A comprehensive study of multiplicative attribute graph model

Graphs are powerful tools to describe social, technological and biological networks, with nodes representing agents (people, websites, gene, etc.) and edges (or links) representing relations (or interactions) between agents. Examples of real-world networks include social networks, the World Wide Web, collaboration networks, protein networks, etc. Researchers often model these networks as random graphs. In this dissertation, we study a recently introduced social network model, named the Multiplicative Attribute Graph model (MAG), which takes into account the randomness of nodal attributes in the process of link formation (i.e., the probability of a link existing between two nodes depends on their attributes). Kim and Lesckovec, who defined the model, have claimed that this model exhibit some of the properties a real world social network is expected to have. Focusing on a homogeneous version of this model, we investigate the existence of zero-one laws for graph properties, e.g., the absence of isolated nodes, graph connectivity and the emergence of triangles. We obtain conditions on the parameters of the model, so that these properties occur with high or vanishingly probability as the number of nodes becomes unboundedly large. In that regime, we also investigate the property of triadic closure and the nodal degree distribution.

Impact of Cryptosporidium spp. interaction with co-occurring microorganisms on moderate-to-severe diarrhea in the developing world

Diarrheal illness is responsible for over a quarter of all deaths in children under 5 years of age in sub-Saharan Africa and South Asia. Recent findings have identified the parasite Cryptosporidium as a contributor to enteric disease. We examined 9,348 cases and 13,128 controls from the Global Enteric Multicenter Study to assess whether Cryptosporidium interacted with co-occurring pathogens based on adjusted odds of moderate-to-severe diarrhea (MSD). Cryptosporidium was found to interact negatively with Shigella spp., with multiplicative interaction score of 0.16 (95% CI: 0.07 to 0.37, p-value=0.000), and an additive interaction score of -9.81 (95% CI: -13.61 to -6.01, p-value=0.000). Cryptosporidium also interacted negatively with Aeromonas spp., Adenovirus, Norovirus, and Astrovirus with marginal significance. Odds of MSD for Cryptosporidium co-infection with Shigella spp., Aeromonas spp., Adenovirus, Norovirus, or Astrovirus are lower than odds of MSD with either organism alone. This may reduce the efficacy of intervention strategies targeted at Cryptosporidium.

The relationship of early social, mental, and behavioral experiences with adult obesity and Alcohol Use Disorder

Stressful life events early in life, including symptoms of mental disorders or childhood maltreatment, may increase risk for worse mental and physical health outcomes in adulthood. The purpose of this dissertation was to examine the effects of childhood Attention Deficit Hyperactivity Disorder (ADHD) symptoms and maltreatment experience on two adult outcomes: obesity and alcohol use disorder (AUD). Mediational effects of adolescent characteristics were explored. This dissertation used Waves I, III, and IV of the National Longitudinal Study of Adolescent to Adult Health. In Paper 1 (Chapter 3), we investigated the association between multiple types of child maltreatment and adult objective (body mass index; BMI) and subjective (self-rated) obesity, as well as mediating effects by adolescent characteristics including depressive symptoms and BMI. Results showed that after adjusting for sex, race/ethnicity, and maternal education, physical maltreatment was moderately associated with adulthood obesity as measured by BMI and self-reported obesity, while sexual maltreatment was more strongly associated with the objective measure but not the subjective measure. The indirect effects of mediation of adolescent BMI and depressive symptoms were statistically significant. In Paper 2 (Chapter 4), the objective was to examine mediation by adolescent depressive symptoms, alcohol consumption, peer alcohol consumption, and delinquency in the relationship between ADHD symptoms and adult AUD. The indirect effects of mediation of adolescent delinquency, alcohol consumption, and peer alcohol consumption were statistically significant in single and multiple mediator models. In Paper 3 (Chapter 5), the objective was to assess the joint effects of maltreatment/neglect on adult AUD. After adjusting for sex, race/ethnicity, child maltreatment, and parental AUD, ADHD symptoms were significantly associated with increased odds of AUD. There was no strong evidence of multiplicative interaction by maltreatment. This association was stronger for males than females, although the interaction term was not statistically significant. This dissertation adds to the literature by examining relationships between several major public health problems: ADHD symptoms, childhood maltreatment, AUD, depressive symptoms, and obesity. This project has implications for understanding how early life stress increases risk for later physical and mental health problems, and identifying potential intervention targets for adolescents.

THE STOCHASTIC NAVIER STOKES EQUATIONS FOR HEAT CONDUCTING, COMPRESSIBLE FLUIDS

This dissertation is devoted to the equations of motion governing the evolution of a fluid or gas at the macroscopic scale. The classical model is a PDE description known as the Navier-Stokes equations. The behavior of solutions is notoriously complex, leading many in the scientific community to describe fluid mechanics using a statistical language. In the physics literature, this is often done in an ad-hoc manner with limited precision about the sense in which the randomness enters the evolution equation. The stochastic PDE community has begun proposing precise models, where a random perturbation appears explicitly in the evolution equation. Although this has been an active area of study in recent years, the existing literature is almost entirely devoted to incompressible fluids. The purpose of this thesis is to take a step forward in addressing this statistical perspective in the setting of compressible fluids. In particular, we study the well posedness for the corresponding system of Stochastic Navier Stokes equations, satisfied by the density, velocity, and temperature. The evolution of the momentum involves a random forcing which is Brownian in time and colored in space. We allow for multiplicative noise, meaning that spatial correlations may depend locally on the fluid variables. Our main result is a proof of global existence of weak martingale solutions to the Cauchy problem set within a bounded domain, emanating from large initial datum. The proof involves a mix of deterministic and stochastic analysis tools. Fundamentally, the approach is based on weak compactness techniques from the deterministic theory combined with martingale methods. Four layers of approximate stochastic PDE's are built and analyzed. A careful study of the probability laws of our approximating sequences is required. We prove appropriate tightness results and appeal to a recent generalization of the Skorohod theorem. This ultimately allows us to deduce analogues of the weak compactness tools of Lions and Feireisl, appropriately interpreted in the stochastic setting.