This paper considers the stochastic 3-D incompressible anisotropic Navier-Stokes equations. We establish the global existence of a strong solution in probability when either the horizontal component of the initial data and external force is sufficiently small or the horizontal viscosity coefficient is sufficiently large.

BACKGROUND:Foods contain pro-inflammatory and anti-inflammatory components that may influence mood. This study aims to investigate the association between dietary inflammation, assessed by the Dietary Inflammatory Index (DII), and anxiety and depression. METHODS:DII was calculated from 29 food items in a 24-h diet recall questionnaire from the UK Biobank. Depression and anxiety disorders were identified using International Classification of Diseases codes from hospital records, while depressive and anxious moods were assessed using the Patient Health Questionnaire-9 and Generalized Anxiety Disorder-7 questionnaires. Cox proportional hazards models were used to assess the association between baseline dietary inflammation and future depression/anxiety disorders. RESULTS:Over a median follow-up of 14.1 years among 189,835 participants, the incidence of depression and anxiety disorders was 257.25 and 272.10 per 100,000 person-years, respectively. The mean DII was -0.435, with a range from -6.566 to 5.449. Individuals with higher DII scores exhibited an elevated risk of depressive mood (OR [95 % CI] = 1.137 [1.111,1.162], P < 0.001), depression disorders (HR [95 % CI] = 1.063 [1.046,1.082], P < 0.001), anxiety mood (OR [95 % CI] = 1.094 [1.079-1.108], P < 0.001), and anxiety disorders (HR [95 % CI] = 1.023 [1.007,1.040], P < 0.001), after adjusting for sociodemographic, lifestyle, and medical condition factors. CONCLUSIONS:Diets with pro-inflammatory traits, reflected by a higher DII, were strongly linked to an increased risk of developing depression and anxiety in the future. An anti-inflammatory diet, guided by the DII, may offer a promising protective approach against these mental health issues.

This paper establishes the global existence of the pathwise solutions for the stochastic 3-D incompressible Euler equations with the axially symmetric initial data and axially symmetric additive noise.

OBJECTIVE:Although metabolic abnormalities are implicated in the etiology of neurodegenerative diseases, their role in the development of amyotrophic lateral sclerosis (ALS) remains a subject of controversy. We aimed to identify the association between metabolic syndrome (MetS) and the risk of ALS. METHODS:This study included 395,987 participants from the UK Biobank to investigate the relationship between MetS and ALS. Cox regression model was used to estimate hazard ratios (HR). Stratified analyses were performed based on gender, body mass index (BMI), smoking status, and education level. Mediation analysis was conducted to explore potential mechanisms. RESULTS:In this study, a total of 539 cases of ALS were recorded after a median follow-up of 13.7 years. Patients with MetS (defined harmonized) had a higher risk of developing ALS after adjusting for confounding factors (HR: 1.50, 95% CI: 1.19-1.89). Specifically, hypertension and high triglycerides were linked to a higher risk of ALS (HR: 1.53, 95% CI: 1.19-1.95; HR: 1.31, 95% CI: 1.06-1.61, respectively). Moreover, the quantity of metabolic abnormalities showed significant results. Stratified analysis revealed that these associations are particularly significant in individuals with a BMI <25. These findings remained stable after sensitivity analysis. Notably, mediation analysis identified potential metabolites and metabolomic mediators, including alkaline phosphatase, cystatin C, γ-glutamyl transferase, saturated fatty acids to total fatty acids percentage, and omega-6 fatty acids to omega-3 fatty acids ratio. INTERPRETATION:MetS exhibits a robust association with an increased susceptibility to ALS, particularly in individuals with a lower BMI. Furthermore, metabolites and metabolomics, as potential mediators, provide invaluable insights into the intricate biological mechanisms. ANN NEUROL 2024;96:788-801.

BACKGROUND:Previous studies have observed liver abnormalities in amyotrophic lateral sclerosis (ALS) patients. This study aimed to investigate whether early signs of liver disease, measured by magnetic resonance imaging-derived iron-corrected T1-mapping (cT1), are risk factors for developing ALS. METHODS:cT1 and proton density fat fraction were measured and automatically analyzed using LiverMultiScan® software. The Fibrosis-4 index was calculated using an established formula based on age and blood markers. Cox proportional hazard models were used to examine the relationship between liver disease, liver biomarkers, and incident ALS. RESULTS:In a cohort of 533,707 individuals from UK Biobank, 24 ALS cases were identified among 28,328 participants with liver disease during the follow-up period. Among a total of 33,959 individuals with complete liver imaging data, 15 incident ALS cases were observed during a median follow-up period of 5.6 years. Individuals with liver disease had a higher risk of developing ALS, with an adjusted hazard ratio of 7.35 (95% CI 4.47-12.09; p < 0.001). An increase in cT1 was also associated with a higher risk of ALS. After adjusting for age, sex, Townsend deprivation index, smoking status, alcohol intake frequency, body mass index, proton density fat fraction, Fibrosis-4, and metabolic syndrome, an increase in cT1 remained significantly associated with a higher risk of ALS, with an adjusted hazard ratio of 3.15 (95% CI 1.79-5.55) per 1-SD increase. Sensitivity analyses confirmed these robust results. INTERPRETATION:Liver disease activity, indicated by cT1, increases the risk of developing ALS, independent of metabolic syndrome, liver fat, or fibrosis. ANN NEUROL 2025;97:270-280.

