We investigate the tail behavior of the first-passage time for Sinai’s random walk in a random environment. Our method relies on the connection between Sinai’s walk and branching processes with immigration in a random environment, and the analysis on some important quantities of these branching processes such as extinction time, maximum population, and total population.

We consider linear-fractional branching processes (one-type and two-type) with immigration in varying environments. For $n\ge0$, let $Z_n$ count the number of individuals of the nth generation, which excludes the immigrant who enters the system at time n. We call n a regeneration time if $Z_n=0$. For both the one-type and two-type cases, we give criteria for the finiteness or infiniteness of the number of regeneration times. We then construct some concrete examples to exhibit the strange phenomena caused by the so-called varying environments. For example, it may happen that the process is extinct, but there are only finitely many regeneration times. We also study the asymptotics of the number of regeneration times of the model in the example.

Previous studies have indicated an association between vitamin D and thyroid- and parathyroid-related diseases. However, it remains unclear whether it is a cause of the disease, a side effect of treatment or a consequence of the disease. The Mendelian randomisation (MR) study strengthens the causal inference by controlling for non-heritable environmental confounders and reverse causation. In this study, a two-sample bidirectional MR analysis was conducted to investigate the causal relationship between serum vitamin D levels and thyroid- and parathyroid-related diseases. Inverse variance weighted, weighted median and MR-Egger methods were performed, the Cochran Q test was used to evaluate the heterogeneity and the MR-PRESSO and MR-Egger intercepts were utilised to assess the possibility of pleiotropy. The Bonferroni-corrected significance threshold was 0·0038. At the Bonferroni-corrected significance level, we found that vitamin D levels suggestively decreased the risk of benign parathyroid adenoma (OR = 0·244; 95 % CI 0·074, 0·802; P = 0·0202) in the MR analyses. In the reverse MR study, a genetically predicted risk of thyroid cancer suggestively increased the risk of elevated vitamin D (OR = 1·007; 95 % CI 1·010, 1·013; P = 0·0284), chronic thyroiditis significantly increased the risk of elevated vitamin D (OR = 1·007; 95 % CI 1·002, 1·011; P = 0·0030) and thyroid nodules was significantly decreased the vitamin D levels (OR = 0·991; 95 % CI 0·985, 0·997; P = 0·0034). The findings might be less susceptible to horizontal pleiotropy and heterogeneity (P > 0·05). This study from a gene perspective indicated that chronic thyroiditis and thyroid nodules may impact vitamin D levels, but the underlying mechanisms require further investigation.

Studies on obesity and risk factors from a life-course perspective among residents in the Tibet Plateau with recent economic growth and increasing obesity are important and urgently needed. The birth cohort in this area provides a unique opportunity to examine the association between maternal dietary practice and neonatal obesity. The study aims to detect the prevalence of obesity among neonates, associated with maternal diet and other factors, supporting life-course strategies for obesity control. A cohort of pregnant women was enrolled in Tibet Plateau and followed till childbirth. Dietary practice during pregnancy was assessed using the Chinese FFQ – Tibet Plateau version, food items and other variables were associated with the risk for obesity of neonates followed by logistic regression, classification and regression trees (CART) and random forest. Of the total 1226 mother–neonate pairs, 40·5 % were Tibetan and 5·4 % of neonates with obesity. Consuming fruits as a protective factor for obesity of neonates with OR (95 % CI) = 0·61 (0·43, 0·87) from logistic regression; as well as OR = 0·20 (0·12, 0·35) for consuming fruits (≥ weekly) from CART. Removing fruit consumption to avoid overshadowing effects of other factors, the following were influential from CART: maternal education (more than middle school, OR = 0·22 (0·13, 0·37)) and consumption of Tibetan food (daily, OR = 3·44 (2·08, 5·69). Obesity among neonates is prevalent in the study population. Promoting healthy diets during pregnancy and strengthening maternal education should be part of the life-course strategies for obesity control.

As a member of the Scathophagidae family, Scathophaga stercoraria (S. stercoraria) is widely distributed globally and is closely associated with animal feces. It is also a species of great interest to many scientific studies. However, its phylogenetic relationships are poorly understood. In this study, S. stercoraria was found in plateau pikas for the first time. The potential cause of its presence in the plateau pikas was discussed and it was speculated that the presence of S. stercoraria was related to the yak feces. In addition, 2 nuclear genes (18SrDNA and 28SrDNA), 1 mitochondrial gene (COI), and the complete mitochondrial genome of S. stercoraria were sequenced. Phylogenetic trees constructed based on 13 Protein coding genes (13PCGs), 18S and 28S rDNA showed that S. stercoraria is closely related to the Calliphoridae family; phylogenetic results based on COI suggest that within the family Scathophagidae, S. stercoraria is more closely related to the genus Leptopa, Micropselapha, Parallelomma and Americina. Divergence times estimated using the COI gene suggest that the divergence formation of the genus Scathophaga is closely related to changes in biogeographic scenarios and potentially driven by a combination of uplift of the Qinghai-Tibetan Plateau (QTP) and dramatic climate changes. These results provide valuable information for further studies on the phylogeny and differentiation of the Scathophaga genus in the future.

