Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.

Globalizing the Sculptural Landscapes of the Sarapis and Isis Cults in Hellenistic and Roman Greece

“Globalizing the Sculptural Landscape of Isis and Sarapis Cults in Roman Greece,” asks questions of cross-cultural exchange and viewership of sculptural assemblages set up in sanctuaries to the Egyptian gods. Focusing on cognitive dissonance, cultural imagining, and manipulations of time and space, I theorize ancient globalization as a set of loosely related processes that shifted a community's connections with place. My case studies range from the 3rd century BCE to the 2nd century CE, including sanctuaries at Rhodes, Thessaloniki, Dion, Marathon, Gortyna, and Delos. At these sites, devotees combined mainstream Greco-Roman sculptures, Egyptian imports, and locally produced imitations of Egyptian artifacts. In the last case, local sculptors represented Egyptian subjects with Greco-Roman naturalistic styles, creating an exoticized visual ideal that had both local and global resonance. My dissertation argues that the sculptural assemblages set up in Egyptian sanctuaries allowed each community to construct complex narratives about the nature of the Egyptian gods. Further, these images participated in a form of globalization that motivated local communities to adopt foreign gods and reinterpret them to suit local needs.

I begin my dissertation by examining how Isis and Sarapis were represented in Greece. My first chapter focuses on single statues of Egyptian gods, describing their iconographies and stylistic tendencies through examples from Corinth and Gortyna. By comparing Greek examples with images of Sarapis, Isis, and Harpokrates from around the Mediterranean, I demonstrate that Greek communities relied on globally available visual tropes rather than creating site or region-specific interpretations. In the next section, I examine what other sources viewers drew upon to inform their experiences of Egyptian sculpture. In Chapter 3, I survey the textual evidence for Isiac cult practice in Greece as a way to reconstruct devotees’ expectations of sculptures in sanctuary contexts. At the core of this analysis are Apuleius’ Metamorphoses and Plutarch’s De Iside et Osiride, which offer a Greek perspective on the cult’s theology. These literary works rely on a tradition of aretalogical inscriptions—long hymns produced from roughly the late 4th century B.C.E. into the 4th century C.E. that describe the expansive syncretistic powers of Isis, Sarapis, and Harpokrates. This chapter argues that the textual evidence suggests that devotees may have expected their images to be especially miraculous and likely to intervene on their behalf, particularly when involved in ritual activity inside the sanctuary.

In the final two chapters, I consider sculptural programs and ritual activity in concert with sanctuary architecture. My fourth chapter focuses on sanctuaries where large amounts of sculpture were found in underground water crypts: Thessaloniki and Rhodes. These groups of statues can be connected to a particular sanctuary space, but their precise display contexts are not known. By reading these images together, I argue that local communities used these globally available images to construct new interpretations of these gods, ones that explored the complex intersections of Egyptian, Greek, and Roman identities in a globalized Mediterranean. My final chapter explores the Egyptian sanctuary at Marathon, a site where exceptional preservation allows us to study how viewers would have experienced images in architectural space. Using the Isiac visuality established in Chapter 3, I reconstruct the viewer's experience, arguing that the patron, Herodes Atticus, intended his viewer to inform his experience with the complex theology of Middle Platonism and prevailing elite attitudes about Roman imperialism.

Throughout my dissertation, I diverge from traditional approaches to culture change that center on the concepts of Romanization and identity. In order to access local experiences of globalization, I examine viewership on a micro-scale. I argue that viewers brought their concerns about culture change into dialogue with elements of cult, social status, art, and text to create new interpretations of Roman sculpture sensitive to the challenges of a highly connected Mediterranean world. In turn, these transcultural perspectives motivated Isiac devotees to create assemblages that combined elements from multiple cultures. These expansive attitudes also inspired Isiac devotees to commission exoticized images that brought together disparate cultures and styles in an eclectic manner that mirrored the haphazard way that travel brought change to the Mediterranean world. My dissertation thus offers a more theoretically rigorous way of modeling culture change in antiquity that recognizes local communities’ agency in producing their cultural landscapes, reconciling some of the problems of scale that have plagued earlier approaches to provincial Roman art.

