A residual-set framework is introduced for analyzing additive prime conjectures, with particular emphasis on the Strong Goldbach Conjecture (SGC). For each even integer $E_n\ge 4$, the residual set $ℛ\left(E_n\right)=\{E_n-p\mid$ $p<E_n,p\in \mathbb{P}\}$ is defined, and the universal residual set ${ℛ}_{\mathbb{E}}={{{\displaystyle \cup }}^{\text{}}}_{E_n}ℛ\left(E_n\right)$ is constructed. It is shown that ${ℛ}_{\mathbb{E}}$ contains infinitely many primes. A nontrivial constructive lower bound is derived, establishing that the number of Goldbach partitions satisfies $G\left(E\right)\ge 2$ for all $E\ge 8$, and that the cumulative partition count satisfies ${\displaystyle \sum }_{E\le N}G\left(E\right)\gg \frac{N^2}{{\text{log}}^{4}N}$. An optimized deterministic algorithm is implemented to verify the SGC for even integers up to 16,000 digits. Each computed partition $E_n=p+q$ is validated using elliptic curve primality testing, and no exceptions are observed. Runtime variability observed in the empirical tests corresponds with known fluctuations in prime density and modular residue distribution. A recursive construction is formulated for generating Goldbach partitions, using residual descent and leveraging properties of the residual sets. The method extends naturally to Lemoine's Conjecture, asserting that every odd integer $n\ge 7$ can be expressed as $n=p+2q$, where $p,q\in \mathbb{P}$. A corresponding residual formulation is developed, and it is proven that at least two valid partitions exist for all $n\ge 9$. Comparative analysis with the Hardy-Littlewood and Chen estimates is provided to contextualize the cumulative growth rate. The residual-set methodology offers a deterministic, scalable, and structurally grounded approach to additive problems in prime number theory, supported by both theoretical results and large-scale computational evidence.

The Mambaka watershed is extends between latitudes 1 3°45'E and 14°15'E and longitudes 7°16'N and 6°45'N. The geology, various tectonic and structural events that have affected the Adamawa Plateau in Cameroon make it rich in multi-substance mining. The objective of this study is to map rare earth (REE) geochemical anomalies in the sediments of the watershed streams west of Mambaka, and to trace their origins and geochemical processes. Predictive maps from inverse distance interpolations (IDW), factor analysis (F1) or principal component analysis (PCA) and hierarchical bottom-up classification maps provided a better understanding of the central tendency, distribution and dispersion of REE in the samples and in the study area, based on standard deviation and variance values that generated two factors F1 (Ho-Tm-Er-Yb-Lu-Dy-Tb-Gd-Eu-Sm) and F2 (Pr-Nd-Ce-La-Sm) representing 92.44% of the total cumulative variance. The ratios Ce/Ce* > 0.78 and Eu/Eu* > 1 demonstrate positive anomalies in Ce and Eu, and clear differentiation. The normalized concentrations used to calculate fractionation ratios show that the values for LaN/YbN (0.58 to 1.34), LaN/SmN (0.61 to 0.88) and LaN/LuN (0.62 to 1.43) suggest higher fractionation in SS09 and lower fractionation in SS01. Similarly, the ratios La/Lu (61.71 to 143.46), La/Yb (9.00 to 20.72), La/Sm (4.02 to 5.83) and La/ Lu (61.71 to 143.46) confirm these higher ratios in SS09 and lower in SS01. The REE in the study area comes from hydrothermal processes based on high lineament densities at sampling points in igneous rocks with a mean ∑REE value of between 174-219 ppm.

