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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

Two mathematical aspects of the centuries-old Japanese sashiko stitching form hitomezashi are discussed: the encoding of designs using words from a binary alphabet, and duality. Traditional hitomezashi designs are analysed using these two ideas. Self-dual hitomezashi designs related to Fibonacci snowflakes, which we term Pell persimmon polyomino patterns, are proposed. Both these designs and the binary words used to generate them appear to be new to their respective literatures., Comment: 25 pages; 21 figures

We report on a particular example of noise and data representation interacting to introduce systematic error. Many instruments collect integer digitized values and appy nonlinear coding, in particular square-root coding, to compress the data for transfer or downlink; this can introduce surprising systematic errors when they are decoded for analysis. Square root coding and subsequent decoding typically introduces a variable, $\pm 1$ count value-dependent systematic bias in the data after reconstitution. This is significant when large numbers of measurements (e.g., image pixels) are averaged together. Using direct modeling of the probabiliity distribution of particular coded values in the presence of instrument noise, one may apply Bayes' Theorem to construct a decoding table that reduces this error source to a very small fraction of a digitizer step; in our example, systematic error from square root coding is reduced by a factor of 20 from 0.23 count RMS to 0.013 count RMS. The method is suitable both for new experiments such as the upcoming PUNCH mission, and also for post facto application to existing data sets -- even if the instrument noise properties are only loosely known. Further, the method does not depend on the specifics of the coding formula, and may be applied to other forms of nonlinear coding or representation of data values., Comment: Accepted to Astrophysical Journal

Early college high schools are powerful instruments for success for young men of color, and school leaders must take an intentional approach to remove systemic barriers to their engagement. This report outlines strategies to better recruit and retain young men of color in early college programs and provides examples of successful and emerging practices that support all youth in preparing for their future careers through early college programs.

We report observations of a unique, large prominence eruption that was observed in the He II 304 {\AA} passband of the the Extreme Ultraviolet Imager/Full Sun Imager telescope aboard Solar Orbiter on 15-16 February 2022. Observations from several vantage points (Solar Orbiter, the Solar-Terrestrial Relations Observatory, the Solar and Heliospheric Observatory, and Earth-orbiting satellites) were used to measure the kinematics of the erupting prominence and the associated coronal mass ejection. Three-dimensional reconstruction was used to calculate the deprojected positions and speeds of different parts of the prominence. Observations in several passbands allowed us to analyse the radiative properties of the erupting prominence. The leading parts of the erupting prominence and the leading edge of the corresponding coronal mass ejection propagate at speeds of around 1700 km/s and 2200 km/s, respectively, while the trailing parts of the prominence are significantly slower (around 500 km/s). Parts of the prominence are tracked up to heights of over $6 R_\sun$. The He II emission is probably produced via collisional excitation rather than scattering. Surprisingly, the brightness of a trailing feature increases with height. The reported prominence is the first observed in He II 304 {\AA} emission at such a great height (above 6 $R_\sun$).

This document identifies guiding principles that intermediary staff members and leaders can use to support equitable career outcomes for youth--particularly Black and Latinx youth and young people who are experiencing poverty. These four principles are imperatives for how staff members at intermediary organizations can design strategies for guiding and engaging with youth.

We investigate the effects of the evolutionary processes in the internal magnetic structure of two interplanetary coronal mass ejections (ICMEs) detected in situ between 2020 November 29 and December 1 by Parker Solar Probe (PSP). The sources of the ICMEs were observed remotely at the Sun in EUV and subsequently tracked to their coronal counterparts in white light. This period is of particular interest to the community since it has been identified as the first widespread solar energetic particle event of Solar Cycle 25. The distribution of various solar and heliospheric-dedicated spacecraft throughout the inner heliosphere during PSP observations of these large-scale magnetic structures enables a comprehensive analysis of the internal evolution and topology of such structures. By assembling different models and techniques, we identify the signatures of interaction between the two consecutive ICMEs and the implications for their internal structure. We use multispacecraft observations in combination with a remote-sensing forward modeling technique, numerical propagation models, and in-situ reconstruction techniques. The outcome, from the full reconciliations, demonstrates that the two CMEs are interacting in the vicinity of PSP. Thus, we identify the in-situ observations based on the physical processes that are associated with the interaction and collision of both CMEs. We also expand the flux rope modeling and in-situ reconstruction technique to incorporate the aging and expansion effects in a distorted internal magnetic structure and explore the implications of both effects in the magnetic configuration of the ICMEs.

