This paper proves the energy equality for distributional solutions to fractional Navier-Stokes equations, which gives a new proof and covers the classical result of Galdi [Proc. Amer. Math. Soc. 147 (2019), 785–792].

This paper presents a feedforward compensation approach for musculoskeletal systems (MSs). Compared with traditional rigid robots, human arms have the advantages of flexibility and safety in operation in unstructured environments. However, the influence of external unknown disturbances, inner friction effects, and dynamic uncertainties of the MS makes it difficult to model and practically apply. In order to reduce the inner friction effects of the hardware platform and the over-relaxation/tension of the cable-pull drive, a feedforward friction compensation method for the cable-pulled artificial muscle unit is proposed. The method analyzes the friction causes of the hardware structure and establishes a mapping network relationship between the joint variables and the muscle force error in the muscle space. The experimental results show that the method can effectively improve the control accuracy and reduce the artificial muscle over-relaxation/tension instability.

The sequential occurrence of three layers of smooth muscle layers (SML) in human embryos and fetus is not known. Here, we investigated the process of gut SML development in human embryos and fetuses and compared the morphology of SML in fetuses and neonates. The H&E, Masson trichrome staining, and Immunohistochemistry were conducted on 6–12 gestation week human embryos and fetuses and on normal neonatal intestine. We showed that no lumen was seen in 6–7th gestation week embryonic gut, neither gut wall nor SML was developed in this period. In 8–9th gestation week embryonic and fetal gut, primitive inner circular SML (IC-SML) was identified in a narrow and discontinuous gut lumen with some vacuoles. In 10th gestation week fetal gut, the outer longitudinal SML (OL-SML) in gut wall was clearly identifiable, both the inner and outer SML expressed α-SMA. In 11–12th gestation week fetal gut, in addition to the IC-SML and OL-SML, the muscularis mucosae started to develop as revealed by α-SMA immune-reactivity beneath the developing mucosal epithelial layer. Comparing with the gut of fetuses of 11–12th week of gestation, the muscularis mucosae, IC-SML, and OL-SML of neonatal intestine displayed different morphology, including branching into glands of lamina propria in mucosa and increased thickness. In conclusions, in the human developing gut between week-8 to week-12 of gestation, the IC-SML develops and forms at week-8, followed by the formation of OL-SML at week-10, and the muscularis mucosae develops and forms last at week-12.

Aiming at the problem of low accuracy of robot joint fault diagnosis, a fault diagnosis method of robot joint based on BP neural network is designed. In this paper, the UR10 robot is taken as the research object, and the end pose data of the robot are collected in real time. By injecting different joint errors and changing the sampling frequency, the joint fault database is collected and established, and the BP neural network is used for training to obtain the robot neural network fault diagnosis model. The fault diagnosis model can output the joint fault of the input end pose data. And we analyzed the influence of different joint angle errors and different training sets on the accuracy of joint fault diagnosis of the robot. The results show that when the sampling frequency is 250 Hz, the simulation result of joint fault diagnosis accuracy with the fault degree of 0.5° is 99.17%, and the experimental result is 97.87%. Compared with traditional data-driven methods, it has higher accuracy and diagnostic efficiency, and compared with existing machine learning methods, it also achieves a high accuracy while reducing the network complexity. The effectiveness of the BP neural network robot joint fault diagnosis method is verified by experiments.

This work aims to investigate experimentally the effect of the Reynolds number Re, based on the nozzle diameter D, on jet mixing manipulation using an unsteady radial minijet. A novel artificial intelligence (AI) control system has been developed to manipulate the jet over Re = 5800–40 000. The system may optimize simultaneously the control law and a time-independent parameter, which dictate the actuation ON/OFF states and amplitude, respectively. The control parameters include the mass flow rate, excitation frequency and diameter ratios (Cm, fe/f0 and d/D) of the minijet to the main jet as well as the duty cycle (α) of minijet injection. Jet mixing is quantified using Ke and K0, where K is the decay rate of the jet centreline mean velocity, and subscripts e and 0 denote the manipulated and unforced jets, respectively. It has been found that the maximum Ke achievable does not vary with Re. Scaling analysis of the huge volume of experimental data obtained from the AI system reveals that the relationship Ke = g1 (Cm, fe/f0, α, d/D, Re, K0) may be reduced to Ke/K0 = g2 $(\zeta )$, where g1 and g2 are different functions and the scaling factor $\zeta = ({C_m}/\alpha ){(D/d)^{1 - n}}(1/Re){({f_e}/{f_{e,opt}})^m}$, m and 1 − n are the power indices, and subscript opt denotes the value at which Ke is maximum. The scaling law is discussed in detail, along with the physical meanings of the dimensionless parameters Ke/K0, ζ, $({C_m}/\alpha ){(D/d)^{1 - n}}(1/Re)$ and ${({f_e}/{f_{e,opt}})^m}$.

