We present the discovery of a large gradual apparent fading event in optical and near-infrared wavelengths in a quasar at z=1.767 by a factor of 20-30 (in optical) over a period of ~20 years in the observed frame. This pronounced fading trend in brightness was first identified by comparing the magnitudes measured in the Subaru/Hyper Suprime-Cam (HSC) images with those in the Sloan Digital Sky Survey (SDSS) images for ~3x10^4 quasars spectroscopically identified by SDSS. We performed follow-up observations, including optical imaging and spectroscopy as well as near-infrared imaging, with >4m-class telescopes such as Subaru, GTC, Keck, and SOAR telescopes. We combine these new data with the archival data to examine the variability behavior over ~20 years in detail and even the longer-term trend of the variability over ~70 years in the observed frame. We find that (i) the AGN component likely faded by a factor of ~50 from the early 2000s to 2023 and (ii) the observed brightness decline is best explained by a substantial decrease in accretion rate rather than time-varying line-of-sight dust obscuration. These findings are derived from multi-component (time-varying AGN + constant galaxy) spectral energy distribution fitting over multi-epochs, which is well consistent with the optical spectra. The Eddington ratio decreases by a factor of ~50, from ~0.4 to ~0.008 if we use the black hole mass measured with the SDSS spectrum, which could be highly uncertain because of the very large variability. The total brightness is dominated by the host galaxy in the rest-frame optical wavelength rather than the AGN as of 2023.

Though U-Net has achieved tremendous success in medical image segmentation tasks, it lacks the ability to explicitly model long-range dependencies. Therefore, Vision Transformers have emerged as alternative segmentation structures recently, for their innate ability of capturing long-range correlations through Self-Attention (SA). However, Transformers usually rely on large-scale pre-training and have high computational complexity. Furthermore, SA can only model self-affinities within a single sample, ignoring the potential correlations of the overall dataset. To address these problems, we propose a novel Transformer module named Mixed Transformer Module (MTM) for simultaneous inter- and intra- affinities learning. MTM first calculates self-affinities efficiently through our well-designed Local-Global Gaussian-Weighted Self-Attention (LGG-SA). Then, it mines inter-connections between data samples through External Attention (EA). By using MTM, we construct a U-shaped model named Mixed Transformer U-Net (MT-UNet) for accurate medical image segmentation. We test our method on two different public datasets, and the experimental results show that the proposed method achieves better performance over other state-of-the-art methods. The code is available at: this https URL.

MRC 0600-399, in the merging galaxy cluster Abell 3376, is one of the unique Head-Tail radio galaxies having abruptly bending structures, the origin of which is still under discussion. A previous study suggested that the interaction between the jets and the magnetic fields on the cold front has produced such an outstanding feature; however, it is still not known how the jet propagates the long distance keeping the sharp shape. In this study, we performed a polarization analysis of MRC 0600-399 and a nearby radio source using MeerKAT L-band data. To interpret the Faraday structure, we constructed the Pseudo-3D visualization map of the reconstructed Faraday dispersion function 3D cube. MRC 0600-399 has a complicated Faraday depth structure, and some of the Faraday depth features are in good agreement with the 2D structure on the celestial sphere. For the northern jet of MRC 0600-399, the Faraday depth values show a clear gap at the tip region. Based on the polarization analysis and comparison with the other observation, we concluded that the synchrotron radiation from the tip region of the northern jet originates from the magnetic field on the cold front.

As a natural generalization of the Legendre symbol, the $q$-th power residue symbol $(a/p)_q$ is defined for primes $p$ and $q$ with $p\equiv 1 \bmod q$. In this paper, we generalize the second supplementary law by providing an explicit condition for $(q/p)_q = 1$, when $p$ has a special form $p = \sum_{i=0}^{q-1} m^i n^{q-1-i}$. This condition is expressed in terms of the polylogarithm $\mathrm{Li}_{1-q}(x)$ of negative index. Our proof relies on an argument similar to Lemmermeyer's proof of Euler's conjectures for cubic residue.

