Path Integrals and p-adic L-functions
We prove an arithmetic path integral formula for the inverse p-adic absolute values of the Kubota-Leopoldt p-adic L-functions at roots of unity.
math.NT↗
arXiv subjects
Dohyeong Kim
Publications and source records attributed to Dohyeong Kim.
KOBEST: Korean Balanced Evaluation of Significant Tasks
A well-formulated benchmark plays a critical role in spurring advancements in the natural language processing (NLP) field, as it allows objective and precise evaluation of diverse models. As modern language models (LMs) have become more elaborate and sophisticated, more difficult benchmarks that require linguistic knowledge and reasoning have been proposed. However, most of these benchmarks only support English, and great effort is necessary to construct benchmarks for other low resource languages. To this end, we propose a new benchmark named Korean balanced evaluation of significant tasks (KoBEST), which consists of five Korean-language downstream tasks. Professional Korean linguists designed the tasks that require advanced Korean linguistic knowledge. Moreover, our data is purely annotated by humans and thoroughly reviewed to guarantee high data quality. We also provide baseline models and human performance results. Our dataset is available on the Huggingface.
cs.CL↗
Semi-Supervised Imitation Learning with Mixed Qualities of Demonstrations for Autonomous Driving
In this paper, we consider the problem of autonomous driving using imitation learning in a semi-supervised manner. In particular, both labeled and unlabeled demonstrations are leveraged during training by estimating the quality of each unlabeled demonstration. If the provided demonstrations are corrupted and have a low signal-to-noise ratio, the performance of the imitation learning agent can be degraded significantly. To mitigate this problem, we propose a method called semi-supervised imitation learning (SSIL). SSIL first learns how to discriminate and evaluate each state-action pair's reliability in unlabeled demonstrations by assigning higher reliability values to demonstrations similar to labeled expert demonstrations. This reliability value is called leverage. After this discrimination process, both labeled and unlabeled demonstrations with estimated leverage values are utilized while training the policy in a semi-supervised manner. The experimental results demonstrate the validity of the proposed algorithm using unlabeled trajectories with mixed qualities. Moreover, the hardware experiments using an RC car are conducted to show that the proposed method can be applied to real-world applications.
cs.RO↗
Batalin-Vilkovisky formalism in the $p$-adic Dwork theory
The goal of this article is to develop BV (Batalin-Vilkovisky) formalism in the $p$-adic Dwork theory. Based on this formalism, we explicitly construct a $p$-adic dGBV algebra (differential Gerstenhaber-Batalin-Vilkovisky algebra) for a smooth projective complete intersection variety $X$ over a finite field, whose cohomology gives the $p$-adic Dwork cohomology of $X$, and its cochain endomorphism (the $p$-adic Dwork Frobenius operator) which encodes the information of the zeta function $X$. As a consequence, we give a modern deformation theoretic interpretation of Dwork's theory of the zeta function of $X$ and derive a formula for the $p$-adic Dwork Frobenius operator in terms of homotopy Lie morphisms and the Bell polynomials.
math.NT↗
The Infrared Medium-deep Survey. VIII. Quasar Luminosity Function at $z\sim5$
Faint $z\sim5$ quasars with $M_{1450}\sim-23$ mag are known to be the potentially important contributors to the ultraviolet ionizing background in the post-reionization era. However, their number density has not been well determined, making it difficult to assess their role in the early ionization of the intergalactic medium (IGM). In this work, we present the updated results of our $z\sim5$ quasar survey using the Infrared Medium-deep Survey (IMS), a near-infrared imaging survey covering an area of 85 deg$^{2}$. From our spectroscopic observations with the Gemini Multi-Object Spectrograph (GMOS) on the Gemini-South 8 m Telescope, we discovered eight new quasars at $z\sim5$ with $-26.1\leq M_{1450} \leq -23.3$. Combining our IMS faint quasars ($M_{1450}>-27$ mag) with the brighter Sloan Digital Sky Survey (SDSS) quasars ($M_{1450}<-27$ mag), we derive the $z\sim5$ quasar luminosity function (QLF) without any fixed parameters down to the magnitude limit of $M_{1450}=-23$ mag. We find that the faint-end slope of the QLF is very flat ($α=-1.2^{+1.4}_{-0.6}$), with a characteristic luminosity of $M^{*}_{1450}=-25.8^{+1.4}_{-1.1}$ mag. The number density of $z\sim5$ quasars from the QLF gives an ionizing emissivity at 912 $\unicode{x212B}$ of $ε_{912}=(3.7$--$7.1)\times10^{23}$ erg s$^{-1}$ Hz$^{-1}$ Mpc$^{-3}$ and an ionizing photon density of $\dot{n}_{\rm ion}=(3.0$--$5.7)\times10^{49}$ Mpc$^{-3}$ s$^{-1}$. These results imply that quasars are responsible for only 10-20% (up to 50% even in the extreme case) of the photons required to completely ionize the IGM at $z\sim5$, disfavoring the idea that quasars alone could have ionized the IGM at $z\sim5$.