Background: Maternity leave, whether paid or unpaid, is a critical resource that can significantly impact maternal well-being and newborn outcomes. However, its availability and utilization among mothers living in poverty remain understudied. Education is widely recognized as a key factor that increases access to both paid and unpaid leave. However, the theory of Minorities’ Diminished Returns (MDRs) posits that structural racism, segregation, and labor market discrimination limit the benefits of socioeconomic resources, such as education, for Black and Latino individuals. This suggests that the effects of education on maternity leave may not be uniform across racial and ethnic groups. Objective: This study aimed to examine the MDRs of education on access to unpaid and paid maternity leave among Black and Latino mothers compared to White mothers giving birth while living in poverty. Methods: We utilized baseline data from the Baby’s First Years Study (BFY), a longitudinal investigation of the effects of poverty on child development. The sample consisted of 1,050 mothers living in poverty who had recently given birth. Maternity leave (paid and unpaid) was assessed via self-report, and educational attainment was measured in years of schooling. Structural equation modeling (SEM) and interaction terms were employed to analyze racial and ethnic differences in the relationship between education and access to maternity leave. Results: Educational attainment was positively associated with access to unpaid maternity leave for the overall sample of mothers giving birth in poverty, but this association was weaker for Black and Latino mothers compared to non-Latino White mothers. Education did not significantly increase the likelihood of paid maternity leave, and there were no group differences for this association. Conclusion: This study highlights the urgent needs to address structural racism, labor market discrimination, and residential segregation that diminish the impact of education on living conditions for Black and Latino mothers, compared to non-Latino White mothers, even for those living under poverty. Policymakers and practitioners should develop targeted interventions to reduce racial and ethnic disparities in access to paid and unpaid maternity leave and other critical resources, particularly for new mothers living in poverty. Addressing these inequities is essential for improving maternal and newborn health outcomes and promoting social justice.

Background: Financial well-being is a key domain of overall well-being, encompassing an individual's ability to meet financial obligations, secure their financial future, and maintain a sense of financial freedom. Education is often viewed as a critical pathway to enhancing financial well-being. However, the returns of education on financial well-being are not uniform across racial, ethnic, and nativity groups. The theory of Minorities’ Diminished Returns (MDRs) suggests that the positive effects of education on outcomes such as income and financial security are weaker for marginalized groups, including Black individuals, Latinos, and immigrants. Objective: This study examines the diminished returns of education on financial well-being among Black, Latino, and immigrant populations in the United States. We aim to investigate how structural inequalities contribute to weaker financial returns on education for these groups compared to their White and native-born counterparts. Methods: We utilized data from the Understanding America Study (UAS 2014) to conduct a cross-sectional analysis of adult respondents. The study assessed financial well-being outcomes (e.g., income, savings, and financial security) and their association with educational attainment across racial, ethnic, and nativity groups. Regression models were employed to test for interaction effects between education and race/ethnicity/nativity, adjusting for sociodemographic factors such as age, gender, employment, and family structure. Results: Our analysis included 8,121 individuals. The mean age of the respondents was 48 years (SD = 16). High education was associated with higher financial well-being (B = 1.284, 95% CI: 1.157, 1.410). The interaction terms between education and immigrant status (B = -0.507, 95% CI: -0.930, -0.084), race (Black) (B = -0.770, 95% CI: -1.208, -0.331), and ethnicity (Hispanic) (B = -0.589, 95% CI: -0.969, -0.210) were all significant, suggesting that immigrant, Black, and Hispanic individuals experience diminished returns on education in terms of financial well-being, relative to US-born non-Hispanic White individuals. The significant negative interactions between education and minority statuses (Black, Hispanic, and immigrant) indicate that while education generally improves financial well-being, the magnitude of this improvement is substantially smaller for these marginalized groups. Conclusion: Understanding how education translates to financial well-being across different racial, ethnic, and nativity groups is critical for addressing persistent financial disparities.

In this study, we have investigated the status of faults in terms of precession and subsequence, and their relationship with vein mineralization in Kaybarkuh intrusive body in East of Iran. At least, three generations of faults are evidenced in Dasht-e-Bayaz (DB) fault terminal. During formation of faults, the stress orientation in the region has changed at least once probably due to DB fault evolution. Mineralization, especially gold and copper, is formed along the third-generation faults and sometimes on the fault surfaces. It can be predicted that mineralization also happened in the tensioned area of Kal-Shur covered by salt playa and Quaternary sediments, which requires subsurface and geophysics studies.

