In his 1984 AMS Memoir, Andrews introduced the family of functions $c\phi_k(n)$, the number of k-coloured generalized Frobenius partitions of n. In 2019, Chan, Wang and Yang systematically studied the arithmetic properties of $\textrm{C}\Phi_k(q)$ for $2\leq k\leq17$ by utilizing the theory of modular forms, where $\textrm{C}\Phi_k(q)$ denotes the generating function of $c\phi_k(n)$. In this paper, we first establish another expression of $\textrm{C}\Phi_{12}(q)$ with integer coefficients, then prove some congruences modulo small powers of 3 for $c\phi_{12}(n)$ by using some parameterized identities of theta functions due to A. Alaca, S. Alaca and Williams. Finally, we conjecture three families of congruences modulo powers of 3 satisfied by $c\phi_{12}(n)$.

Polarized electron beam production via laser wakefield acceleration in pre-polarized plasma is investigated by particle-in-cell simulations. The evolution of the electron beam polarization is studied based on the Thomas–Bargmann–Michel–Telegdi equation for the transverse and longitudinal self-injection, and the depolarization process is found to be influenced by the injection schemes. In the case of transverse self-injection, as found typically in the bubble regime, the spin precession of the accelerated electrons is mainly influenced by the wakefield. However, in the case of longitudinal injection in the quasi-1D regime (for example, F. Y. Li et al., Phys. Rev. Lett. 110, 135002 (2013)), the direction of electron spin oscillates in the laser field. Since the electrons move around the laser axis, the net influence of the laser field is nearly zero and the contribution of the wakefield can be ignored. Finally, an ultra-short electron beam with polarization of $99\%$ can be obtained using longitudinal self-injection.

Echinococcosis poses a significant threat to public health. The Chinese government has implemented prevention and control measures to mitigate the impact of the disease. By analyzing data from the Chinese Center for Disease Control and Prevention and the State Council of the People’s Republic of China, we found that implementation of these measures has reduced the infection rate by nearly 50% between 2004 to 2022 (from 0.3975 to 0.1944 per 100,000 person-years). Nonetheless, some regions still bear a significant disease burden, and lack of detailed information limites further evaluation of the effects on both alveolar and cystic echinococcosis. Our analysis supports the continuing implementation of these measures and suggests that enhanced wildlife management, case-based strategies, and surveillance systems will facilitate disease control.

The Lawson criterion for proton-boron (p-11B) thermonuclear fusion is substantially higher than that for deuterium-tritium (DT) because the fusion cross section is lower and peaks at higher ion energies. The Maxwellian averaged p-11B reactivity peaks at several hundred keV, where bremsstrahlung radiation emission may dominate over fusion reactions if electrons and ions are in thermal equilibrium and the losses are unrestricted. Nonequilibrium burn has often been suggested to realize the benefits of this aneutronic reaction, but the predominance of elastic scattering over fusion reactivity makes this difficult to achieve. The development of ultrashort pulse lasers (USPL) has opened new possibilities for initiating nonequilibrium thermonuclear burns and significant numbers of p-11B alpha particles have been reported from several experiments. We present an analysis that shows that these significant alpha yields are the result of beam fusion reactions that do not scale to net energy gain. We further find that the yields can be explained by experimental parameters and recently updated cross sections such that a postulated avalanche mechanism is not required. We use this analysis to understand the underlying physics of USPL-driven nonequilibrium fusion reactions and whether they can be used to initiate fusion burns. We conclude by outlining a path to increasing the p-11B reactivity towards the goal of achieving ignition and describing the design principles that we will use to develop a computational point design.

This study advances a coopetition perspective to argue that an intangibility gap, defined as the difference in intangible asset intensity between industry-frontier foreign firms and local firms, generates both competitive threats and cooperative opportunities for local firms. Thus, an intangibility gap may affect local firms’ internal research and development (R&D) efforts beyond a linear, catching-up way of thinking. Using a sample of manufacturing firms in China, we find that intangibility gap has an inverted U-shaped relationship with the internal R&D intensity of local firms such that a moderate intangibility gap is more likely to stimulate local firms’ R&D than a small or large intangibility gap. Moreover, the results show that export intensity and state ownership of local firms serve as two boundary conditions under which the inverted U-shaped relationship becomes less and more pronounced, respectively.