astro-ph.GA↗
Gemini Multi-Object Spectrograph Integral Field Unit Spectroscopy of the Double-peaked Broad Emission Line of a Red Active Galactic Nucleus
Galaxy mergers are expected to produce multiple supermassive black holes (SMBHs) in close-separation, but the detection of such SMBHs has been difficult. 2MASS J165939.7$+$183436 is a red active galactic nucleus (AGN) that is a prospective merging SMBH candidate owing to its merging features in Hubble Space Telescope imaging and double-peaked broad emission lines (BELs). Herein, we report a Gemini Multi-Object Spectrograph Integral Field Unit observation of a double-peaked broad H$α$ line of 2MASS J165939.7$+$183436. Furthermore, we confirm the existence of two BEL peaks that are kinematically separated by 3000\,$\rm km\,s^{-1}$, with the SMBH of each BEL component weighing at $10^{8.92\pm0.06}\,M_{\rm \odot}$ and $10^{7.13\pm0.06}\,M_{\rm \odot}$, if they arise from independent BELs near the two SMBHs. The BEL components were not separated at $>0\farcs1$; however, under several plausible assumptions regarding the fitting of each spaxel, the two components are found to be spatially separated at $0\farcs085$ ($\sim250$\,pc). Different assumptions for the fitting can lead to a null ($< 0\farcs05$) or a larger spatial separation ($\sim0\farcs15$). Given the uncertainty regarding the spatial separation, various models, such as the disk emitter and multiple SMBH models, are viable solutions to explain the double BEL components. These results will promote future research for finding more multiple SMBH systems in red AGNs, and higher-resolution imaging validates these different models.
astro-ph.GA↗
The Infrared Medium-deep Survey. \Romannum{7}. Faint Quasars at $z \sim 5$ in the ELAIS-N1 Field
The intergalactic medium (IGM) at $z\sim$ 5 to 6 is largely ionized, and yet the main source for the IGM ionization in the early universe is uncertain. Of the possible contributors are faint quasars with $-26 \lesssim M_{\rm 1450} \lesssim -23$, but their number density is poorly constrained at $z\sim5$. In this paper, we present our survey of faint quasars at $z\sim5$ in the European Large-Area {\it ISO} Survey-North 1 (ELAIS-N1) field over a survey area of 6.51 deg$^2$ and examine if such quasars can be the dominant source of the IGM ionization. We use the deep optical/near-infrared data of the ELAIS-N1 field as well as the additional medium-band observations to find $z \sim 5$ quasars through a two-step approach using the broadband color selection, and SED fitting with the medium-band information included. Adopting Bayesian information criterion, we identify ten promising quasar candidates. Spectra of three of the candidates are obtained, confirming all of them to be quasars at $z\sim5$ and supporting the reliability of the quasar selection. Using the promising candidates, we derive the $z\sim5$ quasar luminosity function at $-26 \lesssim M_{\rm 1450} \lesssim -23$. The number density of faint $z\sim5$ quasars in the ELAIS-N1 field is consistent with several previous results that quasars are not the main contributors to the IGM-ionizing photons at $z\sim5$
astro-ph.GA↗
More connected, more active: galaxy clusters and groups at z~1 and the connection between their quiescent galaxy fractions and large-scale environments
High-redshift galaxy clusters, unlike local counterparts, show diverse star formation activities. However, it is still unclear what keeps some of the high-redshift clusters active in star formation. To address this issue, we performed a multi-object spectroscopic (MOS) observation of 226 high-redshift (0.8 < z < 1.3) galaxies in galaxy cluster candidates and the areas surrounding them. Our spectroscopic observation reveals six to eight clusters/groups at z ~ 0.9 and z ~ 1.3. The redshift measurements demonstrate the reliability of our photometric redshift measurements, which in turn gives credibility for using photometric redshift members for the analysis of large-scale structures (LSSs). Our investigation of the large-scale environment (~10 Mpc) surrounding each galaxy cluster reveals LSSs --- structures up to ~10 Mpc scale --- around many of, but not all, the confirmed overdensities and the cluster candidates. We investigate the correlation between quiescent galaxy fraction of galaxy overdensities and their surrounding LSSs, with a larger sample of ~ 20 overdensities including photometrically selected overdensities at 0.6 < z < 0.9. Interestingly, galaxy overdensities embedded within these extended LSSs show a lower fraction of quiescent galaxies (~ 20 %) than isolated ones at similar redshifts (with a quiescent galaxy fraction of ~ 50 %). Furthermore, we find a possible indication that clusters/groups with a high quiescent galaxy fraction are more centrally concentrated. Based on these results, we suggest that LSSs are the main reservoirs of gas and star-forming galaxies to keep galaxy clusters fresh and extended in size at z ~ 1.
