, subdomain boundary conditions, and other properties of the DDM. While some work has been done on optimizing these parameters, it has mostly focused on the one-level setting or special cases such as structured-grid discretizations with regular subdomain construction. In this paper, we propose multigrid graph neural networks (MG-GNN), a novel GNN architecture for learning optimized parameters in two-level DDMs\@. We train MG-GNN using a new unsupervised loss function, enabling effective training on small problems that yields robust performance on unstructured grids that are orders of magnitude larger than those in the training set. We show that MG-GNN outperforms popular hierarchical graph network architectures for this optimization and that our proposed loss function is critical to achieving this improved performance.

Algebraic Multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their performance. Reduction-based AMG (AMGr) algorithms attempt to formalize these heuristics by providing two-level convergence bounds that depend concretely on properties of the partitioning of the given matrix into its fine- and coarse-grid degrees of freedom. MacLachlan and Saad (SISC 2007) proved that the AMGr method yields provably robust two-level convergence for symmetric and positive-definite matrices that are diagonally dominant, with a convergence factor bounded as a function of a coarsening parameter. However, when applying AMGr algorithms to matrices that are not diagonally dominant, not only do the convergence factor bounds not hold, but measured performance is notably degraded. Here, we present modifications to the classical AMGr algorithm that improve its performance on matrices that are not diagonally dominant, making use of strength of connection, sparse approximate inverse (SPAI) techniques, and interpolation truncation and rescaling, to improve robustness while maintaining control of the algorithmic costs. We present numerical results demonstrating the robustness of this approach for both classical isotropic diffusion problems and for non-diagonally dominant systems coming from anisotropic diffusion.

Proof Blocks is a software tool that provides students with a scaffolded proof-writing experience, allowing them to drag and drop prewritten proof lines into the correct order instead of starting from scratch. In this paper we describe a randomized controlled trial designed to measure the learning gains of using Proof Blocks for students learning proof by induction. The study participants were 332 students recruited after completing the first month of their discrete mathematics course. Students in the study took a pretest and read lecture notes on proof by induction, completed a brief (less than 1 hour) learning activity, and then returned one week later to complete the posttest. Depending on the experimental condition that each student was assigned to, they either completed only Proof Blocks problems, completed some Proof Blocks problems and some written proofs, or completed only written proofs for their learning activity. We find that students in the early phases of learning about proof by induction are able to learn just as much from reading lecture notes and using Proof Blocks as by reading lecture notes and writing proofs from scratch, but in far less time on task. This finding complements previous findings that Proof Blocks are useful exam questions and are viewed positively by students., Comment: To be presented at SIGCSE 2023

The middle corona, the region roughly spanning heliocentric altitudes from $1.5$ to $6\,R_\odot$, encompasses almost all of the influential physical transitions and processes that govern the behavior of coronal outflow into the heliosphere. Eruptions that could disrupt the near-Earth environment propagate through it. Importantly, it modulates inflow from above that can drive dynamic changes at lower heights in the inner corona. Consequently, this region is essential for comprehensively connecting the corona to the heliosphere and for developing corresponding global models. Nonetheless, because it is challenging to observe, the middle corona has been poorly studied by major solar remote sensing missions and instruments, extending back to the Solar and Heliospheric Observatory (SoHO) era. Thanks to recent advances in instrumentation, observational processing techniques, and a realization of the importance of the region, interest in the middle corona has increased. Although the region cannot be intrinsically separated from other regions of the solar atmosphere, there has emerged a need to define the region in terms of its location and extension in the solar atmosphere, its composition, the physical transitions it covers, and the underlying physics believed to be encapsulated by the region. This paper aims to define the middle corona and give an overview of the processes that occur there., Comment: Working draft prepared by the middle corona heliophysics working group

Evolution of disease in a large population is a function of the top-down policy measures from a centralized planner, as well as the self-interested decisions (to be socially active) of individual agents in a large heterogeneous population. This paper is concerned with understanding the latter based on a mean-field type optimal control model. Specifically, the model is used to investigate the role of partial information on an agent's decision-making, and study the impact of such decisions by a large number of agents on the spread of the virus in the population. The motivation comes from the presymptomatic and asymptomatic spread of the COVID-19 virus where an agent unwittingly spreads the virus. We show that even in a setting with fully rational agents, limited information on the viral state can result in an epidemic growth., Comment: arXiv admin note: text overlap with arXiv:2111.10422

