We consider the system $\dot {x}=(A+ P(t,\epsilon )) x, x\in \mathbb {R}^{3}, $ where $A, P$ are both three-dimensional skew symmetric matrices, A is a constant matrix with eigenvalues $\pm i\unicode{x3bb} $ and 0, $P(t,\epsilon )$ is $C^{m}(m=0,1)$-smooth in $\epsilon $ and analytic quasi-periodic with respect to t with basic frequencies $\omega =(1,\alpha )$, with $\alpha $ being irrational, and $\epsilon $ is a small parameter. Under some non-resonant conditions about the basic frequencies and the eigenvalues of the constant matrix and without any non-degeneracy condition, it is proved that for many sufficiently small parameters, this system can be reduced to a rotation system. Furthermore, if the basic frequencies satisfy that $ 0\leq \beta (\alpha ) < r,$ where $\beta (\alpha )=\limsup \nolimits _{n\rightarrow \infty } {\ln q_{n+1}}/{q_{n}},$ $q_{n}$ is the sequence of denominations of the best rational approximations for $\alpha \in \mathbb {R} \setminus \mathbb {Q},$ r is the initial radius of analytic domain, it is proved that for many sufficiently small parameters, this system can be reduced to a constant system.

Obesity is an established risk factor for hypertension, but the mechanisms are only partially understood. We examined whether body mass index (BMI)-related DNA methylation (DNAm) variation would mediate the association of BMI with blood pressure (BP). We first conducted a genomewide DNA methylation analysis in monozygotic twin pairs to detect BMI-related DNAm variation and then evaluated the mediating effect of DNAm on the relationship between BMI and BP levels using the causal inference test (CIT) method and mediation analysis. Ontology enrichment analysis was performed for CpGs using the GREAT tool. A total of 60 twin pairs for BMI and systolic blood pressure (SBP) and 58 twin pairs for BMI and diastolic blood pressure (DBP) were included. BMI was positively associated with SBP (β = 1.86, p = .0004). The association between BMI and DNAm of 85 CpGs reached p < 1×10–4 level. Eleven BMI-related differentially methylated regions (DMRs) within LNCPRESS1, OGDHL, RNU1-44P, NPHS1, ECEL1P2, LLGL2, RNY4P15, MOGAT3, PHACTR3, and BAI2 were found. Of the 85 CpGs, 9 mapped to C10orf71-AS1, NDUFB5P1, KRT80, BAI2, ABCA2, PEX11G and FGF4 were significantly associated with SBP levels. Of the 9 CpGs, 2 within ABCA2 negatively mediated the association between BMI and SBP, with a mediating effect of −0.24 (95% CI [−0.65, −0.01]). BMI was also positively associated with DBP (β = 0.60, p = .0495). The association between BMI and DNAm of 193 CpGs reached p < 1×10−4 level. Twenty-five BMI-related DMRs within OGDHL, POU4F2, ECEL1P2, TTC6, SMPD4, EP400, TUBA1C and AGAP2 were found. Of the 193 CpGs, 33 mapped to ABCA2, ADORA2B, CTNNBIP1, KDM4B, NAA60, RSPH6A, SLC25A19 and STIL were significantly associated with DBP levels. Of the 33 CpGs, 12 within ABCA2, SLC25A19, KDM4B, PTPRN2, DNASE1, TFCP2L1, LMNB2 and C10orf71-AS1 negatively mediated the association between BMI and DBP, with a total mediation effect of −0.66 (95% CI [−1.07, −0.30]). Interestingly, BMI might also negatively mediate the association between the DNAm of most CpG mediators mentioned above and BP. The mediating effect of DNAm was also found when stratified by sex. In conclusion, DNAm variation may partially negatively mediate the association of BMI with BP. Our findings may provide new clues to further elucidate the pathogenesis of obesity to hypertension and identify new diagnostic biomarkers and therapeutic targets for hypertension.

