A cyanoacrylate direct bonding system of orthodontic attachments

Thesis (M.Sc.D.)--Boston University School of Graduate Dentistry, 1973. Orthodontics.Bibliography included

On the Reconstruction of Geodesic Subspaces of RN\mathbb{R}^N

We consider the topological and geometric reconstruction of a geodesic subspace of $\mathbb{R}^N$ both from the \v{C}ech and Vietoris-Rips filtrations on a finite, Hausdorff-close, Euclidean sample. Our reconstruction technique leverages the intrinsic length metric induced by the geodesics on the subspace. We consider the distortion and convexity radius as our sampling parameters for a successful reconstruction. For a geodesic subspace with finite distortion and positive convexity radius, we guarantee a correct computation of its homotopy and homology groups from the sample. For geodesic subspaces of $\mathbb{R}^2$, we also devise an algorithm to output a homotopy equivalent geometric complex that has a very small Hausdorff distance to the unknown shape of interest

Introduction to the R package TDA

We present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given some data, provide topological information about the underlying space, such as the distance function, the distance to a measure, the kNN density estimator, the kernel density estimator, and the kernel distance. The salient topological features of the sublevel sets (or superlevel sets) of these functions can be quantified with persistent homology. We provide an R interface for the efficient algorithms of the C++ libraries GUDHI, Dionysus and PHAT, including a function for the persistent homology of the Rips filtration, and one for the persistent homology of sublevel sets (or superlevel sets) of arbitrary functions evaluated over a grid of points. The significance of the features in the resulting persistence diagrams can be analyzed with functions that implement recently developed statistical methods. The R package TDA also includes the implementation of an algorithm for density clustering, which allows us to identify the spatial organization of the probability mass associated to a density function and visualize it by means of a dendrogram, the cluster tree

Stochastic Convergence of Persistence Landscapes and Silhouettes

Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly to a random sample of diagrams. Instead, we can summarize the persistent homology with the persistence landscape, introduced by Bubenik, which converts a diagram into a well-behaved real-valued function. We investigate the statistical properties of landscapes, such as weak convergence of the average landscapes and convergence of the bootstrap. In addition, we introduce an alternate functional summary of persistent homology, which we call the silhouette, and derive an analogous statistical theory

MONITORING AND CONTROLLING OF TEMPERATURE IN A GAS PLANT VIA CASCADE ARCHITECTURE

This report discusses the development and implementation of computer eoutrol on an industrial process plant. The objectives of the project is to design and tune two different PID controller for the control of temperature in a gaseous pilot plant. The gaseous pilot plant, located at Universiti Teknologi PETRONAS, is used in the case study. The focus of the project is on the control and monitoring of the temperature of gas in the pilot plant. The PID controller will be designed and simulated via MATLAB/Simulink. The work involves two main stages, modeling and simulation, and real-time implementation. Once the PID controller has been designed and simulated via MA TLAB/Simulink, the model will be interfaced to the plant via an xPC target card for real-time analysis. The result of this investigation shows that the cascade control architecture would be a viable method to be used in plant process control. The cascade configuration that indicates the better performance can specifically be defines to use the Ziegler Nichols closed loop tuning method for the primary loop, while for the secondary loop the Cohen Coon tuning method is preferable

On the Bootstrap for Persistence Diagrams and Landscapes

Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular, we derive confidence sets for persistence diagrams and confidence bands for persistence landscapes