Although it is well-known that there is a relationship between socio-physical dis- tance and edge probability in interpersonal networks, the predictive power of such distances for total network structure has not been established. Here, it is shown that upper bounds on the marginal edge probabilities for farflung dyads can be used to place a lower bound on the predictive power of distance, and one such bound is de- rived. Application of this bound to the special case of uniformly placed vertices on the plane suggests that only modest constraints are required for distance effects to dominate at large physical scales.

Interpersonal interaction over short time scales is frequently understood in terms of actions, which can be thought of as discrete events in which one individual emits a behavior directed at one or more other entities in his or her environment (possibly including him or herself). Here, we introduce a highly flexible framework for modeling actions within social settings, which permits likelihood-based inference for behavioral mechanisms with complex dependence. The utility of the framework is illustrated via an application to dynamic modeling of responder radio communications during the early hours of the World Trade Center disaster.

With climate change upon us, the development of energy storage technologies to increase the integration of renewable energy systems is critical. Thus, a variety of energy storage systems are required to meet the wide array of demands from grid-level storage to high-power, fast-charging electric vehicles. This dissertation presents the introduction of novel Li- and Na-ion chemistries and materials systems for energy storage (Chapter 3 and 5) and demonstrates further development of full-cell chemistries for industrial applications (Chapter 4). In Chapter 3, we present a method for high-power electrode development from high ionic conductivity solid-state electrolytes in a model Na-ion system: Na-β alumina (NBA). The substitution of a redox active ion, Fe, for Al within the NBA structure enabled development of a high-power Na-ion battery electrode with 75% capacity retention at a 20C-rate. This work demonstrates a new avenue for materials research development in high-power materials design and improved interface compatibility of electrodes with solid state electrolytes. In Chapter 4, we present high-power Li-ion devices, which can deliver charge in a matter of minutes instead of hours, that could transform the electric vehicle market as well as consumer electronics and ‘internet-of-things’ (IOT) devices. The Nb2O5-based devices demonstrate the advantage of pseudocapacitive materials, those with capacitor-like kinetics, in full-cell battery systems. Energy storage devices with the demonstrated power-density capabilities are necessary to realize the clean energy goals of the upcoming decades and mark a significant step from lab-scale to practical applications. Finally, in Chapter 5, a combination of high-power and high-energy is demonstrated in amorphous sulfides: a-WSx and a-TaSy. This is the first demonstration to date of high-power, amorphous materials for energy storage with evidence of multielectron, anionic redox. The development of amorphous sulfide materials highlights the advantage of amorphous over crystalline structures for multielectron, anionic redox reversibility as well as the importance of local atomic ordering compared with long-range order for fast charging capabilities. Taken together, the work presented here delivers pathways for future materials development and design in Na- and Li-ion battery systems from fundamental materials properties for high energy and high power to full-cell, prototype devices.

Exponential family models for random graphs (ERGs, also known as p∗ models) are an increasingly popular tool for the analysis of social networks. ERGs allow for the parameterization of complex dependence among edges within a likelihood-based framework, and are often used to model local influences on global structure. This paper introduces a family of cycle statistics, which allow for the modeling of long-range dependence within ERGs. These statistics are shown to arise from a family of partial conditional dependence assumptions based on an extended form of reciprocity, here called reciprocal path dependence. Algorithms for computing cycle statistic changescores and the cycle census are provided, as are analytical expressions for the first and approximate second moments of the cycle census under a Bernoulli null model. An illustrative application of ERG modeling using cycle statistics is also provided.

Time-varying networks and techniques developed to study them have been used to analyze dynamic systems in social, computational, biological, and other contexts. Significant progress has been made in this area in recent years, resulting from a combination of statistical advances and improved computational resources, giving rise to a range of new research questions. This thesis addresses problems related to three lines of inquiry involving dynamic networks: data collection designs; the conditions needed for structural stability of an evolving network; and the computational scalability of statistical models for network dynamics. The first contribution involves a commonly neglected problem concerning data collection protocols for dynamic network data: the impact of in-design missingness. A systematic formalization is offered for the widely used class of retrospective life history designs, and it is shown that design parameters have nontrivial effects on both the quantity of missingness and the impact of such missingness on network modeling and reconstruction. Using a simulation study, we also show how the consequences of design parameters for inference vary as a function of look-back time relative to the time of measurement. The second contribution of this thesis is related to a fundamental question of network dynamics: when or where are changes in a network most likely to occur? A novel approach is taken to this question, by exploring its complement -- what factors stabilize a network (or subgraphs thereof) and make it resistant to change? For networks whose behavior can be parameterized in exponential family form, a formal characterization of the graph-stabilizing region of the parameter space is shown to correspond to a convex polytope in the parameter space. A related construction can be used to find subgraphs that are or are not stable with respect to a given parameter vector, and to identify edge variables that are most vulnerable to perturbation. Finally, the third contribution of this thesis is to scalable parameter estimation for a class of temporal exponential family random graph models (TERGM) from sampled data. An algorithm is proposed that allows accurate approximation of maximum likelihood estimates for certain classes of TERGMs from egocentrically sampled retrospective life history data, without requiring simulation of the underlying network (a major bottleneck when the network size is large). Estimation time for this algorithm scales with the data size, and not with the size of the network, allowing it to be employed on very large populations.