Developmental signals and environmental stresses regulate carbon distribution in the vegetative and reproductive organs of plants and affect seed yield. Cleistogenes songorica is a xerophytic grass with great potential application value in ecological restoration. However, how carbohydrate transport and distribution during grain filling affect the seed yield of C. songorica under water stress is not clear. The present study showed that the soluble sugar and starch contents of cleistogamous (CL) spikes and chasmogamous (CH) spikes were significantly higher at the milk stage, which was attributed to a significantly higher seed number and seed yield per spike under water stress conditions than under well-watered conditions (P < 0.01). RNA-seq data revealed a total of 54,525 differentially expressed genes (DEGs) under water stress conditions, but only 3744 DEGs were shared among all comparison groups. Weighted gene co-expression network analysis showed that the transport and distribution of carbohydrates were regulated by ABA-responsive genes (CsABA8OX1_1, CsABA8OX1_2, CsABA8OX2_1, CsABA8OX2_2, CsNCED3, CsNCED1_1, CsNCED1_2 and CsNCED4_1) and sugar transport and starch synthesis genes (CsSUS1, CsSUS2, CsSUS3, CsAGP1, CsAGP4, CsAGP5, CsSSS1 and CsSBE5) under water stress conditions. These genes jointly regulated carbohydrate remobilization in sources (stems, leaves and sheaths) to promote grain filling and improve seed yield. The present study helped to clarify the phenotypic, metabolic and transcriptional response mechanisms of vegetative organs, such as stems and leaves, and reproductive organs, such as CL spikes and CH spikes, to promote carbohydrate redistribution under water stress, and it provides theoretical guidance for improving seed yields.

Thyroid cancer (TC) incidence has increased greatly during the past decades with a few established risk factors, while no study is available that has assessed the association of the Chinese Health Dietary Index (CHDI) with TC. We conducted a 1:1 matched case–control study in two hospitals in Shanghai, China. Diet-quality scores were calculated according to CHDI using a validated and reliable FFQ. Conditional logistic regression analysis and restricted cubic spline analysis were used to reveal potential associations between CHDI score and TC risk. A total of 414 pairs of historically confirmed TC patients and healthy controls were recruited from November 2012 to December 2015. The total score of cases and controls were 67·5 and 72·8, respectively (P < 0·001). The median score of total vegetables, fruit, diary products, dark green and orange vegetables, fish, shellfish and mollusk, soyabean, whole grains, dry bean and tuber in cases was significantly lower than those in controls. Compared with the reference group (≤60 points), the average (60–80 points) and high (≥80 points) levels of the CHDI score were associated with a reduced risk of TC (OR: 0·40, 95 % CI 0·26, 0·63 for 60–80 points; OR: 0·22, 95 % CI 0·12, 0·38 for ≥80 points). In age-stratified analyses, the favourable association remained significant among participants who are younger than 50 years old. Our data suggested that high diet quality as determined by CHDI was associated with lower risk of TC.

Thanks to the ability to perform imaging and manipulation at the nanoscale, atomic force microscopy (AFM) has been widely used in biology, materials, chemistry, and other fields. However, as common error sources, vertical drift and illusory slope severely impair AFM imaging quality. To address this issue, this paper proposes a robust algorithm to synchronously correct the image distortion caused by vertical drift and slope, thus achieving accurate morphology characterization. Specifically, to eliminate the damage of abnormal points and feature areas on the correction accuracy, the laser spot voltage error acquired in the AFM scanning process is first utilized to preprocess the morphology height data of the sample, so as to obtain the refined alternative data suitable for line fitting. Subsequently, this paper proposes a novel line fitting algorithm based on sparse sample consensus, which accurately simulates vertical drift and slope in the cross-sectional profile of the topographic image, thereby achieving effective correction of the image distortion. In the experiments and applications, a nanoscale optical grating sample and a biological cell sample are adopted to perform topography imaging and distortion correction, so as to verify the ability of the proposed algorithm to promote AFM imaging quality.

