Functional central limit theorem with mean-uncertainty under sublinear expectation

In this paper, we introduce a fundamental model for independent and identically distributed sequence with model uncertainty on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels. Thanks to the well-defined upper and lower variances, we obtain a new functional central limit theorem with mean-uncertainty on the canonical space by the method based on the martingale central limit theorem and stability of stochastic integral in the classical probability theory. Then we extend it to the general sublinear expectation space through a new representation theorem. Our results generalize Peng's central limit theorem with zero-mean to the case of mean-uncertainty and provides a purely probabilistic proof instead of the existing nonlinear partial differential equation approach. As an application, we consider the two-armed bandit problem and generalize the corresponding central limit theorem from the case of mean-certainty to mean-uncertainty.Comment: 31 pages. arXiv admin note: substantial text overlap with arXiv:2203.0017

Volunteer Participation in the Health eHeart Study: A Comparison with the US Population.

Direct volunteer "eCohort" recruitment can be an efficient way of recruiting large numbers of participants, but there is potential for volunteer bias. We compared self-selected participants in the Health eHeart Study to participants in the National Health And Nutrition Examination Survey (NHANES) 2013-14, a cross-sectional survey of the US population. Compared with the US population (represented by 5,769 NHANES participants), the 12,280 Health eHeart participants with complete survey data were more likely to be female (adjusted odds ratio (ORadj) = 3.1; 95% confidence interval (CI) 2.9-3.5); less likely to be Black, Hispanic, or Asian versus White/non-Hispanic (ORadj's = 0.4-0.6, p < 0.01); more likely to be college-educated (ORadj = 15.8 (13-19) versus ≤high school); more likely to have cardiovascular diseases and risk factors (ORadj's = 1.1-2.8, p < 0.05) except diabetes (ORadj = 0.8 (0.7-0.9); more likely to be in excellent general health (ORadj = 0.6 (0.5-0.8) for "Good" versus "Excellent"); and less likely to be current smokers (ORadj = 0.3 (0.3-0.4)). While most self-selection patterns held for Health eHeart users of Bluetooth blood pressure cuff technology, there were some striking differences; for example, the gender ratio was reversed (ORadj = 0.6 (0.4-0.7) for female gender). Volunteer participation in this cardiovascular health-focused eCohort was not uniform among US adults nor for different components of the study

SCALE: Online Self-Supervised Lifelong Learning without Prior Knowledge

Unsupervised lifelong learning refers to the ability to learn over time while memorizing previous patterns without supervision. Previous works assumed strong prior knowledge about the incoming data (e.g., knowing the class boundaries) which can be impossible to obtain in complex and unpredictable environments. In this paper, motivated by real-world scenarios, we formally define the online unsupervised lifelong learning problem with class-incremental streaming data, which is non-iid and single-pass. The problem is more challenging than existing lifelong learning problems due to the absence of labels and prior knowledge. To address the issue, we propose Self-Supervised ContrAstive Lifelong LEarning (SCALE) which extracts and memorizes knowledge on-the-fly. SCALE is designed around three major components: a pseudo-supervised contrastive loss, a self-supervised forgetting loss, and an online memory update for uniform subset selection. All three components are designed to work collaboratively to maximize learning performance. Our loss functions leverage pairwise similarity thus remove the dependency on supervision or prior knowledge. We perform comprehensive experiments of SCALE under iid and four non-iid data streams. SCALE outperforms the best state-of-the-art algorithm on all settings with improvements of up to 3.83%, 2.77% and 5.86% kNN accuracy on CIFAR-10, CIFAR-100 and SubImageNet datasets.Comment: Submitted for revie

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

Rarefied gas flow in a three-dimensional enclosure induced by nonuniform temperature distribution is numerically investigated. The enclosure has a square channel-like geometry with alternatively heated closed ends and lateral walls with a linear temperature distribution. A recently proposed implicit discrete velocity method with a memory reduction technique is used to numerically simulate the problem based on the nonlinear Shakhov kinetic equation. The Knudsen number dependencies of the vortices pattern, slip velocity at the planar walls and edges, and heat transfer are investigated. The influences of the temperature ratio imposed at the ends of the enclosure and the geometric aspect ratio are also evaluated. The overall flow pattern shows similarities with those observed in two-dimensional configurations in literature. However, features due to the three-dimensionality are observed with vortices that are not identified in previous studies on similar two-dimensional enclosures at high Knudsen and small aspect ratios

