Spatial and temporal components play a critical role in explaining variability across geographic regions and time, and are necessary components to space-time epidemiological research. Until recent years, most spatial epidemiological studies have used simple space-time analyses, but the continuous advancements in statistical modeling software and geographic information systems have made more complex spatial analyses readily available. However, methods may be problematic and several ongoing statistical weaknesses have been documented, including failing to account for three significant correlative factors - spatial, temporal, and spatiotemporal autocorrelations. Using Eastern Equine Encephalitis (EEE) human incidence data, this Master's thesis aimed to answer the research question, is there a northeastern shift in human EEE incidence within the United States, by identifying a statistical model that adjusts for spatial, temporal, and spatiotemporal autocorrelations. This thesis introduced the spatial autoregressive distributed lag (SADL) model, a model that adjusts for spatial, temporal, and spatiotemporal autocorrelations. However, results demonstrated that EEE is too rare an event for the SADL model to be appropriate, and a non-autocorrelation model was used as the final model. Results showed that EEE incidence is significantly increasing over time for all infected regions of the United States, with a significant difference of 1.4 cases/10 million between 1964 and 2015. Results did not demonstrate a northeastern shift in EEE incidence as the northeastern US had the highest expected incidence across the entire study period (1964-1967: 2.9/10 million; 2012-2015: 6.8/10 million), but results did demonstrate that the northeastern US had the quickest increasing risk for EEE as compared to other infected regions of the US with an increase in expected incidence of 3.9/10 million between 1964 and 2015.

Turing theory plays an important role in real biological pattern formation problems, such as solid tumor growth and animal coat patterns. To understand how patterns form and develop over time due to growth, we consider spatiotemporal patterns, in particular Turing patterns, for reaction diffusion systems on growing surfaces with curvature. Of particular interest is isotropic growth of the sphere, where growth of the domain occurs in the same proportion in all directions. Applying a modified linear stability analysis and a separation of timescales argument, we derive the necessary and sufficient conditions for a diffusion driven instability of the steady state and for the emergence of spatial patterns. Finally, we explore these results using numerical simulations.

Temporal and spatial distribution in species composition and abundance of hydromedusae in relation to hydrographic variables in the waters surrounding Taiwan were investigated from February to November, 2004. A total of 101 species belonging to 65 genera and 34 families hydromedusae were identified, with the mean abundance of 557 ¡Ó 90 inds./1000m3. The abundance of hydromedusae showed no significant seasonal change but generally was higher in spring and fall, and lower in summer. The eight dominant species were Aglaura hemistoma¡BSolmundella bitentaculata¡BEutima levuka¡BLiriope tetraphylla¡BAglantha elata¡BLaodicea indica¡BRhopalonema velatum and Sminthea eurygaster, which together contributed 85% of the total hydromedusae. Hydromedusae showed higher abundance in the waters northwest off Taiwan, while the species number and diversity were higher in the waters east and south off Taiwan. Hydromedusa communities showed significant difference among water masses, higher abundance in China Costal Current, meanwhile higher species number and diversity in Kuroshio Current. Different dominant species showed different distribution patterns. The total abundance of hydromedusae showed no significant correlation with temperature or salinity, but were positive correlated with zooplankton abundance, while species richness were negatively correlated with zooplankton abundance. Different dominant hydromedusae species showed different correlationships with environmental factors; Aglaura hemistoma showed significant positive correlation with salinity, but Solmundella bitentaculata showed significant negative corelation with salinity. The correlationship between the abundance of each dominant species and evironmental factors varied seasonally.

Philosophical analyses of causation take many forms but one major difficulty they all aim to address is that of the spatiotemporal continuity between causes and their effects. Bertrand Russell in 1913 brought the problem to its most transparent form and made it a case against the notion of causation in physics. The issue highlighted in Russell's argument is that of temporal contiguity between cause and effect. This tension arises from the imposition of a spectrum of discrete events occupying spacetime points upon a background of spacetime continuum. An immediate and natural solution is to superpose instead spatiotemporally continuous entities, or processes, on the spacetime continuum. This is indeed the process view of physical causation advocated by Wesley Salmon and Phil Dowe. This view takes the continuous trajectories of physical objects (worldlines) as the causal connection whereby causal influences in the form of conserved quantities are transported amongst events. Because of their reliance on spatiotemporal continuity, these theories have difficulty when confronted with the discontinuous processes in the quantum domain. This thesis is concerned with process theories. It has two parts. The first part introduces and criticizes these theories, which leads to my proposal of the History Conserved Quantity Theory with Transmission. The second part considers the extension of the idea of causal processes to quantum physics. I show how a probability distribution generated by the Schrodinger wavefunction can be regarded as a conserved quantity that makes the spacetime evolution of the wavefunction a quantum causal process. However, there are conceptual problems in the interpretation of the wavefunction, chiefly to do, as I shall argue, with the difference in the behaviours of probabilistic potentials between quantum and classical physics. I propose in the final chapter, the Feynman Path Integral formulation of quantum mechanics (with the Feynman histories) as an alternative approach to incorporating the probabilistic potentials in quantum physics. This account of how to introduce causal processes in quantum mechanics fares better, I claim, than the previous one in dealing with the situational aspect of quantum phenomena that requires the consideration of events at more than one time.

