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We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it to Abelian semigroup operations using the characterization of associative symmetric polynomials. Both models take advantage of the analytic invertibility of invertible neural networks. For each case, by repeating the binary operations, we can represent a function for multiset input thanks to the algebraic structure. Naturally, our multiset architecture has size-generalization ability, which has not been obtained in existing methods. Further, we present modeling the Abelian group operation itself is useful in a word analogy task. We train our models over fixed word embeddings and demonstrate improved performance over the original word2vec and another naive learning method.

The orientals are the free strict $\omega$-categories on the simplices introduced by Street. The aim of this paper is to show that they are also the free weak $\omega$-categories on the same generating data. More precisely, we exhibit the Street nerves of the orientals as fibrant replacements of the simplices in Verity's model structure for complicial sets., Comment: v2: 24 pages. Major revision. Published version

We present a catalog of eclipsing binaries in the northern Galactic Plane from the Kiso Wide-Field Camera Intensive Survey of the Galactic Plane (KISOGP). We visually identified 7055 eclipsing binaries spread across $\sim$330 square degrees, including 4197 W Ursa Majoris/EW-, 1458 $\beta$ Lyrae/EB-, and 1400 Algol/EA-type eclipsing binaries. For all systems, $I$-band light curves were used to obtain accurate system parameters. We derived the distances and extinction values for the EW-type objects from their period--luminosity relation. We also obtained the structure of the thin disk from the distribution of our sample of eclipsing binary systems, combined with those of high-mass star-forming regions and Cepheid tracers. We found that the thin disk is inhomogeneous in number density as a function of Galactic longitude. Using this new set of distance tracers, we constrain the detailed structure of the thin disk. Finally, we report a global parallax zero-point offset of $ \Delta \pi=-42.1\pm1.9\mbox{(stat.)}\pm12.9\mbox{(syst.)}$ $\mu$as between our carefully calibrated EW-type eclipsing binary positions and those provided by Gaia Early Data Release 3. Implementation of the officially recommended parallax zero-point correction results in a significantly reduced offset. Additionally, we provide a photometric characterization of our EW-type eclipsing binaries that can be applied to further analyses., Comment: 17 pages, 9 figures, 2 tables. Accepted for publication in AJ

We consider the min-max $r$-gathering problem described as follows: We are given a set of users and facilities in a metric space. We open some of the facilities and assign each user to an opened facility such that each facility has at least $r$ users. The goal is to minimize the maximum distance between the users and the assigned facility. We also consider the min-max $r$-gather clustering problem, which is a special case of the $r$-gathering problem in which the facilities are located everywhere. In this paper, we study the tractability and the hardness when the underlying metric space is a spider, which answers the open question posed by Ahmed et al. [WALCOM'19]. First, we show that the problems are NP-hard even if the underlying space is a spider. Then, we propose FPT algorithms parameterized by the degree $d$ of the center. This improves the previous algorithms because they are parameterized by both $r$ and $d$. Finally, we propose PTASes to the problems. These are best possible because there are no FPTASes unless P=NP., Comment: This is work is a merger of arXiv:1907.04088 and arXiv:1907.04087

We study Graph Convolutional Networks (GCN) from the graph signal processing viewpoint by addressing a difference between learning graph filters with fully connected weights versus trainable polynomial coefficients. We find that by stacking graph filters with learnable polynomial parameters, we can build a highly adaptive and robust vertex classification model. Our treatment here relaxes the low-frequency (or equivalently, high homophily) assumptions in existing vertex classification models, resulting a more ubiquitous solution in terms of spectral properties. Empirically, by using only one hyper-parameter setting, our model achieves strong results on most benchmark datasets across the frequency spectrum., Comment: Source code is provided at github.com/gear/sgf

We report the latest statistical analyses of superflares on solar-type (G-type main-sequence; effective temperature is 5100 - 6000 K) stars using all of the $Kepler$ primary mission data, and $Gaia$-DR2 (Data Release 2) catalog. We updated the flare detection method from our previous studies by using high-pass filter to remove rotational variations caused by starspots. We also examined the sample biases on the frequency of superflares, taking into account gyrochronology and flare detection completeness. The sample size of solar-type stars and Sun-like stars (effective temperature is 5600 - 6000 K and rotation period is over 20 days in solar-type stars) are $\sim$4 and $\sim$12 times, respectively, compared with Notsu et al. (2019, ApJ, 876, 58). As a result, we found 2341 superflares on 265 solar-type stars, and 26 superflares on 15 Sun-like stars: the former increased from 527 to 2341 and the latter from 3 to 26 events compared with our previous study. This enabled us to have a more well-established view on the statistical properties of superflares. The observed upper limit of the flare energy decreases as the rotation period increases in solar-type stars. The frequency of superflares decreases as the stellar rotation period increases. The maximum energy we found on Sun-like stars is $4 \times 10^{34}$ erg. Our analysis of Sun-like stars suggest that the Sun can cause superflares with energies of $\sim 7 \times 10^{33}$ erg ($\sim$X700-class flares) and $\sim 1 \times 10^{34}$ erg ($\sim$X1000-class flares) once every $\sim$3,000 years and $\sim$6,000 years, respectively., Comment: 49 pages, 22 figures, 6 tables, supplementary table, Accepted for publication in The Astrophysical Journal (03-Nov-2020)