We compute univariate and multigraded Hilbert series of invariants and covariants of representations of the circle and orthogonal group $\operatorname{O}_2$. The multigradings considered include the maximal grading associated to the decomposition of the representation into irreducibles as well as the bigrading associated to a cotangent-lifted representation, or equivalently, the bigrading associated to the holomorphic and antiholomorphic parts of the real invariants and covariants. This bigrading induces a bigrading on the algebra of on-shell invariants of the symplectic quotient, and the corresponding Hilbert series are computed as well. We also compute the first few Laurent coefficients of the univariate Hilbert series, give sample calculations of the multigraded Laurent coefficients, and give an example to illustrate the extension of these techniques to the semidirect product of the circle by other finite groups. We describe an algorithm to compute each of the associated Hilbert series., Comment: v2: 26 pages, corrected typos and error in Theorem 3.14, improved exposition

Within an imaging instrument's field of view, there may be many observational targets of interest. Similarly, within a spectrograph's bandpass, there may be many emission lines of interest. The brightness of these targets and lines can be orders of magnitude different, which poses a challenge to instrument and mission design. A single exposure can saturate the bright emission and/or have a low signal to noise ratio (SNR) for faint emission. Traditional high dynamic range (HDR) techniques solve this problem by either combining multiple sequential exposures of varied duration or splitting the light to different sensors. These methods, however, can result in the loss of science capability, reduced observational efficiency, or increased complexity and cost. The simultaneous HDR method described in this paper avoids these issues by utilizing a special type of detector whose rows can be read independently to define zones that are then composited, resulting in areas with short or long exposure measured simultaneously. We demonstrate this technique for the sun, which is bright on disk and faint off disk. We emulated these conditions in the lab to validate the method. We built an instrument simulator to demonstrate the method for a realistic solar imager and input. We then calculated SNRs, finding a value of 45 for a faint coronal mass ejection (CME) and 200 for a bright CME, both at 3.5 $R_{\odot}$ -- meeting or far exceeding the international standard for digital photography that defines a SNR of 10 as acceptable and 40 as excellent. Future missions should consider this type of hardware and technique in their trade studies for instrument design., Comment: 9 pages, 5 figures, accepted to ApJ

Motivated by the existence of superconductivity in pyrite-structure CuS$_2$, we explore the possibility of ionic-liquid-gating-induced superconductivity in the proximal antiferromagnetic Mott insulator NiS$_2$. A clear gating-induced transition from a two-dimensional insulating state to a three-dimensional metallic state is observed at positive gate bias on single crystal surfaces. No evidence for superconductivity is observed down to the lowest measured temperature of 0.45 K, however. Based on transport, energy-dispersive X-ray spectroscopy, X-ray photoelectron spectroscopy, atomic force microscopy, and other techniques, we deduce an electrochemical gating mechanism involving a substantial decrease in the S:Ni ratio (over hundreds of nm), which is both non-volatile and irreversible. This is in striking contrast to the reversible, volatile, surface-limited, electrostatic gate effect in pyrite FeS$_2$. We attribute this stark difference in electrochemical vs. electrostatic gating response in NiS$_2$ and FeS$_2$ to the much larger S diffusion coefficient in NiS$_2$, analogous to the different behaviors observed among electrolyte-gated oxides with differing O-vacancy diffusivities. The gating irreversibility, on the other hand, is associated with the lack of atmospheric S; this is in contrast to the better understood oxide case, where electrolysis of atmospheric H$_2$O provides an O reservoir. This study of NiS$_2$ thus provides new insight into electrolyte gating mechanisms in functional materials, in a previously unexplored limit., Comment: 4 figures, included supplement

