Long-time existence for semi-linear Klein-Gordon equations with quadratic potential

We prove that small smooth solutions of semi-linear Klein-Gordon equations with quadratic potential exist over a longer interval than the one given by local existence theory, for almost every value of mass. We use normal form for the Sobolev energy. The difficulty in comparison with some similar results on the sphere comes from the fact that two successive eigenvalues $\lambda, \lambda'$ of $\sqrt{-\Delta+|x|^2}$ may be separated by a distance as small as $\frac{1}{\sqrt{\lambda}}$

On Fila-King Conjecture in Dimension Four

We consider the following Cauchy problem for the four-dimensional energy critical heat equation \begin{equation*} \begin{cases} u_t=\Delta u+u^{3} ~&\mbox{ in }~ {\mathbb R}^4 \times (0,\infty),\\ u(x,0)=u_0(x) ~&\mbox{ in }~ {\mathbb R}^4. \end{cases} \end{equation*} We construct a positive infinite time blow-up solution $u(x,t)$ with the blow-up rate $\| u(\cdot,t)\|_{L^\infty({\mathbb R}^4)} \sim \ln t$ as $t\to \infty$ and show the stability of the infinite time blow-up. This gives a rigorous proof of a conjecture by Fila and King \cite[Conjecture 1.1]{filaking12}.Comment: 61 pages; any comment welcom

Trichotomy dynamics of the 1-equivariant harmonic map flow

For the 1-equivariant harmonic map flow from $R^2$ into $S^2$ \begin{equation*} \left\{ \begin{aligned} &v_t=v_{rr}+\frac{v_r}{r} - \frac{\sin(2v)}{2r^2} , ~\quad(r,t)\in R_+\times (t_0,+\infty),\\ &v(r,t_0)=v_0, \qquad\qquad\qquad\quad r\in R_+, \end{aligned} \right. \end{equation*} we construct global growing, bounded and decaying solutions with the initial data $v_0(r)$ satisfying v_0(0)=\pi ~\mbox{ and }~ v_0(r)\sim r^{1-\gamma} ~\mbox{ as }~ r\to+\infty, \quad \gamma>1. These global solutions exhibit the following trichotomy long-time asymptotic behavior \begin{equation*} \| v_r(\cdot,t) \|_{L^\infty ([0,\infty))} \sim \begin{cases} t^{\frac{\gamma-2}{2}}\ln t ~&\mbox{ if }~ 1<\gamma<2,\\ 1 ~&\mbox{ if }~ \gamma=2,\\ \ln t ~&\mbox{ if }~ \gamma>2,\\ \end{cases} ~\mbox{ as }~ t\to +\infty. \end{equation*}Comment: 30 pages; comments welcom

Overexpression of IGF2 affects mouse weight and glycolipid metabolism and IGF2 is positively related to macrosomia

ObjectiveTo investigate the effects of insulin-like growth factor 2 (IGF2) on growth and glycolipid metabolism, as well as the underlying mechanism.MethodsA mouse model of IGF2 overexpression was constructed to measure weight gain before adulthood, to obtain the values of adult glycolipid metabolism indicators in the peripheral blood and to detect the expression of genes in the IGF2 signaling pathway in different mouse tissues. The present study also explored the independent association between the IGF2 gene and macrosomia by detecting and comparing the expression levels of IGF2 mRNA/H19 RNA in maternal peripheral blood and fetal cord blood of 26 human pregnancies.ResultsIn the mouse model, weights of the IGF2-overexpressing mice were significantly higher than those of the control mice at the age of 5-10 weeks. The glucose concentration, total cholesterol and high-density lipoprotein cholesterol (HDL-C) levels of IGF2-overexpressing mice were significantly lower than those of wild-type (WT) mice. Compared with the WT mice, the expression of H19 was significantly decreased in the pancreas and IGF1R was significantly decreased in the muscle of mice with IGF2 overexpression. The expression levels of STAT3 and AKT2 showed significant decrease in liver, muscle and increase in muscle of IGF2-overexpressing mice, respectively. GLUT2 expression showed significant increase in liver, kidney, muscle and decrease in pancreas of mice with IGF2 overexpression. This study also found that in normal mothers with the similar clinical characteristics, IGF2 expression in the maternal peripheral blood and fetal cord blood is an independent factor influencing macrosomia. ConclusionIGF2 expression was independently correlated with the occurrence of macrosomia, and overexpression of IGF2 significantly increased the weights of mice at the age of 5-10 weeks and significantly affected the values of adult glycolipid metabolism indicators, which might be the result of changes in the IGF2-IGF1R-STAT3/AKT2-GLUT2/GLUT4 pathway. These findings might suggest that IGF2 plays an important role in growth and glycolipid metabolism during both pregnancy and postnatal development

The proportion of HIV disclosure to sexual partners among people diagnosed with HIV in China: A systematic review and meta-analysis