In this paper, we present the results from spectroscopic and photometric observations of the M-type flare star YZ CMi in the framework of the Optical and Infrared Synergetic Telescopes for Education and Research (OISTER) collaborations during the Transiting Exoplanet Survey Satellite (TESS) observation period. We detected 145 white-light flares from the TESS light curve and 4 H$\alpha$ flares from the OISTER observations performed between 2019-01-16 and 2019-01-18. Among them, 3 H$\alpha$ flares were associated with white-light flares. However, one of them did not show clear brightening in continuum; during this flare, the H$\alpha$ line exhibited blue-asymmetry which has lasted for $\sim 60$ min. The line of sight velocity of the blue-shifted component is $-80$ - $-100$ km s$^{-1}$. This suggests that there can be upward flows of chromospheric cool plasma even without detectable red/NIR continuum brightening. By assuming that the blue-asymmetry in H$\alpha$ line was caused by a prominence eruption on YZ CMi, we estimated the mass and kinetic energy of the upward-moving material to be $10^{16}$ - $10^{18}$ g and $10^{29.5}$ - $10^{31.5}$ erg, respectively. The estimated mass is comparable to expectations from the empirical relation between the flare X-ray energy and mass of upward-moving material for stellar flares and solar CMEs. In contrast, the estimated kinetic energy for the non-white-light flare on YZ CMi is roughly $2$ orders of magnitude smaller than that expected from the relation between flare X-ray energy and kinetic energy for solar CMEs. This could be understood by the difference in the velocity between CMEs and prominence eruptions., Comment: 39 pages, 15 figures, supplementary table (CSV format); accepted for publication in PASJ

A matroid has been one of the most important combinatorial structures since it was introduced by Whitney as an abstraction of linear independence. As an important property of a matroid, it can be characterized by several different (but equivalent) axioms, such as the augmentation, the base exchange, or the rank axiom. A supermatroid is a generalization of a matroid defined on lattices. Here, the central question is whether a supermatroid can be characterized by several equivalent axioms similar to a matroid. Barnabei, Nicoletti, and Pezzoli characterized supermatroids on distributive lattices, and Fujishige, Koshevoy, and Sano generalized the results for cg-matroids (supermatroids on lower locally distributive lattices). In this study, we focus on modular lattices, which are an important superclass of distributive lattices, and provide equivalent characterizations of supermatroids on modular lattices. We characterize supermatroids on modular lattices using the rank axiom in which the rank function is a directional DR-submodular function, which is a generalization of a submodular function introduced by the authors. Using a characterization based on rank functions, we further prove the strong exchange property of a supermatroid, which has application in optimization. We also reveal the relation between the axioms of a supermatroid on lower semimodular lattices, which is a common superclass of a lower locally distributive lattice and a modular lattice., Comment: 32pages, 8 figures

Radar and optical simultaneous observations of meteors are important to understand the size distribution of the interplanetary dust. However, faint meteors detected by high power large aperture radar observations, which are typically as faint as 10 mag. in optical, have not been detected until recently in optical observations, mainly due to insufficient sensitivity of the optical observations. In this paper, two radar and optical simultaneous observations were organized. The first observation was carried out in 2009 to 2010 using Middle and Upper Atmosphere Radar (MU radar) and an image-intensified CCD camera. The second observation was carried out in 2018 using the MU radar and a mosaic CMOS camera, Tomo-e Gozen, mounted on the 1.05-m Kiso Schmidt Telescope. In total, 331 simultaneous meteors were detected. The relationship between radar cross sections and optical V-band magnitudes was well approximated by a linear function. A transformation function from the radar cross section to the V-band magnitude was derived for sporadic meteors. The transformation function was applied to about 150,000 meteors detected by the MU radar in 2009--2015, large part of which are sporadic, and a luminosity function was derived in the magnitude range of $-1.5$ to $9.5$ mag. The luminosity function was well approximated by a single power-law function with the population index of $r = 3.52{\pm}0.12$. The present observation indicates that the MU radar has capability to detect interplanetary dust of $10^{-5}$ to $10^{0}$ g in mass as meteors., Comment: Accepted for publication in Planetary & Space Science. 20 pages, 8 figures

