Applications of shuffle product to restricted decomposition formulas for multiple zeta values

In this paper we obtain a recursive formula for the shuffle product and apply it to derive two restricted decomposition formulas for multiple zeta values (MZVs). The first formula generalizes the decomposition formula of Euler and is similar to the restricted formula of Eie and Wei for MZVs with one strings of 1's. The second formula generalizes the previous results to the product of two MZVs with one and two strings of 1's respectively.Comment: 11 page

Application of Genome Editing Technology to MicroRNA Research in Mammalians

Targeted nucleases have recently emerged as a powerful genome editing tool. The ability of introducing targeted, desired changes into mammalian genome makes them an invaluable tool to unravel functions of miRNAs in biology and disease. In combination with homologous donor vector, targeted nucleases can achieve high efficiency and precision, enabling bi-allelic ablation of miRNA in cultured somatic cells. Here we review the structure and function of miRNA as well as the unique implementation of genome editing technology in modifying miRNA sequences in mammalians. This chapter discusses the four mainstay genome editing technologies: meganuclease, zinc finger nuclease (ZFN), transcription activator-like effector nuclease (TALEN) and clustered regularly interspaced short palindromic repeat-associated nuclease Cas9 (CRISPR-Cas9), focusing on TALEN

Generative Action Description Prompts for Skeleton-based Action Recognition

Skeleton-based action recognition has recently received considerable attention. Current approaches to skeleton-based action recognition are typically formulated as one-hot classification tasks and do not fully exploit the semantic relations between actions. For example, "make victory sign" and "thumb up" are two actions of hand gestures, whose major difference lies in the movement of hands. This information is agnostic from the categorical one-hot encoding of action classes but could be unveiled from the action description. Therefore, utilizing action description in training could potentially benefit representation learning. In this work, we propose a Generative Action-description Prompts (GAP) approach for skeleton-based action recognition. More specifically, we employ a pre-trained large-scale language model as the knowledge engine to automatically generate text descriptions for body parts movements of actions, and propose a multi-modal training scheme by utilizing the text encoder to generate feature vectors for different body parts and supervise the skeleton encoder for action representation learning. Experiments show that our proposed GAP method achieves noticeable improvements over various baseline models without extra computation cost at inference. GAP achieves new state-of-the-arts on popular skeleton-based action recognition benchmarks, including NTU RGB+D, NTU RGB+D 120 and NW-UCLA. The source code is available at https://github.com/MartinXM/GAP.Comment: Accepted by ICCV2

3,3-Dinitro­azetidinium 2-hy­droxy­benzoate

In the title gem-dinitro­azetidinium 2-hy­droxy­benzoate salt, C3H6N3O4 +·C7H5O3 −, the azetidine ring is virtually planar, with a mean deviation from the plane of 0.0242 Å. The dihedral angle between the two nitro groups is 87.5 (1)°

Delayed Feedback Control on a Class of Generalized Gyroscope Systems under Parametric Excitation

AbstractThe nonlinear dynamics of the parametrically excited vibrations of a class of generalized gyroscope systems under delayed feedback control is investigated by the averaging method and simulations in this paper. The influence of feedback control on the stability of the trivial solution and the amplitude of the periodic vibrations is presented based on Routh-Hurwitz criterion and the Levenberg-Marquardt method respectively. It is shown that the stability of the trivial solution can be varied when feedback control and time delay are employed. The amplitudes of periodic solutions can also be modulated greatly by feedback gain and time delay. However, the influence of time delay on amplitudes is periodic. The simulations obtained by numerically integrating the original system are in good agreement with the analytical results