We study several parameters of a random Bienaymé–Galton–Watson tree $T_n$ of size $n$ defined in terms of an offspring distribution $\xi$ with mean $1$ and nonzero finite variance $\sigma ^2$ . Let $f(s)=\mathbb{E}\{s^\xi \}$ be the generating function of the random variable $\xi$ . We show that the independence number is in probability asymptotic to $qn$ , where $q$ is the unique solution to $q = f(1-q)$ . One of the many algorithms for finding the largest independent set of nodes uses a notion of repeated peeling away of all leaves and their parents. The number of rounds of peeling is shown to be in probability asymptotic to $\log n/\log (1/f'(1-q))$ . Finally, we study a related parameter which we call the leaf-height. Also sometimes called the protection number, this is the maximal shortest path length between any node and a leaf in its subtree. If $p_1 = \mathbb{P}\{\xi =1\}\gt 0$ , then we show that the maximum leaf-height over all nodes in $T_n$ is in probability asymptotic to $\log n/\log (1/p_1)$ . If $p_1 = 0$ and $\kappa$ is the first integer $i\gt 1$ with $\mathbb{P}\{\xi =i\}\gt 0$ , then the leaf-height is in probability asymptotic to $\log _\kappa \log n$ .

The incidence of scarlet fever has increased dramatically in recent years in Chongqing, China, but there has no effective method to forecast it. This study aimed to develop a forecasting model of the incidence of scarlet fever using a seasonal autoregressive integrated moving average (SARIMA) model. Monthly scarlet fever data between 2011 and 2019 in Chongqing, China were retrieved from the Notifiable Infectious Disease Surveillance System. From 2011 to 2019, a total of 5073 scarlet fever cases were reported in Chongqing, the male-to-female ratio was 1.44:1, children aged 3–9 years old accounted for 81.86% of the cases, while 42.70 and 42.58% of the reported cases were students and kindergarten children, respectively. The data from 2011 to 2018 were used to fit a SARIMA model and data in 2019 were used to validate the model. The normalised Bayesian information criterion (BIC), the coefficient of determination (R2) and the root mean squared error (RMSE) were used to evaluate the goodness-of-fit of the fitted model. The optimal SARIMA model was identified as (3, 1, 3) (3, 1, 0)12. The RMSE and mean absolute per cent error (MAPE) were used to assess the accuracy of the model. The RMSE and MAPE of the predicted values were 19.40 and 0.25 respectively, indicating that the predicted values matched the observed values reasonably well. Taken together, the SARIMA model could be employed to forecast scarlet fever incidence trend, providing support for scarlet fever control and prevention.

Public health measures associated with coronavirus disease (COVID-19) have accelerated the adoption of virtual health care across Canada. We explore the opportunities that virtual care presents in achieving the Quadruple Aim and challenges to navigate, through the lens of care for older adults. In particular, we recommend virtual care-related policies related to older adults that address (a) limited uptake among the socio-economically disadvantaged, (b) user-centered design of virtual care technologies, and (c) integration of iterative evaluations to ensure equitable and efficient achievement of desired outcomes. As virtual care accelerates forward, we must not leave older Canadians behind.

A shock-induced separation loss reduction method, using local blade suction surface shape modification (smooth ramp structure) with constant adverse pressure gradient with the consideration of radial equilibrium effect to split a single shock foot into multiple weaker shock wave configuration, is investigated on the NASA Rotor 37 for promoting aerodynamic performance of a transonic compressor rotor. Numerical investigation on baseline blade and improved one with blade modification on suction side has been conducted employing the Reynolds-averaged Navier–Stokes method to reveal flow physics of ramp structure. The results indicate that the passage shock foot of baseline is replaced with a family of compression waves and a weaker shock foot generating moderate adverse pressure gradient on ramp profile, which is beneficial for mitigating the shock foot and shrinking flow separation region as well. In addition, the radial secondary flow of low-momentum fluids within boundary layer is decreased significantly in the region of passage shock-wave/boundary-layer interaction on blade suction side, which mitigates the mass flow and mixing intensity of tip leakage flow. With the reduction of flow separation loss induced by passage shock, the adiabatic efficiency and total pressure ratio of improved rotor are superior to baseline model. This study herein implies a potential application of ramp profile in design method of transonic and supersonic compressors.

