On 4n4n-dimensional neither pointed nor semisimple Hopf algebras and the associated weak Hopf algebras

For a class of neither pointed nor semisimple Hopf algebras $H_{4n}$ of dimension $4n$, it is shown that they are quasi-triangular, which universal $R$-matrices are described. The corresponding weak Hopf algebras $\mathfrak{w}H_{4n}$ and their representations are constructed. Finally, their duality and their Green rings are established by generators and relations explicitly. It turns out that the Green rings of the associated weak Hopf algebras are not commutative even if the Green rings of $H_{4n}$ are commutative.Comment: 18 page

Molecular Dynamics Investigations Suggest a Non-specific Recognition Strategy of 14-3-3σ Protein by Tweezer: Implication for the Inhibition Mechanism

The supramolecular complex formed between protein and designed molecule has become one of the most efficient ways to modify protein functions. As one of the more well-studied model systems, 14-3-3 family proteins play an important role in regulating intracellular signaling pathways via protein-protein interactions. In this work, we selected 14-3-3σ as the target protein. Molecular dynamics simulations and binding free energy calculations were applied to identify the possible binding sites and understand its recognition ability of the supramolecular inhibitor, the tweezer molecule (CLR01). On the basis of our simulation, major interactions between lysine residues and CLR01 come from the van der Waals interactions between the long alkyl chain of lysine and the cavity formed by the norbornadiene and benzene rings of the inhibitor. Apart from K214, which was found to be crystallized with this inhibitor, other lysine sites have also shown their abilities to form inclusion complexes with the inhibitor. Such non-specific recognition features of CLR01 against 14-3-3σ can be used in the modification of protein functions via supramolecular chemistry

Generalized core inverses of matrices

[EN] n this paper, we introduce two new generalized inverses of matrices, namely, the -core inverse and the (j, m)-core inverse. The -core inverse of a complex matrix extends the notions of the core inverse defined by Baksalary and Trenkler [1] and the core-EP inverse defined by Manjunatha Prasad and Mohana [10]. The (j, m)-core inverse of a complex matrix extends the notions of the core inverse and the DMP-inverse defined by Malik and Thome [9]. Moreover, the formulae and properties of these two new concepts are investigated by using matrix decompositions and matrix powers.This research is supported by the National Natural Science Foundation of China (NO. 11771076 and No. 11471186). The first author is grateful to China Scholarship Council for giving him a purse for his further study in Universitat Politecnica de Valencia, Spain.Xu, S.; Chen, J.; Benítez López, J.; Wang, D. (2019). Generalized core inverses of matrices. Miskolc Mathematical Notes (Online). 20(1):565-584. https://doi.org/10.18514/MMN.2019.2594S56558420

GPU Accelerated Quantum Virtual Screening: Application for the Natural Inhibitors of New Dehli Metalloprotein (NDM-1)

Quantum mechanical approaches for the massive computation on large biological system such as virtual screening in drug design and development have presented a challenge to computational chemists for many years. In this study, we demonstrated that by taking advantage of rapid growth of GPU-based hardware and software (i.e., teraChem), it is feasible to perform virtual screening of a refined chemical library at quantum mechanical level in order to identify the lead compounds with improved accuracy, especially for the drug targets such as metalloproteins in which significant charge transfer and polarization occur amongst the metal ions and their coordinated amino acids. Our calculations predicted four nature compounds (i.e., Curcumin, Catechin, menthol, and Ferulic acid) as the suitable inhibitors for antibiotics resistance against New Delhi Metallo-β-lactamase-1 (NDM-1). Molecular orbitals (MOs) of the QM region of metal ions and their coordinated residues indicate that the bridged hydroxide ion delocalized the electron over the Zn-OH-Zn group at HOMO, different from MOs when the OH− is not presented in NDM-1. This indicates that the bridged hydroxide ion plays an important role in the design of antibiotics and other inhibitors targeting the metalloproteins

