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

The Light and Period Variations of the Eclipsing Binary BX Draconis

New CCD photometric observations of BX Dra were obtained for 26 nights from 2009 April to 2010 June. The long-term photometric behaviors of the system are presented from detailed studies of the period and light variations, based on the historical data and our new observations. All available light curves display total eclipses at secondary minima and inverse O'Connell effects with Max I fainter than Max II, which are satisfactorily modeled by adding the slightly time-varying hot spot on the primary star. A total of 87 times of minimum light spanning over about 74 yrs, including our 22 timing measurements, were used for ephemeris computations. Detailed analysis of the O-C diagram showed that the orbital period has changed in combinations with an upward parabola and a sinusoidal variation. The continuous period increase with a rate of +5.65 \times 10^-7 d yr^-1 is consistent with that calculated from the Wilson-Devinney synthesis code. It can be interpreted as a mass transfer from the secondary to the primary star at a rate of 2.74 \times 10^-7 M\odot yr^-1, which is one of the largest rates for contact systems. The most likely explanation of the sinusoidal variation with a period of 30.2 yrs and a semi-amplitude of 0.0062 d is a light-traveltime effect due to the existence of a circumbinary object. We suggest that BX Dra is probably a triple system, consisting of a primary star with a spectral type of F0, its secondary component of spectral type F1-2, and an unseen circumbinary object with a minimum mass of M3 = 0.23 M\odot.Comment: 24 pages, including 5 figures and 9 tables, accepted for publication in PAS

AAVR-Displaying Interfaces: Serotype-Independent Adeno-Associated Virus Capture and Local Delivery Systems.

Interfacing gene delivery vehicles with biomaterials has the potential to play a key role in diversifying gene transfer capabilities, including localized, patterned, and controlled delivery. However, strategies for modifying biomaterials to interact with delivery vectors must be redesigned whenever new delivery vehicles and applications are explored. We have developed a vector-independent biomaterial platform capable of interacting with various adeno-associated viral (AAV) serotypes. A water-soluble, cysteine-tagged, recombinant protein version of the recently discovered multi-AAV serotype receptor (AAVR), referred to as cys-AAVR, was conjugated to maleimide-displaying polycaprolactone (PCL) materials using click chemistry. The resulting cys-AAVR-PCL system bound to a broad range of therapeutically relevant AAV serotypes, thereby providing a platform capable of modulating the delivery of all AAV serotypes. Intramuscular injection of cys-AAVR-PCL microspheres with bound AAV vectors resulted in localized and sustained gene delivery as well as reduced spread to off-target organs compared to a vector solution. This cys-AAVR-PCL system is thus an effective approach for biomaterial-based AAV gene delivery for a broad range of therapeutic applications