In this paper, we present a policy gradient method that avoids exploratory noise injection and performs policy search over the deterministic landscape. By avoiding noise injection all sources of estimation variance can be eliminated in systems with deterministic dynamics (up to the initial state distribution). Since deterministic policy regularization is impossible using traditional non-metric measures such as the KL divergence, we derive a Wasserstein-based quadratic model for our purposes. We state conditions on the system model under which it is possible to establish a monotonic policy improvement guarantee, propose a surrogate function for policy gradient estimation, and show that it is possible to compute exact advantage estimates if both the state transition model and the policy are deterministic. Finally, we describe two novel robotic control environments -- one with non-local rewards in the frequency domain and the other with a long horizon (8000 time-steps) -- for which our policy gradient method (TDPO) significantly outperforms existing methods (PPO, TRPO, DDPG, and TD3). Our implementation with all the experimental settings is available at https://github.com/ehsansaleh/code_tdpo

Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Yet the optimal construction of these methods requires tedious analysis and is often available only in simplified, structured-grid settings, limiting their use for more complex problems. In this work, we generalize optimized Schwarz domain decomposition methods to unstructured-grid problems, using Graph Convolutional Neural Networks (GCNNs) and unsupervised learning to learn optimal modifications at subdomain interfaces. A key ingredient in our approach is an improved loss function, enabling effective training on relatively small problems, but robust performance on arbitrarily large problems, with computational cost linear in problem size. The performance of the learned linear solvers is compared with both classical and optimized domain decomposition algorithms, for both structured- and unstructured-grid problems.

Proof Blocks is a software tool that allows students to practice writing mathematical proofs by dragging and dropping lines instead of writing proofs from scratch. Proof Blocks offers the capability of assigning partial credit and providing solution quality feedback to students. This is done by computing the edit distance from a student's submission to some predefined set of solutions. In this work, we propose an algorithm for the edit distance problem that significantly outperforms the baseline procedure of exhaustively enumerating over the entire search space. Our algorithm relies on a reduction to the minimum vertex cover problem. We benchmark our algorithm on thousands of student submissions from multiple courses, showing that the baseline algorithm is intractable, and that our proposed algorithm is critical to enable classroom deployment. Our new algorithm has also been used for problems in many other domains where the solution space can be modeled as a DAG, including but not limited to Parsons Problems for writing code, helping students understand packet ordering in networking protocols, and helping students sketch solution steps for physics problems. Integrated into multiple learning management systems, the algorithm serves thousands of students each year., Comment: Accepted for AIED 2023 in Tokyo, Japan

Linear polarized light has been used to view the solar corona for over 150 years. While the familiar Stokes representation for polarimetry is complete, it is best matched to a laboratory setting and therefore is not the most convenient representation either for coronal instrument design or for coronal data analysis. Over the last 100 years of development of coronagraphs and heliospheric imagers, various representations have been used both for direct measurement and analysis. These systems include famous representations such as the (B, pB) system that is analogous to the Stokes system in solar observing coordinates, and also internal representations such as in-instrument Stokes parameters with fixed or variable "vertical" direction, and brightness values through a particular polarizing optic or set thereof. Many polarimetric instruments currently use a symmetric three-polarizer measurement and representation system, which we refer to as "(M, Z, P)", to derive the (B, pB) or Stokes parameters. We present a symmetric derivation of (B, pB) and Stokes parameters from (M, Z, P), analyze the noise properties of (M, Z, P) in the context of instrument design, develop (M, Z, P) as a useful intermediate system for data analysis including background subtraction, and draw a helpful analogy between linear polarimetric systems and the large existing body of work on photometric colorimetry., Comment: 15 pages; 2 figures; accepted to ApJ

This paper is concerned with developing mean-field game models for the evolution of epidemics. Specifically, an agent's decision -- to be socially active in the midst of an epidemic -- is modeled as a mean-field game with health-related costs and activity-related rewards. By considering the fully and partially observed versions of this problem, the role of information in guiding an agent's rational decision is highlighted. The main contributions of the paper are to derive the equations for the mean-field game in both fully and partially observed settings of the problem, to present a complete analysis of the fully observed case, and to present some analytical results for the partially observed case.