Neuroscience focuses largely on how the brain mediates perception and cognition. However, this leaves open the basic organization and hierarchies of the brain’s neural activity by itself prior to and independent of its role in cognition. A recent model characterizes the brain’s intrinsic features in terms of temporo- spatial dynamical (rather than cognitive) terms – the brain’s spatiotemporal hierarchies shape what is called ‘brain’s intrinsicality’. The brain’s intrinsicality may provide potential applications in designing artificial intelligence (AI). In this dissertation, I explore ‘intrinsic neural timescales’ and their spatial topography as one main building block of the brain’s intrinsicality. First, I present empirical investigation of temporal hierarchy and information flux as two basic facets of brain’s intrinsicality using magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI) data. That is complemented by introducing the notion of intrinsicality through intrinsic neural timescales and how they shape input processing in the brain. Then, I propose a model for input processing through intrinsic neural timescales and provide some notes on how that model can be implemented in an artificial agent. I conclude that the spatiotemporal dynamics of the brain’s intrinsicality provides potential key insights for Artificial General Intelligence (AGI).

Tennessee has a long history of floods that have caused property damage and loss of life. In the face of climate change and variability, it is imperative to look at trends to ascertain if there is a significant change in current flood regimes versus past flood events. Trend Analysis and Emerging Hotspot Analysis are useful geospatial tools that can effectively display changes over time and space. This study aims to evaluate the history of flood events in Tennessee to identify spatiotemporal trends and hot spots. A total of 902 flood events from 1996-2021 recorded in the National Oceanic Atmospheric Agency (NOAA) storm events database were analyzed using the number of events per county and the total damages per county at an annual time step. Two 26-year space-time cubes were built in ArcGIS Pro (version 3.0) for flood events and damages using an annual time step, with counties as the spatial unit. GeoGa software (version 1.20.0.22) was used to weight the distance between Tennessee counties to define a statistically significant neighborhood distance at 37km fixed distance. Trend Analysis and Emerging Hotspot Analysis was conducted to assess spatiotemporal trends in flooding events and damages (in dollars). Trend analysis revealed an increasing trend of flood events in eleven counties in middle Tennessee (Davidson, Wilson, Rutherford, Coffee, Marion, Putnam, Overton, Maury, Lawrence and Dickson counties) and Carter county in east Tennessee. Decreasing trends were observed in two counties (Lake and Bradley), all at a 90% or greater confidence level. Increasing trends in flood damages were identified in Cumberland, Putnam, Lawrence, Blount, Sullivan and Green counties, all in east and middle Tennessee. Decreasing trends were identified in Lake, Obion, Dyer, and Tipton, all in west Tennessee. East Tennessee was identified as a sporadic flooding hot spot (Hawkins, Green and Washington counties) with no significant hot spots in middle and west Tennessee. There were no hot spots nor cold spots in flood-related damages across Tennessee. The results indicate that flood events and related damages are decreasing in west Tennessee while parts of middle Tennessee and east Tennessee are experiencing increased flood events. This study is an important step to better understand spatiotemporal trends in flooding and flooding damages and will be useful in hazard mitigation planning in Tennessee at both state and county levels.

The nonlinear and chaotic dynamics of a shallow fluid layer are investigated numerically using large-scale parallel numerical simulations. Two particular situations are studied in detail. First, a fluid layer is placed between rigid boundaries and heated from below to yield the chaotic dynamics of thermal convection rolls (Rayleigh-Bénard convection). Second is a free-surface fluid layer placed on a shaker to yield nonlinear surface waves (Faraday waves). In both cases the full governing partial differential equations are solved using parallel spectral element methods. Rayleigh-Bénard convection is studied in a cylindrical dish with realistic boundaries. The complete flow field is obtained as well as the spectrum of Lyapunov exponents and Lyapunov vectors. The Lyapunov exponents and their corresponding perturbation fields are used to determine when and where events occur that contribute most to the chaotic dynamics. Roll pinch-off and roll mergers are found to be the largest contributors. Two dimensional and three dimensional Faraday waves are studied with periodic boundary conditions. The full Navier-Stokes equations are solved including the complex dynamics of the free surface waves to gain a better understanding of the interplay between the viscous boundary layers, the nonlinear streaming flow, and the bulk flow. The vortices in the bulk flow are weak compared to the flow in the viscous boundary layers. The surface waves are found to be non-sinusoidal and the time evolution of the waves are explored for both large and small amplitude waves. / Master of Science

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Finding frequent patterns plays a vital role in many analytics tasks such as finding itemsets, associations, correlations, and sequences. In recent decades, spatiotemporal frequent pattern mining has emerged with the main goal focused on developing data-driven analysis frameworks for understanding underlying spatial and temporal characteristics in massive datasets. In this thesis, we will focus on discovering spatiotemporal event sequences from large-scale region trajectory datasetes with event annotations. Spatiotemporal event sequences are the series of event types whose trajectory-based instances follow each other in spatiotemporal context. We introduce new data models for storing and processing evolving region trajectories, provide a novel framework for modeling spatiotemporal follow relationships, and present novel spatiotemporal event sequence mining algorithms.