The Full Periodicity Kernel for σ Maps

AbstractLet σ be the topological space formed by the points (x, y) of R2 such that either x2 + y2 = 1, or 0 ≤ x ≤ 2 and y = 1. A σ map ƒ is a continuous self-map of σ having the branching point (0, 1) as a fixed point. We denote by Per(ƒ) the set of periods of all periodic points of ƒ, and by N the set of positive integers. We prove that if ƒ is a σ map and {2, 3, 4, 5, 7} ⊆ Per(ƒ), then Per(ƒ) = N. Conversely, if S ⊆ N is a set such that for every σ map ƒ S ⊆ Per(ƒ) implies Per(ƒ) = N, then {2, 3, 4, 5, 7} ⊆ S

Risk factors for incident dementia among older Cubans

Introduction: Little is known about risk factors of dementia in Latin American countries. We aimed to identify socio-demographic, health and lifestyle risk factors of incident dementia in Cuban older adults. Methods: Data were from 1,846 participants in the Cuban cohort of the 10/66 Dementia Research Group. Participants completed questionnaires, health examinations, and cognitive tests at baseline (2003-2006) and 4.5 years later (2007-2010). Associations between risk factors (baseline) and incident dementia (follow-up) were examined using logistic regression. Results: Just over 9% of participants developed dementia. Overall, older age and low physical activity were associated with incident dementia. In those 65-74 years of age, depression, stroke and low physical activity were associated with incident dementia. In those ≥75 years of age, low physical activity, never eating fish, and smoking were associated with incident dementia. Conclusions: Modifiable lifestyle factors play an important role in developing dementia in Cuban older adults. This knowledge opens up opportunities for preventive strategies

Prevalence and Incidence of Parkinson\u27s Disease in Latin America: A Meta-Analysis

\ua9 2023 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society. Background: Parkinson\u27s disease (PD) is a rapidly growing neurodegenerative disorder, but up-to-date epidemiological data are lacking in Latin America. We sought to estimate the prevalence and incidence of PD and parkinsonism in Latin America. Methods: We searched Medline, Embase, Scopus, Web of Science, Scientific Electronic Library Online, and Literatura Latino-Americana e do Caribe em Ci\ueancias da Sa\ufade or the Latin American and Caribbean Health Science Literature databases for epidemiological studies reporting the prevalence or incidence of PD or parkinsonism in Latin America from their inception to 2022. Quality of studies was assessed using the Joanna Briggs Institute (JBI) Critical Appraisal Checklist. Data were pooled via random-effects meta-analysis and analyzed by data source (cohort studies or administrative databases), sex, and age group. Significant differences between groups were determined by meta-regression. Results: Eighteen studies from 13 Latin American countries were included in the review. Meta-analyses of 17 studies (nearly 4 million participants) found a prevalence of 472 (95% CI, 271–820) per 100,000 and three studies an incidence of 31 (95% CI, 23–40) per 100,000 person-years for PD; and seven studies found a prevalence of 4300 (95% CI, 1863–9613) per 100,000 for parkinsonism. The prevalence of PD differed by data source (cohort studies, 733 [95% CI, 427–1255] vs. administrative databases. 114 [95% CI, 63–209] per 100,000, P < 0.01), age group (P < 0.01), but not sex (P = 0.73). PD prevalence in ≥60 years also differed significantly by data source (cohort studies. 1229 [95% CI, 741–2032] vs. administrative databases, 593 [95% CI, 480–733] per 100,000, P < 0.01). Similar patterns were observed for parkinsonism. Conclusions: The overall prevalence and incidence of PD in Latin America were estimated. PD prevalence differed significantly by the data source and age, but not sex. \ua9 2023 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society

Burden of Parkinsonism and Parkinson\u27s Disease on Health Service Use and Outcomes in Latin America

\ua9 2023 - The authors. Published by IOS Press.Background: Little is known about the burden of parkinsonism and Parkinson\u27s disease (PD) in Latin America. Better understanding of health service use and clinical outcomes in PD is needed to improve its prognosis. Objective: The aim of the study was to estimate the burden of parkinsonism and PD in six Latin American countries. Methods: 12,865 participants aged 65 years and older from the 10/66 population-based cohort study were analysed. Baseline assessments were conducted in 2003-2007 and followed-up 4 years later. Parkinsonism and PD were defined using current clinical criteria or self-reported diagnosis. Logistic regression models assessed the association between parkinsonism/PD with baseline health service use (community-based care or hospitalisation in the last 3 months) and Cox proportional hazards regression models with incident dependency (subjective assessment by interviewer based on informant interview) and mortality. Separate analyses for each country were combined via fixed effect meta-analysis. Results: At baseline, the prevalence of parkinsonism and PD was 7.9% (n = 934) and 2.6% (n = 317), respectively. Only parkinsonism was associated with hospital admission at baseline (OR 1.89, 95% CI 1.30-2.74). Among 7,296 participants without dependency at baseline, parkinsonism (HR 2.34, 95% CI 1.81-3.03) and PD (2.10, 1.37-3.24) were associated with incident dependency. Among 10,315 participants with vital status, parkinsonism (1.73, 1.50-1.99) and PD (1.38, 1.07-1.78) were associated with mortality. The Higgins I2 tests showed low to moderate levels of heterogeneity across countries. Conclusions: Our findings show that older people with parkinsonism or PD living in Latin America have higher risks of developing dependency and mortality but may have limited access to health services