Properties of GH4169 Superalloy Characterized by Nonlinear Ultrasonic Waves

The nonlinear wave motion equation is solved by the perturbation method. The nonlinear ultrasonic coefficients β and δ are related to the fundamental and harmonic amplitudes. The nonlinear ultrasonic testing system is used to detect received signals during tensile testing and bending fatigue testing of GH4169 superalloy. The results show that the curves of nonlinear ultrasonic parameters as a function of tensile stress or fatigue life are approximately saddle. There are two stages in relationship curves of relative nonlinear coefficients β′ and δ′ versus stress and fatigue life. The relative nonlinear coefficients β′ and δ′ increase with tensile stress when tensile stress is lower than 65.8% of the yield strength, and they decrease with tensile stress when tensile stress is higher than 65.8% of the yield strength. The nonlinear coefficients have the extreme values at 53.3% of fatigue life. For the second order relative nonlinear coefficient β′, there is good agreement between the experimental data and the comprehensive model. For the third order relative nonlinear coefficient δ′, however, the experiment data does not accord with the theoretical model

Interactions between curcumin and human salt-induced kinase 3 elucidated from computational tools and experimental methods

Natural products are widely used for treating mitochondrial dysfunction-related diseases and cancers. Curcumin, a well-known natural product, can be potentially used to treat cancer. Human salt-induced kinase 3 (SIK3) is one of the target proteins for curcumin. However, the interactions between curcumin and human SIK3 have not yet been investigated in detail. In this study, we studied the binding models for the interactions between curcumin and human SIK3 using computational tools such as homology modeling, molecular docking, molecular dynamics simulations, and binding free energy calculations. The open activity loop conformation of SIK3 with the ketoenol form of curcumin was the optimal binding model. The I72, V80, A93, Y144, A145, and L195 residues played a key role for curcumin binding with human SIK3. The interactions between curcumin and human SIK3 were also investigated using the kinase assay. Moreover, curcumin exhibited an IC50 (half-maximal inhibitory concentration) value of 131 nM, and it showed significant antiproliferative activities of 9.62 ± 0.33 µM and 72.37 ± 0.37 µM against the MCF-7 and MDA-MB-23 cell lines, respectively. This study provides detailed information on the binding of curcumin with human SIK3 and may facilitate the design of novel salt-inducible kinases inhibitors

Evaluation of Pseudo-Haptic Interactions with Soft Objects in Virtual Environments

This paper proposes a pseudo-haptic feedback method conveying simulated soft surface stiffness information through a visual interface. The method exploits a combination of two feedback techniques, namely visual feedback of soft surface deformation and control of the indenter avatar speed, to convey stiffness information of a simulated surface of a soft object in virtual environments. The proposed method was effective in distinguishing different sizes of virtual hard nodules integrated into the simulated soft bodies. To further improve the interactive experience, the approach was extended creating a multi-point pseudo-haptic feedback system. A comparison with regards to (a) nodule detection sensitivity and (b) elapsed time as performance indicators in hard nodule detection experiments to a tablet computer incorporating vibration feedback was conducted. The multi-point pseudo-haptic interaction is shown to be more time-efficient than the single-point pseudo-haptic interaction. It is noted that multi-point pseudo-haptic feedback performs similarly well when compared to a vibration-based feedback method based on both performance measures elapsed time and nodule detection sensitivity. This proves that the proposed method can be used to convey detailed haptic information for virtual environmental tasks, even subtle ones, using either a computer mouse or a pressure sensitive device as an input device. This pseudo-haptic feedback method provides an opportunity for low-cost simulation of objects with soft surfaces and hard inclusions, as, for example, occurring in ever more realistic video games with increasing emphasis on interaction with the physical environment and minimally invasive surgery in the form of soft tissue organs with embedded cancer nodules. Hence, the method can be used in many low-budget applications where haptic sensation is required, such as surgeon training or video games, either using desktop computers or portable devices, showing reasonably high fidelity in conveying stiffness perception to the user

Crack Assessment of Wheel Hubs via an Ultrasonic Transducer and Industrial Robot

Crack assessment when making fitness-for-service decisions requires a thorough examination of crack location and size in critical areas. An ultrasonic transducer is used for such assessments, but traditional methods cannot cope with complex rotators, such as wheel hubs. We present a model of robot-assisted crack growth assessment in wheel hubs. We integrate a six-degrees-of-freedom (DOF) industrial robot and a turntable to form a robot-assisted ultrasonic testing (UT) system that does not use traditional UT equipment. Ultrasonic beams are focused at certain depths appropriate for achieving maximum sensitivity. We quantitatively analysed wheel hubs with longitudinal and transverse series of pre-cracks, and concluded that our system autonomously detected cracks