Compatible structures of operads by polarization, their Koszul duality and Manin products

Algebraic structures with multiple copies of a given type of operations interrelated by various compatibility conditions have long being studied in mathematics and mathematical physics. They are broadly referred as linearly compatible, matching, and totally compatible structures. This paper gives a unified approach to these structures in the context of operads. We first generalize the process of polarization for polynomials in invariant theory to the one for operads, leading to the general notion of linearly compatible operads. Refining the polarization by partitioning it into foliations, we obtain a notion of matching operads consolidating those appeared recently from applications of regularity structures, and Volterra integral equations. Distinguished among them is the leveled matching compatibility, which is unique with respect to a fix ordering of the vertices in tree monomials. Equating all matching compatibilities of a given operad leads to the totally compatible operad of this operad. For unary/binary quadratic operads, the linear compatibility and the total compatibility are in Koszul dual to each other, and there is a Koszul self-duality among the matching compatibilities. In particular, the leveled matching compatibility is Koszul self-dual. For binary quadratic operads, these three compatible operads can also be obtained by taking Manin black and white products. For finitely generated binary quadratic operad, we prove that the Koszulity is preserved under taking each of the linear and total compatibilities, as well as the leveled matching compatibility.Comment: 30 page

Jia-Wei-Kai-Xin-San treatment alleviated mild cognitive impairment through anti-inflammatory and antiapoptotic mechanisms in SAMP8 mice

Background. Alleviating mild cognitive impairment (MCI) is crucial to delay the progression of Alzheimer’s disease (AD). Jia-Wei-Kai-Xin-San (JWKXS) is applied for treating AD with MCI. However, the mechanism of JWKXS in the treatment of MCI is unclear. Thus, this study aimed to investigate the effect and mechanism of JWKXS in SAMP8 mice models of MCI. Methods. MCI models were established to examine learning and memory ability and explore the pathomechanisms in brain of SAMP8 mice at 4, 6, and 8 months. The mice were treated for 8 weeks and the effects of JWKXS on MCI were characterized through Morris water maze and HE/Nissl’s/immunohistochemical staining. Its mechanism was predicted by the combination of UPLC-Q-TOF/MS and system pharmacology analysis, further verified with SAMP8 mice, BV2 microglial cells, and PC12 cells. Results. It was found that 4-month-old SAMP8 mice exhibited MCI. Two months of JWKXS treatment improved the learning and memory ability, alleviated the hippocampal tissue and neuron damage. Through network pharmacology, four key signaling pathways were found to be involved in treatment of MCI by JWKXS, including TLR4/NF-κB pathway, NLRP3 inflammasome activation, and intrinsic and extrinsic apoptosis. In vitro and in vivo experiments demonstrated that JWKXS attenuated neuroinflammation by inhibiting microglia activation, suppressing TLR4/NF-κB and NLRP3 inflammasome pathways, and blocking the extrinsic and intrinsic apoptotic pathways leading to neuronal apoptosis suppression in the hippocampus. Conclusion. JWKXS treatment improved the learning and memory ability and conferred neuroprotective effects against MCI by inducing anti-inflammation and antiapoptosis. Limitations. The small sample size and short duration of the intervention limit in-depth investigation of the mechanisms. Future Prospects. This provides a direction for further clarification of the anti-AD mechanism, and provides certain data support for the formulation to move toward clinical practice

Failure Mechanisms and Constitutive Model of Composite Rock under Dynamic Loading

AbstractIn order to investigate the dynamic response characteristics of composite rock with different joint angles, static compression test and dynamic impact test are carried out using WDW-300E servo pressure-testing machine and split Hopkinson pressure bar (SHPB) test system. The dynamic compressive strength, energy dissipation, and failure modes are compared between rock coal (R-C) and coal rock (C-R). Furthermore, a 3D SHPB simulation system is constructed using coupling finite difference method and discrete element method (FDM-DEM) to reproduce the energy evolution and failure modes of composite rock with different joint angles, and the fabric tensor is obtained based on secondary development. Finally, a constitutive model of composite rock is established considering joint angles. The results of experiment, simulation, and theoretical analysis show that for the case of uniaxial compression test, with the increase of joint angle, the peak stress of composite rock shows obvious U-shaped change, and the elastic modulus increases gradually while the peak strain decreases gradually. For the case of dynamic impact test, the peak stress, strain, and energy dissipation values of composite rock decrease first and then increase with the increase of angle, and the elastic modulus of composite rock increases monotonically after a slight fluctuation of 30°. The stress, energy dissipation and elastic modulus of composite rock R-C are larger than that of composite rock C-R. However, the strain value of composite rock R-C is generally less than of composite rock C-R. The failure mode of composite rock with small and large angle is mainly splitting under dynamic impact, and the fracture fragmentation is relatively small with high energy absorption rate, while the fracture fragmentation is mainly shear and splitting mixed failure with low energy absorption rate. The energy accumulation and transformation process inside the composite rock are analyzed by 3D simulation system, and the damage of the composite rock under impact is mainly concentrated on the coal side, and peak values of contact number and contact force with different joint angles are calculated by using fabric tensor. Based on Weibull distribution, a constitutive model of composite rock is constructed considering initial damage and dynamic failure effect, which is in good agreement with experimental and simulation results, verifying the correctness of the constructed model