Gender-specific association of decreased estimated glomerular filtration rate and left vertical geometry in the general population from rural Northeast China

Abstract Background Left ventricular hypertrophy (LVH) is common and associated with cardiovascular outcomes among patients with known chronic kidney disease (CKD). However, the link between decreased estimated glomerular filtration rate (eGFR) and left ventricular (LV) geometry remains poorly explored in general population. In this study, we examined the gender-specific association between eGFR and LVH in the general population from rural Northeast China. Methods This survey was conducted from July 2012 to August 2013. A total of 10907 participants (5,013 men and 5,894 women) from the rural Northeast China were randomly selected and examined. LV mass index (LVMI) was used to define LVH (LVMI\u2009>\u200946.7\ua0g/m 2.7 in women; > 49.2\ua0g/m 2.7 in men). LV geometry was defined as normal, or with concentric remodeling, eccentric or concentric hypertrophy, according to relative wall thickness (RWT) and LVMI. Mildly decreased eGFR was defined as eGFR\u2009\u2265\u200960 and\u2009<\u200990\ua0ml/min/1.73\ua0m 2 , and moderate-severely decreased eGFR was defined as eGFR\u2009<\u200960\ua0ml/min/1.73\ua0m 2 . Results As eGFR decreased, LVH showed a gradual increase in the entire study population. Multivariate analysis revealed a gender-specific relationship between eGFR and LV geometry. Only in men, mildly decreased eGFR was associated with concentric remodeling [odds ratio (OR): =1.58; 95% CI: 1.14\u20132.20; P \u2009<\u20090.01] and concentric LVH OR \u2009=\u20091.63; 95% CI: 1.15\u20132.31; P \u2009<\u20090.01). And only in men, moderate-severely decreased eGFR was a risk factor for concentric LVH ( OR \u2009=\u20094.56; 95% CI: 2.14\u20139.73; P \u2009<\u20090.001) after adjusting for confounding factors. Conclusions These findings suggested that decreased eGFR was a risk factor for LV geometry in men, and a gender-specific difference should be taken into account in clinical practice

Effect of short-term exercise intervention on cardiovascular functions and quality of life of chronic heart failure patients: A meta-analysis

AbstractObjectiveThe purpose of this study was to comprehensively evaluate the effect of short-term exercise intervention on the cardiovascular functions and quality of life (QoL) of patients with chronic heart failure (CHF).MethodsThis meta-analysis was analyzed using RevMan5.3 and Stata 13.0. The parameters of cardiovascular functions and QoL were assessed. Weighted mean differences and their corresponding 95% confidence intervals (CIs) were computed for continuous variables.ResultsData from 2533 CHF patients enrolled in 28 published studies of randomized controlled trials (RCTs) were collated. There were significant differences in VO2 max prior to and after exercise intervention in CHF patients who are 50–55 years old (5 RCTs; 95% CI, −4.86 to −2.29; I2 = 50.5%), 60–65 years old (10 RCTs; 95% CI, −2.66 to −2.04; I2 = 0%), and 69–75 years old (5 RCTs; 95% CI, −1.88 to −0.34; I2 = 38.5%). VO2 max was significantly increased by aerobic exercise (9 RCTs; 95% CI, −3.45 to −1.92; I2 = 37.7%) and combined aerobic resistance exercise (4 RCTs; 95% CI, −4.41 to −0.26; I2 = 76.6%). There were significant differences in cardiac output (n = 303; 95% CI, −0.25 to −0.02; I2 = 12%) and QoL (n = 299; 95% CI, 3.19 to 9.70; I2 = 17%) prior to and after short-term exercise.ConclusionAerobic exercise and aerobic with resistance exercise can significantly improve the aerobic capacity of CHF patients, whereas resistance exercise cannot. The improvement in aerobic capacity caused by aerobic exercise and aerobic with resistance exercise decreases with age. Systolic blood pressure and ventricle structures and functions of CHF patients show no significant changes after the short-term exercise intervention