Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some instances, the objective is to discover part of the hidden physics from the available data, and PIML has been shown to be particularly effective for such problems for which conventional methods may fail. Unlike commercial machine learning where training of deep neural networks requires big data, in PIML big data are not available. Instead, we can train such networks from additional information obtained by employing the physical laws and evaluating them at random points in the space–time domain. Such PIML integrates multimodality and multifidelity data with mathematical models, and implements them using neural networks or graph networks. Here, we review some of the prevailing trends in embedding physics into machine learning, using physics-informed neural networks (PINNs) based primarily on feed-forward neural networks and automatic differentiation. For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs). We present representative examples for both forward and inverse problems and discuss what advances are needed to scale up PINNs, PIGNs and more broadly GNNs for large-scale engineering problems.

Resistance to carbapenems in human pathogens is a growing clinical and public health concern. The carbapenems are in an antimicrobial class considered last-resort, they are used to treat human infections caused by multidrug-resistant Enterobacterales, and they are classified by the World Health Organization as ‘High Priority Critically Important Antimicrobials’. The presence of carbapenem-resistant Enterobacterales (CREs) of animal-origin is of concern because targeted studies of Canadian retail seafood revealed the presence of carbapenem resistance in a small number of Enterobacterales isolates. To further investigate this issue, a risk profile was developed examining shrimp and salmon, the two most important seafood commodities consumed by Canadians and Escherichia coli, a member of the Enterobacterales order. Carbapenem-resistant E. coli (CREc) isolates have been identified in shrimp and other seafood products. Although carbapenem use in aquaculture has not been reported, several classes of antimicrobials are utilised globally and co-selection of antimicrobial-resistant microorganisms in an aquaculture setting is also of concern. CREs have been identified in retail seafood purchased in Canada and are currently thought to be uncommon. However, data concerning CRE or CREc occurrence and distribution in seafood are limited, and argue for implementation of ongoing or periodic surveillance.

Scrub typhus is a common bacterial infection in Asia caused by Orientia tsutsugamushi. This serological cohort study estimated the incidence of infection in a rural population in South India. Participants were enrolled through systematic sampling in 46 villages at baseline, and revisited the following year. Blood samples were tested for IgG antibodies using ELISA, followed by indirect immunofluorescence assays (IFA) in those positive for ELISA at both rounds. A case was defined as sero-conversion (ELISA), or at least a 4-fold titre increase (IFA), between the two time points. In addition to crude incidence rate estimates, we used piecewise linear rates across calendar months, with rates proportional to the monthly incidence of local hospital cases to address seasonality and unequal follow-up times. Of 402 participants, 61.7% were female. The mean age was 46.7 years, (range 13–88). 21 participants showed evidence for serological infection. The estimated incidence was 4.4 per 100 person-years (95% CI 2.8–6.7). The piecewise linear rates approach resulted in a similar estimate of 4.6 per 100 person years (95% CI 2.9–6.9). Considering previous estimates of symptomatic scrub typhus incidence in the same study population, only about 2–5% of infections may result in clinically relevant disease.

We study the so-called frog model on ${\mathbb{Z}}$ with two types of lazy frogs, with parameters $p_1,p_2\in (0,1]$ respectively, and a finite expected number of dormant frogs per site. We show that for any such $p_1$ and $p_2$ there is positive probability that the two types coexist (i.e. that both types activate infinitely many frogs). This answers a question of Deijfen, Hirscher, and Lopes in dimension one.