This paper retrospectively analysed the prevalence of macrolide-resistant Mycoplasma pneumoniae (MRMP) in some parts of China. Between January 2013 and December 2019, we collected 4,145 respiratory samples, including pharyngeal swabs and alveolar lavage fluid. The highest PCR-positive rate of M. pneumoniae was 74.5% in Beijing, the highest resistance rate was 100% in Shanghai, and Gansu was the lowest with 20%. The highest PCR-positive rate of M. pneumoniae was 74.5% in 2013, and the highest MRMP was 97.4% in 2019; the PCR-positive rate of M. pneumoniae for adults in Beijing was 17.9% and the MRMP was 10.48%. Among the children diagnosed with community-acquired pneumonia (CAP), the PCR-positive and macrolide-resistant rates of M. pneumoniae were both higher in the severe ones. A2063G in domain V of 23S rRNA was the major macrolide-resistant mutation, accounting for more than 90%. The MIC values of all MRMP to erythromycin and azithromycin were ≥ 64 μg/ml, and the MICs of tetracycline and levofloxacin were ≤ 0.5 μg/ml and ≤ 1 μg/ml, respectively. The macrolide resistance varied in different regions and years. Among inpatients, the macrolide-resistant rate was higher in severe pneumonia. A2063G was the common mutation, and we found no resistance to tetracycline and levofloxacin.

In this paper, we study the singular boundary value problem

$$ \begin{align*} \begin{cases} \Delta_\infty^h u=\lambda f(x,u,Du) \quad &\mathrm{in}\; \Omega, \\ u>0\quad &\mathrm{in}\; \Omega,\\ u=0 \quad &\mathrm{on} \;\partial\Omega, \end{cases} \end{align*} $$

where $\lambda>0$ is a parameter, $h>1$ and $\Delta _\infty ^h u=|Du|^{h-3} \langle D^2uDu,Du \rangle $ is the highly degenerate and h-homogeneous operator related to the infinity Laplacian. The nonlinear term $f(x,t,p):\Omega \times (0,\infty )\times \mathbb {R}^{n}\rightarrow \mathbb {R}$ is a continuous function and may exhibit singularity at $t\rightarrow 0^{+}$. We establish the comparison principle by the double variables method for the general equation $\Delta _\infty ^h u=F(x,u,Du)$ under some conditions on the term $F(x,t,p)$. Then, we establish the existence of viscosity solutions to the singular boundary value problem in a bounded domain based on Perron’s method and the comparison principle. Finally, we obtain the existence result in the entire Euclidean space by the approximation procedure. In this procedure, we also establish the local Lipschitz continuity of the viscosity solution.

We prove that the local time of random walks conditioned to stay positive converges to the corresponding local time of three-dimensional Bessel processes by proper scaling. Our proof is based on Tanaka’s pathwise construction for conditioned random walks and the derivation of asymptotics for mixed moments of the local time.

Adsorption of the ${\text{AuCl}}_4^{-}$ complex by kaolinites of different crystallinities (Kao-1 and Kao-2) from 100 mL of AuCl3·HCl·4H2O solutions containing 10,000, 500 and 50 µg/L Au and 1 g of kaolinite was measured at pH 3 to 9 at ambient temperature and 120°C. Adsorption from the 50, 500 and 10,000 µg Au/L solutions ranged from 64 to 100% at ambient temperature and from 68 to 100% at 120°C for both kaolinites. Adsorption was pH dependent with a maximum at pH <5 and a minimum at neutral and alkaline pHs. Up to 1 mg Au/g kaolinite was adsorbed by the kaolinites at both ambient temperature and 120°C. In a separate Au adsorption experiment using 100 mL of 4000 µg Au/L solutions and 0.02 to 1.0 g of Kao-1, up to 8.55 mg Au/ g of kaolinite was adsorbed. The pH dependence of Au adsorption suggests that surface complexation of Au to alumina sites at the edges of kaolinite particles might be involved. Protonation of kaolinite surface sites might facilitate adsorption of the anionic Au complex. Both kaolinites adsorbed ~100% of added Au at low pH values, but the less crystalline kaolinite (Kao-2) adsorbed more Au at high pH. Greater Au adsorption would be expected for the less crystalline Kao-2 sample if adsorption occurred at the edges of kaolinite particles.