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

Let $G$ be a complex reductive group and $V$ a $G$-module. There is a natural moment mapping $\mu\colon V\oplus V^*\to\mathfrak{g}^*$ and we denote $\mu^{-1}(0)$ (the shell) by $N_V$. We use invariant theory and results of Musta\c{t}\u{a} [Mus01] to find criteria for $N_V$ to have rational singularities and for the categorical quotient $N_V /\!\!/ G$ to have symplectic singularities, the latter results improving upon [HSS20]. It turns out that for ``most'' $G$-modules $V$, the shell $N_V$ has rational singularities. For the case of direct sums of classical representations of the classical groups, $N_V$ has rational singularities and $N_V /\!\!/ G$ has symplectic singularities if $N_V$ is a reduced and irreducible complete intersection. Another important special case is $V=p\,\mathfrak{g}$ (the direct sum of $p$ copies of the Lie algebra of $G$) where $p\geq 2$. We show that $N_V$ has rational singularities and that $N_V /\!\!/ G$ has symplectic singularities, improving upon results of [Bud19], [AA16], [Kap19] and [GH20]. Let $\pi=\pi_1(\Sigma)$ where $\Sigma$ is a closed Riemann surface of genus $p\geq 2$. Let $G$ be semisimple and let $\operatorname{Hom}(\pi,G)$ and $\mathscr X\!(\pi,G)$ be the corresponding representation variety and character variety. We show that $\operatorname{Hom}(\pi,G)$ is a complete intersection with rational singularities and that $\mathscr X\!(\pi,G)$ has symplectic singularities. If $p>2$ or $G$ contains no simple factor of rank $1$, then the singularities of $\operatorname{Hom}(\pi,G)$ and $\mathscr X\!(\pi,G)$ are in codimension at least four and $\operatorname{Hom}(\pi,G)$ is locally factorial. If, in addition, $G$ is simply connected, then $\mathscr X\!(\pi,G)$ is locally factorial., Comment: 21 pages. v2: 22 pages, clarified and improved arguments in Section 3, improved exposition and minor corrections. v3: 30 pages, reformatted, minor corrections. v4, 31 pages, improved exposition and minor corrections following referee's remarks

Let $n\ge 1$ and $A$ be a commutative algebra of the form $\boldsymbol k[x_1,x_2,\dots, x_n]/I$ where $\boldsymbol k$ is a field of characteristic $0$ and $I\subseteq \boldsymbol k[x_1,x_2,\dots, x_n]$ is an ideal. Assume that there is a Poisson bracket $\{\:,\:\}$ on $S$ such that $\{I,S\}\subseteq I$ and let us denote the induced bracket on $A$ by $\{\:,\:\}$ as well. It is well-known that $[\mathrm d x_i,\mathrm d x_j]:=\mathrm d\{x_i,x_j\}$ defines a Lie bracket on the $A$-module $\Omega_{A|\boldsymbol k}$ of K\"ahler differentials making $(A,\Omega_{A|\boldsymbol k})$ a Lie-Rinehart pair. Recall that $A$ is regular if and only if $\Omega_{A|\boldsymbol k}$ is projective as an $A$-module. If $A$ is not regular, the cotangent complex $\mathbb L_{A|\boldsymbol k}$ may serve as a replacement for the $A$-module $\Omega_{A|\boldsymbol k}$. We prove that there is a structure of an $L_\infty$-algebroid on $\mathbb L_{A|\boldsymbol k}$, compatible with the Lie-Rinehart pair $(A,\Omega_{A|\boldsymbol k})$. The $L_\infty$-algebroid on $\mathbb L_{A|\boldsymbol k}$ actually comes from a $P_\infty$-algebra structure on the resolvent of the morphism $k[x_1,x_2,\dots, x_n]\to A$. We identify examples when this $L_\infty$-algebroid simplifies to a dg Lie algebroid. For aesthetic reasons we concentrate on cases when $ \boldsymbol k[x_1,x_2,\dots, x_n]$ carries a (possibly nonstandard) $\mathbb Z_{\ge 0}$-grading and both $I$ and $\{\:,\:\}$ are homogeneous., Comment: 32 pages, 2 tables. V2: We corrected an error in the bracket table of the invariants of the Kleinian singularity E_7 (which does not appear in the published version in IMRN, https://doi.org/10.1093/imrn/rnac170) that was identified by William Osnayder Clavijo Esquivel; we express our appreciation for identifying this error

The "middle corona" is a critical transition between the highly disparate physical regimes of the lower and outer solar corona. Nonetheless, it remains poorly understood due to the difficulty of observing this faint region (1.5-3 solar radii). New observations from the GOES Solar Ultraviolet Imager in August and September 2018 provide the first comprehensive look at this region's characteristics and long-term evolution in extreme ultraviolet (EUV). Our analysis shows that the dominant emission mechanism here is resonant scattering rather than collisional excitation, consistent with recent model predictions. Our observations highlight that solar wind structures in the heliosphere originate from complex dynamics manifesting in the middle corona that do not occur at lower heights. These data emphasize that low-coronal phenomena can be strongly influenced by inflows from above, not only by photospheric motion, a factor largely overlooked in current models of coronal evolution. This study reveals the full kinematic profile of the initiation of several coronal mass ejections, filling a crucial observational gap that has hindered understanding of the origins of solar eruptions. These new data uniquely demonstrate how EUV observations of the middle corona provide strong new constraints on models seeking to unify the corona and heliosphere., Comment: Send requests for associated animations to the corresponding author