Recently, a variety of vision transformers have been developed as their capability of modeling long-range dependency. In current transformer-based backbones for medical image segmentation, convolutional layers were replaced with pure transformers, or transformers were added to the deepest encoder to learn global context. However, there are mainly two challenges in a scale-wise perspective: (1) intra-scale problem: the existing methods lacked in extracting local-global cues in each scale, which may impact the signal propagation of small objects; (2) inter-scale problem: the existing methods failed to explore distinctive information from multiple scales, which may hinder the representation learning from objects with widely variable size, shape and location. To address these limitations, we propose a novel backbone, namely ScaleFormer, with two appealing designs: (1) A scale-wise intra-scale transformer is designed to couple the CNN-based local features with the transformer-based global cues in each scale, where the row-wise and column-wise global dependencies can be extracted by a lightweight Dual-Axis MSA. (2) A simple and effective spatial-aware inter-scale transformer is designed to interact among consensual regions in multiple scales, which can highlight the cross-scale dependency and resolve the complex scale variations. Experimental results on different benchmarks demonstrate that our Scale-Former outperforms the current state-of-the-art methods. The code is publicly available at: this https URL

An input-output table is an important data for analyzing the economic situation of a region. Generally, the input-output table for each region (regional input-output table) in Japan is not always publicly available, so it is necessary to estimate the table. In particular, various methods have been developed for estimating input coefficients, which are an important part of the input-output table. Currently, non-survey methods are often used to estimate input coefficients because they require less data and computation, but these methods have some problems, such as discarding information and requiring additional data for estimation. In this study, the input coefficients are estimated by approximating the generation process with an artificial neural network (ANN) to mitigate the problems of the non-survey methods and to estimate the input coefficients with higher precision. To avoid over-fitting due to the small data used, data augmentation, called mixup, is introduced to increase the data size by generating virtual regions through region composition and scaling. By comparing the estimates of the input coefficients with those of Japan as a whole, it is shown that the accuracy of the method of this research is higher and more stable than that of the conventional non-survey methods. In addition, the estimated input coefficients for the three cities in Japan are generally close to the published values for each city.

An exact solution for a nonrotating boson star in (2+1) dimensional gravity with a negative cosmological constant is found. The relations among mass, particle number, and radius of the (2+1) dimensional boson star are shown.

The recent analysis of the Planck 2018 polarization data shows a nonzero isotropic cosmic birefringence (ICB) that is not explained within the $\Lambda$CDM paradigm. We then explore the question of whether the nonzero ICB is interpreted by the framework of the Standard Model Effective Field Theory (SMEFT), or at the energy scales of the cosmic microwave background, the low-energy EFT (LEFT) whose dynamical degrees of freedom are five SM quarks and all neutral and charged leptons. Our systematic study reveals that any operator in the EFT on a cosmological background would not give the reported ICB angle, which is observationally consistent with frequency independence. In particular, we estimate the size of the ICB angle generated by the effect that the cosmic microwave background photons travel through the medium of the cosmic neutrino background with parity-violating neutrino-photon interactions and find that it would be too small to explain the data. If the reported ICB angle should be confirmed, then our result would indicate the existence of a new particle that is lighter than the electroweak scale and feebly interacting with the SM particles.

We discuss phenomenological consequences of the recently-introduced refinements of the de Sitter swampland conjecture. The conjecture constraints the first and the second derivatives of the scalar potential in terms of two $O(1)$ constants $c$ and $c'$, leading to interesting constraints on particle phenomenology, especially inflationary model building. Our work can also be regarded as bottom-up constraints on the values of $c$ and $c'$.

We consider a six-dimensional $U(1)$ gauge theory compactified on two-dimensional manifolds. The number of chiral fermions is determined by the flux quantization number on the two-dimensional compact manifolds. Using the Swampland Conjectures, we find constraints among the parameters of the theory: the flux quantization number, the compactification scale, and the string scale. Specifically, the Weak Gravity Conjecture and the Trans-Planckian Censorship Conjecture give non-trivial bounds.

Observations have found black holes spanning ten orders of magnitude in mass across most of cosmic history. The Kerr black hole solution is however provisional as its behavior at infinity is incompatible with an expanding universe. Black hole models with realistic behavior at infinity predict that the gravitating mass of a black hole can increase with the expansion of the universe independently of accretion or mergers, in a manner that depends on the black hole's interior solution. We test this prediction by considering the growth of supermassive black holes in elliptical galaxies over $0

We investigate symmetric equilibria of mutual reinforcement learning when both players alternately learn the optimal memory-two strategies against the opponent in the repeated prisoners' dilemma game. We provide a necessary condition for memory-two deterministic strategies to form symmetric equilibria. We then provide three examples of memory-two deterministic strategies which form symmetric mutual reinforcement learning equilibria. We also prove that mutual reinforcement learning equilibria formed by memory-two strategies are also mutual reinforcement learning equilibria when both players use reinforcement learning of memory-$n$ strategies with $n>2$.

We introduce the concept of deformed zero-determinant strategies in repeated games. We then show that the Tit-for-Tat strategy in the repeated prisoner's dilemma game is a deformed zero-determinant strategy, which unilaterally equalizes the probability distribution functions of payoffs of two players.

