A handlebody link is a union of handlebodies of positive genus embedded in 3-space, which generalises the notion of links in classical knot theory. In this paper, we consider handlebody links with a genus two handlebody and $n-1$ solid tori, $n>1$ . Our main result is the classification of such handlebody links with six crossings or less, up to ambient isotopy.

In this paper, effects of discharge parameters and modulation frequency on the signal of laser-induced fluorescence measurements of ion velocity distribution functions are investigated in the LIF Test Source. A maximum modulation frequency is found for each given set of parameters, beyond which the signal gradually declines. Meanwhile, this maximum modulation frequency occurred consistently at ~1/10 of the theoretical frequency limit and photon counts received by a photomultiplier tube, which indicates that as modulation frequency and the associated per-pulse-excitation-event count decrease, the transition from the macroscopic statistical signal to the microscopic probabilistic signal is a gradual process.

For individual cultures, findings on regulating embryo density by changing the microdrop volume are contradictory. The aim of this study was to investigate the relationship between embryo density and the developmental outcome of day 3 embryos after adjusting covariates. In total, 1196 embryos from 206 couples who had undergone in vitro fertilization treatment were analyzed retrospectively. Three embryo densities were used routinely, i.e. one embryo in a drop (30 μl/embryo), two embryos in a drop (15 μl/embryo) and three embryos in a drop (10 μl/embryo). Embryo quality on day 3 was evaluated, both the cell number of day 3 embryos and the proportion of successful implantations served as endpoints. Maternal age, paternal age, antral follicles and level of anti-Müllerian hormone, type of infertility, controlled ovarian stimulation protocol, length of stimulation, number of retrieved oocytes, number of zygotes (two pronuclei) and insemination type were covariates and adjusted. After adjusting fully for all covariates, the cell number of day 3 embryos was significantly increased by 0.40 (95% CI 0.00, 0.79; P = 0.048) and 0.78 (95% CI 0.02, 1.54; P = 0.044) in the 15 μl/embryo and 10 μl/embryo group separately, compared with the 30 μl/embryo group. The proportions of implanted embryos were 42.1%, 48.7% and 0.0% in the 30 μl/embryo, 15 μl/embryo and 10 μl/embryo groups respectively. There was no statistical significance (P = 0.22) between the 30 μl/embryo group and the 15 μl/embryo group. After adjusting for confounders that were significant in univariate analysis, embryo density was still not associated with day 3 embryo implantation potential (P > 0.05). In a 30-μl microdrop, culturing embryos with an embryo density of both 15 and 10 μl/embryo increased the cell number of day 3 embryos, which did not benefit embryo implanting potential, compared with individual culture of 30 μl/embryo.

In this paper, we present explicit and computable error bounds for the asymptotic expansions of the Hermite polynomials with Plancherel–Rotach scale. Three cases, depending on whether the scaled variable lies in the outer or oscillatory interval, or it is the turning point, are considered separately. We introduce the ‘branch cut’ technique to express the error terms as integrals on the contour taken as the one-sided limit of curves approaching the branch cut. This new technique enables us to derive simple error bounds in terms of elementary functions. We also provide recursive procedures for the computation of the coefficients appearing in the asymptotic expansions.

Climbing robots have broad application prospects in aerospace equipment inspection, forest farm monitoring, and pipeline maintenance. Different types of climbing robots in existing research have different advantages. However, the self-adaptability and stability have not been achieved at the same time. In order to realize the self-adaptability of holding and climbing stability, this work proposes a new type of climbing robot under the premise of minimizing the driving source. The robot realizes stable multifinger holding and wheeled movement through two motors. At the same time, the robot has two different working modes, namely pole climbing and ground crawling. The holding adaptability and climbing stability are realized by underactuated holding mechanism and model reference adaptive controller (MRAC). On the basis of model design and parameter analysis, a prototype of the climbing robot is built. Experiments prove that the proposed climbing robot has the ability to stably climb poles of different shapes. The holding and climbing stability, self-adaptability, and climbing and crawling speed of the proposed climbing robot are verified by experiments.