Ascaridia galli (Nematoda: Ascaridiidae) is the most common intestinal roundworm of chickens and other birds with a worldwide distribution. Although A. galli has been extensively studied, knowledge of the genetic variation of this parasite in detail is still insufficient. The present study examined genetic variation in the mitochondrial cytochrome c oxidase subunit 1 (cox1) gene among A. galli isolates (n = 26) from domestic chickens in Hunan Province, China. A portion of the cox1 (pcox1) gene was amplified by polymerase chain reaction separately from adult A. galli individuals and the amplicons were subjected to sequencing from both directions. The length of the sequences of pcox1 is 441 bp. Although the intra-specific sequence variation within A. galli is 0–7.7%, the inter-specific sequence differences among other members of the infraorder Ascaridomorpha were 11.4–18.9%. Phylogenetic analyses based on the maximum likelihood method using the sequences of pcox1 confirmed that all of the Ascaridia isolates were A. galli, and also resolved three distinct clades. Taken together, the findings suggest that A. galli may represent a complex of cryptic species. Our results provide an additional genetic marker for the management of A. galli in chickens and other birds.

Steinernema populi n. sp. was recovered by baiting from beneath poplar trees in China. Morphological and molecular features provided evidence for placing the new species into the Kushidai clade. The new species is characterized by the following morphological features: third-stage infective juveniles (IJ) with a body length of 1095 (973–1172) μm, a distance from the anterior end to excretory pore of 77 (70–86) μm and a tail length of 64 (55–72) μm. The Body length/Tail length (c) ratio and Anterior end to Excretory pore/ Tail length × 100 (E%) of S. populi n. sp. are substantially greater than those of all other ‘Feltiae–Kushidai–Monticolum’ group members. The first-generation males can be recognized by a spicule length of 66 (57–77) μm and a gubernaculum length of 46 (38–60) μm. The new species is further characterized by sequences of the internal transcribed spacer and partial 28S regions of the ribosomal DNA. Phylogenetic analyses show that Steinernema akhursti and Steinernema kushidai are the closest relatives to S. populi n. sp.

We use a continuous wavelet transform to analyse the daily hemispheric sunspot area data from the Greenwich Royal Observatory during cycles 12–24 and then study the cause of the appearance or disappearance of the Rieger-type periodicity in the northern and southern hemispheres during a certain cycle. The Rieger-type periodicity in the northern and southern hemispheres should be developed independently in the two hemispheres. This periodicity in the northern hemisphere is generally anti-correlated with the long-term variations in the mean solar cycle strength of hemispheric activity, but the correlation of the two parameters in the southern hemisphere shows a weak correlation. The appearance or disappearance of Rieger-type periodicity in the northern and southern hemispheres during a certain solar cycle is not directly correlated with their corresponding hemispheric mean activity strength but should be related to the strength of the hemispheric activity during sunspot maximum times, which hints the Rieger-type periodicity is more related to temporal evolution of toroidal magnetic field. The Rieger-type periodicity in the two hemispheres disappears in those solar cycles with relatively weak hemispheric activity during sunspot maximum times. The reason for the disappearance of this periodicity may be due to the combined influence of relatively weak toroidal magnetic fields and torsional oscillations, the differential rotation parameters vary through the solar cycle and may not remain more or less unchanged during some time, which does not permit the strong growth of magnetic Rossby waves.