To investigate temporal trends in coronavirus disease 2019 (COVID-19)-related outcomes and to evaluate whether the impacts of potential risk factors and disparities changed over time, we conducted a retrospective cohort study with 249 075 patients tested or treated for COVID-19 at Michigan Medicine (MM), from 10 March 2020 to 3 May 2021. Among these patients, 26 289 were diagnosed with COVID-19. According to the calendar time in which they first tested positive, the COVID-19-positive cohort were stratified into three-time segments (T1: March–June, 2020; T2: July–December, 2020; T3: January–May, 2021). Potential risk factors that we examined included demographics, residential-level socioeconomic characteristics and preexisting comorbidities. The main outcomes included COVID-19-related hospitalisation and intensive care unit (ICU) admission. The hospitalisation rate for COVID-positive patients decreased from 36.2% in T1 to 14.2% in T3, and the ICU admission rate decreased from 16.9% to 2.9% from T1 to T3. These findings confirm that COVID-19-related hospitalisation and ICU admission rates were decreasing throughout the pandemic from March 2020 to May 2021. Black patients had significantly higher (compared to White patients) hospitalisation rates (19.6% vs. 11.0%) and ICU admission rates (6.3% vs. 2.8%) in the full COVID-19-positive cohort. A time-stratified analysis showed that racial disparities in hospitalisation rates persisted over time and the estimates of the odds ratios (ORs) stayed above unity in both unadjusted [full cohort: OR = 1.98, 95% confidence interval (CI) (1.79, 2.19); T1: OR = 1.70, 95% CI (1.36, 2.12); T2: OR = 1.40, 95% CI (1.17, 1.68); T3: OR = 1.55, 95% CI (1.29, 1.86)] and adjusted analysis, accounting for differences in demographics, socioeconomic status, and preexisting comorbid conditions (full cohort: OR = 1.45, 95% CI (1.25, 1.68); T1: OR = 1.26, 95% CI (0.90, 1.76); T2: OR = 1.29, 95% CI (1.01, 1.64); T3: OR = 1.29, 95% CI (1.00, 1.67)).

The evolution of an instability in a transitional hypersonic boundary layer and its effects on aerodynamic cooling are investigated over 260-mm-long flared cone models with smooth and porous surfaces. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors and an infrared camera. Calculations are performed based on both direct numerical simulations (DNS) and linear stability theory (LST). The unit Reynolds number is $9.7 \times 10^6\ \textrm {m}^{-1}$. It is confirmed that a cooled region appears downstream of the local heat peak as the second-mode instability evolves over the smooth-surface model, as found in other studies. Comparisons between the DNS and LST results show that the nonlinear interaction of the second mode causes the phase difference $\phi _{p\theta }$ to change between the periodic pressure and dilatation waves. This forms a negative cycle-averaged pressure dilatation near the wall and creates the cooled region. Further, by using porous steel to modify the sound admittance of the model surface, it is possible to artificially obtain negative cycle-averaged pressure dilatation near the wall, and thus reduce the surface heat flux by approximately 28 %. These results indicate the possibility of precisely controlling the pressure-dilatation-induced aerodynamic heating through the modification of surface sound admittance.

In this paper, the generation of relativistic electron mirrors (REM) and the reflection of an ultra-short laser off the mirrors are discussed, applying two-dimension particle-in-cell 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 rapid expansion. 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 to the resonance between laser and REM. The reflected radiation near this interval and corresponding spectra will be amplified due to the resonance. Through adjusting the arriving time of the probe laser, a certain part of the reflected field could be selectively amplified or depressed, leading to the selective adjustment of the corresponding spectra.

Identification of the electromagnetic-wave (EM) counterparts of gravitational-wave (GW) sources can significantly broaden the research scope of GW astronomy, by pinpointing the exact locations of GW events and their environments, and using GW sources as standard sirens for cosmology. Yet, only one GW event has been found to be associated with an EM counterpart so far. Here, we outline the challenges of identifying EM counterparts of GW events, and describe our global network of telescopes that has been used to uncover GW EM counterparts. We also introduce a new facility in construction, the 7-dimensional telescope (7DT). Our GECKO observations have demonstrated that we can cover 50 deg2 within one hour to find kilonovae at a few hundred Mpc away. Furthermore, 7DT will produce a low resolution spectral map of the GW localization area, facilitating the EM counterpart search.

Porphyromonas gingivalis has been linked to the development and progression of oesophageal squamous cell carcinoma (ESCC), and is considered to be a high-risk factor for ESCC. Currently, the commonly used methods for P. gingivalis detection are culture or DNA extraction-based, which are either time and labour intensive especially for high-throughput applications. We aimed to establish and evaluate a rapid and sensitive direct quantitative polymerase chain reaction (qPCR) protocol for the detection of P. gingivalis without DNA extraction which is suitable for large-scale epidemiological studies. Paired gingival swab samples from 192 subjects undergoing general medical examinations were analysed using two direct and one extraction-based qPCR assays for P. gingivalis. Tris-EDTA buffer-based direct qPCR (TE-direct qPCR), lysis-based direct qPCR (lysis-direct qPCR) and DNA extraction-based qPCR (kit-qPCR) were used, respectively, in 192, 132 and 60 of these samples for quantification of P. gingivalis. The sensitivity and specificity of TE-direct qPCR was 95.24% and 100% compared with lysis-direct qPCR, which was 100% and 97.30% when compared with kit-qPCR; TE-direct qPCR had an almost perfect agreement with lysis-direct qPCR (κ = 0.954) and kit-qPCR (κ = 0.965). Moreover, the assay time used for TE-direct qPCR was 1.5 h. In conclusion, the TE-direct qPCR assay is a simple and efficient method for the quantification of oral P. gingivalis and showed high sensitivity and specificity compared with routine qPCR.