Since the advent of direct-acting antiviral therapy, the elimination of hepatitis c virus (HCV) as a public health concern is now possible. However, identification of those who remain undiagnosed, and re-engagement of those who are diagnosed but remain untreated, will be essential to achieve this. We examined the extent of HCV infection among individuals undergoing liver function tests (LFT) in primary care. Residual biochemistry samples for 6007 patients, who had venous blood collected in primary care for LFT between July 2016 and January 2017, were tested for HCV antibody. Through data linkage to national and sentinel HCV surveillance databases, we also examined the extent of diagnosed infection, attendance at specialist service and HCV treatment for those found to be HCV positive. Overall HCV antibody prevalence was 4.0% and highest for males (5.0%), those aged 37–50 years (6.2%), and with an ALT result of 70 or greater (7.1%). Of those testing positive, 68.9% had been diagnosed with HCV in the past, 84.9% before the study period. Most (92.5%) of those diagnosed with chronic infection had attended specialist liver services and while 67.7% had ever been treated only 38% had successfully cleared infection. More than half of HCV-positive people required assessment, and potentially treatment, for their HCV infection but were not engaged with services during the study period. LFT in primary care are a key opportunity to diagnose, re-diagnose and re-engage patients with HCV infection and highlight the importance of GPs in efforts to eliminate HCV as a public health concern.

We derive closed-form solutions to some discounted optimal stopping problems related to the perpetual American cancellable dividend-paying put and call option pricing problems in an extension of the Black–Merton–Scholes model. The cancellation times are assumed to occur when the underlying risky asset price process hits some unobservable random thresholds. The optimal stopping times are shown to be the first times at which the asset price reaches stochastic boundaries depending on the current values of its running maximum and minimum processes. The proof is based on the reduction of the original optimal stopping problems to the associated free-boundary problems and the solution of the latter problems by means of the smooth-fit and modified normal-reflection conditions. We show that the optimal stopping boundaries are characterised as the maximal and minimal solutions of certain first-order nonlinear ordinary differential equations.

This paper examines the value-at-risk (VaR) implications of mean-variance hedging. We derive an equivalence between the VaR-based hedge and the mean-variance hedging. This method transfers the investor's subjective risk-aversion coefficient into the estimated VaR measure. As a result, we characterize the collapse probability bounds under which the VaR-based hedge could be insignificantly different from the minimum-variance hedge in the presence of estimation risk. The results indicate that the squared information ratio of futures returns is the primary factor determining the difference between the minimum-variance and VaR-based hedges.

Mycoplasma genitalium (MG) and Chlamydia trachomatis (CT) are the most common sexually transmitted pathogens, which can cause cervicitis, pelvic inflammation and infertility in female. In the present study, we collected the basic information, clinical results of leucorrhoea and human papillomavirus (HPV) infection of patients, who were involved in both MG and CT RNA detection in West China Second Hospital of Sichuan University from January 2019 to April 2021, ranging from 18 to 50 years old. The results showed that the infection frequencies of MG and CT were 2.6% and 6.5%, respectively. The infection rate of CT in gynaecological patients was significantly higher than that of MG (P < 0.001). Moreover, patients with CT infection often had symptoms of gynaecological diseases, while patients with MG infection remain often asymptomatic. By exploring the connection between MG or CT infection and vaginal secretions, we found that the infection of MG or CT promoted to the increase of vaginal leukocytes, and CT infection exacerbated the decrease of the number of Lactobacillus in the vagina. Further analysis suggested that independent infection and co-infection of MG or CT resulted in abnormal vaginal secretion, affecting the stability of vaginal environment, which may induce vaginal diseases. Unexpectedly, our study found no association between MG or CT infection and high-risk HPV infection. In conclusion, our study explored the infection of MG and CT among women in Southwest China for the first time, and revealed that the infection of MG or CT would affect the homeostasis of vaginal environment, which laid a foundation for the clinical diagnosis and treatment of MG and CT infection.

In this work the $\ell_q$-norms of points chosen uniformly at random in a centered regular simplex in high dimensions are studied. Berry–Esseen bounds in the regime $1\leq q < \infty$ are derived and complemented by a non-central limit theorem together with moderate and large deviations in the case where $q=\infty$. An application to the intersection volume of a regular simplex with an $\ell_p^n$-ball is also carried out.