Associations between education and dementia in the Caribbean and the United States: An international comparison

Introduction: Despite high dementia prevalence in Hispanic populations globally, especially Caribbean Hispanics, no study has comparatively examined the association between education and dementia among Hispanics living in the Caribbean Islands and older adults in the United States. Methods: We used data on 6107 respondents aged 65 and older in the baseline wave of the population-based and harmonized 10/66 survey from Cuba, the Dominican Republic, and Puerto Rico, collected between 2003 and 2008, and 11,032 respondents aged 65 and older from the U.S.-based Health and Retirement Study data in 2014, a total of 17,139 individuals. We estimated multivariable logistic regression models examining the association between education and dementia, adjusted for age, income, assets, and occupation. The models were estimated separately for the Caribbean population (pooled and by setting) and the U.S. population by race/ethnicity (Hispanic, Black, and White), followed by pooled models across all populations. Results: In the Caribbean population, the relative risk of dementia among low versus high educated adults was 1.45 for women (95% confidence interval [CI] 1.17, 1.74) and 1.92 (95% CI 1.35, 2.49) for men, smaller compared to those in the United States, especially among non-Hispanic Whites (women: 2.78, 95% CI 1.94, 3.61; men: 5.98, 95% CI 4.02, 7.95). Discussion: The differential associations between education and dementia across the Caribbean and US settings may be explained by greater disparities in social conditions in the United States compared to the Caribbean, such as access to health care, healthy behaviors, and social stressors, which serve as potentially important mediators

Leg length, skull circumference, and the incidence of dementia in Latin America and China: A 10/66 population-based cohort study

\ua9 2018 Prince et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Background Adult leg length is influenced by nutrition in the first few years of life. Adult head circumference is an indicator of brain growth. Cross-sectional studies indicate inverse associations with dementia risk, but there have been few prospective studies. Methods Population-based cohort studies in urban sites in Cuba, Dominican Republic Puerto Rico and Venezuela, and rural and urban sites in Peru, Mexico and China. Sociodemographic and risk factor questionnaires were administered to all participants, and anthropometric measures taken, with ascertainment of incident dementia, and mortality, three to five years later. Results Of the original at risk cohort of 13,587 persons aged 65 years and over, 2,443 (18.0%) were lost to follow-up; 10,540 persons with skull circumference assessments were followed up for 40,466 person years, and 10,400 with leg length assessments were followed up for 39,954 person years. There were 1,009 cases of incident dementia, and 1,605 dementia free deaths. The fixed effect pooled meta-analysed adjusted subhazard ratio (ASHR) for leg length (highest vs. lowest quarter) was 0.80 (95% CI, 0.66–0.97) and for skull circumference was 1.02 (95% CI, 0.84–1.25), with no heterogeneity of effect between sites (I2 = 0%). Leg length measurements tended to be shorter at follow-up, particularly for those with baseline cognitive impairment and dementia. However, leg length change was not associated with dementia incidence (ASHR, per cm 1.006, 95% CI 0.992–1.020), and the effect of leg length was little altered after adjusting for baseline frailty (ASHR 0.82, 95% CI 0.67–0.99). A priori hypotheses regarding effect modification by gender or educational level were not supported. However, the effect of skull circumference was modified by gender (M vs F ASHR 0.86, 95% CI 0.75–0.98), but in the opposite direction to that hypothesized with a greater protective effect of larger skull dimensions in men. Conclusions Consistent findings across settings provide quite strong support for an association between adult leg length and dementia incidence in late-life. Leg length is a relatively stable marker of early life nutritional programming, which may confer brain reserve and protect against neu-rodegeneration in later life through mitigation of cardiometabolic risk. Further clarification of these associations could inform predictive models for future dementia incidence in the context of secular trends in adult height, and invigorate global efforts to improve childhood nutrition, growth and development

Prediction of dementia risk in low-income and middle-income countries (the 10/66 Study): an independent external validation of existing models