This paper considers coverage games in which a group of agents are tasked with identifying the highest-value subset of resources; in this context, game-theoretic approaches are known to yield Nash equilibria within a factor of 2 of optimal. We consider the case that some of the agents suffer a communication failure and cannot observe the actions of other agents; in this case, recent work has shown that if there are k>0 compromised agents, Nash equilibria are only guaranteed to be within a factor of k+1 of optimal. However, the present paper shows that this worst-case guarantee is fragile; in a sense which we make precise, we show that if a problem instance has a very poor worst-case guarantee, then it is necessarily very "close" to a problem instance with an optimal Nash equilibrium. Conversely, an instance that is far from one with an optimal Nash equilibrium necessarily has relatively good worst-case performance guarantees. To contextualize this fragility, we perform simulations using the log-linear learning algorithm and show that average performance on worst-case instances is considerably better even than our improved analytical guarantees. This suggests that the fragility of the price of anarchy can be exploited algorithmically to compensate for online communication failures., Comment: 6 pages, 4 figures

D-forms have in the past been created from inflexible materials, or considered as abstract mathematical objects. This paper describes a number of realisations of D-forms, and the related pita-forms, in textiles. Examples are given in which the created 3D space is purposefully employed and others in which ornamentation of the constituent surfaces is the highlighted feature. In particular, a set of biscornu has been fashioned to provide a 3D sampler of the axial point group $D_{4d}$ and its subgroups, using hitomezashi., Comment: 11 pages, 19 figures

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"

In the shock-ignition inertial confinement fusion scheme, high-intensity lasers propagate through an inhomogeneous coronal plasma, driving a shock designed to cause fuel ignition. During the high-intensity ignitor laser pulse, SRS backscatter in the long scale-length coronal plasma is likely to be in the kinetic regime. In this work, we use one-dimensional particle-in-cell simulations to show that there is a non-linear frequency shift caused by kinetic effects, resulting in the growth of Stimulated Raman Scattering (SRS) in an inhomogeneous plasma far exceeding the predictions of the fluid theory, so-called inflationary SRS or iSRS. We find that iSRS occurs over a wide range of density scale-lengths relevant to shock-ignition and other directly-driven inertial confinement fusion schemes. The presence of iSRS in shock-ignition plasmas has implications for the theoretical gains from shock-ignition inertial confinement fusion. Here we quantify the intensity threshold for the onset of iSRS for shock-ignition relevant parameters., Comment: 9 pages, 7 figures

Eilers et al. have recently completed the geometric classification of unital graph $C^\ast$-algebras up to Morita equivalence using a set of moves on the corresponding digraphs. We explore the question of whether these moves preserve the nonzero elements of the spectrum of a finite digraph, which in this paper is allowed to have loops and parallel edges. We consider several different digraph spectra that have been studied in the literature, answering this question for the Laplace and adjacency spectra, their skew counterparts, the symmetric adjacency spectrum, the adjacency spectrum of the line digraph, the Hermitian adjacency spectrum, and the normalized Laplacian, considering in most cases two ways that these spectra can be defined in the presence of parallel edges. We show that the adjacency spectra of the digraph and line digraph are preserved by a subset of the moves, and the skew adjacency and Laplace spectra are preserved by the Cuntz splice. We give counterexamples to show that the other spectra are not preserved by the remaining moves. The same results hold if one restricts to the class of strongly connected digraphs., Comment: 29 pages, 8 figures, 2 tables. v2: corrected errors, improved exposition, added Example 5.3

We compute the Hilbert series of the graded algebra of real regular functions on a linear symplectic quotient by the $2$-torus as well as the first four coefficients of the Laurent expansion of this Hilbert series at $t = 1$. We describe an algorithm to compute the Hilbert series as well as the Laurent coefficients in explicit examples., Comment: 22 pages