astro-ph.GA↗
Medium-resolution Optical and Near-Infrared Spectral Atlas of 16 2MASS-selected NIR-red Active Galactic Nuclei at $z \sim 0.3$
We present medium-resolution spectra ($R \sim 2000$--4000) at 0.4--1.0\,$μ$m and 0.7--2.5\,$μ$m of 16 active galactic nuclei (AGNs) selected with red color in the near-infrared (NIR) of $J - K > 2.0$ mag at $z \sim 0.3$. We fit the H$β$, H$α$, P$β$, and P$α$ lines from these spectra to obtain their luminosities and line widths. We derive the $E(B-V)$ color excess values of the NIR-red AGNs using two methods, one based on the line-luminosity ratios and another based on the continuum slopes. The two $E(B-V)$ values agree with each other at rms dispersion $\sim$ 0.249. About half of the NIR-red AGNs have $g'-K < 5$ magnitude, and we find that these NIR red, but blue in optical-NIR AGNs, have $E(B-V) \sim 0$, suggesting that a significant fraction of the NIR color-selected red AGNs are unobscured or only mildly obscured. After correcting for the dust extinction, we estimate the black hole (BH) masses and the bolometric luminosities of the NIR-red AGNs using the Paschen lines to calculate their Eddington ratios ($λ_{\rm Edd}$). The median Eddington ratios of nine NIR-red AGNs ($\log (λ_{\rm Edd}) \simeq -0.654 \pm 0.176$) are only mildly higher than those of unobscured type 1 AGNs ($\log (λ_{\rm Edd}) \simeq -0.961 \pm 0.008$). Moreover, we find that the $M_{\rm BH}$--$σ_{\ast}$ relation for three NIR-red AGNs is consistent with that of unobscured type 1 AGNs at similar redshift. These results suggest that the NIR red color selection alone is not effective at picking up dusty, intermediate-stage AGNs.
astro-ph.GA↗
The Infrared Medium-deep Survey. VI. Discovery of Faint Quasars at $z\sim5$ with a Medium-band-based Approach
The faint quasars with $M_{1450}>-24$ mag are known to hold the key to the determination of the ultraviolet emissivity for the cosmic re-ionization. But only a few have been identified so far because of the limitations on the survey data. Here, we present the first results of the $z\sim5$ faint quasar survey with the Infrared Medium-deep Survey (IMS), which covers $\sim100$ deg$^{2}$ areas in $J$-band to the depths of $J_{\rm AB}\sim23$ mag. To improve selection methods, the medium-band follow-up imaging has been carried out using the SED camera for QUasars in Early uNiverse (SQUEAN) on the Otto Struve 2.1 m Telescope. The optical spectra of the candidates were obtained with 8-m class telescopes. We newly discovered 10 quasars with $-25<M_{1450}<-23$ at $z\sim5$, among which three have been missed in a previous survey using the same optical data over the same area, implying the necessity for improvements in high redshift faint quasars selection. We derived photometric redshifts from the medium-band data, and find that they have high accuracies of $\langle|Δz|/(1+z)\rangle=0.016$. The medium-band-based approach allows us to rule out many of the interlopers that contaminate $\gtrsim20~\%$ of the broad-band-selected quasar candidates. These results suggest that the medium-band-based approach is a powerful way to identify $z\sim5$ quasars and measure their redshifts at high accuracy (1-2 %). It is also a cost-effective way to understand the contribution of quasars to the cosmic re-ionization history.