To determine the association between hearing loss and environmental Pb, Cd and Se exposure, a total of 1503 American adults from National Health and Nutrition Examination Survey (NHANES) (2011–2012) were assessed. The average of four audiometric frequencies (0·5, 1, 2 and 4 kHz) was used to identify speech-frequency hearing loss (SFHL), while the average of 3 audiometric frequencies (3, 4 and 6 kHz) was used to identify high-frequency hearing loss (HFHL). HFHL adjusted OR determined by comparing the highest and lowest blood Pb and Cd quartiles were 1·98 (95 % CI: 1·27, 3·10) and 1·81 (95 % CI: 1·13, 2·90), respectively. SFHL was significantly associated with blood Cd with the OR = 2·42 for the highest quartile. When further stratified by age, this association appeared to be limited to adults aged 35–52 years. After stratified by gender, except for Pb and Cd, we observed that blood Se showed a dose-dependent association with SFHL in men. In women, only Cd showed a dose-dependent association with speech and high-frequency hearing loss. Hearing loss was positively associated with blood levels of Pb and Cd. Additionally, our study provided novel evidence suggesting that excessive Se supplement would increase SFHL risk in men.

In this paper, we study a dissipative systems modelling electrohydrodynamics in incompressible viscous fluids. The system consists of the Navier–Stokes equations coupled with a classical Poisson–Nernst–Planck equations. In the three-dimensional case, we establish a global regularity criteria in terms of the middle eigenvalue of the strain tensor in the framework of the anisotropic Lorentz spaces for local smooth solution. The proof relies on the identity for entropy growth introduced by Miller in the Arch. Ration. Mech. Anal. [16].

The aim of the present study was to compare the rate of preterm birth (PTB) and growth from birth to 18 years between twins conceived by in vitro fertilization (IVF) and twins conceived by spontaneous conception (SC) in mainland China. The retrospective cohort study included 1164 twins resulting from IVF and 25,654 twins conceived spontaneously, of which 494 from IVF and 6338 from SC were opposite-sex twins. PTB and low birth weight (LBW), and growth, including length/height and weight, were compared between the two groups at five stages: infancy (0 year), toddler period (1–2 years), preschool (3–5 years), primary or elementary school (6–11 years), and adolescence (10–18 years). Few statistically significant differences were found for LBW and growth between the two groups after adjusting for PTB and other confounders. Twins born by IVF faced an increased risk of PTB compared with those born by SC (adjusted odds ratio [aOR] 8.21, 95% confidence interval [CI] [3.19, 21.13], p < .001 in all twins and aOR 10.12, 95% CI [2.32, 44.04], p = .002 in opposite-sex twins). Twins born by IVF experienced a similar growth at five stages (0–18 years old) when compared with those born by SC. PTB risk, however, is significantly higher for twins conceived by IVF than those conceived by SC.

In clinical environments, orthopedic implants are associated with a risk of infection during implantation. However, the growth paths of bacteria on metal, which is nontransparent, are difficult to observe. In this study, we visualized the DH5-alpha Escherichia coli bacterial growth path on the surface of magnesium by using scanning electron microscope (SEM) images and constructed a convolutional neural network-based artificial intelligence (AI) system to identify metal surfaces, bacteria, and its generated products to grade the growth stage of the bacteria implanted on the magnesium. The detection result of the E. coli growth stage by the AI system was close to that manually marked by experts, and it may greatly accelerate the investigation of the bacterial growth process in various types of metallic material.

DNA methylation is one of the most important epigenetic modifications in breast cancer (BC) development, and long-term dietary habits can alter DNA methylation. Cadherin-4 (CDH4, a member of the cadherin family) encodes Ca2+-dependent cell–cell adhesion glycoproteins. We conducted a case–control study (380 newly diagnosed BC and 439 cancer-free controls) to explore the relationship of CDH4 methylation in peripheral blood leukocyte DNA (PBL DNA), as well as its combined and interactive effects with dietary factors on BC risk. A case-only study (335 newly diagnosed BC) was conducted to analyse the association between CDH4 methylation in breast tissue DNA and dietary factors. CDH4 methylation was detected using quantitative methylation-specific PCR. Unconditional logistic regressions were used to analyse the association of CDH4 methylation in PBL DNA and BC risk. Cross-over analysis and unconditional logistic regression were used to calculate the combined and interactive effects between CDH4 methylation in PBL DNA and dietary factors in BC. CDH4 hypermethylation was significantly associated with increased BC risk in PBL DNA (ORadjusted (ORadj) = 2·70, (95 % CI 1·90, 3·83), P < 0·001). CDH4 hypermethylation also showed significant combined effects with the consumption of vegetables (ORadj = 4·33, (95 % CI 2·63, 7·10)), allium vegetables (ORadj = 7·00, (95 % CI 4·17, 11·77)), fish (ORadj = 7·92, (95 % CI 3·79, 16·53)), milk (ORadj = 6·30, (95 % CI 3·41, 11·66)), overnight food (ORadj = 4·63, (95 % CI 2·69, 7·99)), pork (ORadj = 5·59, (95 % CI 2·94, 10·62)) and physical activity (ORadj = 4·72, (95 % CI 2·87, 7·76)). Moreover, consuming milk was significantly related with decreased risk of CDH4 methylation (OR = 0·61, (95 % CI 0·38, 0·99)) in breast tissue. Our findings may provide direct guidance on the dietary intake for specific methylated carriers to decrease their risk for developing BC.

