Path description for qq-characters of fundamental modules in type CC

In this paper, we investigate the behavior of monomials in the $q$-characters of the fundamental modules over a quantum affine algebra of untwisted type C. As a result, we give simple closed formulae for the $q$-characters of the fundamental modules in terms of sequences of vertices in $\mathbb{R}^2$, so-called paths, with an admissible condition. This may be viewed as a type C analog of the path description of $q$-characters in types A and B due to Mukhin--Young.Comment: v4: minor revision; v3: 23 pages, revised introduction and abstract, reference added, comments added on Remark 2.1, 3.1, 3.2, 4.5, 4.9, 4.10, added Section 4.2 to explain connected components, added Examples 2.4, 4.4, added Lemma 4.6, revised proof of Theorem 4.7, and several typos corrected; v2: 15 pages, typos corrected, reference correcte

Bivariate Beta-LSTM

Long Short-Term Memory (LSTM) infers the long term dependency through a cell state maintained by the input and the forget gate structures, which models a gate output as a value in [0,1] through a sigmoid function. However, due to the graduality of the sigmoid function, the sigmoid gate is not flexible in representing multi-modality or skewness. Besides, the previous models lack modeling on the correlation between the gates, which would be a new method to adopt inductive bias for a relationship between previous and current input. This paper proposes a new gate structure with the bivariate Beta distribution. The proposed gate structure enables probabilistic modeling on the gates within the LSTM cell so that the modelers can customize the cell state flow with priors and distributions. Moreover, we theoretically show the higher upper bound of the gradient compared to the sigmoid function, and we empirically observed that the bivariate Beta distribution gate structure provides higher gradient values in training. We demonstrate the effectiveness of bivariate Beta gate structure on the sentence classification, image classification, polyphonic music modeling, and image caption generation.Comment: AAAI 202

Crystal base of the negative half of the quantum superalgebra Uq(gl(m∣n))U_q(\mathfrak{gl}(m|n))

We construct a crystal base of $U_q(\mathfrak{gl}(m|n))^-$, the negative half of the quantum superalgebra $U_q(\mathfrak{gl}(m|n))$. We give a combinatorial description of the associated crystal $\mathscr{B}_{m|n}(\infty)$, which is equal to the limit of the crystals of the ($q$-deformed) Kac modules $K(\lambda)$. We also construct a crystal base of a parabolic Verma module $X(\lambda)$ associated with the subalgebra $U_q(\mathfrak{gl}_{0|n})$, and show that it is compatible with the crystal base of $U_q(\mathfrak{gl}(m|n))^-$ and the Kac module $K(\lambda)$ under the canonical embedding and projection of $X(\lambda)$ to $U_q(\mathfrak{gl}(m|n))^-$ and $K(\lambda)$, respectively.Comment: 43 page

Tensile Behavior and Cracking Pattern of an Ultra-High Performance Mortar Reinforced by Polyethylene Fiber

This paper presents an experimental study of the compressive strength, tensile behavior (including the tensile strength, tensile strain capacity, and toughness), and cracking patterns of an ultra-high performance mortar (UHPM) reinforced by polyethylene (PE) fiber as well as a discussion of the different tensile behaviors of the UHPM according to the types and contents of fibers used. The UHPM reinforced by microsteel fiber of 1.5 vol% and the UHPM reinforced by PE fibers with three different fiber contents were designed and prepared. A series of experiments was undertaken to assess the effect of PE fiber on the properties of the UHPM. The results found a lower strength level, higher tensile strain capacity and toughness, and a larger crack width in the PE fiber-reinforced UHPM compared to microsteel fiber-reinforced UHPM. It was also demonstrated that tensile strain capacity and toughness of 4.05% and 0.454 MPa m/m, respectively, can be attained when using the proposed polyethylene-fiber-reinforced UHPM

Quantization of virtual Grothendieck rings and their structure including quantum cluster algebras