Almost all creatinine is excreted by the kidney in individuals. Serum creatinine concentration, a widely used renal function index in clinical practice, can be affected by both genetic and environmental factors, as evidenced by current research exploring the relationship between these factors and kidney function. However, few studies have explored the heritability of serum creatinine in Asian populations. Therefore, we explored the genetic and environmental factors that affect the serum creatinine level in Asian populations. Participants in this study came from the Qingdao Twin Registry in China, and 374 pairs of twins were included, of which 139 pairs were dizygotic twins, whose ages ranged from 40 to 80 years old, and the serum creatinine level ranged from 10 to 126 μmol/L. Structural equation models were constructed using Mx software to calculate heritability, with adjusted covariates being age, sex, and body mass index. The results of heritability analysis showed that ACE was the best fit model. Serum creatinine level is influenced by genetic and environmental factors. The result of heritability was 35.44%, and the influence of shared environmental factors accounted for 52.13%. This study provided the relevant basis for future research on genetic and environmental factors affecting serum creatinine levels in Asian populations.

An abnormal alanine aminotransferase (ALT) level is predictive of disease and all-cause mortality and may indicate liver injury. Using twin modeling, the genetic and environmental factors that affect human serum ALT levels have been well studied for the populations in the different countries, and the results showed moderate-to-high heritability. However, the heritability of ALT level has not been explored in Chinese population. Thus, we recruited 369 pairs of twins (233 monozygotic and 136 dizygotic) from the Qingdao Twin Registry in China with a median age of 50 years (40−80 years). Correlation analysis and a structural equation model (SEM) were conducted to evaluate the heritability of ALT level. The data for age, gender, body mass index and alcohol consumption were set as covariates. Intrapair correlation in monozygotic twins was 0.64 (95%CI [.56, .71]) and 0.42 (95% CI [.28, .55]) in dizygotic twins. The SEM analysis indicated that 65% (95% CI [57%, 71%]) of the variation in ALT levels can be explained by additive genetics and 35% (95% CI [29%, 44%]) of the variation is attributed to unique environmental factors or residuals. Shared environmental influences were not significant. In conclusion, serum ALT variations exhibited strong genetic effects. The variation could also be explained by unique environmental factors. However, shared environmental factors have a minor impact on the serum ALT level.

We explored the genetic architecture of metabolic risk factors of cardiovascular diseases (CVDs) and their clustering in Chinese boys and girls. Seven metabolic traits (body mass index [BMI], waist circumference [WC], systolic blood pressure [SBP], diastolic blood pressure [DBP], total cholesterol [TC], triglyceride [TG], and uric acid [UA]) were measured in a sample of 1016 twins between 8 and 17 years of age, recruited from the Qingdao Twin Registry. Cholesky, independent pathway, and common pathway models were used to identify the latent genetic structure behind the clustering of these metabolic traits. Genetic architecture of these metabolic traits was largely similar in boys and girls. The highest heritability was found for BMI (a2 = 0.63) in boys and TC (a2 = .69) in girls. Three heritable factors, adiposity (BMI and WC), blood pressure (SBP and DBP), and metabolite factors (TC, TG, and UA), which formed one higher-order latent phenotype, were identified. Latent genetic, common environmental, and unique environmental factors indirectly impacted the three factors through one single latent factor. Our results suggest that there is one latent factor influencing several metabolic traits, which are known risk factors of CVDs in young Chinese twins. Latent genetic, common environmental, and unique environmental factors indirectly imposed on them. These results inform strategies for gene pleiotropic discovery and intervening of CVD risk factors during childhood and adolescence.

