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Background and aimsAge-related cognitive impairment impacts a significant portion of the elderly population. Remnant cholesterol (RC) has attracted increased attention in relation to cardiovascular disease, diabetes, hypertension, and fatty liver disease. Nevertheless, its role in cognitive function is still enigmatic, prompting our exploration into the potential associations between them.MethodsA total of 1,331 participants from the NHANES (2011–2014) database, all aged over 60, were included in this investigation. Cognitive function was assessed using four widely applied tests, including the Consortium to Establish a Registry for Alzheimer’s Disease Word Learning (CERAD-WL), CERAD Delayed Recall (CERAD-DR), Animal Fluency Test (AFT), as well as Digit Symbol Substitution test (DSST). Z-score is calculated by scores from the above four tests. The association between RC, total cholesterol (TC) to RC and cognitive performance was assessed by logistic regression analyses. In addition, restricted cubic spline (RCS) regression was performed to assess non-linearity between RC and cognitive function. Subgroup analysis was performed to evaluate the robustness of the results in populations with relevant covariate variables.ResultsThose with Z-scores below the 25% quartile are defined as having cognitive impairment, totaling 498 individuals. Observationally, higher RC levels and a lower TC/RC were associated with an increased risk of cognitive impairment. After adjusting for confounding factors, the impact of RC levels on cognitive performance quartiles was consistent across various subgroups, except in individuals with trouble sleeping, no/unknown alcohol use, and no hypertension. Americans with high RC levels and trouble sleeping are more likely to develop cognitive impairment, with an odds ratio of 2.33 (95% CI: 1.18–4.59).ConclusionThis study suggests that higher RC levels and lower levels of TC/RC are associated with an increased likelihood of cognitive impairment, suggesting that RC can serve as a novel and convenient indicator for predicting the risk of cognitive impairment in the US population.

We propose a real-space formalism of the topological Euler class, which characterizes the fragile topology of two-dimensional systems with real wave functions. This real-space description is characterized by local Euler markers whose macroscopic average coincides with the Euler number, and it applies equally well to periodic and open boundary conditions for both crystals and noncrystalline systems. We validate this by diagnosing topological phase transitions in clean and disordered crystalline systems with the reality endowed by the space-time inversion symmetry $\mathcal{I}_{ST}$. Furthermore, we demonstrated the topological Euler phases in quasicrystals and even in amorphous lattices lacking any spatial symmetries. Our work not only provides a local characterization of the fragile topology but also significantly extends its territory beyond $\mathcal{I}_{ST}$-symmetric crystalline materials.