Deterministic Random Walks on Regular Trees

Jim Propp's rotor router model is a deterministic analogue of a random walk on a graph. Instead of distributing chips randomly, each vertex serves its neighbors in a fixed order. Cooper and Spencer (Comb. Probab. Comput. (2006)) show a remarkable similarity of both models. If an (almost) arbitrary population of chips is placed on the vertices of a grid $\Z^d$ and does a simultaneous walk in the Propp model, then at all times and on each vertex, the number of chips on this vertex deviates from the expected number the random walk would have gotten there by at most a constant. This constant is independent of the starting configuration and the order in which each vertex serves its neighbors. This result raises the question if all graphs do have this property. With quite some effort, we are now able to answer this question negatively. For the graph being an infinite $k$-ary tree ($k \ge 3$), we show that for any deviation $D$ there is an initial configuration of chips such that after running the Propp model for a certain time there is a vertex with at least $D$ more chips than expected in the random walk model. However, to achieve a deviation of $D$ it is necessary that at least $\exp(\Omega(D^2))$ vertices contribute by being occupied by a number of chips not divisible by $k$ at a certain time.Comment: 15 pages, to appear in Random Structures and Algorithm

A 50 MHz FMCW radar for the study of E-region coherent backscatter

A 50~MHz E-region coherent backscatter radar was designed based on frequency modulated continuous wave (FMCW) radar techniques. This thesis presents the theory behind the FMCW technique and its implementation in a practical radar system. The system was designed and constructed at the University of Saskatchewan and was field tested at a radar site a few kilometres from the university. This thesis demonstrates that an FMCW radar is technically possible and functional as a research tool for E-region coherent backscatter studies. The primary goal of this research is to develop a better understanding of the plasma processes responsible for the radar echoes. FMCW techniques offer a compromise between the pulsed and continuous wave (CW) radar techniques, which have previously been used for E-region experiments. CW techniques provide excellent spectral measurements but are limited in their ability to determine range information. Pulsed techniques offer excellent range resolution but may be limited in their ability to make detailed high resolution Doppler measurements of E-region radar backscatter. The implementation of FMCW techniques provides a simple and effective method of simultaneously obtaining excellent Doppler and range measurements. The use of FMCW techniques is a novel approach to E-region coherent backscatter studies. Data analysis techniques were developed to extract the range and Doppler information from FMCW radar echoes. In the first few months of operation, the radar observed all four typical E-region radar signatures, Type I to Type IV, plus meteor trail echoes. Observations of each type of radar echo are presented, without interpretation, to illustrate the performance of the radar

Trinity Restoration Inc.: Southside Cultural Center Economic Impact Study

Economic development has shifted from location-oriented business models towards a more all-encompassing model that recognizes the advancement of human capital or intellectual property as continuously increasing in value. This microcosmic characteristic of development extends to aid in the growth of society as a whole. The Arts and Culture attract a demographic of inspired and motivated people to the area. It results in the development of the society surrounding art venues. The general population will always seek out entertainment, by installing a venue of artistic expression in South Providence that will motivate the community and propel development. This phenomena has been proven, as denoted through the historical evaluation of artistic venues across America that have generated economic growth in their respective communities

Crossroads Rhode Island: Proposed Social Enterprise Business Plan

Crossroads Rhode Island provides their clients with a continuum of care that includes basic emergency needs, shelter, housing, case management and vocational services for individuals and families. In order to provide these services they rely on the generosity of their donors and supporters who have helped Crossroads to become the largest homeless services organization in Rhode Island. It is important to Crossroads that they stick to their core values of safety, respect, and effectiveness when helping the homeless or at-risk individuals and families secure stable homes

Visiting Nurse Services of Newport and Bristol County: Increasing Program Awareness for the Help at Home Program

We came up with the idea of using a cost analysis to clearly demonstrate the advantage of home care vs. hospitalization. John Hopkins Bay view Medical Center conducted a study within their geriatrics unit to test their Hospital At Home program against typical on-site care at the hospital. The study was held over the course of 30 days involving hundreds of patients across three cities and the results were staggering. Not only was at home care 32% cheaper ($5,081 versus$7,480) but also overall customer satisfaction was significantly higher

Efficient Irregular Wavefront Propagation Algorithms on Hybrid CPU-GPU Machines

In this paper, we address the problem of efficient execution of a computation pattern, referred to here as the irregular wavefront propagation pattern (IWPP), on hybrid systems with multiple CPUs and GPUs. The IWPP is common in several image processing operations. In the IWPP, data elements in the wavefront propagate waves to their neighboring elements on a grid if a propagation condition is satisfied. Elements receiving the propagated waves become part of the wavefront. This pattern results in irregular data accesses and computations. We develop and evaluate strategies for efficient computation and propagation of wavefronts using a multi-level queue structure. This queue structure improves the utilization of fast memories in a GPU and reduces synchronization overheads. We also develop a tile-based parallelization strategy to support execution on multiple CPUs and GPUs. We evaluate our approaches on a state-of-the-art GPU accelerated machine (equipped with 3 GPUs and 2 multicore CPUs) using the IWPP implementations of two widely used image processing operations: morphological reconstruction and euclidean distance transform. Our results show significant performance improvements on GPUs. The use of multiple CPUs and GPUs cooperatively attains speedups of 50x and 85x with respect to single core CPU executions for morphological reconstruction and euclidean distance transform, respectively.Comment: 37 pages, 16 figure

On the length of a random minimum spanning tree

We study the expected value of the length $L_n$ of the minimum spanning tree of the complete graph $K_n$ when each edge $e$ is given an independent uniform $[0,1]$ edge weight. We sharpen the result of Frieze \cite{F1} that \lim_{n\to\infty}\E(L_n)=\z(3) and show that \E(L_n)=\z(3)+\frac{c_1}{n}+\frac{c_2+o(1)}{n^{4/3}} where $c_1,c_2$ are explicitly defined constants.Comment: Added next term and two co-author