The effect of coffee consumption on functional disability has been scarcely investigated. Thus, this study aimed to examine the association between coffee consumption and functional disability in older American adults. Participants (≥60 years old, n 7704) were from the National Health and Nutrition Examination Survey 2007–2016. Coffee consumption was assessed through two 24-h dietary recall interviews. Five domains of functional disability including lower extremity mobility (LEM), general physical activity (GPA), leisure and social activities (LSA), activities of daily living (ADL) and instrumental activities of daily living (IADL) were self-reported. Age- and multivariate-adjusted logistic regression models and restricted cubic spline analyses were used. Total coffee consumption was inversely associated with LEM, GPA, LSA and IADL disability. Compared with non-drinkers of total coffee, those who consumed ≥2 cups/d reported lower odds of LEM (OR 0·67, 95 % CI 0·50, 0·91), GPA (OR 0·65, 95 % CI 0·47, 0·88), LSA (OR 0·61, 95 % CI 0·45, 0·83) and IADL (OR 0·59, 95 % CI 0·44, 0·78) disability. The dose–response analyses confirmed these relationships. Intake of ≥2 cups/d caffeinated coffee was also inversely linked to GPA (OR 0·67, 95 % CI 0·48, 0·92), LSA (OR 0·66, 95 % CI 0·46, 0·93) and IADL (OR 0·57, 95 % CI 0·43, 0·75) disability, whereas the inverse association of 2+ cups/d decaffeinated coffee was only on LEM (OR 0·43, 95 % CI 0·23, 0·81) and LSA (OR 0·39, 95 % CI 0·16, 0·94) disability. The present study suggested that coffee consumption was inversely associated with functional disability in older American adults. Those associations of diverse coffee types differed across domains of functional disability.

In this paper we consider the following nonlinear quasi-periodic system:

$$\begin{eqnarray}{\dot{x}}=(A+\unicode[STIX]{x1D716}P(t,\unicode[STIX]{x1D716}))x+\unicode[STIX]{x1D716}g(t,\unicode[STIX]{x1D716})+h(x,t,\unicode[STIX]{x1D716}),\quad x\in \mathbb{R}^{d},\end{eqnarray}$$

$A$

$d\times d$

$\unicode[STIX]{x1D716}g(t,\unicode[STIX]{x1D716})$

$\unicode[STIX]{x1D716}$

$h(x,t,\unicode[STIX]{x1D716})=O(x^{2})$

$x\rightarrow 0$

$P,g$

$h$

$t$

$\unicode[STIX]{x1D714}=(1,\unicode[STIX]{x1D6FC})$

$\unicode[STIX]{x1D6FC}$

$\unicode[STIX]{x1D716}$

$$\begin{eqnarray}{\dot{x}}=(A+B_{\ast }(t))x+h_{\ast }(x,t,\unicode[STIX]{x1D716}),\quad x\in \mathbb{R}^{d},\end{eqnarray}$$

$h_{\ast }(x,t,\unicode[STIX]{x1D716})=O(x^{2})~(x\rightarrow 0)$

$\unicode[STIX]{x1D714}=(1,\unicode[STIX]{x1D6FC})$

$\unicode[STIX]{x1D716}$

Depression is an important public health problem. The aim of the study is to explore the associations of total protein intake and protein sources with the risk of depressive symptoms. This cross-sectional study used data from the National Health and Nutrition Examination Survey for the years 2007–2014. Dietary protein intake was obtained from two 24-h dietary recall interviews. Depressive symptoms were assessed by a nine-item Patient Health Questionnaire. Logistic regression models and restricted cubic spline models were used to estimate the associations of total protein intake (g/kg per d) and protein sources with the risk of depressive symptoms. A total of 17 845 individuals aged 18 years and older were included in this study. Total protein intake was inversely associated with the risk of depressive symptoms. The full-adjusted OR of depressive symptoms was 0·34 (95 % CI 0·17, 0·68) for quartile (Q) 4 v. Q1 of total protein intake. For protein intake from milk and milk products, the association with depressive symptoms was significant both for Q2 v. Q1 (OR 0·61; 95 % CI 0·41, 0·93) and Q3 v. Q1 (OR 0·37; 95 % CI 0·24, 0·59) in the full-adjusted model. In the dose–response analysis, the shape of the associations of total protein intake and protein intake from milk and milk products with the risk of depressive symptoms was approximately L-shaped and U-shaped, respectively. The present study demonstrated that total protein intake and protein intake from milk and milk products might reduce the risk of depressive symptoms in US adults.

