Historic research into the Virginia Springs reveals a collection of vital interconnected seasonal communities centered on retreat from the unhealthy environs of the coast and devoted to resort in the mountains. Prior to the Civil War the Virginia Springs became renowned internationally as the summer home of the region's and the nation's elite. The collapse of the southern economy during and following the war meant the reorganization and often the failure of most of the Springs. A revival of sorts took place among the Virginia Springs during the late 19th century, consciously referencing the earlier "golden age." Many Springs found new life as schools, church camps, retirement homes and smaller hotels. Many simply left the scene altogether. Today little remains in the landscape to suggest the scale and vitality of many of these dynamic seasonal communities. And yet retreat to a wilderness setting remains appealing. Perhaps most compelling are the persistence of landscape qualities that contributed to their reputations as places of healing and retreat, namely the mountain air, the wild scenery and the healing waters. The Virginia Springs are in fact at an ideal location and represent ideal conditions for a new chapter in our own relationship with wild nature. Preservation efforts ought to focus on articulating such a relationship of building to landscape. While the scale of such a retreat might not equal that of its predecessors, a revived Virginia Spring, such as the Healing Springs of Bath County, can say much about how we find retreat in the 21st century. / Master of Landscape Architecture

Many real-world network data can be formulated as graphs, where a binary relation exists between nodes. One of the fundamental problems in network data analysis is community detection, clustering the nodes into different groups. Statistically, this problem can be formulated as hypothesis testing: under the null hypothesis, there is no community structure, while under the alternative hypothesis, community structure exists. One is of the method is to use the largest eigenvalues of the scaled adjacency matrix proposed by Bickel and Sarkar (2016), which works for dense graph. Another one is the subgraph counting method proposed by Gao and Lafferty (2017a), valid for sparse network. In this paper, firstly, we empirically study the BS or GL methods to see whether either of them works for moderately sparse network; secondly, we propose a subsampling method to reduce the computation of the BS method and run simulations to evaluate the performance.

In certain areas such as Pharmacokinetic(PK) and Pharmacodynamic(PD), the hazard rate function, denoted by ??, plays a central role in modeling the instantaneous risk of failure time data. In the context of assessing the appropriateness of a given parametric hazard rate model, Huh and Hutmacher [22] showed that their hazard-based visual predictive check is as good as a visual predictive check based on the survival function. Even though Huh and Hutmacher’s visual method is simple to implement and interpret, the final decision reached there depends on the personal experience of the user. In this thesis, our primary aim is to develop nonparametric goodness-ofit tests for hazard rate functions to help bring objectivity in hazard rate model selections or to augment subjective procedures like Huh and Hutmacher’s visual predictive check. Toward that aim two nonparametric goodnessofit (g-o) test statistics are proposed and they are referred to as chi-square g-o test and kernel-based nonparametric goodness-ofit test for hazard rate functions, respectively. On one hand, the asymptotic distribution of the chi-square goodness-ofit test for hazard rate functions is derived under the null hypothesis ??0 : ??(??) = ??0(??) ??? ? R + as well as under the fixed alternative hypothesis ??1 : ??(??) = ??1(??) ??? ? R +. The results as expected are asymptotically similar to those of the usual Pearson chi-square test. That is, under the null hypothesis the proposed test converges to a chi-square distribution and under the fixed alternative hypothesis it converges to a non-central chi-square distribution. On the other hand, we showed that the power properties of the kernel-based nonparametric goodness-ofit test for hazard rate functions are equivalent to those of the Bickel and Rosenblatt test, meaning the proposed kernel-based nonparametric goodness-ofit test can detect alternatives converging to the null at the rate of ???? , ?? < 1/2, where ?? is the sample size. Unlike the latter, the convergence rate of the kernel-base nonparametric g-o test is much greater; that is, one does not need a very large sample size for able to use the asymptotic distribution of the test in practice.