The dimension growth conjecture, polynomial in the degree and without logarithmic factors

We address Heath-Brown's and Serre's dimension growth conjecture (proved by Salberger), when the degree $d$ grows. Recall that Salberger's dimension growth results give bounds of the form $O_{X, \varepsilon} (B^{\dim X+\varepsilon})$ for the number of rational points of height at most $B$ on any integral subvariety $X$ of ${\mathbb P}^n_{\mathbb Q}$ of degree $d\geq 2$, where one can write $O_{d,n, \varepsilon}$ instead of $O_{X, \varepsilon}$ as soon as $d\geq 4$. Our main contribution is to remove the factor $B^\varepsilon$ as soon as $d \geq 5$, without introducing a factor $\log B$, while moreover obtaining polynomial dependence on $d$ of the implied constant. Working polynomially in $d$ allows us to give a self-contained and slightly simplified treatment of dimension growth for degree $d \geq 16$, while in the range $5 \leq d \leq 15$ we invoke results by Browning, Heath-Brown and Salberger. Along the way we improve the well-known bounds due to Bombieri and Pila on the number of integral points of bounded height on affine curves and those by Walsh on the number of rational points of bounded height on projective curves. The former improvement leads to a slight sharpening of a recent estimate due to Bhargava, Shankar, Taniguchi, Thorne, Tsimerman and Zhao on the size of the $2$-torsion subgroup of the class group of a degree $d$ number field. Our treatment builds on recent work by Salberger which brings in many primes in Heath-Brown's variant of the determinant method, and on recent work by Walsh and Ellenberg--Venkatesh, who bring in the size of the defining polynomial. We also obtain lower bounds showing that one cannot do better than polynomial dependence on $d$

Interventions Towards Sustainable Watershed Management as Demonstrated by Hydrologic Simulation

Increasing population, changing climate, and on-going legacies of environmental mismanagement motivate our need for deeper understanding of the process and limits of adaptation towards sustainable management of water resources. Movements towards open-science and transdisciplinary research have enabled deeper assessments of the co-evolution of human society and changing landscapes. Policies and decisions enabling environmental restoration or sustainable resource use have been actively pursued for decades. The social barriers that prevent adaptations to succeed are deep and entrenched, but equally important are the physical barriers. Successful adaptations in water resource management need to explicitly consider the joint interactions of intervention magnitude, or intensity, over the feasible extent of its operation. While a seemingly simple concept, many solutions to water resource management would be impossible to achieve without adequate consideration of these constraints.In these three studies specific management practices were evaluated in the context of whole watershed responses and found to characterize this common constraint despite the diversity of applications. The three studies impose alternative management practices within a model of watershed-scale hydrologic processes, and the success of each practice was ultimately determined by the geographic constraints over which it could act, not by any deficiency in the policy’s capacity to affect a sufficient intensity of change. In Chapter 1, current rates of road salt loading and potential levels of aquatic habitat impairment are estimated for a New England watershed. The potential for reducing impairment through a combination of reduced salt application and buildout are investigated. Chapter 2 examines issues of aquifer sustainability in the Pacific Northwest and evaluates tradeoffs in modernizing irrigation technology. As irrigation efficiency increased less water recharged the aquifer, which exacerbated aquifer drawdown. Drawdown was offset by enhanced aquifer recharge directly from the river. The study analyzes the constraints under which aquifer drawdown can be eliminated while minimizing any reduction in streamflow. Chapter 3 evaluates the efficacy of two programs that incentivize the restoration of wetlands within the Mississippi River basin to reduce nitrogen export as nitrate export to the Gulf of Mexico. A more thorough consideration of geographic and engineering constraints on restoration illustrates how complementary management practices would be necessary to meet nutrient reduction goals. Finally, Chapter 4 analyzes the three studies and develops the concepts of intensity and extensity in successful practices in watershed management. Chapter 4 also lays out the common methodology of model experimentation in silico used throughout these studies, and defends the epistemological framework chosen

Agent-Driven Representations, Algorithms, and Metrics for Automated Organizational Design.

As cooperative multiagent systems (MASs) increase in interconnectivity, complexity, size, and longevity, coordinating the agents' reasoning and behaviors becomes increasingly difficult. One approach to address these issues is to use insights from human organizations to design structures within which the agents can more efficiently reason and interact. Generally speaking, an organization influences each agent such that, by following its respective influences, an agent can make globally-useful local decisions without having to explicitly reason about the complete joint coordination problem. For example, an organizational influence might constrain and/or inform which actions an agent performs. If these influences are well-constructed to be cohesive and correlated across the agents, then each agent is influenced into reasoning about and performing only the actions that are appropriate for its (organizationally-designated) portion of the joint coordination problem. In this dissertation, I develop an agent-driven approach to organizations, wherein the foundation for representing and reasoning about an organization stems from the needs of the agents in the MAS. I create an organizational specification language to express the possible ways in which an organization could influence the agents' decision making processes, and leverage details from those decision processes to establish quantitative, principled metrics for organizational performance based on the expected impact that an organization will have on the agents' reasoning and behaviors. Building upon my agent-driven organizational representations, I identify a strategy for automating the organizational design process~(ODP), wherein my ODP computes a quantitative description of organizational patterns and then searches through those possible patterns to identify an (approximately) optimal set of organizational influences for the MAS. Evaluating my ODP reveals that it can create organizations that both influence the MAS into effective patterns of joint policies and also streamline the agents' decision making in a coordinate manner. Finally, I use my agent-driven approach to identify characteristics of effective abstractions over organizational influences and a heuristic strategy for converging on a good abstraction.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113616/1/jsleight_1.pd