astro-ph.GA↗
Intra-night optical variability of AGN in the COSMOS field with the KMTNet
Active Galactic Nucleus (AGN) variability can be used to study the physics of the region in the vicinity of the central black hole. In this paper, we investigated intra-night optical variability of AGN in the COSMOS field in order to understand the AGN instability at the smallest scale. Observations were performed using the KMTNet on three separate nights for 2.5-5 hour at a cadence of 20-30 min. We find that the observation enables the detection of the short-term variability as small as $\sim$ 0.02 and 0.1 mag for $R \sim$ 18 and 20 mag sources, respectively. Using four selection methods (X-rays, mid-infrared, radio, and matching with SDSS quasars), 394 AGNs are detected in the 4 deg$^2$ field of view. After differential photometry and $χ^2-$test, we classify intra-night variable AGNs. But the fraction of variable AGNs (0-8 %) is consistent with a statistical fluctuation from null result. Eight out of 394 AGNs are found to be intra-night variable in two filters or two nights with a variability level of 0.1 mag, suggesting that they are strong candidates for intra-night variable AGNs. Still they represent a small population (2 %). There is no sub-category of AGNs that shows a statistically significant intra-night variability.
astro-ph.GA↗
Discrete Hodge star operator on 3-manifolds
Scott Wilson introduced the notion of combinatorial Hodge star operators on a compact oriented triangulated manifold $M$, which act on the singular cohomology ring of $M$. Such an operator depends on both a triangulation $\mathscr K$ of $M$ and a metric on the simplicial cochain complex of $\mathscr K$. Taking the discrete metric, we arrive at the notion of the discrete Hodge star operator for each pair $(M,\mathscr K)$. We prove, when $M$ is a $3$-manifold, that the discrete Hodge star operators acting on the cuspidal cohomology groups $H^i_\mathrm{cusp}(M,\mathbb Q)$ are independent of $\mathscr K$ for $i=1,2$. As an application, we construct a canonical positive definite symmetric quadratic form on $H^i_\mathrm{cusp}(M,\mathbb Q)$ for $i=1,2$. On the other hand, we will interpret our result from a point of view on the Langlands Program; we provide a supporting evidence for the conjecture of Prasanna and Venkatesh, which predicts a degree-shifting action of a motivic cohomology group on the cohomology ring of an arithmetic group.
math.AT↗
The Infrared Medium-deep Survey. IV. Low Eddington Ratio of A Faint Quasar at $z\sim6$: Not Every Supermassive Black Hole is Growing Fast in the Early Universe
To date, most of the luminous quasars known at $z\sim6$ have been found to be in maximal accretion with the Eddington ratios, $λ_{\rm{Edd}}\sim1$, suggesting enhanced nuclear activities in the early universe. However, this may not be the whole picture of supermassive black hole (SMBH) growth since previous studies have not reached on faint quasars that are more likely to harbor SMBHs with low $λ_{\rm{Edd}}$. To gain a better understanding on the accretion activities in quasars in the early universe, we obtained a deep near-infrared (NIR) spectrum of a quasar, IMS J220417.92+011144.8 (hereafter IMS J2204+0112), one of the faintest quasars that have been identified at $z\sim6$. From the redshifted C IV $λ1549$ emission line in the NIR spectrum, we find that IMS J2204+0112 harbors a SMBH with about a billion solar mass and $λ_{\rm{Edd}} \sim 0.1$, but with a large uncertainty in both quantities (0.41 dex). IMS J2204+0112 has one of the lowest Eddington ratios among quasars at $z\sim6$, but a common value among quasars at $z\sim2$. Its low $λ_{\rm{Edd}}$ can be explained with two scenarios; the SMBH growth from a stellar mass black hole through short-duration super-Eddington accretion events or from a massive black hole seed ($\sim10^{5}\,M_{\odot}$) with Eddington-limited accretion. NIR spectra of more faint quasars are needed to better understand the accretion activities of SMBHs at $z \sim 6$.
