Likelihood Landscape and Local Minima Structures of Gaussian Mixture Models

In this paper, we study the landscape of the population negative log-likelihood function of Gaussian Mixture Models with a general number of components. Due to nonconvexity, there exist multiple local minima that are not globally optimal, even when the mixture is well-separated. We show that all local minima share the same form of structure that partially identifies the component centers of the true mixture, in the sense that each local minimum involves a non-overlapping combination of fitting multiple Gaussians to a single true component and fitting a single Gaussian to multiple true components. Our results apply to the setting where the true mixture components satisfy a certain separation condition, and are valid even when the number of components is over-or under-specified. For Gaussian mixtures with three components, we obtain sharper results in terms of the scaling with the separation between the components

Entry-Specific Bounds for Low-Rank Matrix Completion under Highly Non-Uniform Sampling

Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying probabilities, potentially with different asymptotic scalings. We show that under structured sampling probabilities, it is often better and sometimes optimal to run estimation algorithms on a smaller submatrix rather than the entire matrix. In particular, we prove error upper bounds customized to each entry, which match the minimax lower bounds under certain conditions. Our bounds characterize the hardness of estimating each entry as a function of the localized sampling probabilities. We provide numerical experiments that confirm our theoretical findings

Positive Solutions for Discrete Boundary Value Problems to One-Dimensional -Laplacian with Delay

We study the existence of positive solutions for discrete boundary value problems to one-dimensional -Laplacian with delay. The proof is based on the Guo-Krasnoselskii fixed-point theorem in cones. Two numerical examples are also provided to illustrate the theoretical results

A data-driven approach design for carbon emission prediction of machining

The issue of carbon emission reduction for manufacturing industry attracts increasing attention. As a major contributor in the manufacturing industry, machining has generated large amounts of carbon emissions through the resource consumption, energy consumption, and waste disposal. The carbon emission prediction of machining is a priori technology for its reduction, and has been established as one of the most crucial research targets. The purpose of this study is to design a carbon emission prediction model of machining through a data-driven approach. First of all, the multiple sources and impact factors of carbon emissions in machining are studied, and the relationship between these factors is also studied to describe the carbon emissions. Then, a data-driven approach is designed to predict the carbon emission of machining, which consists of data collection and preprocessing, feature extraction, prediction model establishment and model validation. The ridge regression, BP neural network based on Genetic Algorithm (GA-BP), root means square error (RMSE) and mean relative percentage error (MPAE) are respectively employed to fulfill the above tasks in the design approach. Finally, an experimental study of a real turning machining is proposed to verify the feasibility and merits of the designed approach

Association between urinary arsenic species and vitamin D deficiency: a cross-sectional study in Chinese pregnant women

BackgroundAn increasing number of studies suggest that environmental pollution may increase the risk of vitamin D deficiency (VDD). However, less is known about arsenic (As) exposure and VDD, particularly in Chinese pregnant women.ObjectivesThis study examines the correlations of different urinary As species with serum 25 (OH) D and VDD prevalence.MethodsWe measured urinary arsenite (As3+), arsenate (As5+), monomethylarsonic acid (MMA), and dimethylarsinic acid (DMA) levels and serum 25(OH)D2, 25(OH)D3, 25(OH) D levels in 391 pregnant women in Tianjin, China. The diagnosis of VDD was based on 25(OH) D serum levels. Linear relationship, Logistic regression, and Bayesian kernel machine regression (BKMR) were used to examine the associations between urinary As species and VDD.ResultsOf the 391 pregnant women, 60 received a diagnosis of VDD. Baseline information showed significant differences in As3+, DMA, and tAs distribution between pregnant women with and without VDD. Logistic regression showed that As3+ was significantly and positively correlated with VDD (OR: 4.65, 95% CI: 1.79, 13.32). Meanwhile, there was a marginally significant positive correlation between tAs and VDD (OR: 4.27, 95% CI: 1.01, 19.59). BKMR revealed positive correlations between As3+, MMA and VDD. However, negative correlations were found between As5+, DMA and VDD.ConclusionAccording to our study, there were positive correlations between iAs, especially As3+, MMA and VDD, but negative correlations between other As species and VDD. Further studies are needed to determine the mechanisms that exist between different As species and VDD

Neuroprotective Effect of Xueshuantong for Injection (Lyophilized) in Transient and Permanent Rat Cerebral Ischemia Model

