IST Austria Thesis

This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph. For triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton. In the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars

Topology-Constrained Network Design

International audienc

The detailed velocity structure and distribution of 13CO emission in the Galactic plane

Studying the detailed velocity structure of molecular gas in our Galaxy is of fundamental importance for understanding structure formation in the interstellar medium. Knowledge about the detailed gas kinematics is moreover essential to map the distribution and dynamics of the molecular gas in the Milky Way. In this thesis I use the method of spectral decomposition to analyse the 13CO (1-0) observations of the Galactic Ring Survey (GRS). I developed the GaussPy+ package, specifically designed for the fully automated decomposition of large Galactic plane surveys, to fit the ~2.3 million spectra of this large emission line data set. After extensive validation of the algorithm using synthetic spectra and a GRS test field, I use GaussPy+ to fit the entire data set of the GRS, resulting in ~4.6 million Gaussian fit components. These decomposition results provide a new way to analyse the dynamics of the molecular gas over a wide extent of the Galactic plane and study how its velocity structure looks like and varies at Galactic to sub-cloud scales. I find that the velocity dispersion of the gas is increased in the midplane and towards the inner Galaxy, and establish that the integrated emission of the velocity components correlates well with the complexity of the gas emission and the amount of dust emission along the line of sight. Moreover, I uncover qualitatively similar fluctuations in the centroid velocities of the gas components throughout the entire GRS data set, and demonstrate how the fitted linewidths enable the separation of blended gas emission features that originate from nearby regions and far distances. Finally, I use a Bayesian approach to obtain the current best assessment of the Galactic distribution of 13CO. As prior information, I use the presently most precise knowledge about the structure and kinematics of the Milky Way and an extensive compilation of distances from literature. I perform two different distance calculations that either include or exclude a prior for a model of Galactic features, which allows me to characterise possible biases of the distance estimates and establish more reliable limits on the 13CO distribution. I establish that the majority (76% to 84%) of the 13CO emission is associated with spiral arm features. However, I do not find significant differences between the gas emission properties associated with spiral arm and interarm features. I conclude that the decomposition results provide a wealth of data enabling new and unexplored ways to interpret the detailed gas velocity structure of large Galactic plane surveys. The methodology and results presented in this thesis allowed for a homogeneous study of the dynamics and distribution of the molecular gas over a large fraction of the Galactic disk. As demonstrated in this work, the information extracted from the detailed gas kinematics and its combination with complementary tracers of the interstellar medium has enormous potential to further our knowledge about the physical processes and mechanisms shaping the interstellar medium

University of Maryland walking robot: A design project for undergraduate students

The design and construction required that the walking robot machine be capable of completing a number of tasks including walking in a straight line, turning to change direction, and maneuvering over an obstable such as a set of stairs. The machine consists of two sets of four telescoping legs that alternately support the entire structure. A gear-box and crank-arm assembly is connected to the leg sets to provide the power required for the translational motion of the machine. By retracting all eight legs, the robot comes to rest on a central Bigfoot support. Turning is accomplished by rotating the machine about this support. The machine can be controlled by using either a user operated remote tether or the on-board computer for the execution of control commands. Absolute encoders are attached to all motors (leg, main drive, and Bigfoot) to provide the control computer with information regarding the status of the motors (up-down motion, forward or reverse rotation). Long and short range infrared sensors provide the computer with feedback information regarding the machine's relative position to a series of stripes and reflectors. These infrared sensors simulate how the robot might sense and gain information about the environment of Mars

Topology Considerations in Hybrid Electric Vehicle Powertrain Architecture Design.

Optimal system architecture (topology or configuration) design has been a challenging design problem because of its combinatorial nature. Parametric optimization studies make design decisions assuming a given architecture but there has been no general methodology that addresses design decisions on the system architecture itself. Hybrid Electric Vehicle (HEV) powertrains allow various architecture alternatives created by connecting the engine, motor/generators and the output shaft in different ways through planetary gear systems. Addition of clutches to HEV powertrains allows changing the connection arrangement (configuration) among the powertrain components during the vehicle operation. Architectures with this capability are referred to as multi-mode architectures while architectures with fixed configurations are referred to as single-mode architectures. HEV architecture optimization requires designing the powertrain’s configuration and its sizing simultaneously. Additionally, evaluation of an HEV architecture design depends on a power management (control) strategy that distributes the power demand to the engine and motor/generators. Including this control problem increases the complexity of the HEV architecture design problem. This dissertation focuses on a general methodology to make design decisions on HEV powertrain architecture and component sizes. The representation of the architecture design problem is critical to solving this problem. A new general representation capable of describing all architecture alternatives is introduced. Using the representation, all feasible configurations are generated where these feasible configurations are used to create single- and multi-mode HEV architectures. Single-mode and multi-mode architecture design problems considering fuel economy, vehicle performance and architecture complexity are formulated separately and solution strategies are developed. The high complexity of the resulting optimization problem does not allow us to claim true optimality rigorously; therefore, the terms ``promising" or ``near-optimal" are more accurate in characterizing our results. The results show that different architectures must be designed for different applications. The case studies designing architectures for some available vehicles from the market find the architectures already implemented in these vehicles under some design constraints. Alternative architectures that improve these designs under different design constraints are also demonstrated. Architectures for a new application that is not available in the market are also designed.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111412/1/bayrak_1.pd