Exponents Associated with YY-Systems and their Relationship with qq-Series

Let $X_r$ be a finite type Dynkin diagram, and $\ell$ be a positive integer greater than or equal to two. The $Y$-system of type $X_r$ with level $\ell$ is a system of algebraic relations, whose solutions have been proved to have periodicity. For any pair $(X_r, \ell)$, we define an integer sequence called exponents using formulation of the $Y$-system by cluster algebras. We give a conjectural formula expressing the exponents by the root system of type $X_r$, and prove this conjecture for $(A_1,\ell)$ and $(A_r, 2)$ cases. We point out that a specialization of this conjecture gives a relationship between the exponents and the asymptotic dimension of an integrable highest weight module of an affine Lie algebra. We also give a point of view from $q$-series identities for this relationship

A Giant Green Pea Identified in the Spectroscopy of Spatially Extended [OIII] Sources

We present the results of the deep Subaru/FOCAS and Keck/MOSFIRE spectroscopy for four spatially extended [O III]$\lambda\lambda$4959,5007 sources, dubbed [O III] blobs, at $z=0.6-0.8$ that are originally pinpointed by large-area Subaru imaging surveys. The line diagnostics of the rest-frame optical lines suggests that only one [O III] blob, OIIIB-3, presents an AGN signature, indicating that hot gas of the rest of the [O III] blobs is heated by star formation. One of such star-forming [O III] blobs, OIIIB-4, at $z=0.838$ has an [O III] equivalent width of $845\pm27$ \r{A} and an [O III] to [O II]$\lambda\lambda$3726,3729 ratio of [O III]/[O II]= $6.5\pm2.7$ that are as high as those of typical green peas (Cardamone et al. 2009). The spatially resolved spectrum of OIIIB-4 shows [O III]/[O II]= $5-10$ over $14$ kpc in the entire large [O III] extended regions of OIIIB-4, unlike the known green peas whose strong [O III] emission region is compact. Moreover, OIIIB-4 presents no high ionization emission lines, unlike green beans that have extended [O III] emission with a type-2 AGN. OIIIB-4 is thus a giant green pea, which is a low stellar mass ($7\times10^7$ $M_\odot$) galaxy with a very high specific star formation rate (sSFR = $2\times10^2\, {\rm Gyr}^{-1}$), a high ionization parameter ($q_{ion} \sim 3\times10^8\, {\rm cm\,s^{-1}}$), and a low metallicity similar to those of green peas. Neither an AGN-light echo nor a fast radiative shock likely takes place due to the line diagnostics for spatially-resolved components of OIIIB-4 and no detections of He II$\lambda$4686 or [Ne V]$\lambda\lambda$3346,3426 lines that are fast-radiative shock signatures. There is a possibility that the spatially-extended [O III] emission of OIIIB-4 is originated from outflowing gas produced by the intense star formation in a density-bounded ionization state.Comment: 17 pages, 12 figures, 4 tables, Accepted for publication in Ap

Functional Dynamics by Intention Recognition in Iterated Games

Intention recognition is an important characteristic of intelligent agents. In their interactions with others, they try to read others' intentions and make an image of others to choose their actions accordingly. While the way in which players choose their actions depending on such intentions has been investigated in game theory, how dynamic changes in intentions by mutually reading others' intentions are incorporated into game theory has not been explored. We present a novel formulation of game theory in which players read others' intentions and change their own through an iterated game. Here, intention is given as a function of the other's action and the own action to be taken accordingly as the dependent variable, while the mutual recognition of intention is represented as the functional dynamics. It is shown that a player suffers no disadvantage when he/she recognizes the other's intention, whereas the functional dynamics reach equilibria in which both players' intentions are optimized. These cover a classical Nash and Stackelberg equilibria but we extend them in this study: Novel equilibria exist depending on the degree of mutual recognition. Moreover, the degree to which each player recognizes the other can also differ. This formulation is applied to resource competition, duopoly, and prisoner's dilemma games. For example, in the resource competition game with player-dependent capacity on gaining the resource, the superior player's recognition leads to the exploitation of the other, while the inferior player's recognition leads to cooperation through which both players' payoffs increase.Comment: 20 pages, 6 figures, and supplementary materia

Schwartz type model selection for ergodic stochastic differential equation models

We study the construction of the theoretical foundation of model comparison for ergodic stochastic differential equation (SDE) models and an extension of the applicable scope of the conventional Bayesian information criterion. Different from previous studies, we suppose that the candidate models are possibly misspecified models, and we consider both Wiener and a pure-jump L\'{e}vy noise driven SDE. Based on the asymptotic behavior of the marginal quasi-log likelihood, the Schwarz type statistics and stepwise model selection procedure are proposed. We also prove the model selection consistency of the proposed statistics with respect to an optimal model. We conduct some numerical experiments and they support our theoretical findings

Scene Segmentation-Based Luminance Adjustment for Multi-Exposure Image Fusion

We propose a novel method for adjusting luminance for multi-exposure image fusion. For the adjustment, two novel scene segmentation approaches based on luminance distribution are also proposed. Multi-exposure image fusion is a method for producing images that are expected to be more informative and perceptually appealing than any of the input ones, by directly fusing photos taken with different exposures. However, existing fusion methods often produce unclear fused images when input images do not have a sufficient number of different exposure levels. In this paper, we point out that adjusting the luminance of input images makes it possible to improve the quality of the final fused images. This insight is the basis of the proposed method. The proposed method enables us to produce high-quality images, even when undesirable inputs are given. Visual comparison results show that the proposed method can produce images that clearly represent a whole scene. In addition, multi-exposure image fusion with the proposed method outperforms state-of-the-art fusion methods in terms of MEF-SSIM, discrete entropy, tone mapped image quality index, and statistical naturalness.Comment: will be published in IEEE Transactions on Image Processin