Xueshuantong for Injection (Lyophilized) (XST), a Chinese Materia Medica standardized product extracted from Panax notoginseng (Burk.), is used extensively for the treatment of cerebrovascular diseases such as acutely cerebral infarction clinically in China. In the present study, we evaluated the acute and extended protective effects of XST in different rat cerebral ischemic model and explored its effect on peroxiredoxin (Prx) 6-toll-like receptor (TLR) 4 signaling pathway. We found that XST treatment for 3 days could significantly inhibit transient middle cerebral artery occlusion (MCAO) induced infarct volume and swelling percent and regulate the mRNA expression of interleukin-1β (IL-1β), IL-17, IL-23p19, tumor necrosis factor-α (TNFα), and inducible nitric oxide synthase (iNOS) in brain. Further study demonstrated that treatment with XST suppressed the protein expression of peroxiredoxin (Prx) 6-toll-like receptor (TLR) 4 and phosphorylation level of p38 and upregulated the phosphorylation level of STAT3. In permanent MCAO rats, XST could reduce the infarct volume and swelling percent. Moreover, our results revealed that XST treatment could increase the rats’ weight and improve a batch of functional outcomes. In conclusion, the present data suggested that XST could protect against ischemia injury in transient and permanent MCAO rats, which might be related to Prx6-TLR4 pathway

Patterns of co-morbidity with anxiety disorders in Chinese women with recurrent major depression

BACKGROUND: Studies conducted in Europe and the USA have shown that co-morbidity between major depressive disorder (MDD) and anxiety disorders is associated with various MDD-related features, including clinical symptoms, degree of familial aggregation and socio-economic status. However, few studies have investigated whether these patterns of association vary across different co-morbid anxiety disorders. Here, using a large cohort of Chinese women with recurrent MDD, we examine the prevalence and associated clinical features of co-morbid anxiety disorders. METHOD: A total of 1970 female Chinese MDD patients with or without seven co-morbid anxiety disorders [including generalized anxiety disorder (GAD), panic disorder, and five phobia subtypes] were ascertained in the CONVERGE study. Generalized linear models were used to model association between co-morbid anxiety disorders and various MDD features. RESULTS: The lifetime prevalence rate for any type of co-morbid anxiety disorder is 60.2%. Panic and social phobia significantly predict an increased family history of MDD. GAD and animal phobia predict an earlier onset of MDD and a higher number of MDD episodes, respectively. Panic and GAD predict a higher number of DSM-IV diagnostic criteria. GAD and blood-injury phobia are both significantly associated with suicidal attempt with opposite effects. All seven co-morbid anxiety disorders predict higher neuroticism. CONCLUSIONS: Patterns of co-morbidity between MDD and anxiety are consistent with findings from the US and European studies; the seven co-morbid anxiety disorders are heterogeneous when tested for association with various MDD features

Ultra-high pressure balloon angioplasty for pulmonary artery stenosis in children with congenital heart defects: Short- to mid-term follow-up results from a retrospective cohort in a single tertiary center

ObjectiveBalloon angioplasty (BA) has been the treatment of choice for pulmonary artery stenosis (PAS) in children. There remains, however, a significant proportion of resistant lesions. The ultra-high pressure (UHP) balloons might be effective in a subset of these lesions. In this study, we analyzed the safety and efficacy with short- to mid-term follow-up results of UHP BA for PAS in children with congenital heart defects (CHD) in our center.MethodsThis is a retrospective cohort study in a single tertiary heart center. Children diagnosed with PAS associated with CHD were referred for UHP BA. All data with these children were collected for analysis with updated follow-up.ResultsA total of 37 UHP BAs were performed consecutively in 28 children. The success rate was 78.4%. A significantly (P = 0.005) larger ratio of the balloon to the minimal luminal diameter at the stenotic waist (balloon/waist ratio) was present in the success group (median 3.00, 1.64–8.33) compared to that in the failure group (median 1.94, 1.41 ± 4.00). Stepwise logistic regression analysis further identified that the balloon/waist ratio and the presence of therapeutic tears were two independent predictors of procedural success. The receiver operating characteristic curve revealed a cut-off value of 2.57 for the balloon/waist ratio to best differentiate success from failure cases. Signs of therapeutic tears were present in eight cases, all of whom were in the success group. Perioperative acute adverse events were recorded in 16 patients, including 11 pulmonary artery injuries, three pulmonary hemorrhages, and two pulmonary artery aneurysms. During a median follow-up period of 10.4 (0.1–21.0) months, nine cases experienced restenosis at a median time of 40 (4–325) days after angioplasty.ConclusionsThe UHP BA is safe and effective for the primary treatment of PAS in infants and children with CHD. The success rate is high with a low incidence of severe complications. The predictors of success are a larger balloon/waist ratio and the presence of therapeutic tears. The occurrence of restenosis during follow-up, however, remains a problem. A larger number of cases and longer periods of follow-up are needed for further study