The government of Mexico City carried out the introduction of palm trees in the 50s to increase the visual appearance of the main avenues. As a result of introduction of these exotic species, phytosanitary problems appeared. Currently there is scarce information on how to evaluate the health of these majestic monocots, in this sense, it is necessary to implement assessment scales to determine the health condition of the most frequently found species to advance on their care and management. The present study had the following objectives: 1) To determine the current state of health of palm trees by means of a scale of visual evaluation of the crown; 2) To know the diversity and structural characteristics of palm trees and 3) To determine the influence of composite variables on the ecosystem services such as the amount of shade provided. Health of palm trees were evaluated two times (dry and rainy seasons in 2022) on 35 transects of 200 m length. An imaginary circle divided into twelfths was overlapped on palm tree “crowns”, and through it, two absolute variables, Live Crown Ratio (LCR) and Crown Quality (CQ) were evaluated. Composite variables were also calculated. The 12/12 health scale adapted in the present study was useful. Four health categories were obtained for the Live crown ratio (LCR): 7.62% of the palm trees were in critical condition, 7.80% were in intermediate condition, 80.36% were in normal condition, and 4.20% were in excellent condition. Meanwhile, for crown quality (CQ), the percentages were 13.50%, 20.00%, 56.96% and 0.43%, respectively. The total height and “crown” diameter showed a positive correlation with the volume composite variables. The shadow area projected as an important ecosystem service increased as the health of the palm trees improved. This is the first study on palm trees health assessment in Mexico City.

A new parameter was proposed, with the help of which a specific disperse system was characterized. In addition, a regularity was found showing the relationship between the structural characteristics of structural units (particle size distribution, standard deviation, intensity and average diameter). Various highly dispersed systems have been investigated, including polystyrene latex, Sucrose and latex.

The focus of this study was to determine the influence of religious literacy and multicultural teaching competence on the teaching self-efficacy of Religious and Moral Education (RME) teachers in public basic schools within the Kumasi Metropolis. The research employed a cross-sectional survey design with a sample of 308 RME teachers selected through the stratified sampling technique from 165 basic schools across 14 circuits. Data were collected using questionnaires and analysed using Partial Least Squares Structural Equation Modelling (PLS-SEM). The findings revealed that religious literacy significantly and positively influenced teachers’ self-efficacy (β = 0.487, p < 0.05), accounting for 23.7% of the variance. Similarly, multicultural teaching competence demonstrated a strong positive effect on teaching self-efficacy (β = 0.711, p < 0.05), explaining 50.6% of the variance. Finally, the study found that religious literacy and multicultural teaching competence together contributed 52.2% to RME teachers' teaching self-efficacy (SD = 0.692, p < 0.05, R² = 0.522). The study recommended that the Ghana Education Service (GES) and the National Council for Curriculum and Assessment (NaCCA) should design and mandate regular in-service training programmes focused specifically on religious literacy for RME teachers. Also, it was recommended that pre-service and in-service training should emphasise awareness of personal biases, deep knowledge of learners’ cultural and religious backgrounds, and practical skills for culturally responsive pedagogy.