A flexible treatment for gas- and aerosol-phase chemical processes has been developed for models of diverse scale, from box models up to global models. At the core of this novel framework is an "abstracted aerosol representation" that allows a given chemical mechanism to be solved in atmospheric models with different aerosol representations (e.g., sectional, modal, or particle-resolved). This is accomplished by treating aerosols as a collection of condensed phases that are implemented according to the aerosol representation of the host model. The framework also allows multiple chemical processes (e.g., gas- and aerosol-phase chemical reactions, emissions, deposition, photolysis, and mass-transfer) to be solved simultaneously as a single system. The flexibility of the model is achieved by (1) using an object-oriented design that facilitates extensibility to new types of chemical processes and to new ways of representing aerosol systems; (2) runtime model configuration using JSON input files that permits making changes to any part of the chemical mechanism without recompiling the model; this widely used, human-readable format allows entire gas- and aerosol-phase chemical mechanisms to be described with as much complexity as necessary; and (3) automated comprehensive testing that ensures stability of the code as new functionality is introduced. Together, these design choices enable users to build a customized multiphase mechanism, without having to handle pre-processors, solvers or compilers. This new treatment compiles as a stand-alone library and has been deployed in the particle-resolved PartMC model and in the MONARCH chemical weather prediction system for use at regional and global scales. Results from the initial deployment will be discussed, along with future extension to more complex gas-aerosol systems, and the integration of GPU-based solvers.

Understanding the resistive switching behavior, or the resistance change, of oxide-based memristor devices, is critical to predicting their responses with known electrical inputs. Also, with the known electrical response of a memristor, one can confirm its usefulness in non-volatile memory and/or in artificial neural networks. Although bi- or multi-layered oxides have been reported to improve the switching performance, compared to the single oxide layer, the detailed explanation about why the switching can easily be improved for some oxides combinations is still missing. Herein, we fabricated two types of bi-layered heterostructure devices, quasi-HfO$_x$/AlO$_y$ and AlO$_y$/HfO$_x$ sandwiched between Au electrodes, and their electrical responses are investigated. For a deeper understanding of the switching mechanism, the performance of a HfOx only device is also considered, which serves as a control device. The role of bi-layered heterostructures is investigated using both the experimental and simulated results. Our results suggest that synergistic switching performance can be achieved with a proper combination of these materials and/or devices. These results open the avenue for designing more efficient double- or multi-layers memristor devices for an analog response., Comment: 7 pages, 5 figures

Proof Blocks is a software tool which enables students to write proofs by dragging and dropping prewritten proof lines into the correct order. These proofs can be graded completely automatically, enabling students to receive rapid feedback on how they are doing with their proofs. When constructing a problem, the instructor specifies the dependency graph of the lines of the proof, so that any correct arrangement of the lines can receive full credit. This innovation can improve assessment tools by increasing the types of questions we can ask students about proofs, and can give greater access to proof knowledge by increasing the amount that students can learn on their own with the help of a computer.

Large sparse linear systems of equations are ubiquitous in science and engineering, such as those arising from discretizations of partial differential equations. Algebraic multigrid (AMG) methods are one of the most common methods of solving such linear systems, with an extensive body of underlying mathematical theory. A system of linear equations defines a graph on the set of unknowns and each level of a multigrid solver requires the selection of an appropriate coarse graph along with restriction and interpolation operators that map to and from the coarse representation. The efficiency of the multigrid solver depends critically on this selection and many selection methods have been developed over the years. Recently, it has been demonstrated that it is possible to directly learn the AMG interpolation and restriction operators, given a coarse graph selection. In this paper, we consider the complementary problem of learning to coarsen graphs for a multigrid solver, a necessary step in developing fully learnable AMG methods. We propose a method using a reinforcement learning (RL) agent based on graph neural networks (GNNs), which can learn to perform graph coarsening on small planar training graphs and then be applied to unstructured large planar graphs, assuming bounded node degree. We demonstrate that this method can produce better coarse graphs than existing algorithms, even as the graph size increases and other properties of the graph are varied. We also propose an efficient inference procedure for performing graph coarsening that results in linear time complexity in graph size., Comment: Advances in Neural Information Processing Systems (NeurIPS2021)