Two-step estimation of ergodic L\'evy driven SDE

We consider high frequency samples from ergodic L\'evy driven stochastic differential equation (SDE) with drift coefficient $a(x,\alpha)$ and scale coefficient $c(x,\gamma)$ involving unknown parameters $\alpha$ and $\gamma$. We suppose that the L\'evy measure $\nu_{0}$, has all order moments but is not fully specified. We will prove the joint asymptotic normality of some estimators of $\alpha$, $\gamma$ and a class of functional parameter $\int\varphi(z)\nu_0(dz)$, which are constructed in a two-step manner: first, we use the Gaussian quasi-likelihood for estimation of $(\alpha,\gamma)$, and then, for estimating $\int\varphi(z)\nu_0(dz)$ we makes use of the method of moments based on the Euler-type residual with the the previously obtained quasi-likelihood estimator

Convolutional Neural Networks Considering Local and Global features for Image Enhancement

In this paper, we propose a novel convolutional neural network (CNN) architecture considering both local and global features for image enhancement. Most conventional image enhancement methods, including Retinex-based methods, cannot restore lost pixel values caused by clipping and quantizing. CNN-based methods have recently been proposed to solve the problem, but they still have a limited performance due to network architectures not handling global features. To handle both local and global features, the proposed architecture consists of three networks: a local encoder, a global encoder, and a decoder. In addition, high dynamic range (HDR) images are used for generating training data for our networks. The use of HDR images makes it possible to train CNNs with better-quality images than images directly captured with cameras. Experimental results show that the proposed method can produce higher-quality images than conventional image enhancement methods including CNN-based methods, in terms of various objective quality metrics: TMQI, entropy, NIQE, and BRISQUE.Comment: To appear in Proc. ICIP2019. arXiv admin note: text overlap with arXiv:1901.0568

Emergence of Exploitation as Symmetry Breaking in Iterated Prisoner's Dilemma

In society, mutual cooperation, defection, and asymmetric exploitative relationships are common. Whereas cooperation and defection are studied extensively in the literature on game theory, asymmetric exploitative relationships between players are little explored. In a recent study, Press and Dyson demonstrate that if only one player can learn about the other, asymmetric exploitation is achieved in the prisoner's dilemma game. In contrast, however, it is unknown whether such one-way exploitation is stably established when both players learn about each other symmetrically and try to optimize their payoffs. Here, we first formulate a dynamical system that describes the change in a player's probabilistic strategy with reinforcement learning to obtain greater payoffs, based on the recognition of the other player. By applying this formulation to the standard prisoner's dilemma game, we numerically and analytically demonstrate that an exploitative relationship can be achieved despite symmetric strategy dynamics and symmetric rule of games. This exploitative relationship is stable, even though the exploited player, who receives a lower payoff than the exploiting player, has optimized the own strategy. Whether the final equilibrium state is mutual cooperation, defection, or exploitation, crucially depends on the initial conditions: Punishment against a defector oscillates between the players, and thus a complicated basin structure to the final equilibrium appears. In other words, slight differences in the initial state may lead to drastic changes in the final state. Considering the generality of the result, this study provides a new perspective on the origin of exploitation in society.Comment: 19 pages, 7 figures, + supplement(8 pages, 2 figures

Design and Analysis on a Cryogenic Current Amplifier with a Superconducting Microwave Resonator

We propose a new type of cryogenic current amplifiers, in which low-frequency power spectrum of current can be measured through a measurement of microwave response of a superconducting resonant circuit shunted by a series array of Josephson junctions. From numerical analysis on the equivalent circuit, the numerical value of the input-referred current noise of the proposed amplifier is found to be two orders of magnitude lower than the noise floor measured with the conventional cryogenic current amplifiers based on high-electron-mobility transistors or superconducting quantum interference devices. Our proposal can open new avenues for investigating low-temperature solid-state devices that require lower noise and wider bandwidth power spectrum measurements of current.Comment: 4 pages, 3 figure

Automatic Exposure Compensation for Multi-Exposure Image Fusion

This paper proposes a novel luminance adjustment method based on automatic exposure compensation for multi-exposure image fusion. Multi-exposure image fusion is a method to produce images without saturation regions, by using photos with different exposures. In conventional works, it has been pointed out that the quality of those multi-exposure images can be improved by adjusting the luminance of them. However, how to determine the degree of adjustment has never been discussed. This paper therefore proposes a way to automatically determines the degree on the basis of the luminance distribution of input multi-exposure images. Moreover, new weights, called "simple weights", for image fusion are also considered for the proposed luminance adjustment method. Experimental results show that the multi-exposure images adjusted by the proposed method have better quality than the input multi-exposure ones in terms of the well-exposedness. It is also confirmed that the proposed simple weights provide the highest score of statistical naturalness and discrete entropy in all fusion methods.Comment: To appear in Proc. ICIP2018 October 07-10, 2018, Athens, Greec