BackgroundTo date, dementia prediction models have been exclusively developed and tested in high-income countries (HICs). However, most people with dementia live in low-income and middle-income countries (LMICs), where dementia risk prediction research is almost non-existent and the ability of current models to predict dementia is unknown. This study investigated whether dementia prediction models developed in HICs are applicable to LMICs.MethodsData were from the 10/66 Study. Individuals aged 65 years or older and without dementia at baseline were selected from China, Cuba, the Dominican Republic, Mexico, Peru, Puerto Rico, and Venezuela. Dementia incidence was assessed over 3–5 years, with diagnosis according to the 10/66 Study diagnostic algorithm. Discrimination and calibration were tested for five models: the Cardiovascular Risk Factors, Aging and Dementia risk score (CAIDE); the Study on Aging, Cognition and Dementia (AgeCoDe) model; the Australian National University Alzheimer's Disease Risk Index (ANU-ADRI); the Brief Dementia Screening Indicator (BDSI); and the Rotterdam Study Basic Dementia Risk Model (BDRM). Models were tested with use of Cox regression. The discriminative accuracy of each model was assessed using Harrell's concordance (c)-statistic, with a value of 0·70 or higher considered to indicate acceptable discriminative ability. Calibration (model fit) was assessed statistically using the Grønnesby and Borgan test.Findings11 143 individuals without baseline dementia and with available follow-up data were included in the analysis. During follow-up (mean 3·8 years [SD 1·3]), 1069 people progressed to dementia across all sites (incidence rate 24·9 cases per 1000 person-years). Performance of the models varied. Across countries, the discriminative ability of the CAIDE (0·52≤c≤0·63) and AgeCoDe (0·57≤c≤0·74) models was poor. By contrast, the ANU-ADRI (0·66≤c≤0·78), BDSI (0·62≤c≤0·78), and BDRM (0·66≤c≤0·78) models showed similar levels of discriminative ability to those of the development cohorts. All models showed good calibration, especially at low and intermediate levels of predicted risk. The models validated best in Peru and poorest in the Dominican Republic and China.InterpretationNot all dementia prediction models developed in HICs can be simply extrapolated to LMICs. Further work defining what number and which combination of risk variables works best for predicting risk of dementia in LMICs is needed. However, models that transport well could be used immediately for dementia prevention research and targeted risk reduction in LMICs

Prevalence of dementia in Latin America: a collaborative study of population-based cohorts

Background: Dementia is becoming a major public health problem in Latin America (LA), yet epidemiological information on dementia remains scarce in this region. This study analyzes data from epidemiological studies on the prevalence of dementia in LA and compares the prevalence of dementia and its causes across countries in LA and attempts to clarify differences from those of developed regions of the world. Methods: A database search for population studies on rates of dementia in LA was performed. Abstracts were also included in the search. Authors of the publications were invited to participate in this collaborative study by sharing missing or more recent data analysis with the group. Results: Eight studies from six countries were included. The global prevalence of dementia in the elderly (≥65 years) was 7.1% (95% CI: 6.8–7.4), mirroring the rates of developed countries. However, prevalence in relatively young subjects (65–69 years) was higher in LA studies The rate of illiteracy among the elderly was 9.3% and the prevalence of dementia in illiterates was two times higher than in literates. Alzheimer’s disease was the most common cause of dementia. Conclusions: Compared with studies from developed countries, the global prevalence of dementia in LA proved similar, although a higher prevalence of dementia in relatively young subjects was evidenced, which may be related to the association between low educational level and lower cognitive reserve, causing earlier emergence of clinical signs of dementia in the LA elderly population

A novel presenilin 1 mutation (L174M) in a large Cuban family with early onset Alzheimer disease.

We studied a Cuban family with presenile dementia (autosomal dominant) consisting of 281 members within six generations, the proband descended from a Spanish founder. Mean age at onset was 59 years of age. Memory impairment was the main symptom in all patients, additionally, ischemic episodes were described in 4 (n = 18) patients. Neuropathological examination of brain material (1 patient) revealed neuronal loss, amyloid plaques, and neurofibrillary tangles. Thirty DNA samples were genotyped (regions on chromosome 1, 3, 10, 12, 14, 17, 19, 20, and 21). A maximum Lod score of 3.79 at theta = 0 was obtained for marker D14S43, located in a 9-cM interval in which all patients shared the same haplotype. Sequencing of the PSEN1 gene revealed a heterozygous base substitution, C520A (exon 6), which is predicted to cause an amino acid change from leucine to methionine in the TMIII of the presenilin 1 protein. The mutation was found to co-segregate with the disease phenotype and the associated disease haplotype. The C --> A change was not observed in 80 control chromosomes from the Cuban population. Leucine at position 174 is highly conserved among species and is identical in prese