Viruses present an amazing genetic variability. An ensemble of infecting viruses, also called a viral quasispecies, is a cloud of mutants centered around a specific genotype. The simplest model of evolution, whose equilibrium state is described by the quasispecies equation, is the Moran–Kingman model. For the sharp-peak landscape, we perform several exact computations and derive several exact formulas. We also obtain an exact formula for the quasispecies distribution, involving a series and the mean fitness. A very simple formula for the mean Hamming distance is derived, which is exact and does not require a specific asymptotic expansion (such as sending the length of the macromolecules to $\infty$ or the mutation probability to 0). With the help of these formulas, we present an original proof for the well-known phenomenon of the error threshold. We recover the limiting quasispecies distribution in the long-chain regime. We try also to extend these formulas to a general fitness landscape. We obtain an equation involving the covariance of the fitness and the Hamming class number in the quasispecies distribution. Going beyond the sharp-peak landscape, we consider fitness landscapes having finitely many peaks and a plateau-type landscape. Finally, within this framework, we prove rigorously the possible occurrence of the survival of the flattest, a phenomenon which was previously discovered by Wilke et al. (Nature 412, 2001) and which has been investigated in several works (see e.g. Codoñer et al. (PLOS Pathogens 2, 2006), Franklin et al. (Artificial Life 25, 2019), Sardanyés et al. (J. Theoret. Biol. 250, 2008), and Tejero et al. (BMC Evolutionary Biol. 11, 2011)).

Increasing transboundary crises necessitate the development of crisis management capabilities that transcend boundaries. In such situations, inter-governmental and cross-functional collaboration has become a common practice to address the complexities of governance challenges. This study employs Social Network Analysis to examine the structure, function, and evolution of policy collaboration networks in China in response to COVID-19 and SARS. Since the SARS outbreak, China has embraced a collaborative governance approach, considering the transboundary nature of COVID-19. This approach has led to the involvement of numerous specialized organizations engaged in economic and social development, contributing to the establishment of a larger and more loosely connected collaboration network. While the health department bears the primary responsibility for coordinating public health emergency management, diverse organizations with social governance and economic management functions have also emerged as key actors, providing crucial anti-epidemic information, knowledge, and resources to address this significant cross-border crisis.

The literature on representation has shown that those who reflect the characteristics, traits, and/or experiences of a group (descriptive representation) are more likely to represent that group’s interests (substantive representation). In this paper, we argue that questions about representation should be considered with regard to generational identity. Drawing upon research that shows the importance of the Millennial Generation identity for understanding Millennials’ attitudes and policy preferences, we look at whether this identity matters for the legislative representation of group interests by examining bill sponsorship activity in 31 state legislatures. Our results tentatively support the expectation that the Millennial generation identity conditions the sponsorship of Millennial interest bills. Millennial legislators are more likely than non-Millennial legislators to sponsor bills that disproportionately impact their group members. This result is observed among both Democrat and Republican legislators, but at different magnitudes and for different issue priorities. These findings suggest that the Millennial generation identity is a meaningful determinant of legislative behavior, even when examined alongside partisanship.

Leader exemplification involves implicit and explicit claims of high moral values made by a leader. We employed a 2 × 3 experimental design with samples of 265 students in Study 1 and 142 working adults in Study 2 to examine the effects of leader exemplification (exemplification versus no exemplification) and ethical conduct (self-serving, self-sacrificial, and self-other focus) on perceived leader authenticity, trust in leader, and organizational advocacy. In Study 1, we found that exemplification produced elevated levels of perceived authenticity, trust, and advocacy in the form of employment and investment recommendations. We also showed that leader ethical conduct moderated this effect, as ratings were highest following a leader’s self-sacrificial conduct, lowest for self-serving conduct, and moderate for conduct reflecting self-other concerns. In Study 2, we replicated these findings for perceived authenticity and trust, but not organizational advocacy, which yielded mixed results. The leadership implications and future research directions are discussed.

One-bit coding metasurfaces combine two basic unit cells with out-of-phase responses. Their potential in achieving diffuse scattering has already been demonstrated. These metasurfaces can subsequently be applied to radar-signature control. This paper presents a theoretical analysis linking the scattered field to the autocorrelation of the code that encodes the metasurface. This analysis leads to a focus on Minimum Peak Sidelobes codes with autocorrelation characteristics similar to the unit impulse. Advances in other research areas have greatly enhanced the search for these kind of codes, making them directly usable for coding diffuse scattering metasurfaces. This approach is compared with existing codes, specifically examining how it performs against the optimal code found through exhaustive search in small-scale scenarios. Then, it is shown that this coding strategy facilitates the design of metasurfaces with any and large electrical sizes, achieving results comparable to those obtained through optimization-based approaches, at a significantly reduced computational workload.

Biber, Szmrecsanyi, Reppen & Larsson (2023) argue for a more liberal inclusion of genitive variants, evoking Labov's principle of accountability (Labov 1969: 737–8, fn. 20, 1972), which calls for the inclusion of all variants that are functionally equivalent and allow variation. They suggest that the term ‘genitive’ should be defined grammatically, as a restrictive modifier to the head noun, rather than semantically in terms of a possessive relation, thus redefining the linguistic variable for English genitive variation. In particular, they include noun modifiers as a third genitive variant (with s-genitives and of-genitives). In this reply I argue that the authors proceed from a notion of ‘genitive’ that is too broad, including variants that are not functionally equivalent and contexts that are not variable, thus actually violating the principle of accountability.