The comparisons among 126 14C dates of Carex samples including separated leaf and root parts with acid (A)-treatment and acid-base-acid (ABA)-treatment, and 48 published 14C dates of bulk peat plants on a 92-cm core from Jinchuan Mire in NE China, indicate old carbon influence (OCI) on the 14C dates. The OCI varies with plant species, pretreatment and peat depth. In vascular peat plants such as Carex, humin fractions (remains after ABA treatment) and humic acids are representative of the original plant precursor, while fulvic acids are regarded as the secondary mobile product which should be removed for 14C dating. ABA- treatment removes both fulvic acids and humic acids, whereas A-treatment gets rid of only fulvic acids. Carex roots uptake more dissolved CO2 in peat water. Carex leaves may use more CO2 (involving degassing CO2) above the peat surface. By removing humic acids throughout ABA treatment, the OCI may vary differently over depth (time). ABA treatment cannot eliminate the fixed OCI in humin fractions of vascular peat plants, instead, this treatment may enhance OCI by removing humic acid which may represent the true age of the plants. In addition, Bacon model results on this core could not show rapid changes in accumulation rate.

This paper develops the estimation method of mean and covariance functions of functional data with additional covariate information. With the strength of both local linear smoothing modeling and general weighing scheme, we are able to explicitly characterize the mean and covariance functions with incorporating covariate for irregularly spaced and sparsely observed longitudinal data, as typically encountered in engineering technology or biomedical studies, as well as for functional data which are densely measured. Theoretically, we establish the uniform convergence rates of the estimators in the general weighing scheme. Monte Carlo simulation is conducted to investigate the finite-sample performance of the proposed approach. Two applications including the children growth data and white matter tract dataset obtained from Alzheimer's Disease Neuroimaging Initiative study are also provided.

According to the positive time-discounting assumption of intertemporal decision-making, people prefer to undergo negative events in the future rather than in the present. However, negative discounting has been identified in the intertemporal choice and loss domains, which refers to people’s preference to experience negative events earlier rather than later. Studies have validated and supported the "anticipated dread" as an explanation for negative discounting. This study again explored the effect of anticipated dread on intertemporal choice using content analysis; that is, having participants identify anticipated dread among reasons for negative discounting. This study also validated the effect of anticipated dread on negative discounting by manipulating anticipated dread. This study adds empirical and direct evidence for the role of anticipated dread in negative discounting.

Intertemporal choices involve tradeoffs between outcomes that occur at different times. Most of the research has used pure gains tasks and the discount rates yielding from those tasks to explain and predict real-world behaviors and consequences. However, real decisions are often more complex and involve mixed outcomes (e.g., sooner-gain and later-loss or sooner-loss and later-gain). No study has used mixed gain-loss intertemporal tradeoff tasks to explain and predict real-world behaviors and consequences, and studies involving such tasks are also scarce. Considering that tasks involving a combination of gains and losses may yield different discount rates and that existing pure gains tasks do not explain or predict real-world outcomes well, this study conducted two experiments to compare the discount rates of mixed gain-loss intertemporal tradeoffs with those of pure gains or pure losses (Experiment 1) and to examine whether these tasks predicted different real-world behaviors and consequences (Experiment 2). Experiment 1 suggests that the discount rate ordering of the four tasks was, from highest to lowest, pure gains, sooner-loss and later-gain, pure losses, and sooner-gain and later-loss. Experiment 2 indicates that the evidence supporting the claim that the discount rates of the four tasks were related to different real-world behaviors and consequences was insufficient.

Recently, Scholten and Read (2014) found new violations of dominance in intertemporal choice. Although adding a small receipt before a delayed payment or adding a small delayed receipt after an immediate receipt makes the prospect objectively better, it decreases the preference for that prospect (better is worse). Conversely, although adding a small payment before a delayed receipt or adding a small delayed payment after an immediate payment makes the prospect objectively worse, it increases the preference for that prospect (worse is better). Scholten and Read explained these violations in terms of a preference for improvement. However, to produce violations such as these, we find that the temporal sequences need not be constructed as Scholten and Read suggested. In this study, adding a small receipt before a dated receipt (thus constructed as improving) or adding a receipt after a dated payment (thus constructed as improving) decreases preferences for those prospects. Conversely, adding a small payment after a dated receipt (thus constructed as deteriorating) or adding a small payment before a delayed payment (thus constructed as deteriorating) increases preferences for those prospects.

To study intertemporal choices, researchers typically instruct subjects to choose between smaller and sooner (SS) and larger and later (LL) rewards (e.g., gaining CNY 210 in a week vs. gaining CNY 250 in five weeks). People generally tend to discount steeply and prefer SS to LL rewards in such situations. Jiang, Hu and Zhu (2014) recently showed that adding upfront losses or gains to both SS and LL rewards can reduce people’s discounting, and they provided several possible accounts for this effect, including the salience account and the time scale hypothesis. In the current paper, based on the upfront money effect found in Jiang et al. (2014), we further showed that the effect of discounting decreasing could be extended to adding dated-money between SS and LL rewards and after LL rewards. The results helped us exclude both the time scale hypothesis and another possible explanation: preference for improvement. We hypothesized that all the current findings (recorded in this paper and in Jiang et al.) could be accommodated well using the salience account.