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.

STATISTICAL METHODS FOR ADVANCED ECONOMETRIC MODELS WITH APPLICATIONS TO VEHICLE HOLDING AND SPEED QUANTILES DISTRIBUTION

This dissertation proposes statistical methods to formulate, estimate and apply complex transportation models. Two main problems are part of the analyses conducted and presented in this dissertation. The first method solves an econometric problem and is concerned with the joint estimation of models that contain both discrete and continuous decision variables. The use of ordered models along with a regression is proposed and their effectiveness is evaluated with respect to unordered models. Procedure to calculate and optimize the log-likelihood functions of both discrete-continuous approaches are derived, and difficulties associated with the estimation of unordered models explained. Numerical approximation methods based on the Genz algortithm are implemented in order to solve the multidimensional integral associated with the unordered modeling structure. The problems deriving from the lack of smoothness of the probit model around the maximum of the log-likelihood function, which makes the optimization and the calculation of standard deviations very difficult, are carefully analyzed. A methodology to perform out-of-sample validation in the context of a joint model is proposed. Comprehensive numerical experiments have been conducted on both simulated and real data. In particular, the discrete-continuous models are estimated and applied to vehicle ownership and use models on data extracted from the 2009 National Household Travel Survey. The second part of this work offers a comprehensive statistical analysis of free-flow speed distribution; the method is applied to data collected on a sample of roads in Italy. A linear mixed model that includes speed quantiles in its predictors is estimated. Results show that there is no road effect in the analysis of free-flow speeds, which is particularly important for model transferability. A very general framework to predict random effects with few observations and incomplete access to model covariates is formulated and applied to predict the distribution of free-flow speed quantiles. The speed distribution of most road sections is successfully predicted; jack-knife estimates are calculated and used to explain why some sections are poorly predicted. Eventually, this work contributes to the literature in transportation modeling by proposing econometric model formulations for discrete-continuous variables, more efficient methods for the calculation of multivariate normal probabilities, and random effects models for free-flow speed estimation that takes into account the survey design. All methods are rigorously validated on both real and simulated data.

Near-infrared Instrumentation For Rapid-response Astronomy

Ɣ-ray bursts (GRBs) are the Universe's most luminous transient events. Since the discovery of GRBs was announced in 1973, efforts have been ongoing to obtain data over a broader range of the electromagnetic spectrum at the earliest possible times following the initial detection. The discovery of the theorized ``afterglow'' emission in radio through X-ray bands in the late 1990s confirmed the cosmological nature of these events. At present, GRB afterglows are among the best probes of the early Universe (z ≳ 9). In addition to informing theories about GRBs themselves, observations of afterglows probe the circum-burst medium (CBM), properties of the host galaxies and the progress of cosmic reionization. To explore the early-time variability of afterglows, I have developed a generalized analysis framework which models near-infrared (NIR), optical, ultra-violet (UV) and X-ray light curves without assuming an underlying model. These fits are then used to construct the spectral energy distribution (SED) of afterglows at arbitrary times within the observed window. Physical models are then used to explore the evolution of the SED parameter space with time. I demonstrate that this framework produces evidence of the photodestruction of dust in the CBM of GRB 120119A, similar to the findings from a previous study of this afterglow. The framework is additionally applied to the afterglows of GRB 140419A and GRB 080607. In these cases the evolution of the SEDs appears consistent with the standard fireball model. Having introduced the scientific motivations for early-time observations, I introduce the Rapid Infrared Imager-Spectrometer (RIMAS). Once commissioned on the 4.3 meter Discovery Channel Telescope (DCT), RIMAS will be used to study the afterglows of GRBs through photometric and spectroscopic observations beginning within minutes of the initial burst. The instrument will operate in the NIR, from 0.97 μm to 2.37 μm, permitting the detection of very high redshift (z ≳ 7) afterglows which are attenuated at shorter wavelengths by Lyman-ɑ absorption in the intergalactic medium (IGM). A majority of my graduate work has been spent designing and aligning RIMAS's cryogenic (~80 K) optical systems. Design efforts have included an original camera used to image the field surrounding spectroscopic slits, tolerancing and optimizing all of the instrument's optics, thermal modeling of optomechanical systems, and modeling the diffraction efficiencies for some of the dispersive elements. To align the cryogenic optics, I developed a procedure that was successfully used for a majority of the instrument's sub-assemblies. My work on this cryogenic instrument has necessitated experimental and computational projects to design and validate designs of several subsystems. Two of these projects describe simple and effective measurements of optomechanical components in vacuum and at cryogenic temperatures using an 8-bit CCD camera. Models of heat transfer via electrical harnesses used to provide current to motors located within the cryostat are also presented.