Introduction: Stroke remains one of the leading causes of death and disability worldwide, with ischemic stroke accounting for most cases. Structural vascular factors such as carotid artery tortuosity have gained attention as potential markers of vascular aging and cerebrovascular risk. The carotid tortuosity index (CTI), defined as the ratio of actual vessel length to the straight-line distance between two fixed points, provides a quantitative measure of arterial curvature. A CTI value of ≥1.2 indicates pathological tortuosity. Although noninvasive modalities such as CTA and MRA are frequently used, digital subtraction angiography (DSA) remains the gold standard for evaluating vessel geometry due to its higher spatial precision. This study aimed to determine the association of age, sex, and hypertension with CTI measured by DSA. Methods: A cross-sectional study was conducted from November to December 2025 at the Neurointervention Clinic, RS Pelni Jakarta, Indonesia, involving 61 adult patients who underwent carotid DSA. CTI was measured bilaterally using digital imaging software and classified as <1.2 (non-tortuous) or ≥1.2 (tortuous). Clinical data, including age, sex, and hypertension status, were collected from medical records and analyzed using bivariate tests. Results: Older age (≥65 years), female sex, and hypertension were significantly associated with higher CTI values on both carotid sides. Tortuosity was more common among hypertensive patients and elderly females, indicating the influence of vascular remodeling and chronic hemodynamic stress. Conclusion: Carotid tortuosity increases with age, hypertension, and female sex. DSA-based CTI measurement provides a reliable and precise approach for evaluating vascular changes associated with cerebrovascular risk.

The ultimate goal of this study was to determine the influence of religious literacy and multicultural teaching competence of RME teachers on their teaching self-efficacy in the Accra Metropolis. Grounded in culturally responsive teaching and self-efficacy theory, this study employed a cross-sectional survey design. All 441 RME teachers in the eight (8) circuits in the Metropolis which has seventy-two (72) basic schools were involved in the study through the census method. Data were collected using a questionnaire and analyzed using descriptive statistics and partial least squares structural equation modeling (PLS-SEM). Findings revealed that RME teachers reported high levels of RL, MTC, and TSE. Religious literacy and multicultural teaching competence jointly explained 44.2% of the variance in TSE, with a statistically significant positive effect (p < 0.05). It was recommended that, the curriculum for training RME teachers should include in them topics on RL and MTC.

Background: Resting-state functional MRI (rsfMRI) provides insights into large-scale brain network organization associated with cognitive control, emotion regulation, and attentional processes. The ventral attention network (VAN) is a key salience-driven network that supports attentional re-orienting to behaviorally relevant stimuli. However, little is known about how VAN resting state functional connectivity varies by demographic, socioeconomic, psychosocial, and behavioral factors during early adolescence. Objective: To examine associations between VAN rsfMRI connectivity and multiple demographic, socioeconomic, psychosocial, and behavioral characteristics. Methods: Data came from the baseline and early follow-up waves of the Adolescent Brain Cognitive Development (ABCD) Study. The analytic sample included youth with high-quality baseline rsfMRI data and complete socioeconomic and psychosocial measures. The primary outcome was mean resting-state functional connectivity within the VAN across subcortical and cortical regions of interest (ROIs). Bivariate correlations were computed between VAN connectivity and demographic (age, sex, puberty, race/ethnicity), socioeconomic (income, parental education, marital status, neighborhood income), psychosocial (trauma, discrimination, financial difficulty), trait (impulsivity), and behavioral variables (body mass index, depression, suicide, prodromal symptoms, and substance use). Unadjusted bivariate correlations and adjusted logistic regressions were used for data analysis. Results: VAN connectivity showed small but significant correlations with multiple contextual factors. Higher household income, parental education, and neighborhood affluence were associated with greater connectivity, whereas Black race and Hispanic ethnicity were related to lower connectivity. Youth reporting higher discrimination and financial difficulty exhibited weaker VAN connectivity. Greater VAN connectivity was negatively associated with impulsive reward-driven trait (drive), prodromal symptoms, BMI, and marijuana and alcohol use. Associations between VAN connectivity and suicide, depression, marijuana use, and alcohol use remained significant in age and sex adjusted models. Conclusions: VAN connectivity reflects subtle neural correlates of socioeconomic and psychosocial context in early adolescence. Our results underscore the importance of integrating structural and contextual factors in interpreting brain-behavior associations across diverse populations. These findings are suggestive of stable socioeconomic and psychosocial correlates of network efficiency.