We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$-insertion is related to Gromov-Witten theory of the total space of ${\mathcal O}_X(-D)$ and local Gromov-Witten theory of D.

Specializing to $(X,D)=(S,E)$ for S a del Pezzo surface or a rational elliptic surface and E a smooth anticanonical divisor, we show that maximal contact Gromov-Witten theory of $(S,E)$ is determined by the Gromov-Witten theory of the Calabi-Yau 3-fold ${\mathcal O}_S(-E)$ and the stationary Gromov-Witten theory of the elliptic curve E.

Specializing further to $S={\mathbb P}^2$, we prove that higher genus generating series of maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ are quasimodular and satisfy a holomorphic anomaly equation. The proof combines the quasimodularity results and the holomorphic anomaly equations previously known for local ${\mathbb P}^2$ and the elliptic curve.

Furthermore, using the connection between maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ and Betti numbers of moduli spaces of semistable one-dimensional sheaves on ${\mathbb P}^2$, we obtain a proof of the quasimodularity and holomorphic anomaly equation predicted in the physics literature for the refined topological string free energy of local ${\mathbb P}^2$ in the Nekrasov-Shatashvili limit.

The objective of this study was to analyze differences in birth weight and overweight/obesity in a Shanghai twin cohort. We also wanted to study their association and explore possible risk factors for the discordance of overweight/obesity within twins. This was an internal case–control study designed for twins. The 2012 Shanghai Twin Registration System baseline survey data of a total of 3417 twin pairs were statistically analyzed using SPSS22 software. Results show that the body mass index (BMI) of the Shanghai twin population increased with age. Twins with a high birth weight had a higher BMI and a higher rate of overweight and obesity; 0- to 6-year-old twins, male twins and dizygotic (DZ) twins had higher rates of overweight/obesity than other groups. The greater the discordant birth weight rate of twins, the more obvious the difference in BMI (p < .05). There was a significant difference in overweight/obesity between twins with a relative difference of birth weight ≥15% in DZ twins (p < .05). DZ twins, male twins and 0- to 6-year-old twins were more likely to be discordant in overweight/obese than others. The discordant birth weight within twins was not a risk factor for discordant overweight/obesity. However, attention should be paid to childhood obesity, and appropriate interventions should be made at the appropriate time. Genetics may play an important role in the occurrence and development of overweight/obesity. In conclusion, discordant growth and development in the uterus early in life may not lead to discordant weight development in the future.

When biological samples are first exposed to electrons in cryo-electron microcopy (cryo-EM), proteins exhibit a rapid ‘burst’ phase of beam-induced motion that cannot be corrected with software. This lowers the quality of the initial frames, which are the least damaged by the electrons. Hence, they are commonly excluded or down-weighted during data processing, reducing the undamaged signal and the resolution in the reconstruction. By decreasing the cooling rate during sample preparation, either with a cooling-rate gradient or by increasing the freezing temperature, we show that the quality of the initial frames for various protein and virus samples can be recovered. Incorporation of the initial frames in the reconstruction increases the resolution by an amount equivalent to using ~60% more data. Moreover, these frames preserve the high-quality cryo-EM densities of radiation-sensitive residues, which is often damaged or very weak in canonical three-dimensional reconstruction. The improved freezing conditions can be easily achieved using existing devices and enhance the overall quality of cryo-EM structures.

In this paper, the generation of relativistic electron mirrors (REMs) and the reflection of an ultra-short laser off this mirrors are discussed, applying two-dimensional particle-in-cell (2D-PIC) simulations. REMs with ultra-high acceleration and expanding velocity can be produced from a solid nanofoil illuminated normally by an ultra-intense femtosecond laser pulse with a sharp rising edge. Chirped attosecond pulse can be produced through the reflection of a counter-propagating probe laser off the accelerating REM. In the electron moving frame, the plasma frequency of the REM keeps decreasing due to its rapidly expanding. The laser frequency, on the contrary, keeps increasing due to the acceleration of REM and the relativistic Doppler shift from the lab frame to the electron moving frame. Within an ultra-short time interval, the two frequencies will be equal in the electron moving frame, which leads the resonance between laser and REM. The reflected radiation near this interval and the corresponding spectra will be amplified due to the resonance. Through adjusting the arriving time of the probe laser, certain part of the reflected field could be selectively amplified or depressed, leading to the selectively adjusting of the corresponding spectra.