Relax, no need to round: integrality of clustering formulations

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: $k$-means and $k$-median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and (b) they are generic tools which are relatively parameter-free, not tailored to specific assumptions over the input. More precisely, we consider the distributional setting where there are $k$ clusters in $\mathbb{R}^m$ and data from each cluster consists of $n$ points sampled from a symmetric distribution within a ball of unit radius. We ask: what is the minimal separation distance between cluster centers needed for convex relaxations to exactly recover these $k$ clusters as the optimal integral solution? For the $k$-median linear programming relaxation we show a tight bound: exact recovery is obtained given arbitrarily small pairwise separation $\epsilon > 0$ between the balls. In other words, the pairwise center separation is $\Delta > 2+\epsilon$. Under the same distributional model, the $k$-means LP relaxation fails to recover such clusters at separation as large as $\Delta = 4$. Yet, if we enforce PSD constraints on the $k$-means LP, we get exact cluster recovery at center separation $\Delta > 2\sqrt2(1+\sqrt{1/m})$. In contrast, common heuristics such as Lloyd's algorithm (a.k.a. the $k$-means algorithm) can fail to recover clusters in this setting; even with arbitrarily large cluster separation, k-means++ with overseeding by any constant factor fails with high probability at exact cluster recovery. To complement the theoretical analysis, we provide an experimental study of the recovery guarantees for these various methods, and discuss several open problems which these experiments suggest.Comment: 30 pages, ITCS 201

Paint Sludge Reuse

http://deepblue.lib.umich.edu/bitstream/2027.42/106047/1/ME589F13_881-7_Paint Sludge Reuse_Public Summary.pd

Assessment of knowledge on neonatal resuscitation amongst health care providers in Kenya

Introduction: Competence in neonatal resuscitation, which represents the most urgent pediatric clinical situation, is critical in delivery rooms to ensure safety and health of newly born infants. The challenges experienced by health care providers during this procedure are unique due to different causes of cardio respiratory arrest. This study aimed at assessing the knowledge of health providers on neonatal resuscitation. Methods: Data were gathered among 192 health providers drawn from all counties of Kenya. The clinicians were asked to complete questionnaires which were in two parts as; demographic information and assessment of their knowledge by different scenarios which were formatted in the multiple choice questions. Data were analyzed using SPSS version 15.0 for windows. The results are presented using tables. Results: All the participants were aged 23 years and above with at least a certificate training. Most medical providers had heard of neonatal resuscitation (85.4%) with only 23 receiving formal training. The average duration of neonatal training was 3 hours with 50% having missed out on practical exposure. When asked on steps of resuscitation, only 68 (35.4%) of the participants scored above 85%. More than 70% of them considered their knowledge about neonatal resuscitation inadequate and blamed it on inadequate medical training programs. Conclusion: Health providers, as the key personnel in the management of neonatal resuscitation, in this survey seem to have inadequate training and knowledge on this subject. Increasing the duration and quality of formal training should be considered during the pre-service medical education to ensure acceptable neonatal outcome

Growing Up in the New South Africa

This book presents a qualitative research conducted in the Fish Hoek valley in South Africa with a view to understanding the challenges in the transitions into adulthood in South Africa

ABO Blood Groups Do Not Predict Schistosoma mansoni Infection Profiles in Highly Endemic Villages of Uganda

Schistosoma mansoni is a parasite which causes significant public-health issues, with over 240 mil-lion people infected globally. In Uganda alone, approximately 11.6 million people are affected. Despite over a decade of mass drug administration in this country, hyper-endemic hotspots persist, and individuals who are repeatedly heavily and rapidly reinfected are observed. Human blood-type antigens are known to play a role in the risk of infection for a variety of diseases, due to cross-reactivity between host antibodies and pathogenic antigens. There have been conflicting results on the effect of blood type on schistosomiasis infection and pathology. Moreover, the ef-fect of blood type as a potential intrinsic host factor on S. mansoni prevalence, intensity, clearance, and reinfection dynamics and on co-infection risk remains unknown. Therefore, the epidemio-logical link between host blood type and S. mansoni infection dynamics was assessed in three hyper-endemic communities in Uganda. Longitudinal data incorporating repeated pretreatment S. mansoni infection intensities and clearance rates were used to analyse associations between blood groups in school-aged children. Soil-transmitted helminth coinfection status and biometric parameters were incorporated in a generalised linear mixed regression model including age, gender, and body mass index (BMI), which have previously been established as significant factors influencing the prevalence and intensity of schistosomiasis. The analysis revealed no associations between blood type and S. mansoni prevalence, infection intensity, clearance, reinfection, or coinfection. Variations in infection profiles were significantly different between the villages, and egg burden significantly decreased with age. While blood type has proven to be a predictor of several diseases, the data collected in this study indicate that it does not play a significant role in S. mansoni infection burdens in these high-endemicity communities

Gendered sexual risk patterns and polygamy among HIV sero-discordant couples in Uganda

This study examined the multiple sexual partnerships and HIV sero-discordant relationships are among the most at-risk for HIV transmission.Multiple sexual partnerships and HIV sero-discordant relationships are among the most at-risk for HIV transmission. Polygamy is a common form of multiple-partnered relationships in Eastern Uganda. We investigated the association between HIV risk patterns and polygamy among HIV sero-discordant couples at The AIDS Support Organization in Jinja, Uganda Methods Participants were enrollees in a prospective cohort of HIV sero-discordant couples, the Highly Active Antiretroviral therapy as Prevention (HAARP) Study at TASO Jinja. Descriptive nand bivariate analyses to compare sexual risk patterns among HIV sero-discordant men; in polygamous as compared to single-spouse relationship

Understanding the Risks Factors of Under-Five Child Mortality in Kenya: Random Survival Forest and Accelerated Failure Time Shared Frailty Models

Under-five mortality rates is one of the health indicators of great importance to any country. Kenya is among the countries in the Sub-Saharan Africa with high Under-Five Child Mortality (U5CM) rates. It is therefore important to apply best statistical approaches to establish which factors influence child mortality. This will go a long way to inform the optimal design of health intervention strategies within the country and globally. In this study, Random Survival Forest (RSF) and Accelerated Failure Time Shared Frailty Models have been used to analyze U5CM based on the Kenya Demographic Health Survey (KDHS, 2014) dataset. Akaike Information Criterion (AIC) statistics was used to select the model of best fit. Results obtained from fitting the AFT-shared frailty model, showed that there was presence of unobserved heterogeneity at community level. However, there was no evidence to conclude the existence of unobserved heterogeneity at the household level. Among the variants of the AFT Shared Frailty models analysed, the Log-logistic AFT- model showed that “the sons who have died,” “daughters who have died,” “duration of breastfeeding,” and “months of breastfeeding” had significant influence on the U5CM (p <0.05). The Log-logistic AFT model with Gaussian frailty emerged to be the best model for the U5CM since it had the least Akaike Information Criterion (AIC) statistic. On the other hand, the results from Random Survival Forest, “sons who have died,” “daughters who have died,” “living children plus current pregnancy,” “sex of child,” “duration of breastfeeding,” “number of living children,” and “months of breastfeeding” were ranked as important factors that have influence on the under-five mortality. Furthermore, this study also found out that there was presence of unobserved heterogeneity at community level of clustering. At the household level however, there was no unobserved heterogeneity, hence there was no need for household frailty term