These case studies demonstrate that cultural anxieties played a key role in how viewers experienced artistic imagery in the Hellenistic and Roman Mediterranean. This dissertation thus offers a new component in our understanding of ancient visuality, and, in turn, a better way to analyze how local communities dealt with the rise of connectivity and globalization.

Global Value Chain Analysis: A Primer, 2nd Edition

The first edition of Global Value Chain Analysis: A Primer was released five years ago (May 2011) in order to provide an overview of the key concepts and methodological tools used by Duke University’s Center on Globalization, Governance & Competitiveness (Duke CGGC) a university-based research center that focuses on innovative applications of the GVC framework, which was developed by Duke CGGC’s founding director, Gary Gereffi. The Second Edition of Global Value Chain Analysis: A Primer (July 2016) retains a simple, expository style and use of recent research examples in order to offer an entry point for those wishing to better understand and use the GVC framework as a tool to analyze how local actors (firms, communities, workers) are linked to and affected by major transformations in the global economy. The GVC framework focuses on structural shifts in global industries, anchored by the core concepts of governance and upgrading. This Second Edition highlights some of the refinements in these concepts, and introduces a number of new illustrations drawing from recent Duke CGGC research. The bibliography offers a sampling of the broad array of studies available on the Duke CGGC website and in related academic publications. We hope this work stimulates continued interest in and use of the GVC framework as a tool to promote more dynamic, inclusive and sustainable development outcomes for all economies and the local actors within them.

Distributed Feature Selection in Large n and Large p Regression Problems

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space), and the challenge arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. For sample space partitioning, I propose a MEdian Selection Subset AGgregation Estimator ({\em message}) algorithm for solving these issues. The algorithm applies feature selection in parallel for each subset using regularized regression or Bayesian variable selection method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in sample size, and has theoretical guarantees. I provide extensive experiments to show excellent performance in feature selection, estimation, prediction, and computation time relative to usual competitors.

While sample space partitioning is useful in handling datasets with large sample size, feature space partitioning is more effective when the data dimension is high. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In the thesis, I propose a new embarrassingly parallel framework named {\em DECO} for distributed variable selection and parameter estimation. In {\em DECO}, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

For datasets with both large sample sizes and high dimensionality, I propose a new "divided-and-conquer" framework {\em DEME} (DECO-message) by leveraging both the {\em DECO} and the {\em message} algorithm. The new framework first partitions the dataset in the sample space into row cubes using {\em message} and then partition the feature space of the cubes using {\em DECO}. This procedure is equivalent to partitioning the original data matrix into multiple small blocks, each with a feasible size that can be stored and fitted in a computer in parallel. The results are then synthezied via the {\em DECO} and {\em message} algorithm in a reverse order to produce the final output. The whole framework is extremely scalable.

Periodic Breathing and Behavioral Awakenings at High Altitude.

Objectives. To study the relationship between nocturnal periodic breathing episodes and behavioral awakenings at high altitude. Methods. Observational study. It is 6-day ascent of 4 healthy subjects from Besisahar (760 meters) to Manang (3540 meters) in Nepal in March 2012. A recording pulse oximeter was worn by each subject to measure their oxygen saturation and the presence of periodic breathing continuously through the night. An actigraph was simultaneously worn in order to determine nocturnal behavioral awakenings. There were no interventions. Results. 187-hour sleep at high altitude was analyzed, and of this, 145 hours (78%) had at least one PB event. At high altitude, 10.5% (95% CI 6.5-14.6%) of total sleep time was spent in PB while 15 out of 50 awakenings (30%, 95% CI: 18-45%) occurring at high altitudes were associated with PB (P < 0.001). Conclusions. Our data reveals a higher than expected number of behavioral awakenings associated with PB compared to what would be expected by chance. This suggests that PB likely plays a role in behavioral awakenings at high altitude.