Comparing Features of Three-Dimensional Object Models Using Registration Based on Surface Curvature Signatures

This dissertation presents a technique for comparing local shape properties for similar three-dimensional objects represented by meshes. Our novel shape representation, the curvature map, describes shape as a function of surface curvature in the region around a point. A multi-pass approach is applied to the curvature map to detect features at different scales. The feature detection step does not require user input or parameter tuning. We use features ordered by strength, the similarity of pairs of features, and pruning based on geometric consistency to efficiently determine key corresponding locations on the objects. For genus zero objects, the corresponding locations are used to generate a consistent spherical parameterization that defines the point-to-point correspondence used for the final shape comparison

Impact of Land Model Calibration on Coupled Land-Atmosphere Prediction

Land-atmosphere (L-A) interactions play a critical role in determining the diurnal evolution of both planetary boundary layer (PBL) and land surface heat and moisture budgets, as well as controlling feedbacks with clouds and precipitation that lead to the persistence of dry and wet regimes. Recent efforts to quantify the strength of L-A coupling in prediction models have produced diagnostics that integrate across both the land and PBL components of the system. In this study, we examine the impact of improved specification of land surface states, anomalies, and fluxes on coupled WRF forecasts during the summers of extreme dry and wet land surface conditions in the U.S. Southern Great Plains. The improved land initialization and surface flux parameterizations are obtained through calibration of the Noah land surface model using the new optimization and uncertainty estimation subsystem in NASA's Land Information System (LIS-OPT/UE). The impact of the calibration on the a) spinup of the land surface used as initial conditions, and b) the simulated heat and moisture states and fluxes of the coupled WRF simulations is then assessed. Changes in ambient weather and land-atmosphere coupling are evaluated along with measures of uncertainty propagation into the forecasts. In addition, the sensitivity of this approach to the period of calibration (dry, wet, average) is investigated. Results indicate that the offline calibration leads to systematic improvements in land-PBL fluxes and near-surface temperature and humidity, and in the process provide guidance on the questions of what, how, and when to calibrate land surface models for coupled model prediction

Flow-Based Optimization of Products or Devices

Flow-based optimization of products and devices is an immature field compared to the corresponding topology optimization based on solid mechanics. However, it is an essential part of component development with both internal and/or external flow. The aim of this book is two-fold: (i) to provide state-of-the-art examples of flow-based optimization and (ii) to present a review of topology optimization for fluid-based problems

Heterogeneous volumetric data mapping and its medical applications

With the advance of data acquisition techniques, massive solid geometries are being collected routinely in scientific tasks, these complex and unstructured data need to be effectively correlated for various processing and analysis. Volumetric mapping solves bijective low-distortion correspondence between/among 3D geometric data, and can serve as an important preprocessing step in many tasks in compute-aided design and analysis, industrial manufacturing, medical image analysis, to name a few. This dissertation studied two important volumetric mapping problems: the mapping of heterogeneous volumes (with nonuniform inner structures/layers) and the mapping of sequential dynamic volumes. To effectively handle heterogeneous volumes, first, we studied the feature-aligned harmonic volumetric mapping. Compared to previous harmonic mapping, it supports the point, curve, and iso-surface alignment, which are important low-dimensional structures in heterogeneous volumetric data. Second, we proposed a biharmonic model for volumetric mapping. Unlike the conventional harmonic volumetric mapping that only supports positional continuity on the boundary, this new model allows us to have higher order continuity $C^1$ along the boundary surface. This suggests a potential model to solve the volumetric mapping of complex and big geometries through divide-and-conquer. We also studied the medical applications of our volumetric mapping in lung tumor respiratory motion modeling. We were building an effective digital platform for lung tumor radiotherapy based on effective volumetric CT/MRI image matching and analysis. We developed and integrated in this platform a set of geometric/image processing techniques including advanced image segmentation, finite element meshing, volumetric registration and interpolation. The lung organ/tumor and surrounding tissues are treated as a heterogeneous region and a dynamic 4D registration framework is developed for lung tumor motion modeling and tracking. Compared to the previous 3D pairwise registration, our new 4D parameterization model leads to a significantly improved registration accuracy. The constructed deforming model can hence approximate the deformation of the tissues and tumor