Background: Adolescence is a critical developmental stage for the emergence of major depressive disorder (MDD). Structural and diffusion neuroimaging studies have highlighted the anterior cingulate cortex (ACC) as a key region implicated in emotion regulation, stress reactivity, and mood processing. However, few studies have examined whether microstructural characteristics of the ACC, reflected by mean diffusivity (MD) within gray matter–white matter (GM–WM) contrast regions, are associated with depression in early adolescence. Objective: To examine whether mean diffusivity (MD) within the GM–WM contrast of the left caudal anterior cingulate cortex (ACC) is associated with a past diagnosis of MDD among adolescents in the Adolescent Brain Cognitive Development (ABCD) Study, after accounting for demographic, socioeconomic, and adversity-related factors. Methods: Data were drawn from adolescents with diffusion MRI–derived mean diffusivity measures and diagnostics. The independent variable was mean diffusivity (MD) of the GM–WM contrast in the left caudal ACC. The primary outcome was past MDD diagnosis based on structured psychiatric assessments. Covariates included age, sex, socioeconomic status (SES), and exposure to adverse childhood experiences (ACEs). Logistic regression models tested the association between ACC MD and past MDD. A secondary model evaluated the relationship between ACC MD and past suicide attempt. Results: Mean diffusivity of the left caudal ACC was associated with the odds of past MDD, independent of age, sex, SES, and adversity exposure. In contrast, ACC mean diffusivity was not associated with a history of suicide attempt. Conclusions: Increased mean diffusivity in the caudal ACC may indicate microstructural alterations associated with depressive vulnerability in adolescence. ACC tissue integrity may serve as a sensitive neural correlate of early-onset depression.

Background: Socioeconomic status (SES) is widely associated with improved health, behavioral, and educational outcomes. However, emerging research suggests that these benefits are not uniformly experienced across populations or contexts. The theory of Marginalization-related Diminished Returns (MDRs) has primarily focused on racial and ethnic disparities, showing that individuals from racially marginalized groups often experience weaker protective effects of SES. There is a lack of evidence on geography—particularly rural residence—as a moderator of SES effects. Objective: This review explores how place, especially rural contexts in the U.S., shapes the extent to which SES translates into improved outcomes. We extend the MDRs framework to include place-based and geography-based marginalization, arguing that even among non-Hispanic White populations, rural residence can lead to diminished returns on education, income, and other forms of capital. Content: Drawing on theoretical models such as Fundamental Cause Theory and Bronfenbrenner’s Ecological Systems Theory, and synthesizing empirical findings from studies of academic achievement, substance use, and educational aspirations, this review highlights how structural disadvantages in rural areas weaken the effectiveness of individual and family-level resources. Conclusion: Rural health and educational disparities are not solely due to a lack of resources but may also reflect systemic conditions that erode the value of existing resources. Policy interventions must be place-aware and address the contextual constraints that limit opportunity. Future research should more explicitly test how geography moderates the effects of SES across a range of outcomes and populations.

Background: Sexual and gender minority (SGM) youth are at elevated risk for adverse mental health and substance use outcomes. Stressors such as family conflict, discrimination, and trauma have been suggested as possible mediators of these disparities. Aims: This study examined whether family conflict, discrimination, and trauma mediate the associations between SGM identity and adverse outcomes, including suicide attempt, major depressive disorder (MDD), nicotine use, and marijuana use. Methods: Participants were children from the Adolescent Brain Cognitive Development (ABCD) study. SGM identity was reported at baseline, while outcomes included past MDD and suicide attempts as well as future nicotine and marijuana use. Structural equation modeling (SEM) was used to test both direct and indirect pathways linking SGM identity to mental health and behavioral outcomes. Results: No significant mediation was found through family conflict, discrimination, or trauma. Instead, effects of SGM identity were primarily direct: SGM youth had higher odds of past suicide attempts and MDD, as well as future marijuana use, but not future nicotine use. Stressor variables, however, were independently associated with outcomes. Discrimination predicted all outcomes; trauma was positively associated with suicide, nicotine, and marijuana use but not MDD; and family conflict predicted all outcomes except MDD. Conclusion: Family conflict, discrimination, and trauma did not mediate SGM disparities in mental health and substance use, but each emerged as an independent predictor of risk. These findings highlight the complexity of mechanisms underlying SGM-related disparities and suggest the need for future research to explore additional pathways and contextual influences.