Whether monozygotic (MZ) and dizygotic (DZ) twins differ from each other in a variety of phenotypes is important for genetic twin modeling and for inferences made from twin studies in general. We analyzed whether there were differences in individual, maternal and paternal education between MZ and DZ twins in a large pooled dataset. Information was gathered on individual education for 218,362 adult twins from 27 twin cohorts (53% females; 39% MZ twins), and on maternal and paternal education for 147,315 and 143,056 twins respectively, from 28 twin cohorts (52% females; 38% MZ twins). Together, we had information on individual or parental education from 42 twin cohorts representing 19 countries. The original education classifications were transformed to education years and analyzed using linear regression models. Overall, MZ males had 0.26 (95% CI [0.21, 0.31]) years and MZ females 0.17 (95% CI [0.12, 0.21]) years longer education than DZ twins. The zygosity difference became smaller in more recent birth cohorts for both males and females. Parental education was somewhat longer for fathers of DZ twins in cohorts born in 1990–1999 (0.16 years, 95% CI [0.08, 0.25]) and 2000 or later (0.11 years, 95% CI [0.00, 0.22]), compared with fathers of MZ twins. The results show that the years of both individual and parental education are largely similar in MZ and DZ twins. We suggest that the socio-economic differences between MZ and DZ twins are so small that inferences based upon genetic modeling of twin data are not affected.

The genetic and environmental impacts on correlations between hearing and cognitive functions have not been well studied. Cognitive function was evaluated by the Montreal Cognitive Assessment (MoCA). Hearing function was assessed by audiometric pure-tone hearing thresholds at different frequencies, including 0.5 kHz, 1 kHz, 2 kHz, 4 kHz, 8 kHz, and 12.5 kHz, with the lower hearing thresholds indicating better hearing function. Cognitive and hearing functions were measured on 379 complete twin pairs (240 monozygotic and 139 dizygotic pairs) with a median age of 50 years (range: 40–80 years). Bivariate twin models were fitted to quantify the genetic and environmental components of the correlations between hearing and cognitive functions. The analysis showed significantly high genetic correlation between 2 kHz of hearing and cognition (rG = −1.00, 95% CI [−1.00, −0.46]) and moderate genetic correlation between 4 kHz of hearing and cognition (rG = −0.62, 95% CI [−1.00, −0.14]). We found no significant genetic correlations between low as well as high frequencies of hearing and cognition. Low to moderate common and unique environmental correlations were shown between low frequencies of hearing and cognition (−0.13 to −0.39) and the common environmental correlation between 8 kHz, one of the high frequencies of hearing, and cognition (−0.22). The middle frequencies of hearing and cognitive functions may have a shared genetic basis. Low frequencies of hearing and cognition may share similar common and unique environmental factors. At 8 kHz, the high frequency of hearing and cognition may share similar common environment. This twin study detected a significant genetic and environmental basis in the phenotype correlation between cognition and hearing, which differed across frequencies.

Genetic and environmental influences on predictors of decline in daily functioning, including forced expiratory volume in 1 s (FEV1), forced vital capacity (FVC), handgrip, and five-times-sit-to-stand test (FTSST), have not been addressed in the aging Chinese population. We performed classical twin modeling on FEV1, FVC, handgrip, and FTSST in 379 twin pairs (240 MZ and 139 DZ) with median age of 50 years (40–80 years). Data were analyzed by fitting univariate and bivariate twin models to estimate the genetic and environmental influences on these measures of physical function. Heritability was moderate for FEV1, handgrip, and FTSST (55–60%) but insignificant for FVC. Only FVC showed moderate control, with shared environmental factors accounting for about 50% of the total variance. In contrast, all measures of pulmonary function and muscle strength showed modest influences from the unique environment (40–50%). Bivariate analysis showed highly positive genetic correlations between FEV1 and FVC (rG = 1.00), and moderately negative genetic correlations between FTSST and FEV1 (rG = −0.33) and FVC (rG = −0.42). FEV1 and FVC, as well as FEV1 and handgrip, displayed high common environmental correlations (rC = 1.00), and there were moderate correlations between FVC and handgrip (rC = 0.44). FEV1 and FVC showed high unique environmental correlations (rE = 0.76) and low correlations between handgrip and FEV1 (rE = 0.17), FVC (rE = 0.14), and FTSST (rE = −0.13) with positive or negative direction. We conclude that genetic factors contribute significantly to the individual differences in common indicators of daily functioning (FEV1, handgrip, and FTSST). FEV1 and FVC were genetically and environmentally correlated. Pulmonary function and FTSST may share similar sets of genes but in the negative direction. Pulmonary function and muscle strength may have a shared environmental background.

