Distinguishing Classes of Intersection Graphs of Homothets or Similarities of Two Convex Disks

For smooth convex disks A, i.e., convex compact subsets of the plane with non-empty interior, we classify the classes G^{hom}(A) and G^{sim}(A) of intersection graphs that can be obtained from homothets and similarities of A, respectively. Namely, we prove that G^{hom}(A) = G^{hom}(B) if and only if A and B are affine equivalent, and G^{sim}(A) = G^{sim}(B) if and only if A and B are similar

Discrete Equivalence of Non-positive at Infinity Plane Valuations

Non-positive at infinity valuations are a class of real plane valuations which have a nice geometrical behavior. They are divided in three types. We study the dual graphs of non-positive at infinity valuations and give an algorithm for obtaining them. Moreover we compare these graphs attending the type of their corresponding valuation

Development of Feature Recognition Algorithm for Automated Identification of Duplicate Geometries in CAD Models

This research presents a feature recognition algorithm for the automated identification of duplicate geometries in the CAD assembly. The duplicate geometry is one of the seven indicators of the lazy parts mass reduction method. The lazy parts method is a light weight engineering method that is used for analyzing parts with the mass reduction potential. The duplicate geometry is defined as any geometries lying equal to or within the threshold distance with the user-defined orientation between them and have the percentage similarity that is equal to or greater than the threshold value. The feature recognition system developed in this research for the identification of duplicate geometries is also extended to retrieve the weighted bipartite graph of part connections for the assembly time estimation. The weighted bipartite graph is used as input for the part connectivity based assembly time estimation method. The SolidWorks API software development kit is used in this research to develop a feature recognition system in SolidWorks CAD software package using C++ programming language. The feature recognition system built in the SolidWorks CAD software uses a combination of topology and geometric data for the evaluation of duplicate geometry. The measurement of distances between the sampling points strategy is used for the duplicate geometry feature recognition. The feature recognition algorithm has three phases of evaluation: first, is the evaluation for threshold distance condition of parts in the CAD assembly. Second, the part pairs that have satisfied the threshold distance condition are evaluated for the orientation condition. The threshold distance and orientation are the necessary but not the sufficient conditions for duplicate geometries. In the third phase, the geometries that have satisfied orientation condition are evaluated for the percentage similarity condition. The geometries that satisfy the percentage similarity condition are highlighted in order to help designers review the results of the duplicate geometry analysis. The test cases are used to validate the algorithm against the requirements list. The test cases are designed to check the performance of the algorithm for the evaluation of the threshold distance, orientation, and percentage similarity condition. The results indicate that the duplicate geometry algorithm is able to successfully conduct all the three phases of evaluation. The algorithm is independent of the geometric type and is able to analyze planar, cylindrical, conical, spherical, freeform, and toroidal shapes. The number of sampling points generated on the faces of parts for the orientation and percentage similarity evaluation has the significant effect on the analysis time. The worst case complexity of the algorithm is the big O (nC2x m12 x m22x p4), where n = the number of parts in the assembly m1 = the number of faces in the parts that meet the threshold distance condition m2 = the number of faces that meet the orientation condition p = the number of sampling points on the face The duplicate geometry feature recognition approach is used to demonstrate the applicability in the extraction of assembly relations for the part connectivity based assembly time estimation method. The algorithm is also able to extract part connectivity information for the patterns. Further research is required to automate the identification of other laziness indicators in order to make the lazy parts method a completely automated tool. With regards to the complete automation of part connectivity based assembly time estimation method, the duplicate geometry feature recognition system needs integration with the algorithm for the computation of bipartite graph of part connections for the prediction of assembly time

Lectures on D-branes, gauge theories and Calabi-Yau singularities

These lectures, given at the Chinese Academy of Sciences for the BeiJing/HangZhou International Summer School in Mathematical Physics, are intended to introduce, to the beginning student in string theory and mathematical physics, aspects of the rich and beautiful subject of D-brane gauge theories constructed from local Calabi-Yau spaces. Topics such as orbifolds, toric singularities, del Pezzo surfaces as well as chaotic duality will be covered

Flexible Object Manipulation

Flexible objects are a challenge to manipulate. Their motions are hard to predict, and the high number of degrees of freedom makes sensing, control, and planning difficult. Additionally, they have more complex friction and contact issues than rigid bodies, and they may stretch and compress. In this thesis, I explore two major types of flexible materials: cloth and string. For rigid bodies, one of the most basic problems in manipulation is the development of immobilizing grasps. The same problem exists for flexible objects. I have shown that a simple polygonal piece of cloth can be fully immobilized by grasping all convex vertices and no more than one third of the concave vertices. I also explored simple manipulation methods that make use of gravity to reduce the number of fingers necessary for grasping. I have built a system for folding a T-shirt using a 4 DOF arm and a fixed-length iron bar which simulates two fingers. The main goal with string manipulation has been to tie knots without the use of any sensing. I have developed single-piece fixtures capable of tying knots in fishing line, solder, and wire, along with a more complex track-based system for autonomously tying a knot in steel wire. I have also developed a series of different fixtures that use compressed air to tie knots in string. Additionally, I have designed four-piece fixtures, which demonstrate a way to fully enclose a knot during the insertion process, while guaranteeing that extraction will always succeed

A Conceptual Model of Exploration Wayfinding: An Integrated Theoretical Framework and Computational Methodology

This thesis is an attempt to integrate contending cognitive approaches to modeling wayfinding behavior. The primary goal is to create a plausible model for exploration tasks within indoor environments. This conceptual model can be extended for practical applications in the design, planning, and Social sciences. Using empirical evidence a cognitive schema is designed that accounts for perceptual and behavioral preferences in pedestrian navigation. Using this created schema, as a guiding framework, the use of network analysis and space syntax act as a computational methods to simulate human exploration wayfinding in unfamiliar indoor environments. The conceptual model provided is then implemented in two ways. First of which is by updating an existing agent-based modeling software directly. The second means of deploying the model is using a spatial interaction model that distributed visual attraction and movement permeability across a graph-representation of building floor plans