A popular formalism for multiagent control applies tools from game theory, casting a multiagent decision problem as a cooperation-style game in which individual agents make local choices to optimize their own local utility functions in response to the observable choices made by other agents. When the system-level objective is submodular maximization, it is known that if every agent can observe the action choice of all other agents, then all Nash equilibria of a large class of resulting games are within a factor of $2$ of optimal; that is, the price of anarchy is $1/2$. However, little is known if agents cannot observe the action choices of other relevant agents. To study this, we extend the standard game-theoretic model to one in which a subset of agents either become \emph{blind} (unable to observe others' choices) or \emph{isolated} (blind, and also invisible to other agents), and we prove exact expressions for the price of anarchy as a function of the number of compromised agents. When $k$ agents are compromised (in any combination of blind or isolated), we show that the price of anarchy for a large class of utility functions is exactly $1/(2+k)$. We then show that if agents use marginal-cost utility functions and at least $1$ of the compromised agents is blind (rather than isolated), the price of anarchy improves to $1/(1+k)$. We also provide simulation results demonstrating the effects of these observation denials in a dynamic setting.

For a finitely presented discrete group $\Gamma$, we introduce two generalizations of the orbifold Euler characteristic and $\Gamma$-orbifold Euler characteristic to a class of proper topological groupoids large enough to include all cocompact proper Lie groupoids. The $\Gamma$-Euler characteristic is defined as an integral with respect to the Euler characteristic over the orbit space of the groupoid, and the $\Gamma$-inertia Euler characteristic is the usual Euler characteristic of the $\Gamma$-inertia space associated to the groupoid. A key ingredient is the application of o-minimal structures to study orbit spaces of topological groupoids. Our main result is that the $\Gamma$-Euler characteristic and $\Gamma$-inertia Euler characteristic coincide and generalize the higher-order orbifold Euler characteristics of Gusein-Zade, Luengo, and Melle-Hern\'{a}ndez from the case of a translation groupoid by a compact Lie group and $\Gamma = \mathbb{Z}^\ell$. By realizing the $\Gamma$-Euler characteristic as the usual Euler characteristic of a topological space, we demonstrate that it is Morita invariant in the category of topological groupoids and satisfies familiar properties of the classical Euler characteristic. We give an additional formulation of the $\Gamma$-Euler characteristic for a cocompact proper Lie groupoid in terms of a finite covering by orbispace charts. In the case that the groupoid is an abelian extension of a translation groupoid by a bundle of groups, we relate the $\Gamma$-Euler characteristics to those of the translation groupoid and bundle of groups., Comment: 29 pages. From v1: significant rewriting to clarify the definitions and improve exposition

The Electron Loss and Fields Investigation with a Spatio-Temporal Ambiguity-Resolving option (ELFIN-STAR, or simply: ELFIN) mission comprises two identical 3-Unit (3U) CubeSats on a polar (~93deg inclination), nearly circular, low-Earth (~450 km altitude) orbit. Launched on September 15, 2018, ELFIN is expected to have a >2.5 year lifetime. Its primary science objective is to resolve the mechanism of storm-time relativistic electron precipitation, for which electromagnetic ion cyclotron (EMIC) waves are a prime candidate. From its ionospheric vantage point, ELFIN uses its unique pitch-angle-resolving capability to determine whether measured relativistic electron pitch-angle and energy spectra within the loss cone bear the characteristic signatures of scattering by EMIC waves or whether such scattering may be due to other processes. Pairing identical ELFIN satellites with slowly-variable along-track separation allows disambiguation of spatial and temporal evolution of the precipitation over minutes-to-tens-of-minutes timescales, faster than the orbit period of a single low-altitude satellite (~90min). Each satellite carries an energetic particle detector for electrons (EPDE) that measures 50keV to 5MeV electrons with deltaE/E<40% and a fluxgate magnetometer (FGM) on a ~72cm boom that measures magnetic field waves (e.g., EMIC waves) in the range from DC to 5Hz Nyquist (nominally) with <0.3nT/sqrt(Hz) noise at 1Hz. The spinning satellites (T_spin~3s) are equipped with magnetorquers that permit spin-up/down and reorientation maneuvers. The spin axis is placed normal to the orbit plane, allowing full pitch-angle resolution twice per spin. An energetic particle detector for ions (EPDI) measures 250keV-5MeV ions, addressing secondary science. Funded initially by CalSpace and the University Nanosat Program, ELFIN was selected for flight with joint support from NSF and NASA between 2014 and 2018., Comment: Submitted to Space Science Reviews April 2020. 51 pages, 7 tables, 21 figures

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

Through the hands-on creation of two sashiko pieces of work - a counted thread kogin bookmark and a single running stitched hitomezashi sampler - participants will explore not only the living cultural history of this traditional Japanese needlework but will also experience the mathematics of sashiko in a tangible form, and will take away with them items of simple beauty., Comment: 8 pages, 8 figures, workshop paper intended for Bridges Math Art conference 2020

