<div><div><div><p>Several socially and economically important real-world systems comprise large numbers of interacting constituent entities. Examples include the World Wide Web and Online Social Networks (OSNs). Developing the capability to forecast the macroscopic behavior of such systems based on the microscopic interactions of the constituent parts is of considerable economic importance.</p><p>Previous researchers have investigated phenomenological forecasting models in such contexts as the spread of diseases in the real world and the diffusion of innovations in the OSNs. The previous forecasting models work well in predicting future states of a system that are at equilibrium or near equilibrium. However, forecasting non-equilibrium states – such as the transient emergence of hotspots in web traffic – remains a challenging problem. In this thesis we investigate a hypothesis, rooted in Ludwig Boltzmann's celebrated H-theorem, that the evolutionary dynamics of a large system – such as the World Wide Web – is driven by the system's innate tendency to evolve towards a state of maximum entropy.</p><p>Whereas closed systems may be expected to evolve towards a state of maximum entropy, most real-world systems are not closed. However, the stipulation that if a system is closed then it should asymptotically approach a state of maximum entropy provides a strong constraint on the inverse problem of formulating the microscopic interaction rules that give rise to the observed macroscopic behavior. We make the constraint stronger by insisting that, if closed, a system should evolve monotonically towards a state of maximum entropy and formulate microscopic interaction rules consistent with the stronger constraint.</p><p>We test the microscopic interaction rules that we formulate by applying them to two real world phenomena: the flow of web traffic in the gaming forums on Reddit and the spread of Covid-19 virus. We show that our hypothesis leads to a statistically significant improvement over the existing models in predicting the traffic flow in gaming forums on Reddit. Our interaction rules are also able to qualitatively reproduce the heterogeneity in the number of COVID-19 cases across the cities around the globe. The above experiments provide supporting evidence for our hypothesis, suggesting that our approach is worthy of further investigation.</p><p>In addition to the above stochastic model, we also study a deterministic model of attention flow over a network and establish sufficient conditions that, when met, signal imminent parabolic accretion of attention at a node<br></p></div></div></div>

<div><div>N-body problems, such as simulating the motion of stars in a galaxy and evaluating the spatial statistics through n-point correlation function, are popularly solved. The naive approaches to n-body problems are typically O(n^2) algorithms. Tree codes take advantages of the fact that a group of bodies can be skipped or approximated as a union if their distance is far away from one body’s sight. It reduces the complexity from O(n^2) to O(n*lgn). However, tree codes rely on pointer chasing and have massive branch instructions. These are highly irregular and thus prevent tree codes from being easily parallelized. </div><div><br></div><div>GPU offers the promise of massive, power-efficient parallelism. However, exploiting this parallelism requires the code to be carefully structured to deal with the limitations of the SIMT execution model. This dissertation focusses on optimizations for n-body problems on the heterogeneous system. A general inspector-executor based framework is proposed to automatically schedule GPU threads to achieve high performance. Essentially, the framework lets the GPU execute partial of the tree codes and profile threads behaviors, then it assigns the CPU to re-organize these threads to minimize the divergence before executing the remaining portion of the traversals on the GPU. We apply this framework to six tree traversal algorithms, achieving significant speedups over optimized GPU code that does not perform application-specific scheduling. Further, we show that in many cases, our hybrid approach is able to deliver better performance even than GPU code that uses hand tuned, application-specific scheduling. </div><div> </div><div>For large scale input, ChaNGa is the best-of-breed n-body platform. It uses an asymp-totically-efficient tree traversal strategy known as a dual-tree walk to quickly provide an accurate simulation result. On GPUs, ChaNGa uses a hybrid strategy where the CPU performs the tree walk to determine which bodies interact while the GPU performs the force computation. In this dissertation, we show that a highly optimized single-tree walk approach is able to achieve better GPU performance by significantly accelerating the tree walk and reducing CPU/GPU communication. Our experiments show that this new design can achieve a 8.25x speedup over baseline ChaNGa using one node, one process per node configuration. We also point out that ChaNGa's implementation doesn't satisfy the inclusion condition so that GPU-centric remote tree walk doesn't perform well.</div></div>

<p>The last decade has seen a significant increase in activity within cislunar space. The quantity of missions to the Lunar vicinity will only continue to rise following the collab- orative effort between NASA, ESA, JAXA and the CSA to construct the Gateway space station. One significant engineering challenge is the design of trajectories that deliver space- craft to orbits in the Lunar vicinity. In response, this study employs multi-body dynamics to investigate the geometry of two-maneuver transfers to Earth-Moon libration point or- bits. Zero-Momentum Points are employed to investigate transfer behavior in the circular- restricted 3-body problem. It is found that these points along stable invariant manifolds indicate changes in transfer geometry and represent locations where transfers exhibit limit- ing behaviors. The analysis in the lower-fidelity model is utilized to formulate initial guesses that are transitioned to higher-fidelity, ephemeris models. Retaining the solution geometry of these guesses is prioritized, and adaptations to the transition strategy are presented to circumvent numerical issues. The presented methodologies enable the procurement of desir- able trajectories in higher-fidelity models that reflect the characteristics of the initial guess generated in the circular restricted 3-body problem.</p>