Intrinsically photosensitive retinal ganglion cells (ipRGCs) signal not only anterogradely to drive behavioral responses, but also retrogradely to some amacrine interneurons to modulate retinal physiology. We previously found that all displaced amacrine cells with spiking, tonic excitatory photoresponses receive gap-junction input from ipRGCs, but the connectivity patterns and functional roles of ipRGC-amacrine coupling remained largely unknown. Here, we injected PoPro1 fluorescent tracer into all six types of mouse ipRGCs to identify coupled amacrine cells, and analyzed the latter’s morphological and electrophysiological properties. We also examined how genetically disrupting ipRGC-amacrine coupling affected ipRGC photoresponses. Results showed that ipRGCs couple with not just ON- and ON/OFF-stratified amacrine cells in the ganglion-cell layer as previously reported, but also OFF-stratified amacrine cells in both ganglion-cell and inner nuclear layers. M1- and M3-type ipRGCs couple mainly with ON/OFF-stratified amacrine cells, whereas the other ipRGC types couple almost exclusively with ON-stratified ones. ipRGCs transmit melanopsin-based light responses to at least 93% of the coupled amacrine cells. Some of the ON-stratifying ipRGC-coupled amacrine cells exhibit transient hyperpolarizing light responses. We detected bidirectional electrical transmission between an ipRGC and a coupled amacrine cell, although transmission was asymmetric for this particular cell pair, favoring the ipRGC-to-amacrine direction. We also observed electrical transmission between two amacrine cells coupled to the same ipRGC. In both scenarios of coupling, the coupled cells often spiked synchronously. While ipRGC-amacrine coupling somewhat reduces the peak firing rates of ipRGCs’ intrinsic melanopsin-based photoresponses, it renders these responses more sustained and longer-lasting. In summary, ipRGCs’ gap junctional network involves more amacrine cell types and plays more roles than previously appreciated.

An acute gastroenteritis (AGE) outbreak caused by a norovirus occurred at a hospital in Shanghai, China, was studied for molecular epidemiology, host susceptibility and serological roles. Rectal and environmental swabs, paired serum samples and saliva specimens were collected. Pathogens were detected by real-time polymerase chain reaction and DNA sequencing. Histo-blood group antigens (HBGA) phenotypes of saliva samples and their binding to norovirus protruding proteins were determined by enzyme-linked immunosorbent assay. The HBGA-binding interfaces and the surrounding region were analysed by the MegAlign program of DNAstar 7.1. Twenty-seven individuals in two care units were attacked with AGE at attack rates of 9.02 and 11.68%. Eighteen (78.2%) symptomatic and five (38.4%) asymptomatic individuals were GII.6/b norovirus positive. Saliva-based HBGA phenotyping showed that all symptomatic and asymptomatic cases belonged to A, B, AB or O secretors. Only four (16.7%) out of the 24 tested serum samples showed low blockade activity against HBGA-norovirus binding at the acute phase, whereas 11 (45.8%) samples at the convalescence stage showed seroconversion of such blockade. Specific blockade antibody in the population played an essential role in this norovirus epidemic. A wide HBGA-binding spectrum of GII.6 supports a need for continuous health attention and surveillance in different settings.

Gravitational waves from coalescing neutron stars encode information about nuclear matter at extreme densities, inaccessible by laboratory experiments. The late inspiral is influenced by the presence of tides, which depend on the neutron star equation of state. Neutron star mergers are expected to often produce rapidly rotating remnant neutron stars that emit gravitational waves. These will provide clues to the extremely hot post-merger environment. This signature of nuclear matter in gravitational waves contains most information in the 2–4 kHz frequency band, which is outside of the most sensitive band of current detectors. We present the design concept and science case for a Neutron Star Extreme Matter Observatory (NEMO): a gravitational-wave interferometer optimised to study nuclear physics with merging neutron stars. The concept uses high-circulating laser power, quantum squeezing, and a detector topology specifically designed to achieve the high-frequency sensitivity necessary to probe nuclear matter using gravitational waves. Above 1 kHz, the proposed strain sensitivity is comparable to full third-generation detectors at a fraction of the cost. Such sensitivity changes expected event rates for detection of post-merger remnants from approximately one per few decades with two A+ detectors to a few per year and potentially allow for the first gravitational-wave observations of supernovae, isolated neutron stars, and other exotica.