This literature review delves deeply into the epidemiology, structural and cultural challenges, and management strategies of status epilepticus (SE) in sub-Saharan Africa (SSA). Incidence rates of SE vary significantly between countries, with notable disparities associated with socio-economic contexts, healthcare infrastructures, and cultural perceptions of epilepsy. The management of SE in this region is often hindered by constraints in medical infrastructure, inadequate access to specialist diagnostics such as electroencephalogram, and limited availability of essential anti-epileptic drugs, which are frequently out of reach for rural populations. These challenges are further exacerbated by the social stigma and cultural beliefs surrounding epilepsy, impeding access to care and widening inequalities. Moreover, the scarcity of qualified medical personnel undermines the efficient and prompt management of this neurological emergency. The review underscores the pressing need to enhance healthcare infrastructures, boost the capabilities of healthcare professionals, and conduct community awareness initiatives to destigmatize epilepsy and lessen prejudice. Additionally, practical recommendations are put forward for enhancing local capacity, fostering equity in care access, and mitigating regional health disparities in SSA.

This review article provides a comprehensive anatomical analysis of soccer footwear, delving into the intricate structure and functional roles of its constituent components, including the upper, heel counter, tongue, toe box, outsole/sole plate, studs, and insole. Manufacturing processes influencing these structural elements are also discussed. Current market offerings and patented innovations in soccer cleat technology are examined through a biomechanical lens, highlighting their intended functions and limitations. A critical synthesis of existing knowledge underscores the anatomical and biomechanical distinctions between male and female athletes' feet, arguing for the necessity of sex-specific footwear design. This review culminates in emphasizing the imperative for specifically engineered soccer footwear for female athletes to optimize performance, enhance comfort, and mitigate the elevated risk of lower extremity injuries prevalent in the female game, thereby identifying crucial directions for future research in sports biomechanics and footwear engineering.

Background: Educational attainment is strongly linked to increased employment opportunities, higher income, and greater financial security, making its inverse relationship with reliance on social welfare programs well-documented. However, consistent with the Minorities' Diminished Returns (MDRs) theory, the protective effects of education may be weaker for racial and ethnic minority groups compared to non-Latino Whites. This study examines whether the impact of educational attainment (measured as years of schooling) on social welfare use differs between Caribbean Black and White adults in the United States, focusing on outcomes since age 18 and in the past year. Objective: To investigate the relationship between years of schooling and the likelihood of using social welfare programs, while exploring whether this association varies between Caribbean Black and White adults, in alignment with the MDRs framework. Methods: Data were derived from the National Survey of American Life (NSAL), a nationally representative dataset with a robust sample of Black and White adults in the United States. The study focused on Caribbean Black and White participants aged 18 and older. Structural equation modeling (SEM) was employed to examine the relationship between years of schooling and social welfare use, adjusting for covariates including age, gender, employment status, and marital status. Interaction terms were used to assess potential differences in the returns of education across racial groups. Results: Higher educational attainment was associated with reduced likelihood of using social welfare programs overall. However, consistent with the MDRs framework, the protective effect of education was weaker for Caribbean Black individuals compared to their White counterparts. Caribbean Blacks with similar levels of education as Whites were more likely to report using social welfare programs since age 18 and in the past year, highlighting diminished returns on education for this population. Conclusion: This study extends the MDRs framework to Caribbean Black populations, a group rarely studied in the U.S., revealing significant disparities in the economic benefits of education. The findings underscore the need for policies that address systemic barriers limiting the economic returns of education for racial and ethnic minorities, including Caribbean Blacks, to promote greater equity in social and economic outcomes.