We investigate symmetric equilibria of mutual reinforcement learning when both players alternately learn the optimal memory-two strategies against the opponent in the repeated prisoners' dilemma game. We provide a necessary condition for memory-two deterministic strategies to form symmetric equilibria. We then provide three examples of memory-two deterministic strategies which form symmetric mutual reinforcement learning equilibria. We also prove that mutual reinforcement learning equilibria formed by memory-two strategies are also mutual reinforcement learning equilibria when both players use reinforcement learning of memory-$n$ strategies with $n>2$.

We analyze a decade of 6.7 GHz methanol monitoring data in G9.62+0.20E, confirming the known periodicities of p1 = 241.3 +/- 2.3 d and p2 = 52.5 +/- 0.3 d, and identifying three new cycles at p3 = 127.0 +/- 1.6 d, p4 = 163.9 +/- 2.9 d, and p5 = 204.1 +/- 1.5 d. The 241.3-d and 204.1-d periods occur in multiple velocity channels, while the others are confined to single components. Despite their diverse morphologies and timescales, all flares can be reproduced within a unified Maxwell-Bloch framework operating in the fast-transient superradiance regime, driven by narrow periodic pump excitations. Model fits yield consistent environmental parameters across periodicities (temperatures, collisional timescales), pointing to broadly uniform physical conditions in the masing region. The discovery of new periodicities and their unified Maxwell-Bloch modeling provide a consistent picture of multi-periodic flaring in G9.62+0.20E and support superradiance as a general framework for maser flaring.

Recently del Monaco and Schleißinger addressed an interesting problem whether one can take the limit of multiple Schramm--Loewner evolution (SLE) as the number of slits $N$ goes to infinity. When the $N$ slits grow from points on the real line ${\mathbb{R}}$ in a simultaneous way and go to infinity within the upper half plane ${\mathbb{H}}$, an ordinary differential equation describing time evolution of the conformal map $g_t(z)$ was derived in the $N \to \infty$ limit, which is coupled with a complex Burgers equation in the inviscid limit. It is well known that the complex Burgers equation governs the hydrodynamic limit of the Dyson model defined on ${\mathbb{R}}$ studied in random matrix theory, and when all particles start from the origin, the solution of this Burgers equation is given by the Stieltjes transformation of the measure which follows a time-dependent version of Wigner's semicircle law. In the present paper, first we study the hydrodynamic limit of the multiple SLE in the case that all slits start from the origin. We show that the time-dependent version of Wigner's semicircle law determines the time evolution of the SLE hull, $K_t \subset {\mathbb{H}} \cup {\mathbb{R}}$ , in this hydrodynamic limit. Next we consider the situation such that a half number of the slits start from a>0 and another half of slits start from -a < 0, and determine the multiple SLE in the hydrodynamic limit. After reporting these exact solutions, we will discuss the universal long-term behavior of the multiple SLE and its hull $K_t$ in the hydrodynamic limit.

We present the first results from an all-sky all-frequency (ASAF) search for an anisotropic stochastic gravitational-wave background using the data from the first three observing runs of the Advanced LIGO and Advanced Virgo detectors. Upper limit maps on broadband anisotropies of a persistent stochastic background were published for all observing runs of the LIGO-Virgo detectors. However, a broadband analysis is likely to miss narrowband signals as the signal-to-noise ratio of a narrowband signal can be significantly reduced when combined with detector output from other frequencies. Data folding and the computationally efficient analysis pipeline, {\tt PyStoch}, enable us to perform the radiometer map-making at every frequency bin. We perform the search at 3072 {\tt{HEALPix}} equal area pixels uniformly tiling the sky and in every frequency bin of width $1/32$~Hz in the range $20-1726$~Hz, except for bins that are likely to contain instrumental artefacts and hence are notched. We do not find any statistically significant evidence for the existence of narrowband gravitational-wave signals in the analyzed frequency bins. Therefore, we place $95\%$ confidence upper limits on the gravitational-wave strain for each pixel-frequency pair, the limits are in the range $(0.030 - 9.6) \times10^{-24}$. In addition, we outline a method to identify candidate pixel-frequency pairs that could be followed up by a more sensitive (and potentially computationally expensive) search, e.g., a matched-filtering-based analysis, to look for fainter nearly monochromatic coherent signals. The ASAF analysis is inherently independent of models describing any spectral or spatial distribution of power. We demonstrate that the ASAF results can be appropriately combined over frequencies and sky directions to successfully recover the broadband directional and isotropic results.