Effects of Anthraquinones on Immune Responses and Inflammatory Diseases

The anthraquinones (AQs) and derivatives are widely distributed in nature, including plants, fungi, and insects, with effects of anti-inflammation and anti-oxidation, antibacterial and antiviral, anti-osteoporosis, anti-tumor, etc. Inflammation, including acute and chronic, is a comprehensive response to foreign pathogens under a variety of physiological and pathological processes. AQs could attenuate symptoms and tissue damages through anti-inflammatory or immuno-modulatory effects. The review aims to provide a scientific summary of AQs on immune responses under different pathological conditions, such as digestive diseases, respiratory diseases, central nervous system diseases, etc. It is hoped that the present paper will provide ideas for future studies of the immuno-regulatory effect of AQs and the therapeutic potential for drug development and clinical use of AQs and derivatives

Enhancement of the edible quality and shelf life of soft-boiled chicken using MAP

In order to commercialize soft-boiled chicken, a traditional Asian food, this work was performed to evaluate the effect of the packages on the edible quality. Soft-boiled chickens were packaged with air packaging (AP) or modified atmosphere packaging (MAP, MN:100% N2 and MC:30%CO2/70%N2) conditions. Total viable counts reached the acceptable limit of 4.90 Log CFU/g at 1.5, 2.5, and 4 days of storage under AP, MN, and MC, respectively. However, sensory acceptance limits, based on overall acceptance by the professional panelists, were not reached until one day later. The TVB-N content of MAP was lower than that of the AP. The finding indicated that the shelf life of soft-boiled chicken could be extended by two days using MAP with CO2. These findings will provide basic reference for the packaging of cooked meat and also provide information on poultry processing techniques that could be applied at commercial scales

Edible quality of soft‐boiled chicken processing with chilled carcass was better than that of hot‐fresh carcass

Soft‐boiled chicken is widely popular with its flavor and texture. In a traditional view, the edible quality of soft‐boiled chicken producing with hot‐fresh carcass (without any chilled procedure after evisceration) was better than that of chilled carcass. Hot‐fresh groups with 1, 2, or 4 hr and chilled groups with 24, 48, or 60 hr were used to clarify the view in this study. The results indicated that no significant difference in hardness, springiness, cohesiveness of texture profiles and b* value of skin color was observed between each group, although the highest L* value was obtained in hot‐fresh 4 hr group. Higher contents of succinic acid were found in chilled groups when compared to that of hot‐fresh groups, but there was no difference in lactic acid and pH values. Lower contents of adenosine 5′‐monophosphate (AMP), guanosine 5′‐monophosphate (GMP), inosine and hypoxanthine, and higher inosine‐5′‐monophosphate (IMP) (especially for hot‐fresh 1 hr) were observed in hot‐fresh groups. In addition, although no difference in umami amino acids and bitter amino acid was observed between each tested group, higher amounts of Asp, Met, Ile, Leu, Tyr, and Arg were observed in chilled groups, especially for chilled 60 hr. The finding indicated that the traditional view was lack of scientific evidence, and chilled carcass was suitable for soft‐boiled chicken, substituting for the hot‐fresh carcass

Edible quality of soft‐boiled chicken processing with chilled carcass was better than that of hot‐fresh carcass

Soft‐boiled chicken is widely popular with its flavor and texture. In a traditional view, the edible quality of soft‐boiled chicken producing with hot‐fresh carcass (without any chilled procedure after evisceration) was better than that of chilled carcass. Hot‐fresh groups with 1, 2, or 4 hr and chilled groups with 24, 48, or 60 hr were used to clarify the view in this study. The results indicated that no significant difference in hardness, springiness, cohesiveness of texture profiles and b* value of skin color was observed between each group, although the highest L* value was obtained in hot‐fresh 4 hr group. Higher contents of succinic acid were found in chilled groups when compared to that of hot‐fresh groups, but there was no difference in lactic acid and pH values. Lower contents of adenosine 5′‐monophosphate (AMP), guanosine 5′‐monophosphate (GMP), inosine and hypoxanthine, and higher inosine‐5′‐monophosphate (IMP) (especially for hot‐fresh 1 hr) were observed in hot‐fresh groups. In addition, although no difference in umami amino acids and bitter amino acid was observed between each tested group, higher amounts of Asp, Met, Ile, Leu, Tyr, and Arg were observed in chilled groups, especially for chilled 60 hr. The finding indicated that the traditional view was lack of scientific evidence, and chilled carcass was suitable for soft‐boiled chicken, substituting for the hot‐fresh carcass

Multistage coupling water-enabled electric generator with customizable energy output

Abstract Constant water circulation between land, ocean and atmosphere contains great and sustainable energy, which has been successfully employed to generate electricity by the burgeoning water-enabled electric generator. However, water in various forms (e.g. liquid, moisture) is inevitably discharged after one-time use in current single-stage water-enabled electric generators, resulting in the huge waste of inherent energy within water circulation. Herein, a multistage coupling water-enabled electric generator is proposed, which utilizes the internal liquid flow and subsequently generated moisture to produce electricity synchronously, achieving a maximum output power density of ~92 mW m−2 (~11 W m−3). Furthermore, a distributary design for internal water in different forms enables the integration of water-flow-enabled and moisture-diffusion-enabled electricity generation layers into mc-WEG by a “flexible building blocks” strategy. Through a three-stage adjustment process encompassing size control, space optimization, and large-scale integration, the multistage coupling water-enabled electric generator realizes the customized electricity output for diverse electronics. Twenty-two units connected in series can deliver ~10 V and ~280 μA, which can directly lighten a table lamp for 30 min without aforehand capacitor charging. In addition, multistage coupling water-enabled electric generators exhibit excellent flexibility and environmental adaptability, providing a way for the development of water-enabled electric generators