Although the correlation between cognition and physical function has been well studied in the general population, the genetic and environmental nature of the correlation has been rarely investigated. We conducted a classical twin analysis on cognitive and physical function, including forced expiratory volume in one second (FEV1), forced vital capacity (FVC), handgrip strength, five-times-sit-to-stand test (FTSST), near visual acuity, and number of teeth lost in 379 complete twin pairs. Bivariate twin models were fitted to estimate the genetic and environmental correlation between physical and cognitive function. Bivariate analysis showed mildly positively genetic correlations between cognition and FEV1, rG = 0.23 [95% CI: 0.03, 0.62], as well as FVC, rG = 0.35 [95% CI: 0.06, 1.00]. We found that FTSST and cognition presented very high common environmental correlation, rC = -1.00 [95% CI: -1.00, -0.57], and low but significant unique environmental correlation, rE = -0.11 [95% CI: -0.22, -0.01], all in the negative direction. Meanwhile, near visual acuity and cognition also showed unique environmental correlation, rE = 0.16 [95% CI: 0.03, 0.27]. We found no significantly genetic correlation for cognition with handgrip strength, FTSST, near visual acuity, and number of teeth lost. Cognitive function was genetically related to pulmonary function. The FTSST and cognition shared almost the same common environmental factors but only part of the unique environmental factors, both with negative correlation. In contrast, near visual acuity and cognition may positively share part of the unique environmental factors.

A trend toward greater body size in dizygotic (DZ) than in monozygotic (MZ) twins has been suggested by some but not all studies, and this difference may also vary by age. We analyzed zygosity differences in mean values and variances of height and body mass index (BMI) among male and female twins from infancy to old age. Data were derived from an international database of 54 twin cohorts participating in the COllaborative project of Development of Anthropometrical measures in Twins (CODATwins), and included 842,951 height and BMI measurements from twins aged 1 to 102 years. The results showed that DZ twins were consistently taller than MZ twins, with differences of up to 2.0 cm in childhood and adolescence and up to 0.9 cm in adulthood. Similarly, a greater mean BMI of up to 0.3 kg/m2 in childhood and adolescence and up to 0.2 kg/m2 in adulthood was observed in DZ twins, although the pattern was less consistent. DZ twins presented up to 1.7% greater height and 1.9% greater BMI than MZ twins; these percentage differences were largest in middle and late childhood and decreased with age in both sexes. The variance of height was similar in MZ and DZ twins at most ages. In contrast, the variance of BMI was significantly higher in DZ than in MZ twins, particularly in childhood. In conclusion, DZ twins were generally taller and had greater BMI than MZ twins, but the differences decreased with age in both sexes.

For over 100 years, the genetics of human anthropometric traits has attracted scientific interest. In particular, height and body mass index (BMI, calculated as kg/m2) have been under intensive genetic research. However, it is still largely unknown whether and how heritability estimates vary between human populations. Opportunities to address this question have increased recently because of the establishment of many new twin cohorts and the increasing accumulation of data in established twin cohorts. We started a new research project to analyze systematically (1) the variation of heritability estimates of height, BMI and their trajectories over the life course between birth cohorts, ethnicities and countries, and (2) to study the effects of birth-related factors, education and smoking on these anthropometric traits and whether these effects vary between twin cohorts. We identified 67 twin projects, including both monozygotic (MZ) and dizygotic (DZ) twins, using various sources. We asked for individual level data on height and weight including repeated measurements, birth related traits, background variables, education and smoking. By the end of 2014, 48 projects participated. Together, we have 893,458 height and weight measures (52% females) from 434,723 twin individuals, including 201,192 complete twin pairs (40% monozygotic, 40% same-sex dizygotic and 20% opposite-sex dizygotic) representing 22 countries. This project demonstrates that large-scale international twin studies are feasible and can promote the use of existing data for novel research purposes.