astro-ph.GA↗
What makes red quasars red? Observational evidence for dust extinction from line ratio analysis
Red quasars are very red in the optical through near-infrared (NIR) wavelengths, which is possibly due to dust extinction in their host galaxies as expected in a scenario in which red quasars are an intermediate population between merger-driven star-forming galaxies and unobscured type 1 quasars. However, alternative mechanisms also exist to explain their red colors: (i) an intrinsically red continuum; (ii) an unusual high covering factor of the hot dust component, that is, $\rm CF_{HD} = {\it L}_{HD} / {\it L}_{bol}$, where the ${L}_{\rm HD}$ is the luminosity from the hot dust component and the ${L}_{\rm bol}$ is the bolometric luminosity; and (iii) a moderate viewing angle. In order to investigate why red quasars are red, we studied optical and NIR spectra of 20 red quasars at $z\sim$0.3 and 0.7, where the usage of the NIR spectra allowed us to look into red quasar properties in ways that are little affected by dust extinction. The Paschen to Balmer line ratios were derived for 13 red quasars and the values were found to be $\sim$10 times higher than unobscured type 1 quasars, suggesting a heavy dust extinction with $A_V > 2.5$ mag. Furthermore, the Paschen to Balmer line ratios of red quasars are difficult to explain with plausible physical conditions without adopting the concept of the dust extinction. The $\rm CF_{HD}$ of red quasars are similar to, or marginally higher than, those of unobscured type 1 quasars. The Eddington ratios, computed for 19 out of 20 red quasars, are higher than those of unobscured type 1 quasars (by factors of $3 \sim 5$), and hence the moderate viewing angle scenario is disfavored. Consequently, these results strongly suggest the dust extinction that is connected to an enhanced nuclear activity as the origin of the red color of red quasars, which is consistent with the merger-driven quasar evolution scenario.
astro-ph.GA↗
Arithmetic Chern-Simons Theory II
We apply ideas of Dijkgraaf and Witten on three-dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define classical Chern-Simons actions on spaces of Galois representations. In the subsequent sections, we give formulas for computation in a small class of cases and point towards some arithmetic applications.
math.NT↗
The Infrared Medium-deep Survey. III. Survey of Luminous Quasars at 4.7 $\leq$ z $\leq$ 5.4
We present our first results of the survey for high redshift quasars at $5 \lesssim {\rm z} \lesssim 5.7$. The search for quasars in this redshift range has been known to be challenging due to limitations of filter sets used in previous studies. We conducted a quasar survey for two specific redshift ranges, 4.60 $\leq$ z $\leq$ 5.40 and 5.50 $\leq$ z $\leq$ 6.05, using multi-wavelength data that include observations using custom-designed filters, $is$ and $iz$. Using these filters and a new selection technique, we were able to reduce the fraction of interlopers. Through optical spectroscopy, we confirmed seven quasars at 4.7 $\leq$ z $\leq$ 5.4 with $-27.4 < M_{1450} < -26.4$ which were discovered independently by another group recently. We estimated black hole masses and Eddington ratios of four of these quasars from optical and near-infrared spectra, and found that these quasars are undergoing nearly Eddington-limited accretion which is consistent with the rapid growth of supermassive black holes in luminous quasars at z $\sim$ 5.
astro-ph.GA↗
Abelian arithmetic Chern-Simons theory and arithmetic linking numbers
Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to a precise arithmetic analogue of a 'path-integral formula' for linking numbers.
math.NT↗
The Most Massive Active Galactic Nuclei at $1\lesssim z \lesssim 2$
We obtained near-infrared spectra of 26 SDSS quasars at $0.7<z<2.5$ with reported rest-frame ultraviolet $M_{\rm BH} \sim 10^{10}M_{\odot}$ to critically examine the systematic effects involved with their mass estimations. We find that AGNs heavier than $10^{10}M_{\odot}$ often display double-peaked H$α$ emission, extremely broad FeII complex emission around MgII, and highly blueshifted and broadened CIV emission. The weight of this evidence, combined with previous studies, cautions against the use of $M_{\rm BH}$ values based on any emission line with a width over 8000 km/s. Also, the $M_{\rm BH}$ estimations are not positively biased along the presence of ionized narrow line outflows, anisotropic radiation, or the use of line FWHM instead of $σ$ for our sample, and unbiased with variability, scatter in broad line equivalent width, or obscuration for general type-1 quasars. Removing the systematically uncertain $M_{\rm BH}$ values, $\sim10^{10}M_{\odot}$ BHs in $1\lesssim z \lesssim 2$ AGNs can still be explained by anisotropic motion of the broad line region from $\sim10^{9.5}M_{\odot}$ BHs, although current observations support they are intrinsically most massive, and overmassive to the host's bulge mass.
astro-ph.GA↗