Starspots are thought to be regions of locally strong magnetic fields, similar to sunspots, and they can generate photometric brightness modulations. To deduce stellar and spot properties, such as spot emergence and decay rates, we implement computational code for starspot modeling. It is implemented with an adaptive parallel tempering algorithm and an importance sampling algorithm for parameter estimation and model selection in the Bayesian framework. For evaluating the performance of the code, we apply it to synthetic light curves produced with 3 spots. The light curves are specified in the spot parameters, such as the radii, intensities, latitudes, longitudes, and emergence/decay durations. The spots are circular with specified radii and intensities relative to the photosphere, and the stellar differential rotation coefficient is also included in the light curves. As a result, stellar and spot parameters are uniquely deduced. The number of spots is correctly determined: the 3-spot model is preferable because the model evidence is much greater than that of 2-spot models by orders of magnitude and more than that of 4-spot model by a more modest factor, whereas the light curves are produced to have 2 or 1 local minimum during one equatorial rotation period by adjusting the values of longitude. The spot emergence and decay rates can be estimated with error less than an order of magnitude, considering the difference of the number of spots., Comment: 27 pages, 14 figures, 2 tables, accepted for publication in ApJ

We propose a new model for the theory of $(\infty,n)$-categories (including the case $n=\infty$) in the category of marked cubical sets with connections, similar in flavor to complicial sets of Verity. The model structure characterizing our model is shown to be monoidal with respect to suitably defined (lax and pseudo) Gray tensor products; in particular, these tensor products are both associative and biclosed. Furthermore, we show that the triangulation functor to pre-complicial sets is a left Quillen functor and is strong monoidal with respect to both Gray tensor products., Comment: submitted; 38 pages; v2 minor revisions

We report multi-wavelength monitoring observations of an M-dwarf flare star AD Leonis with Seimei Telescope (6150--7930 {\AA}), SCAT (Spectroscopic Chuo-university Astronomical Telescope; 3700--7500 {\AA}), NICER (Neutron Star Interior Composition Explorer; 0.2--12.0 keV), and collaborations of OISTER (Optical and Infrared Synergetic Telescopes for Education and Research) program. Twelve flares are detected in total which include ten H$\alpha$, four X-ray, and four optical-continuum flares; one of them is a superflare with the total energy of $\sim$ 2.0$\times$10$^{33}$ erg. We found that (1) during the superflare, the H$\alpha$ emission line full width at 1/8 maximum dramatically increases to 14 {\AA} from 8 {\AA} in the low-resolution spectra (R$\sim$ 2000) accompanied with the large white-light flares, (2) some weak H$\alpha$/X-ray flares are not accompanied with white-light emissions, and (3) the non-flaring emissions show clear rotational modulations in X-ray and H$\alpha$ intensity in the same phase. To understand these observational features, one-dimensional hydrodynamic flare simulations are performed by using the RADYN code. As a result of simulations, we found the simulated H$\alpha$ line profiles with hard and high-energy non-thermal electron beams are consistent with that of the initial phase line profiles of the superflares, while those with more soft- and/or weak-energy beam are consistent with those in decay phases, indicating the changes in the energy fluxes injected to the lower atmosphere. Also, we found that the relation between optical continuum and H$\alpha$ intensity is nonlinear, which can be one cause of the non-white-light flares. The flare energy budget exhibits diversity in the observations and models, and more observations of stellar flares are necessary for constraining the occurrence of various emission line phenomena in stellar flares., Comment: 18 pages, 17 figures, Accepted for Publication in PASJ

We present optical and near-infrared observations of SN~Ib~2019ehk. We show that it evolved to a Ca-rich transient according to its spectral properties and evolution in late phases. It, however, shows a few distinguishable properties from the canonical Ca-rich transients: a short-duration first peak in the light curve, high peak luminosity, and association with a star-forming environment. Indeed, some of these features are shared with iPTF14gqr and iPTF16hgs, which are candidates for a special class of core-collapse SNe (CCSNe): the so-called ultra-stripped envelope SNe, i.e., a relatively low-mass He (or C+O) star explosion in a binary as a precursor of double neutron star binaries. The estimated ejecta mass ($0.43 M_\odot$) and explosion energy ($1.7 \times 10^{50} $~erg) are consistent with this scenario. The analysis of the first peak suggests existence of dense circumstellar material in the vicinity of the progenitor, implying a CCSN origin. Based on these analyses, we suggest SN 2019ehk is another candidate for an ultra-stripped envelope SN. These ultra-stripped envelope SN candidates seem to form a subpopulation among Ca-rich transients, associated with young population. We propose that the key to distinguishing this population is the early first peak in their light curves., Comment: submitted to ApJ on Mar 27, 2020