The Sun Coronal Ejection Tracker (SunCET) is an extreme ultraviolet imager and spectrograph instrument concept for tracking coronal mass ejections through the region where they experience the majority of their acceleration: the difficult-to-observe middle corona. It contains a wide field of view (0-4~\Rs) imager and a 1~\AA\ spectral-resolution-irradiance spectrograph spanning 170-340~\AA. It leverages new detector technology to read out different areas of the detector with different integration times, resulting in what we call "simultaneous high dynamic range", as opposed to the traditional high dynamic range camera technique of subsequent full-frame images that are then combined in post-processing. This allows us to image the bright solar disk with short integration time, the middle corona with a long integration time, and the spectra with their own, independent integration time. Thus, SunCET does not require the use of an opaque or filtered occulter. SunCET is also compact -- $\sim$15 $\times$ 15 $\times$ 10~cm in volume -- making it an ideal instrument for a CubeSat or a small, complementary addition to a larger mission. Indeed, SunCET is presently in a NASA-funded, competitive Phase A as a CubeSat and has also been proposed to NASA as an instrument onboard a 184 kg Mission of Opportunity., Comment: 22 pages, 12 figures, 5 tables, in press at Journal of Space Weather and Space Climate special issue called "Space Weather Instrumentation"

We demonstrate a successful navigation and docking control system for the John Deere Tango autonomous mower, using only a single camera as the input. This vision-only system is of interest because it is inexpensive, simple for production, and requires no external sensing. This is in contrast to existing systems that rely on integrated position sensors and global positioning system (GPS) technologies. To produce our system we combined a state-of-the-art object detection architecture, You Only Look Once (YOLO), with a reinforcement learning (RL) architecture, Double Deep QNetworks (Double DQN). The object detection network identifies features on the mower and passes its output to the RL network, providing it with a low-dimensional representation that enables rapid and robust training. Finally, the RL network learns how to navigate the machine to the desired spot in a custom simulation environment. When tested on mower hardware, the system is able to dock with centimeter-level accuracy from arbitrary initial locations and orientations.

The aerosol mixing state significantly affects the climate and health impacts of atmospheric aerosol particles. Simplified aerosol mixing state assumptions, common in Earth System models, can introduce errors in the prediction of these aerosol impacts. The aerosol mixing state index, a metric to quantify aerosol mixing state, is a convenient measure for quantifying these errors. Global estimates of aerosol mixing state indices have recently become available via supervised learning models, but require regionalization to ease spatiotemporal analysis. Here we developed a simple but effective unsupervised learning approach to regionalize predictions of global aerosol mixing state indices. We used the monthly average of aerosol mixing state indices global distribution as the input data. Grid cells were then clustered into regions by the k-means algorithm without explicit spatial information as input. This approach resulted in eleven regions over the globe with specific spatial aggregation patterns. Each region exhibited a unique distribution of mixing state indices and aerosol compositions, showing the effectiveness of the unsupervised regionalization approach. This study defines "aerosol mixing state zones" that could be useful for atmospheric science research., Comment: AI for Earth Sciences Workshop at the 34th Conference on Neural Information Processing Systems (NeurIPS 2020)

Solar eruptions such as Coronal Mass Ejections (CMEs) observed in the inner solar corona (up to 4 R$_{\odot}$) show acceleration profiles which appear as parabolic ridges in height-time plots. Inspired by the white-light automated detection algorithms, Computer Aided CME Tracking System (CACTus) and Solar Eruptive Events Detection System (SEEDS), we employ the parabolic Hough Transform for the first time to automatically detect off-disk solar eruptions {from height-time plots. Due to the limited availability of white-light observations in the inner corona, we use Extreme UltraViolet (EUV) images of the Sun. In this paper we present a new algorithm, CME Identification in Inner Solar Corona (CIISCO), which is based on Fourier motion filtering and the parabolic Hough transform, and demonstrate its implementation using EUV observations taken from {\it Atmospheric Imaging Assembly} (AIA) on-board the Solar Dynamics Observatory (SDO), {\it Extreme Ultra Violet Imager} (EUVI) on-board the STEREO-A and B satellites, and {\it Sun Watcher using Active Pixel System detector and Image Processing} (SWAP) Imager on-board PROBA2. We show that CIISCO is able to identify any {off-disk} outward moving feature in EUV images. The use of automated detection algorithms, like CIISCO, can potentially be used to provide early warnings of CMEs if an EUV telescope is located at $\pm$ 90$^{\circ}$ from the Sun-Earth line, providing CME characteristics and kinematics close to the Sun. This paper also presents the limitations of this algorithm and the prospects for future improvement., Comment: Accepted for publication in Solar Physics; 27 pages, 10 figures, 1 table