BACKGROUND AND AIMS:Little is known about the ability of serological biomarkers to monitor clinical outcomes in patients with Guillain-Barré syndrome (GBS). The objective of this study was to determine the associations of liver function, easily available and convenient biomarkers, with the clinical course and outcome of severe GBS in patients. METHODS:A prospective data collection was conducted in a cohort of 343 GBS patients from multi-centers between September 2019 and December 2023. Serum samples were obtained at four-time points for mechanical ventilation (MV) patients and two-time points for non-MV patients. The primary endpoint was the need for MV during hospitalization, while secondary outcomes included the ability to walk independently and the mortality at 26-week follow-up. RESULTS:(i) A total of 208 patients were eligible, of whom 50 required MV with a median (interquartile range) ventilation duration of 15 (8-27) days. (ii) Hypohepatia, as evidenced by reduced total protein (OR 0.913 [95% CI 0.862-0.967]) and albumin (0.775 [0.679-0.884]) 1 week after treatment, along with raised liver enzymes (2.732 [1.007-7.413]), was associated with the risk of MV after adjusting for confounders. (iii) After 26-week follow-up, patients with hypohepatia were less likely to regain independent walking and exhibited higher mortality in survival analysis (all log-rank p < .05). (iv) In a cross-sectional study spanning up to 4 years of follow-up, patients with prolonged MV (≥15 days) experienced a longer time to regain independent ambulation than those with shorter MV (167 [46-316] vs. 69 [24-106], p = .036). However, no relationships between liver function and prolonged MV were revealed. INTERPRETATION:Dynamically monitoring hepatic metabolism and promptly adjusting, it can aid the improvement of GBS in patients.

Considering the stochastic Boussinesq equations with additive noise, we prove the global existence for the strong solution in the case of strong stable stratification. The averaging theorem is also established.

Considering the stochastic Navier-Stokes system in Rd forced by a multiplicative white noise, we establish the local existence and uniqueness of the strong solution when the initial data take values in the critical space B˙p,rd/p−1(Rd). The proof is based on the contraction mapping principle, stopping time and stochastic estimates. Then we prove the global existence of strong solutions in probability if the initial data are sufficiently small, which contain a class of highly oscillating “large” data.

Considering the stochastic Boussinesq equations in Td with the nonlinear multiplicative noises, we establish the local existence of pathwise solutions. Furthermore, we establish the global existence of pathwise solution when the noises are non-degenerate, which show that the non-degenerate multiplicative noises would provide a regularizing effect: the global existence of solution occurs with high probability if the initial data are sufficiently small, or if the noise coefficients are sufficiently large.

A stochastic three-dimensional Navier-Stokes system with the axisymmetric initial data and white noise is studied. It is shown that if the swirl component of the initial velocity field and the white noise are sufficiently small, then the axisymmetric pathwise solution is global in probability. Moreover, in the absence of the swirl, the pathwise axisymmetric solution is global almost surely. AMS subject classifications: 35Q35, 60H15, 76B03

The stochastic 3D Boussinesq equations with additive noise are considered. We prove the local existence of the strong solution in $H^{s}$ ( $\frac{1}{2}< s\leq 1$ ). We also obtain a new stopping time, which shows that the $H^{\frac{1}{2}^{+}}$ norm of u controls the breakdown of the strong solution. Furthermore, we give the probability estimate of the lifespan larger than δ ( $0<\delta <1$ ).

This paper is concerned with the Cauchy problem of the Quasigeostrophic equation on the torus $${\mathbb {T}}^2$$ . We prove the almost sure existence and uniqueness of the global solution with the random initial data in $${\mathcal {H}}^s({\mathbb {T}}^2), s\in [-1,0)$$ .

Considering the stochastic 3-D incompressible anisotropic Navier-Stokes equations, we prove the local existence of strong solution in H-2(T-3) Moreover, we express the probabilistic estimate of the random time interval for the existence of a local solution in terms of expected values of the initial data and the random noise, and establish the global existence of strong solution in probability if the initial data and the random noise are sufficiently small.

In this paper we consider the Cauchy problem of the incompressible Magnetohydrodynamics (MHD) equations in the periodic space domain TN, where N≥2. After a suitable randomization to the initial data, we obtain the almost sure existence of global weak solutions with the initial data in Hs(TN), s∈(−1,0). Specially, the global weak solution is unique when N=2.