The genetic influences on aging-related phenotypes, including cognition and depression, have been well confirmed in the Western populations. We performed the first twin-based analysis on cognitive performance, memory and depression status in middle-aged and elderly Chinese twins, representing the world's largest and most rapidly aging population. The sample consisted of 384 twin pairs with a median age of 50 years. Cognitive function was measured using the Montreal Cognitive Assessment (MoCA) scale; memory was assessed using the revised Wechsler Adult Intelligence scale; depression symptomatology was evaluated by the self-reported 30-item Geriatric Depression (GDS-30)scale. Both univariate and multivariate twin models were fitted to the three phenotypes with full and nested models and compared to select the best fitting models. Univariate analysis showed moderate-to-high genetic influences with heritability 0.44 for cognition and 0.56 for memory. Multivariate analysis by the reduced Cholesky model estimated significant genetic (rG = 0.69) and unique environmental (rE = 0.25) correlation between cognitive ability and memory. The model also estimated weak but significant inverse genetic correlation for depression with cognition (-0.31) and memory (-0.28). No significant unique environmental correlation was found for depression with other two phenotypes. In conclusion, there can be a common genetic architecture for cognitive ability and memory that weakly correlates with depression symptomatology, but in the opposite direction.

Systolic and diastolic blood pressure, pulse pressure (PP), and body mass index (BMI) are heritable traits in human metabolic health but their common genetic and environmental backgrounds are not well investigated. The aim of this article was to explore the phenotypic and genetic associations among PP, systolic blood pressure (SBP), diastolic blood pressure (DBP), and BMI. The studied sample contained 615 twin pairs (17–84 years) collected in the Qingdao municipality. Univariate and multivariate structural equation models were fitted for assessing the genetic and environmental contributions. The AE model combining additive genetic (A) and unique environmental (E) factors produced the best fit for each four phenotypes. Heritability estimated in univariate analysis ranged from 0.42 to 0.74 with the highest for BMI (95% CI 0.70–0.78), and the lowest for PP (95% CI 0.34–0.49). The multivariate model estimated (1) high genetic correlations for DBP with SBP (0.87), PP with SBP (0.75); (2) low–moderate genetic correlations between PP and DBP (0.32), each BP component and BMI (0.24–0.37); (3) moderate unique environmental correlation for PP with SBP (0.68) and SBP with DBP (0.63); (4) there was no significant unique environmental correlation between PP and BMI. Overall, our multivariate analyses revealed common genetic and environmental backgrounds for PP, BP, and BMI in Chinese twins.

This work focuses on the persistence of lower-dimensional tori with prescribed frequencies and singular normal matrices in reversible systems. By the Kolmogorov–Arnold–Moser theory and the special structure of unperturbed nonlinear terms in the differential equation, we prove that the invariant torus with given frequency persists under small perturbations. Our result is a generalization of X. Wang et al [Degenerate lower dimensional tori in reversible systems. J. Math. Anal. Appl.387 (2012), 776–790].

We evaluated the genetic and environmental contributions to metabolic cardiovascular risk factors and their mutual associations. Eight metabolic factors (body mass index, waist circumference, waist-to-hip ratio, systolic blood pressure, diastolic blood pressure, total serum cholesterol, serum triglycerides, and serum uric acid) were measured in 508 twin pairs aged 8–17 years from the Qingdao Twin Registry, China. Linear structural equation models were used to estimate the heritability of these traits, as well as the genetic and environmental correlations between them. Among boys, body mass index and uric acid showed consistently high heritability (0.49–0.81), whereas other traits showed moderate to high common environmental variance (0.37–0.73) in children (8–12 years) and adolescents (13–17 years) except total cholesterol. For girls, moderate to high heritability (0.39–0.75) were obtained for six metabolic traits in children, while only two traits showed high heritability and others mostly medium to large common environmental variance in adolescents. Genetic correlations between the traits were strong in both boys and girls in children (r g = 0.64–0.99 between body mass index and diastolic blood pressure; r g = 0.71–1.00 between body mass index and waist circumference), but decreased for adolescent girls (r g = 0.51 between body mass index and waist-to-hip ratio; r g = 0.55 between body mass index and uric acid; r g = 0.61 between body mass index and systolic blood pressure). The effect of genetic factors on most metabolic traits decreased from childhood to adolescence. Both common genetic and specific environmental factors influence the mutual associations among most of the metabolic traits.