The European Materials and Modelling Ontology (EMMO) has recently been advanced in the computational molecular engineering and multiscale modelling communities as a top-level ontology, aiming to support semantic interoperability and data integration solutions, e.g., for research data infrastructures. The present work explores how top-level ontologies that are based on the same paradigm - the same set of fundamental postulates - as the EMMO can be applied to models of physical systems and their use in computational engineering practice. This paradigm, which combines mereology (in its extension as mereotopology) and semiotics (following Peirce's approach), is here referred to as mereosemiotics. Multiple conceivable ways of implementing mereosemiotics are compared, and the design space consisting of the possible types of top-level ontologies following this paradigm is characterized., Comment: The co-authors M.T.H. and B.S. acknowledge funding from the German Research Foundation (DFG) through the National Research Data Infrastructure for Catalysis-Related Sciences (NFDI4Cat) within the National Research Data Infrastructure (NFDI) programme of the Joint Science Conference (GWK)

We prove that unital extensions of Kirchberg algebras by separable stable AF algebras have nuclear dimension one. The title follows., Comment: Minor changes. Accepted Version. J. Funct. Anal., to appear

We describe the construction of a new family of developable rollers based on the Platonic solids. In this way kinetic sculptures may be realised, with the Platonic solids quite literally in their heart. We also describe the strong way in which the Platonicons circumscribe the Platonic solids., Comment: 4 pages, 5 figures, submitted for Bridges Helsinki 2020; revised version after reviewing

Correlation and smoothness are terms used to describe a wide variety of random quantities. In time, space, and many other domains, they both imply the same idea: quantities that occur closer together are more similar than those further apart. Two popular statistical models that represent this idea are basis-penalty smoothers (Wood, 2017) and stochastic partial differential equations (SPDE) (Lindgren et al., 2011). In this paper, we discuss how the SPDE can be interpreted as a smoothing penalty and can be fitted using the R package mgcv, allowing practitioners with existing knowledge of smoothing penalties to better understand the implementation and theory behind the SPDE approach., Comment: 23 pages, 4 figures. JABES (2019)

The Virtual Materials Marketplace (VIMMP) project, which develops an open platform for providing and accessing services related to materials modelling, is presented with a focus on its ontology development and data technology aspects. Within VIMMP, a system of marketplace-level ontologies is developed to characterize services, models, and interactions between users; the European Materials and Modelling Ontology (EMMO) is employed as a top-level ontology. The ontologies are used to annotate data that are stored in the ZONTAL Space component of VIMMP and to support the ingest and retrieval of data and metadata at the VIMMP marketplace frontend., Comment: The Virtual Materials Marketplace (VIMMP) project is funded from the European Union's Horizon 2020 research and innovation programme under grant agreement no. 760907

A knot $K_1$ is said to be Gordian adjacent to a knot $K_2$ if $K_1$ is an intermediate knot on an unknotting sequence of $K_2$. We extend previous results on Gordian adjacency by showing sufficient conditions for Gordian adjacency between classes of positive braid knots through manipulations of braid words. In addition, we explore unknotting sequences of positive braid knots and give a proof that there are only finitely many positive braid knots for a given unknotting number., Comment: 20 pages; to appear in Rose-Hulman Undergraduate Mathematics Journal

In order to utilize solar imagery for real-time feature identification and large-scale data science investigations of solar structures, we need maps of the Sun where phenomena, or themes, are labeled. Since solar imagers produce observations every few minutes, it is not feasible to label all images by hand. Here, we compare three machine learning algorithms performing solar image classification using extreme ultraviolet and Hydrogen-alpha images: a maximum likelihood model assuming a single normal probability distribution for each theme from Rigler et al. (2012), a maximum-likelihood model with an underlying Gaussian mixtures distribution, and a random forest model. We create a small database of expert-labeled maps to train and test these algorithms. Due to the ambiguity between the labels created by different experts, a collaborative labeling is used to include all inputs. We find the random forest algorithm performs the best amongst the three algorithms. The advantages of this algorithm are best highlighted in: comparison of outputs to hand-drawn maps; response to short-term variability; and tracking long-term changes on the Sun. Our work indicates that the next generation of solar image classification algorithms would benefit significantly from using spatial structure recognition, compared to only using spectral, pixel-by-pixel brightness distributions.