In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some family of graphs (e.g. paths or non-isomorphic trees). We show that graph homomorphism numbers provide a natural invariant (isomorphism invariant and $\mathcal{F}$-invariant) embedding maps which can be used for graph classification. Viewing the expressive power of a graph classifier by the $\mathcal{F}$-indistinguishable concept, we prove the universality property of graph homomorphism vectors in approximating $\mathcal{F}$-invariant functions. In practice, by choosing $\mathcal{F}$ whose elements have bounded tree-width, we show that the homomorphism method is efficient compared with other methods., Comment: 37th International Conference on Machine Learning (ICML 2020)

We present a systematic approach to effectively evaluate potential risk cost caused by exposure to solar proton events (SPEs) from solar flares for the airline industry. We also evaluate associated health risks from radiation, to provide relevant alternative ways to minimize economic loss and opportunity. The estimated radiation dose induced by each SPE for the passengers of each flight is calculated using ExoKyoto and PHITS. We determine a few scenarios for the estimated dose limit at 1 and 20mSv, corresponding to the effective dose limit for the general public and occupational exposure, respectively, as well as a higher dose induced an extreme superflare. We set a hypothetical airline shutdown scenario at 1mSv for a single flight per passenger, due to legal restrictions under the potential radiation dose. In such a scenario, we calculate the potential loss in direct and opportunity cost under the cancelation of the flight. At the same time, we considered that, even under such a scenario, if the airplane flies at a slightly lower altitude (from 12 to 9.5km: atmospheric depth from 234 to 365g/cm$^{2}$), the total loss becomes much smaller than flight cancelation, and the estimated total dose goes down from 1.2 to 0.45mSv, which is below the effective dose limit for the general public. In case of flying at an even lower altitude (7km: atmospheric depth 484g/cm$^{2}$), the estimated total dose becomes much smaller, 0.12 mSv. If we assume the increase of fuel cost is proportional to the increase in atmospheric depth, the increase in cost becomes 1.56 and 2.07 for the case of flying at 9.5 km and at 7 km, respectively. Lower altitude flights provide more safety for the potential risk of radiation doses induced by severe SPEs. At the same time, since there is total loss caused by flight cancelation, we propose that considering lower flight altitude is the best protection against solar flares., Comment: 16 pages, 3 figures, published in Evolutionary and Institutional Economics Review, 2020 (The accepted version of the manuscript is uploaded in arXiv. The final published version is available in the journal website.)

We construct an $(\infty,2)$-version of the (lax) Gray tensor product. On the 1-categorical level, this is a binary (or more generally an $n$-ary) functor on the category of $\Theta_2$-sets, and it is shown to be left Quillen with respect to Ara's model structure. Moreover we prove that this tensor product forms part of a "homotopical" (biclosed) monoidal structure, or more precisely a normal lax monoidal structure that is associative up to homotopy., Comment: v3: 63 pages. Minor revision. Published version

Data-driven decision-making is performed by solving a parameterized optimization problem, and the optimal decision is given by an optimal solution for unknown true parameters. We often need a solution that satisfies true constraints even though these are unknown. Robust optimization is employed to obtain such a solution, where the uncertainty of the parameter is represented by an ellipsoid, and the scale of robustness is controlled by a coefficient. In this study, we propose an algorithm to determine the scale such that the solution has a good objective value and satisfies the true constraints with a given confidence probability. Under some regularity conditions, the scale obtained by our algorithm is asymptotically $O(1/\sqrt{n})$, whereas the scale obtained by a standard approach is $O(\sqrt{d/n})$. This means that our algorithm is less affected by the dimensionality of the parameters.