The current study investigated associations between variation in the bovine perilipin-2 gene (PLIN2) and milk traits (milk fat content, milk protein content, milk yield and milk fatty acid (FA) component levels) in 409 New Zealand pasture-grazed Holstein-Friesian × Jersey-cross (HF × J-cross or Kiwicross™) cows. Five nucleotide sequence variants were found in three regions of the gene, including c.17C>T in exon 2, c.53A>G in exon 3, c.595+23G>A and c.595+104_595+108del in intron 5, and c.*302T>C in the 3′-untranslated region. The c.*302T>C substitution produces two nucleotide sequence variants (A5 and B5), and this variation was associated with variation in milk protein content and milkfat composition for C10:0, C11:0, C12:0, C13:0 and C16:0 FA and medium-chain fatty acid (MCFA) and long-chain fatty acid (LCFA) groups. After correcting for the effect of variation in the diacylglycerol acyl-CoA acyltransferase 1 gene (DGAT1) that results in the amino acid substitution p.K232A, variation in the FA binding protein 4 gene (FABP4) and variation in the stearoyl-CoA desaturase (Δ-9-desaturase) gene (SCD) that results in the amino acids substitution p.A293V, significant differences between A5A5 and B5B5 cows were found for C10:0, C11:0, C12:0, C13:0, C16:0, and the MCFA, LCFA, total saturated FA and C10:1 index groups. This suggests that nucleotide sequence variation in PLIN2 may be affecting milk FA component levels.

The butterfly plastic zone theory based on Mohr Coulomb criterion has been widely used in coal mine production. In order to verify the universality of the theory, it is necessary to compare the distribution of plastic zone under different strength criteria. Based on the elastic-plastic mechanics, the principal stress distribution function around the circular tunnel is deduced in the paper, and the boundary and radius of the plastic zone under different strength criteria are calculated. The results show that the change laws of the plastic zone around the circular tunnel under different strength criteria has the following commonness: firstly, with the increase of the lateral pressure coefficient, the shape of the plastic zone presents the change laws of “circle ellipse butterfly”; Secondly, with the increase of the lateral pressure coefficient, the radius of the plastic zone is exponential distribution, while the characteristic value is different when the radius of the plastic zone is infinite. At same time, it shows that the butterfly plastic zone has a low sensitivity dependence on the strength criterion, no matter which strength criterion is adopted, and the butterfly plastic zone will inevitably appear in the surrounding rock mass of circular tunnel in the high deviator stress environment; The plastic zone with butterfly shape is highly sensitive to the stress change, and the small stress change may promote the expansion of the plastic zone. This result is significant for us to understand and prevent rock engineering disasters and accidents.

Dietary chitosan (CS) supplementation could improve the growth rate, small intestinal morphology, nutrients apparent digestibility and digestive enzyme activities in pigs, broiler chickens, rats and fish, whereas no data has been reported about the effect of CS on the growing Huoyan geese. Therefore, this study was designed to investigate the effects of CS on growth rate, small intestinal morphology, nutrients apparent utilization and digestive enzyme activities of growing Huoyan geese. Three hundred and twenty (28 days of age, gender balance) Huoyan geese were randomly divided into control, CS100, CS200 and CS400 groups (based on BW) with 20 geese per pen and 4 replicates pen per group, and the feeding experiment lasted for 4 weeks. The 4 diets contained 0, 100, 200 and 400 mg CS per kg feed, respectively. The results showed that CS200 groups had higher average daily gain, final BW, apparent utilization of DM and CP, and lower feed/gain ratio compared with the control group (P < 0.05). Meanwhile, CS100 and CS200 groups had higher villus height, villus height/crypt depth ratio and lower crypt depth in duodenum and jejunum than those in the control group (P < 0.05). The geese in CS100 and CS200 groups had higher villus height, villus height/crypt depth ratio and lower crypt depth of ileum compared with those in control and CS400 groups (P < 0.05). In addition, compared with the control group, CS200 group has higher trypsin activities and lower lipase activities in duodenal, jejunal and ileal contents (P < 0.05). The results suggested that addition of 200 mg/kg CS had positive effects on growth rate, small intestinal morphology, nutrients apparent utilization and digestive enzyme activities of growing Huoyan geese.