For positive integers $n$ and $k$, let $r_{k}(n)$ denote the number of representations of $n$ as a sum of $k$ squares, where representations with different orders and different signs are counted as distinct. For a given positive integer $m$, by means of some properties of binomial coefficients, we derive some infinite families of congruences for $r_{k}(n)$ modulo $2^{m}$. Furthermore, in view of these arithmetic properties of $r_{k}(n)$, we establish many infinite families of congruences for the overpartition function and the overpartition pair function.

Preeclampsia (PE) is now recognised as a cardiovascular risk factor for women. Emerging evidence suggests that children exposed to PE in utero may also be at increased risk of cardiovascular disease (CVD) in later life. Individuals exposed to PE in utero have higher systolic and diastolic blood pressure and higher body mass index (BMI) compared to those not exposed to PE in utero. The aim of this review is to discuss the potential mechanisms driving the relationship between PE and offspring CVD. Exposure to an adverse intrauterine environment as a consequence of the pathophysiological changes that occur during a pregnancy complicated by PE is proposed as one mechanism that programs the fetus for future CVD risk. Consistent with this hypothesis, animal models of PE where progeny have been studied demonstrate causality for programming of offspring cardiovascular health by the preeclamptic environment. Shared alleles between mother and offspring, and shared lifestyle factors between mother and offspring provide alternate pathways explaining associations between PE and offspring CVD risk. In addition, adverse lifestyle habits can also act as second hits for those programmed for increased CVD risk. PE and CVD are both multifactorial diseases and, hence, identifying the relative contribution of PE to offspring risk for CVD is a very complex task. However, considering the emerging strong association between PE and CVD, those exposed to PE in utero may benefit from targeted primary CVD preventive strategies.

Early in a foodborne disease outbreak investigation, illness incubation periods can help focus case interviews, case definitions, clinical and environmental evaluations and predict an aetiology. Data describing incubation periods are limited. We examined foodborne disease outbreaks from laboratory-confirmed, single aetiology, enteric bacterial and viral pathogens reported to United States foodborne disease outbreak surveillance from 1998–2013. We grouped pathogens by clinical presentation and analysed the reported median incubation period among all illnesses from the implicated pathogen for each outbreak as the outbreak incubation period. Outbreaks from preformed bacterial toxins (Staphylococcus aureus, Bacillus cereus and Clostridium perfringens) had the shortest outbreak incubation periods (4–10 h medians), distinct from that of Vibrio parahaemolyticus (17 h median). Norovirus, salmonella and shigella had longer but similar outbreak incubation periods (32–45 h medians); campylobacter and Shiga toxin-producing Escherichia coli had the longest among bacteria (62–87 h medians); hepatitis A had the longest overall (672 h median). Our results can help guide diagnostic and investigative strategies early in an outbreak investigation to suggest or rule out specific etiologies or, when the pathogen is known, the likely timeframe for exposure. They also point to possible differences in pathogenesis among pathogens causing broadly similar syndromes.

Laser–plasma interaction (LPI) at intensities $10^{15}{-}10^{16}~\text{W}\cdot \text{cm}^{-2}$ is dominated by parametric instabilities which can be responsible for a significant amount of non-collisional absorption and generate large fluxes of high-energy nonthermal electrons. Such a regime is of paramount importance for inertial confinement fusion (ICF) and in particular for the shock ignition scheme. In this paper we report on an experiment carried out at the Prague Asterix Laser System (PALS) facility to investigate the extent and time history of stimulated Raman scattering (SRS) and two-plasmon decay (TPD) instabilities, driven by the interaction of an infrared laser pulse at an intensity ${\sim}1.2\times 10^{16}~\text{W}\cdot \text{cm}^{-2}$ with a ${\sim}100~\unicode[STIX]{x03BC}\text{m}$ scalelength plasma produced from irradiation of a flat plastic target. The laser pulse duration (300 ps) and the high value of plasma temperature (${\sim}4~\text{keV}$) expected from hydrodynamic simulations make these results interesting for a deeper understanding of LPI in shock ignition conditions. Experimental results show that absolute TPD/SRS, driven at a quarter of the critical density, and convective SRS, driven at lower plasma densities, are well separated in time, with absolute instabilities driven at early times of interaction and convective backward SRS emerging at the laser peak and persisting all over the tail of the pulse. Side-scattering SRS, driven at low plasma densities, is also clearly observed. Experimental results are compared to fully kinetic large-scale, two-dimensional simulations. Particle-in-cell results, beyond reproducing the framework delineated by the experimental measurements, reveal the importance of filamentation instability in ruling the onset of SRS and stimulated Brillouin scattering instabilities and confirm the crucial role of collisionless absorption in the LPI energy balance.