Coronal waves are large-scale disturbances often driven by coronal mass ejections (CMEs). We investigate a spectacular wave event on 7 March 2012, which is associated with an X5.4 flare (SOL2012-03-07). By using a running center-median (RCM) filtering method for the detection of temporal variations in extreme ultraviolet (EUV) images, we enhance the EUV disturbance observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and the Sun Watcher using Active Pixel System detector and Image Processing (SWAP) onboard the PRoject for Onboard Autonomy 2 (PROBA2). In coronagraph images, a halo front is observed to be the upper counterpart of the EUV disturbance. Based on the EUV and coronagraph images observed from three different perspectives, we have made three-dimensional (3D) reconstructions of the wave surfaces using a new mask-fitting method. The reconstructions are compared with those obtained from forward-fitting methods. We show that the mask fitting method can reflect the inhomogeneous coronal medium by capturing the concave shape of the shock wave front. Subsequently, we trace the developing concave structure and derive the deprojected wave kinematics. The speed of the 3D-wave nose increases from a low value below a few hundred $\mathrm{km\,s^{-1}}$ to a maximum value of about 3800 $\mathrm{km\,s^{-1}}$, and then slowly decreases afterwards. The concave structure starts to decelerate earlier and has significantly lower speeds than those of the wave nose. We also find that the 3D-wave in the extended corona has a much higher speed than the speed of EUV disturbances across the solar disk., Comment: Solar Physics: Topical Collection "Ten Years of Solar Observations with PROBA2", accepted

We present a scalable methodology to verify stochastic hybrid systems. Using the Mori-Zwanzig reduction method, we construct a finite state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain is approximately equivalent to the original system in a distributional sense. Approximate equivalence of the stochastic hybrid system and its Markov chain reduction means that analyzing the Markov chain with respect to a suitably strengthened property, allows us to conclude whether the original stochastic hybrid system meets its temporal logic specifications. We present the first statistical model checking algorithms to verify stochastic hybrid systems against correctness properties, expressed in the linear inequality linear temporal logic (iLTL) or the metric interval temporal logic (MITL).

The large field-of-view of the Sun Watcher using Active Pixel System detector and Image Processing (SWAP) instrument on board the PRoject for Onboard Autonomy 2 (PROBA2) spacecraft provides a unique opportunity to study extended coronal structures observed in EUV in conjunction with global coronal magnetic field simulations. A global non-potential magnetic field model is used to simulate the evolution of the global corona from 1 September 2014 to 31 March 2015, driven by newly emerging bipolar active regions determined from Helioseismic and Magnetic Imager (HMI) magnetograms. We compare the large-scale structure of the simulated magnetic field with structures seen off-limb in SWAP EUV observations. In particular, we investigate how successful the model is in reproducing regions of closed and open structures; the scale of structures; and compare the evolution of a coronal fan observed over several rotations. The model is found to accurately reproduce observed large-scale off-limb structures. When discrepancies do arise they mainly occur off the east solar limb due to active regions emerging on the far side of the Sun, which cannot be incorporated into the model until they are observed on the Earth-facing side. When such ``late'' active region emergences are incorporated into the model, we find that the simulated corona self-corrects within a few days, so that simulated structures off the west limb more closely match what is observed. Where the model is less successful, we consider how this may be addressed, through model developments or additional observational products., Comment: 26 pages, 11 figures