Neural networks using numerous text data have been successfully applied to a variety of tasks. While massive text data is usually compressed using techniques such as grammar compression, almost all of the previous machine learning methods assume already decompressed sequence data as their input. In this paper, we propose a method to directly apply neural sequence models to text data compressed with grammar compression algorithms without decompression. To encode the unique symbols that appear in compression rules, we introduce composer modules to incrementally encode the symbols into vector representations. Through experiments on real datasets, we empirically showed that the proposal model can achieve both memory and computational efficiency while maintaining moderate performance., Comment: 12 pages, 4 Postscript figures

Star spot evolution is visible evidence of the emergence/decay of the magnetic field on stellar surface, and it is therefore important for the understanding of the underlying stellar dynamo and consequential stellar flares. In this paper, we report the temporal evolution of individual star spot area on the hot-Jupiter-hosting active solar-type star Kepler 17 whose transits occur every 1.5 days. The spot longitude and area evolution are estimated (1) from the stellar rotational modulations of Kepler data and (2) from the brightness enhancements during the exoplanet transits caused by existence of large star spots. As a result of the comparison, number of spots, spot locations, and the temporal evolution derived from the rotational modulations is largely different from those of in-transit spots. We confirm that although only two light curve minima appear per rotation, there are clearly many spots present on the star. We find that the observed differential intensity changes are sometimes consistent with the spot pattern detected by transits, but they sometimes do not match with each other. Although the temporal evolution derived from the rotational modulation differs from those of in-transit spots to a certain degree, the emergence/decay rates of in-transit spots are within an order of magnitude of those derived for sunspots as well as our previous research based only on rotational modulations. This supports a hypothesis that the emergence/decay of sunspots and extremely-large star spots on solar-type stars occur through the same underlying processes., Comment: 37 pages, 12 figures, 1 table. Accepted for publication in The Astrophysical Journal

In this work, we explore the state-space formulation of network processes to recover the underlying structure of the network (local connections). To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology inference problem. This approach provides a unified view of the traditional network control theory and signal processing on networks. In addition, it provides theoretical guarantees for the recovery of the topological structure of a deterministic linear dynamical system from input-output observations even though the input and state evolution networks can be different., Comment: Work presented in ITA 2019

Continuing the project described by Kato et al. (2009, PASJ, 61, S395, arXiv/0905.1757), we collected times of superhump maxima for 102 SU UMa-type dwarf novae observed mainly during the 2017 season and characterized these objects. WZ Sge-type stars identified in this study are PT And, ASASSN-17ei, ASASSN-17el, ASASSN-17es, ASASSN-17fn, ASASSN-17fz, ASASSN-17hw, ASASSN-17kd, ASASSN-17la, PNV J20205397+2508145 and TCP J00332502-3518565. We obtained new mass ratios for 7 objects using growing superhumps (stage A). ASASSN-17gf is an EI Psc-type object below the period minimum. CRTS J080941.3+171528 and DDE 51 are objects in the period gap and both showed long-lasting phase of stage A superhumps. We also summarized the recent advances in understanding of SU UMa-type and WZ Sge-type dwarf novae., Comment: The main text and Supporting information are combined in this arXiv version. Accepted for publication in PASJ, author list has been corrected. Follow-up to arXiv:1706.03870, arXiv:1605.06221, ... , arXiv:1009.5444, arXiv:0912.4321

Using a prototype of the Tomo-e Gozen wide-field CMOS mosaic camera, we acquire wide-field optical images at a cadence of 2 Hz and search them for transient sources of duration 1.5 to 11.5 seconds. Over the course of eight nights, our survey encompasses the equivalent of roughly two days on one square degree, to a fluence equivalent to a limiting magnitude about $V = 15.6$ in a 1-second exposure. After examining by eye the candidates identified by a software pipeline, we find no sources which meet all our criteria. We compute upper limits to the rate of optical transients consistent with our survey, and compare those to the rates expected and observed for representative sources of ephemeral optical light., Comment: Accepted for publication in PASJ, 26 pages, 10 figures. The posted version here is our original manuscript, before any changes in response to the referee's comments; to see a copy of the version which was accepted for publication, go to http://spiff.rit.edu/richmond/pub/tomoe_trans.pdf

We report observations of a stellar occultation by the classical Kuiper belt object (50000) Quaoar occurred on 28 June 2019. A single-chord high-cadence (2 Hz) photometry dataset was obtained with the Tomo-e Gozen CMOS camera mounted on the 1.05 m Schmidt telescope at Kiso Observatory. The obtained ingress and egress data do not show any indication of atmospheric refraction and allow to set new $1\sigma$ and $3\sigma$ upper limits of 6 and 16 nbar, respectively, for the surface pressure of a pure methane atmosphere. These upper limits are lower than the saturation vapor pressure of methane at Quaoar's expected mean surface temperature ($T \sim 44$ K) and imply the absence of a $\sim$10 nbar-level global atmosphere formed by methane ice on Quaoar's surface., Comment: 12 pages, 3 figures, accepted for publication in the Astronomical Journal

We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality conclusions including an open case for higher-order output. We find that our proposed technique not only leads to simple proofs of the universality properties but also gives a natural explanation for the tensorization of the previously studied models. Finally, we give some remarks on the connection between our model and the continuous representation of graphs.