Background: Sexual behavior is one of the main routes of HIV/AIDS spread. HIV disclosure to sexual partners has been confirmed to be an important strategy for HIV/AIDS prevention and control. We conducted a systematic review and meta-analysis to pool proportions and characteristics of HIV disclosure to sexual partners among people diagnosed with HIV in China.Methods: We searched eight databases and extracted the data on HIV disclosure to partners. Heterogeneity of the data was tested with I2. Published bias subjectively and objectively analyzed through the funnel plot and Egger's regression test. Subgroup analyses were performed to explore the variation in the proportion by sexual partnership types (unclassified, regular, casual sexual partners), whether being men who have sex with men (MSM), and when to diagnose. The sources of heterogeneity were analyzed. Sensitivity analysis was carried out to evaluate the stability of the results.Results: Out of 3,698 studies, 44 were included in the review; 11 targeted on MSM. The pooled proportion of HIV disclosure to sexual partners was 65% (95% CI: 56%−75%; 34 studies). Sub-group analyses indicated the proportions of HIV disclosure to regular, casual and unclassified sexual partners were 63% (95% CI: 45%−81%; 31 studies), 20% (95% CI: 8%−33%; nine studies), and 66% (95% CI: 59%−73%; 14 studies), respectively. Fifty-seven percent (95% CI: 45%−69%; three studies) disclosed on the day of diagnosis, 62% (95% CI: 42%−82%; four studies) disclosed within 1 month, and 39% (95% CI: 2%−77%; four studies) disclosed 1 month later. Among MSM, the disclosure to regular male partners, regular female sexual partners, spouses, and casual partner were 47% (95% CI: 29%−65%; six studies), 49% (95% CI: 33%−65%; three studies), 48% (95% CI: 18%−78%; seven studies), and 34% (95% CI: 19%−49%; four studies), respectively.Conclusions: The disclosure prevalence of people diagnosed with HIV to sexual partners still need improving in China, and it varies among partner types, key populations, and time being diagnosed. HIV disclosure strategies and procedures need to be developed more detailed and tailored based on the pain points of disclosure status, so as to ultimately prevent HIV transmission through sexual contact.</p

Brown Adipose Tissue Activation Is Inversely Related to Central Obesity and Metabolic Parameters in Adult Human

Background: Recent studies have shown that adult human possess active brown adipose tissue (BAT), which might be important in affecting obesity. However, the supporting evidence on the relationship between BAT and central obesity and metabolic profile in large population based studies is sparse. Methodology/Principal Findings We studied 4011 (2688 males and 1323 females) tumor-free Chinese adults aged 18-89 for BAT activities, visceral/subcutaneous fat areas (VFA/SFA), waist circumferences (WC) and metabolic parameters. We found that the prevalence of BAT was around 2.7% in our study participants, with a significant sexual difference (5.5% in the females vs. 1.3% in the males; p<0.0001). BAT detection was increased in low temperature and declined in elderly subjects. The BAT positive subjects had lower BMI (P<0.0001), less SFA (P<0.01), VFA (P<0.0001), WC (P<0.0001), lower fasting glucose and triglyceride levels (both P<0.01) and increased HDL cholesterol concentrations (P<0.0001), compared with the BAT negative subjects. Robust logistic regression revealed that after adjustment for covariates (including age, sex, BMI, VFA, SFA and WC), age and BMI in the males (0.92 [95%CI, 0.88-0.96] and 0.84 [95% CI, 0.75-0.96], both P ≤0.008) while age and VFA in the females (0.87 [95%CI, 0.83-0.91] and 0.98 [95%CI, 0.97-0.99], respectively, P<0.05) were independently associated with detectable BAT. Conclusions/Significance: Our data suggest that decreased amount of active BAT might be associated with accumulation of visceral fat content and unfavorable metabolic outcomes

Brown Adipose Tissue in Humans Is Activated by Elevated Plasma Catecholamines Levels and Is Inversely Related to Central Obesity

BACKGROUND: Recent studies have shown that adult human possess active brown adipose tissue (BAT), which might be important in controlling obesity. It is known that ß-adrenoceptor-UCP1 system regulates BAT in rodent, but its influence in adult humans remains to be shown. The present study is to determine whether BAT activity can be independently stimulated by elevated catecholamines levels in adult human, and whether it is associated with their adiposity. METHODOLOGY/PRINCIPAL FINDINGS: We studied 14 patients with pheochromocytoma and 14 normal subjects who had performed both ¹⁸F-fluorodeoxyglucose positron emission tomography/computed tomography (¹⁸F-FDG PET/CT) and plasma total metanephrine (TMN) measurements during 2007-2010. The BAT detection rate and the mean BAT activity were significantly higher in patients with elevated TMN levels (Group A: 6/8 and 6.7±2.1 SUVmean· g/ml) than patients with normal TMN concentrations (Group B: 0/6 and 0.4±0.04 SUVmean· g/ml) and normal subjects (Group C: 0/14 and 0.4±0.03 SUVmean·g/ml). BAT activities were positively correlated with TMN levels (R = 0.83, p<0.0001) and were inversely related to body mass index (R = -0.47, p = 0.010), visceral fat areas (R = -0.39, p = 0.044), visceral/total fat areas (R = -0.52, p = 0.0043) and waist circumferences (R = -0.43, p = 0.019). Robust regression revealed that TMN (R = 0.81, p<0.0001) and waist circumferences (R = -0.009, p = 0.009) were the two independent predictors of BAT activities. CONCLUSIONS/SIGNIFICANCE: Brown adipose tissue activity in adult human can be activated by elevated plasma TMN levels, such as in the case of patients with pheochromocytoma, and is negatively associated with central adiposity