The absence of observable innovation data for a firm often leads us to exclude or classify these firms as non-innovators. We assess the reliability of six methods for dealing with unreported innovation using several different counterfactuals for firms without reported R&D or patents. These tests reveal that excluding firms without observable innovation or imputing them as zero innovators and including a dummy variable can lead to biased parameter estimates for observed innovation and other explanatory variables. Excluding firms without patents is especially problematic, leading to false-positive results in empirical tests. Our tests suggest using multiple imputation to handle unreported innovation.

Parasitoid wasps are key agents for controlling insect pests in integrated pest management programs. Although many studies have revealed that the behavior of parasitic wasps can be influenced by insecticides, the strategies of patch time allocation and oviposition have received less attention. In the present study, we forced the endoparasitoid Meteorus pulchricornis to phoxim exposure at the LC30 and tested the foraging behavior within patches with different densities of the host, the larvae of the tobacco cutworm Spodoptera litura. The results showed that phoxim treatment can significantly increase the patch-leaving tendency of female wasps, while host density had no impact. The number of oviposition and the number of previous patch visits also significantly influenced the patch time allocation decisions. The occurrence of oviposition behavior was negatively affected by phoxim exposure; however, progeny production was similar among patches with different host densities. Phoxim exposure shaped the offspring fitness correlates, including longer durations from cocoon to adult wasps, smaller body size, and shorter longevity. The findings of the present study highlight the sublethal effects that reduce the patch residence time and the fitness of parasitoid offspring, suggesting that the application of phoxim in association with M. pulchricornis should be carefully schemed in agroecosystems.

Nutritional Risk Screening index is a standard tool to assess nutritional risk, but epidemiological data are scarce on controlling nutritional status (CONUT) as a prognostic marker in acute haemorrhagic stroke (AHS). We aimed to explore whether the CONUT may predict a 3-month functional outcome in AHS. In total, 349 Chinese patients with incident AHS were consecutively recruited, and their malnutrition risks were determined using a high CONUT score of ≥ 2. The cohort patients were divided into high-CONUT (≥ 2) and low-CONUT (< 2) groups, and primary outcomes were a poor functional prognosis defined as the modified Rankin Scale (mRS) score of ≥ 3 at post-discharge for 3 months. Odds ratios (OR) with 95 % confidence intervals (CI) for the poor functional prognosis at post-discharge were estimated by using a logistic analysis with additional adjustments for unbalanced variables between the high-CONUT and low-CONUT groups. A total of 328 patients (60·38 ± 12·83 years; 66·77 % male) completed the mRS assessment at post-discharge for 3 months, with 172 patients at malnutrition risk at admission and 104 patients with a poor prognosis. The levels of total cholesterol and total lymphocyte counts were significantly lower in high-CONUT patients than low-CONUT patients (P = 0·012 and < 0·001, respectively). At 3-month post discharge, there was a greater risk for the poor outcome in the high-CONUT compared with the low-CONUT patients at admission (OR: 2·32, 95 % CI: 1·28, 4·17). High-CONUT scores independently predict a 3-month poor prognosis in AHS, which helps to identify those who need additional nutritional managements.

Empirical evidence suggests that close to 100 million women are “missing” worldwide. We revisit the empirical evidence for China, the country with the most missing women. Nearly ten million girls born in the 1980s and 1990s who were “missing” according to earlier census data can be found again in the 2010 population census. We discuss two possible explanations for the re-emergence of these formerly missing girls: the delayed registration of girls owing to economic reasons, and the response to amendments to the Chinese Statistics Law in 2009 and policy changes in the 2010 population census. Using the most recent statistics, we document patterns of the underreporting of women over time and across regions as well as explore the basic determinants of underreporting of women. Important policy challenges remain. For the unregistered children, the lack of access to public services will increase their vulnerability and adversely affect their quality of life.