The subshift of finite type property (also known as the Markov property) is ubiquitous in dynamical systems and the simplest and most widely studied class of dynamical systems are $\beta$-shifts, namely transformations of the form $T_{\beta, \alpha} \colon x \mapsto \beta x + \alpha \bmod{1}$ acting on $[-\alpha/(\beta - 1), (1-\alpha)/(\beta - 1)]$, where $(\beta, \alpha) \in \Delta$ is fixed and where $\Delta = \{ (\beta, \alpha) \in \mathbb{R}^{2} \colon \beta \in (1,2) \; \text{and} \; 0 \leq \alpha \leq 2-\beta \}$. Recently, it was shown, by Li et al. (Proc. Amer. Math. Soc. 147(5): 2045-2055, 2019), that the set of $(\beta, \alpha)$ such that $T_{\beta, \alpha}$ has the subshift of finite type property is dense in the parameter space $\Delta$. Here, they proposed the following question. Given a fixed $\beta \in (1, 2)$ which is the $n$-th root of a Perron number, does there exists a dense set of $\alpha$ in the fiber $\{\beta\} \times (0, 2- \beta)$, so that $T_{\beta, \alpha}$ has the subshift of finite type property? We answer this question in the positive for a class of Pisot numbers. Further, we investigate if this question holds true when replacing the subshift of finite type property by the property of beginning sofic (that is a factor of a subshift of finite). In doing so we generalise, a classical result of Schmidt (Bull. London Math. Soc., 12(4): 269-278, 1980) from the case when $\alpha = 0$ to the case when $\alpha \in (0, 2 - \beta)$. That is, we examine the structure of the set of eventually periodic points of $T_{\beta, \alpha}$ when $\beta$ is a Pisot number and when $\beta$ is the $n$-th root of a Pisot number., Comment: 13 pages, 1 figure

We use The Sun Watcher with Active Pixel System detector and Image Processing (SWAP) imager onboard the Project for Onboard Autonomy 2 (PROBA2) mission to study the evolution of large-scale EUV structures in the solar corona observed throughout Solar Cycle 24 (from 2010 to 2019). We discuss the evolution of the on-disk coronal features and at different heights above the solar surface based on EUV intensity changes. We also look at the evolution of the corona in equatorial and polar regions and compare them at different phases of the solar cycle, as well as with sunspot number evolution and with the PROBA2/Lyman-Alpha Radiometer (LYRA) signal. The main results are as follows: The three time series (SWAP on-disk average brightness, sunspot number and LYRA irradiance) are very well correlated, with correlation coefficients around 0.9. The average rotation rate of bright features at latitudes of +15, 0, and -15 degrees was around 15 degree/day throughout the period studied. A secondary peak in EUV averaged intensity at the Poles was observed on the descending phase of SC24. These peaks (at North and South poles respectively) seem to be associated with the start of the development of the (polar) coronal holes. Large-scale off-limb structures were visible from around March 2010 to around March 2016, meaning that they were absent at the minimum phase of solar activity. A fan at the North pole persisted for more than 11 Carrington rotations (February 2014 to March 2015), and it could be seen up to altitudes of 1.6 Rs.

NASA's WB-57 High Altitude Research Program provides a deployable, mobile, stratospheric platform for scientific research. Airborne platforms are of particular value for making coronal observations during total solar eclipses because of their ability both to follow the Moon's shadow and to get above most of the atmospheric airmass that can interfere with astronomical observations. We used the 2017 Aug 21 eclipse as a pathfinding mission for high-altitude airborne solar astronomy, using the existing high-speed visible-light and near-/mid-wave infrared imaging suite mounted in the WB-57 nose cone. In this paper, we describe the aircraft, the instrument, and the 2017 mission; operations and data acquisition; and preliminary analysis of data quality from the existing instrument suite. We describe benefits and technical limitations of this platform for solar and other astronomical observations. We present a preliminary analysis of the visible-light data quality and discuss the limiting factors that must be overcome with future instrumentation. We conclude with a discussion of lessons learned from this pathfinding mission and prospects for future research at upcoming eclipses, as well as an evaluation of the capabilities of the WB-57 platform for future solar astronomy and general astronomical observation., Comment: 17 pages, 10 figures; accepted for publication by the Astrophysical Journal

Probabilistic Computation Tree Logic (PCTL) is frequently used to formally specify control objectives such as probabilistic reachability and safety. In this work, we focus on model checking PCTL specifications statistically on Markov Decision Processes (MDPs) by sampling, e.g., checking whether there exists a feasible policy such that the probability of reaching certain goal states is greater than a threshold. We use reinforcement learning to search for such a feasible policy for PCTL specifications, and then develop a statistical model checking (SMC) method with provable guarantees on its error. Specifically, we first use upper-confidence-bound (UCB) based Q-learning to design an SMC algorithm for bounded-time PCTL specifications, and then extend this algorithm to unbounded-time specifications by identifying a proper truncation time by checking the PCTL specification and its negation at the same time. Finally, we evaluate the proposed method on case studies.