The quantum Grothendieck ring of a certain category of finite-dimensional modules over a quantum loop algebra associated with a complex finite-dimensional simple Lie algebra $\mathfrak{g}$ has a quantum cluster algebra structure of skew-symmetric type. Partly motivated by a search of a ring corresponding to a quantum cluster algebra of {\em skew-symmetrizable} type, the quantum {\em virtual} Grothendieck ring, denoted by $\mathfrak{K}_q(\mathfrak{g})$, is recently introduced by Kashiwara--Oh \cite{KO23} as a subring of the quantum torus based on the $(q,t)$-Cartan matrix specialized at $q=1$. In this paper, we prove that $\mathfrak{K}_q(\mathfrak{g})$ indeed has a quantum cluster algebra structure of skew-symmetrizable type. This task essentially involves constructing distinguished bases of $\mathfrak{K}_q(\mathfrak{g})$ that will be used to make cluster variables and generalizing the quantum $T$-system associated with Kirillov--Reshetikhin modules to establish a quantum exchange relation of cluster variables. Furthermore, these distinguished bases naturally fit into the paradigm of Kazhdan--Lusztig theory and our study of these bases leads to some conjectures on quantum positivity and $q$-commutativity

The Light and Period Variations of the Eclipsing Binary AA Ursae Majoris

We present new multiband CCD photometry for AA UMa made on 8 nights between January and March 2009; the $R$ light curves are the first ever compiled. Historical light curves, as well as ours, display partial eclipses and inverse O'Connell effects with Max I fainter than Max II. Among possible spot models, a cool spot on either of the component stars and its variability with time permit good light-curve representations for the system. A total of 194 eclipse timings over 81 yrs, including our five timings, were used for ephemeris computations. We found that the orbital period of the system has varied due to a periodic oscillation overlaid on an upward parabolic variation. The continuous period increase at a fractional rate of $+$1.3$\times$10$^{-10}$ is consistent with that calculated from the W-D code and can be interpreted as a thermal mass transfer from the less to the more massive secondary star at a rate of 6.6$\times$10$^{-8}$ M$_\odot$ yr$^{-1}$. The periodic component is in satisfactory accord with a light-time effect due to an unseen companion with a period of 28.2 yrs, a semi-amplitude of 0.007 d, and a minimum mass of $M_3 \sin i_3$=0.25 $M_\odot$ but this period variation could also arise from magnetic activity.Comment: 23 pages, including 5 figures and 8 tables, accepted for publication in PAS

Intakes of Dairy Products and Calcium and Obesity in Korean Adults: Korean National Health and Nutrition Examination Surveys (KNHANES) 2007-2009

Background: The possible effects of dairy product intake against obesity have been suggested in animal studies; however, the association is still not well established in epidemiological studies. Few studies in Asian countries with relatively low intake of dairy products exist. Objective: We investigated the association between dairy products and calcium intake and obesity in Korean population with relatively low intake of dairy products. Subjects and Methods Our study population consisted of adults (n = 7173) aged 19–64 among participants of the 2007, 2008 and 2009 Korean National Health and Nutrition Examination Survey who had not made any attempt of intentional weight loss. Dietary intake data from food frequency questionnaire (FFQ) and 24-hour recall were used. Dairy products included milk and yogurt in the FFQ. Obesity was defined as BMI≥25 kg/m2. Results: Higher frequency of dairy product intake was associated with a reduced prevalence of obesity (OR = 0.63; 95% CI = 0.45–0.89 for ≥2 times/day vs. ≤1 time/month; p for trend = 0.003) using the intake data from FFQ. Similarly, high frequency of milk or yogurt intake had an inverse association with obesity. The association between milk and yogurt intake and obesity was similar when the intake from 24-hour recall was examined. Higher calcium intake from dairy products as well as total dietary calcium intake was associated with a decreased prevalence of obesity (OR = 0.83; 95% CI = 0.71–0.98 for highest vs. lowest quintile of dairy calcium intake; p for trend = 0.02, OR = 0.78; 95% CI = 0.64–0.94 for highest vs. lowest quintile of total calcium intake; p for trend = 0.04). The associations appeared to be stronger in women than in men. Conclusion: These results suggest that high consumption of dairy products is associated with a lower prevalence of obesity and that calcium in dairy products may be one of the components contributing to the association. Further longitudinal studies are warranted to replicate our findings