A new mathematical model governing the development of a corrupted hierarchy is derived. This model is based on the Mean Field Games theory. A retrospective problem for that model is considered. From the applied standpoint, this problem amounts to figuring out the past activity of the corrupted hierarchy using the present data for this community. Three new Carleman estimates are derived. These estimates lead to Hölder stability estimates and uniqueness results for both that retrospective problem and its generalized version. Hölder stability estimates characterize the dependence of the error in the solution of the retrospective problem from the error in the input data.
In psychology there is a plethora of different measures and constructs. However, the literature also shows that many of these measures overlap and may even sometimes be redundant. Recognizing such overlap in measures is essential for consolidation and for moving the field forward. Accordingly, we suggest a role herein of the General Factor of Personality (GFP), which emerges from the correlations between specific personality dimensions and reflects a mix of desirable traits (e.g. being sociable, honest, and emotionally stable). It is argued and shown that the GFP is highly correlated with a wide range of psychological traits. We further postulate that this phenomenon provides a parsimonious way of looking at the overlap between many trait measures. This idea is discussed in light of the ongoing debate on the GFP in which some scholars suggest the general factor is substantive and relevant for understanding personality, whereas others consider it to solely reflect a measurement artifact. Irrespective of whether the substantive, artifact, or a mixed explanation of the GFP is adopted, overlooking the presence of a common general factor in psychological measures may, respectively, either impede the development of unifying theories of human behavior, or otherwise compromise measurement validity.
Responsible deployment of AI-assisted video surveillance (A2VS) for public safety requires input from community members and frontline users like security personnel, law enforcement, and small business owners. This study explores their perceptions of A2VS through three in-person focus groups (n = 21) held in June 2025 and a public survey (n = 410) conducted in Charlotte, NC from August to September 2023. Findings show broad support: over 63% of focus group participants expressed positive views, and 85% of survey respondents saw the technology as at least somewhat beneficial. Key concerns included real-time anomaly detection, scalability, and system learning. Random forest analysis of the survey showed education and ethnicity as the top predictors, with white, more educated individuals showing greater support. To synthesize insights, we introduced the Alignment–Tension–Gap (ATG) quadrant map by quantifying cross-group attention and within-group agreement. Alignment topics like notification features were discussed in 100% of groups with 100% agreement. Tension topics like real-time detection appeared in 55% of groups but had only 10% agreement. Emerging gaps like business insights were raised in 25% of groups and showed 70% agreement, pointing to opportunities for innovation.
We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions to the electromagnetic field and imposing additional boundary conditions, after which the problem becomes elliptic. The results are applied to general problems for Maxwell's equations in bounded and unbounded domains, as well as to the transmission problem with inhomogeneities on the right-hand side of the equations and at all boundaries. Relations between the inhomogeneities of the elliptic problem are established that provide a one-to-one correspondence between the solutions of Maxwell's problem and the solutions of the elliptic boundary value problem. As an application, the existence of an orthogonal basis from the eigenfunctions of the general Maxwell's problem is justified.
Despite being more likely to encounter and endure higher levels of psychological distress, African American adults are less likely to seek mental health services. Yet previous research lacks an examination of within-group differences among African Americans' help-seeking attitudes, particularly by generation, gender, or the centrality of race. In this study, we used a nonexperimental correlational research design to examine factors that influence attitudes toward mental health help-seeking in African American adults (N = 190). We examined the potential moderating effects of generation, gender, and race centrality on such attitudes. Using an ordinary least squares regression multiple linear regression analysis, we found that perceived stigmatization of others and self-stigma significantly predicted 22% of the variance in help-seeking attitudes, and the relationship between stigma and mental health help-seeking attitudes was moderated by gender on perceived stigma by others in one's social network and perceived stigma by the general public.