Time-resolved particle image velocimetry (TR-PIV) is employed to investigate the vortex dynamics around the slat cove of a 30P30N multi-element airfoil at a fixed geometric angle of attack of 4 ° within the stowed chord Reynolds number range of 9.3 × 103 ≤ Rec ≤ 5.2 × 104. The results link the frequency properties to the vortex shedding patterns of the slat cusp shear layer. With increasing Rec, three types of vortex dynamics are identified: (i) no vortex shedding from the slat cusp shear layer and the absence of hydrodynamic feedback in the slat cove (9.3 × 103 ≤ Rec ≤ 1.27 × 104); (ii) impingement of shed vortices on the underside of the slat trailing edge at a steady location (1.38 × 104 ≤ Rec ≤ 1.83 × 104); (iii) impingement of shed vortices on the underside of the slat trailing edge at unsteady locations (2.41 × 104 ≤ Rec ≤ 5.2 × 104). The fluctuations generated by shed vortices link the slat cusp and trailing edge by the hydrodynamic feedback in the slat cove. Besides the fundamental frequency and its harmonics, subharmonics and fractional harmonics occur to the slat cusp shear layer in the Rec range of 2.41 × 104–5.2 × 104. Subharmonics make the impingement locations of shed vortices unsteady. Fractional harmonics trigger the secondary instability of the braid region between two consecutive vortices to generate more shed vortices. The vortex dynamics in this Rec range is found to persist to Rec ~ 106.

We study the pricing of timer options in a class of stochastic volatility models, where the volatility is driven by two diffusions—one fast mean-reverting and the other slowly varying. Employing singular and regular perturbation techniques, full second-order asymptotics of the option price are established. In addition, we investigate an implied volatility in terms of effective maturity for the timer options, and derive its second-order expansion based on our pricing asymptotics. A numerical experiment shows that the price approximation formula has a high level of accuracy, and the implied volatility in terms of its effective maturity is illustrated.

Time-resolved particle image velocimetry and hydrogen bubble visualization are used to investigate the wake-induced transition of a 30P30N multi-element airfoil at a fixed angle of attack of 4° within the stowed chord Reynolds-number range of 1.38 × 104 to 3.05 × 104. A special transition routine, strongly affected by the slat wake, is observed in the confluent boundary layer over the 30P30N airfoil. In particular, the effects of slat-wake-triggered double-secondary vortices on the whole transition process are explored in detail. At the initial transition stage, the strong slat-wake disturbances penetrate the boundary layer of the main element and are then amplified by double-exponential growth to generate double-secondary vortices. Compared to the scenarios of simplified geometries (He et al., J. Fluid Mech., vol. 718, 2013, pp. 116–130; He & Wang, Phys. Fluids, vol. 27, 2015, 024106), the double-exponential growth provides stronger fluctuations for the transition. At the intermediate transition stage, the wake disturbances trigger the three-dimensional destabilization of these secondary vortices by direct injection or indirect induction, leading to Λ vortices. The spanwise wavelength of the consequent Λ vortices is therefore locked on by the wake disturbances. At the late transition stage, the Λ vortices evolve into hairpin vortex packets and finally contribute to an attached turbulent boundary layer above the main element. Throughout the transition process, no obvious separation occurs in the mean flow above the main element, revealing potential aerodynamic benefits.

We investigated the effects of botulinum toxin on gait in Parkinson’s disease (PD) patients with foot dystonia. Six patients underwent onabotulinum toxin A injection and were assessed by Burke–Fahn–Marsden Dystonia Rating Scale (BFMDRS), visual analog scale (VAS) of pain, Timed Up and Go (TUG), Berg Balance Test (BBT), and 3D gait analysis at baseline, 1 month, and 3 months. BFMDRS (p = 0.002), VAS (p = 0.024), TUG (p = 0.028), and BBT (p = 0.034) were improved. Foot pressures at Toe 1 (p = 0.028) and Midfoot (p = 0.018) were reduced, indicating botulinum toxin’s effects in alleviating the dystonia severity and pain and improving foot pressures during walking in PD.