Although ethics is increasingly integrated in the curriculum of U.S. medical schools, it remains not well integrated with system issues, and social and structural contexts of illness. Moreover, ethical analysis is not often taught as a clinical skill. To address these issues, an outcomes driven course in Social Sciences, Humanities, Ethics and Professionalism (SHEP) was created. Within the course, a web-based concept mapping device, SHEP Case Analysis Tool (SCAT), was created which schematizes the structure and flow of clinical cases from diagnosis to treatment options, to shared decision making to outcome, and includes key stakeholders, influences, and structural features of the health system. In the course, each student analyzes a case in which they were directly involved using SCAT and presents their analysis to faculty and peers. This exercise 1) reinforces knowledge-based portions of the course pedagogy, 2) supports meta-cognition and critical thinking through concept mapping, 3) applies multidimensional analysis to identify ethical, social, and system issues that impact patient-care. 4) develops problem solving skills, 5) counters the hidden curriculum/support professional identity formation, and 6) develops skills in reflective discourse. This paper outlines the development and use of this concept mapping case analysis tool in an undergraduate medical education curriculum.

This paper explores the intense bond formed between two Qing women, Li Ti and Huang Xunying, as well as their double suicide. The sheer survival of the rich personal and family narratives (in both poetry and prose) surrounding their relationship and suicides represents a startling discovery. By actively resisting the restrictions imposed by the patriarchal family and social order and explicitly defining an unbreakable union marked by moral commitment to and spiritual connection with each other, Li Ti and Huang embody the concept of queerness in today’s usage. The two women’s double suicide, furthermore, posed an extreme form of social protest and an individual quest for freedom. Despite being historically conditioned and ideologically mediated, the excavated primary sources, such as Li Ti’s own poems, challenge not only the norms of their time and place, but also our scholarly consensus about women’s lives in China’s past.

Household income and caregiver mental health are important drivers of children’s health and development. The COVID-19 pandemic created huge economic and mental health disruptions. This study examines financial hardship and its relationship with caregiver and child mental health using Australia’s only representative data spanning three years of the pandemic. Analysis of the repeated, cross-sectional National Child Health Poll included 12,408 caregivers and 20,339 children over six waves (June 2020–April 2023). Caregivers reported their income (dichotomised into low versus not) and deprivation (missing one or more of eight essential items, versus not) and mental health for themselves (Kessler-6, poor versus not) and each child (Self-Rated Mental Health, poor/fair versus good/very good/excellent). Binary logistic models were fitted to predict marginal probabilities of mental health measures by low income and deprivation, over time. Results show that while low income decreased from 41% to 34% over the study period, deprivation increased from 30% to 35%. Poor mental health peaked with stay-at-home orders in 2021 before recovering. Caregivers experiencing low income or deprivation had higher rates of poor mental health throughout the study and slower recovery compared to those without financial hardship. Children in families experiencing financial hardship had slightly higher proportions of poor/fair mental health in 2021–2022, but they were mostly equivalent in June 2020 and April 2023 (range 6–8%). Addressing financial hardship may offer an avenue for improving caregiver mental health. This has implications for post-pandemic recovery and addressing contemporary issues of increasing cost of living and limited mental health supports and services.

Our primary result concerns the positivity of specific kernels constructed using the q-ultraspherical polynomials. In other words, it concerns a two-parameter family of bivariate, compactly supported distributions. Moreover, this family has a property that all its conditional moments are polynomials in the conditioning random variable. The significance of this result is evident for individuals working on distribution theory, orthogonal polynomials, q-series theory, and the so-called quantum polynomials. Therefore, it may have a limited number of interested researchers. That is why, we put our results into a broader context. We recall the theory of Hilbert–Schmidt operators and the idea of Lancaster expansions (LEs) of the bivariate distributions absolutely continuous with respect to the product of their marginal distributions. Applications of LE can be found in Mathematical Statistics or the creation of Markov processes with polynomial conditional moments (the most well-known of these processes is the famous Wiener process).

The neo-Kantian transcendentalist reading of the epistemic status of logical axioms in Frege argues that he is committed to the neo-Kantian idea that we are epistemically justified in accepting logical axioms because accepting them is necessary for achieving epistemically crucial goals. However, I show that Frege hesitates to be fully committed to neo-Kantian transcendentalism because he struggles to accept the idea that such a teleological reason can constitute an epistemic warrant. This interpretation shows some crucial aspects of his philosophy of logic, such as his understanding of the relationship between the simplicity and the sufficiency of logical systems.

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how the perturbation of MCMC affects the convergence speed and approximation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has fast convergence speed and high approximation accuracy as well. Our convergence analysis is conducted under either the Wasserstein metric or the $\chi^2$ metric, both are widely used in the literature. The results can be extended to obtain non-asymptotic error bounds for MCMC estimators. We demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis, Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally, we present some simple numerical examples to verify our theoretical claims.