429 research outputs found
Path description for -characters of fundamental modules in type
In this paper, we investigate the behavior of monomials in the -characters
of the fundamental modules over a quantum affine algebra of untwisted type C.
As a result, we give simple closed formulae for the -characters of the
fundamental modules in terms of sequences of vertices in ,
so-called paths, with an admissible condition. This may be viewed as a type C
analog of the path description of -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
We construct a crystal base of , the negative half
of the quantum superalgebra . We give a combinatorial
description of the associated crystal , which is
equal to the limit of the crystals of the (-deformed) Kac modules
. We also construct a crystal base of a parabolic Verma module
associated with the subalgebra , and
show that it is compatible with the crystal base of
and the Kac module under the canonical embedding and projection of
to and , 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 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
, is recently introduced by Kashiwara--Oh
\cite{KO23} as a subring of the quantum torus based on the -Cartan
matrix specialized at . In this paper, we prove that
indeed has a quantum cluster algebra structure
of skew-symmetrizable type. This task essentially involves constructing
distinguished bases of that will be used to make
cluster variables and generalizing the quantum -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 -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 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 1.310 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
6.610 M yr. 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 =0.25 but this period variation could also arise from
magnetic activity.Comment: 23 pages, including 5 figures and 8 tables, accepted for publication
in PAS
Effect of Ginseng Powder Supplementation on the Physicochemical Properties, Antioxidant Capacity, and Sensory Characteristics of Cream Soup
Ginseng has been used as a medicinal herb in Asian countries for hundreds of years. It contains many kinds of ginsenosides as major active ingredients and is known to have neuroprotective, anti-inflammatory, antitumor, and antidiabetic properties. In this study, we have developed cream soup with different concentrations (0%, 3%, 5%, 7%, and 10%) of ginseng powder (GP) and determined the quality characteristics (color, viscosity, salinity, etc.) and antioxidant activity, along with sensory parameters. After the addition of GP, significant differences in salinity, L* and a*color value, DPPH, and ABTS were found among different concentrations of GP. Cream soup supplemented with GP 10% exhibited the highest values for DPPH and ABTS (83.5% and 87%, respectively), while the contents of total phenolic and saponin were 0.651 ± 0.02 (mg Gallic acid Equiv./g, DW) and 0.797 ± 0.05 (mg Diosgenin Equiv./g, DW), respectively. Moreover, there were no significant changes for °Brix value, pH, acidity, and total flavonoids content compared to control. The sensory characteristics indicated bitterness with the increase in the concentration of GP. However, a non-significant difference was observed between the control and supplemented samples for color, viscosity, and overall preference. Therefore, the supplementation of GP to cream soup could exhibit health benefits and increase the demand for ginseng to promote public health as functional food material
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