Background: Minorities’ Diminished Returns (MDRs) theory posits that the health benefits of socioeconomic resources, such as education, are smaller for marginalized and minoritized populations, including immigrants. While MDRs have been extensively documented for racial and ethnic minorities, less is known about whether these diminished returns extend to immigrant populations. This study tested MDRs of education on various health and cognitive outcomes, including self-rated health (SRH), cognitive function, numeracy, number of chronic medical conditions, and limitations in activities of daily living (ADLs) among immigrants compared to non-immigrants in the United States. Objective. To examine whether educational attainment confers weaker protective effects on SRH, cognitive function, numeracy, chronic medical conditions, and ADLs in immigrants compared to non-immigrants, confirming the presence of MDRs across these domains. Methods: We used data from the Understanding America Study (UAS), a nationally representative survey of U.S. adults. We tested the association between educational attainment and five outcomes—SRH, cognitive function, numeracy, number of chronic medical conditions, and limitations in ADLs—across immigrant and non-immigrant groups. Multivariate regression models were employed, adjusting for key sociodemographic covariates. Results: The protective effects of education on a range of health outcomes were significantly weaker for immigrants compared to non-immigrants. Education level showed weaker associations with SRH, cognitive function, numeracy, number of chronic conditions, and ADLs among immigrants. These findings suggest that even at higher levels of educational attainment, immigrants experience poorer health and cognitive functioning than their U.S.-born counterparts. Conclusion: This study offers strong evidence for the MDRs of education on multiple health outcomes among U.S. immigrants. One possible explanation is that, despite achieving higher levels of education, immigrants often face structural barriers—such as discrimination, limited access to resources, and economic inequities—that constrain the health-related benefits typically associated with educational attainment. Additionally, a portion of immigrant education may be acquired outside the United States, where credentials may not be fully recognized or rewarded within the U.S. labor market. These findings highlight the importance of policies aimed at addressing systemic inequities and improving access to healthcare, employment opportunities, and social support for immigrant communities. Future research should further explore the mechanisms underlying these diminished returns and identify policy solutions to reduce their impact. Keywords: Educational Attainment, Immigrants, Nativity, Self-Rated Health, Chronic Disease, Activities of Daily Living (ADL), Cognitive Function

“To Be Twice as Good to Get Half” is a common mindset among high aspiration and ambition Black individuals in the U.S., capturing the lived reality of Minorities’ Diminished Returns (MDRs). This paper explains that MDRs reflect how, even with high levels of ambition, self-efficacy, education, and income, Black individuals and other marginalized groups do not experience the same protective benefits for health and well-being as White populations. Systemic obstacles embedded within U.S. society weaken the expected returns on socioeconomic achievements for racialized individuals, creating a reality where “being twice as good” still results in lesser outcomes. High-SES Black individuals, for instance, continue to face significant risks for adverse outcomes, such as depression and chronic disease, due to structural inequities across domains like labor market discrimination, segregation, and accumulated disadvantage from childhood. Our analysis identifies key mechanisms—including interpersonal discrimination, lower-quality education, and structural racism in sectors like banking, policing, and real estate—that erode the protective effects of SES across racial lines. Mediating factors, such as chronic stress, allostatic load, and epigenetic changes over the life course, further compound these diminished returns, weakening the expected physical and mental health benefits. Drawing on extensive evidence from U.S. national and local datasets and corroborated by international studies, this paper underscores the necessity of policies that dismantle structural barriers rather than relying solely on SES improvements. Recommendations include implementing multi-sectoral policies, recognizing the unique challenges of middle-class non-White populations, and approaching policy with humility, acknowledging that achieving equity is a long-term endeavor. By challenging the “bootstraps” narrative, this paper advocates for structural interventions aimed at genuine health and economic equity for all racial and socioeconomic groups. While we provide an in-depth analysis of MDRs’ phenomena, mechanisms, mediators, and policy implications, the experience is often distilled as, “I have to be twice as good to get half.”