A Backtracking Algorithm for Determining the Existence of Regular Graphs of Specified Girth and Excess

The study of cages focuses on finding (k, g)-graphs of minimal order. This dissertation generalizes the problem of finding cages to the determination of graphs with specified excess, thereby broadening the significance of the results. The (k, g, ε)-graph problem seeks to determine the existence or nonexistence of k-regular graphs with girth g and excess ε = n(G)−M(k, g) (where M(k, g) represents the Moore bound for cage graphs). Motivated by heuristic methods used to determine properties within the study of cages, we present a backtracking algorithm capable of constructing (k, g, ε)-graphs or determining their nonexistence. Chapter 2 provides our own formalization of well-established definitions and results within the study of cages. Additionally, we establish our own labeling convention to more precisely discuss (k, g, ε)-graph constructions. Historically, the study of cages has lacked a standard labeling convention, and the convention we introduce embeds graph data into vertex labels to improve algorithm efficiency by eliminating some computationally expensive calculations. Chapter 3 of this dissertation provides new information on necessary subgraphs of (k, g, ε)-graphs, if such graphs exist, and methods for determining that a given graph cannot be a subgraph of a (k, g, ε)-graph. The lemmas and theorems in this chapter identify safe edge additions for base graphs and forbidden substructures of (k, g, ε)-graphs. Building on Robertson’s argument that the order of the (4, 5)-cage could not be less than 19, we generalize related concepts for all odd girth (k, g, ε)-graphs and even girth (k, g, ε)-graphs assumed to be bipartite. Chapter 4 provides a backtracking algorithm to construct (k, g, ε)-graphs or determine their nonexistence for all ordered triplets (k, g, ε). Chapter 5 introduces improvements to the algorithm from Chapter 4 that enhance performance and reduce the search space. Enhancements which improve computational efficiency include forced neighbor detection, class-based pruning techniques, and array ordering for quicker traversals of the search space. The intended use of the algorithm is to further the study of the cage problem by determining the existence of k-regular graphs of girth g and specified excess ε, which are not necessarily minimal under these properties. Chapter 6 illustrates the practicality of our algorithm through analyses of experiments performed on (k, g, ε) triples corresponding to known cages as well as triples known to not produce a graph. This chapter demonstrates the algorithm’s ability to both construct existing graphs and determine the nonexistence of graphs associated with specified (k, g, ε) triples. Additionally, the analyses in this chapter highlight the effectiveness of various parameters in efficiently converging to results. This dissertation corrects an error in a frequently cited paper by clarifying a critical gap in O’Keefe and Wong’s analysis of the order of 10-cages, providing a corrected proof that validates their claim. In addition to its theoretical contributions, this dissertation also preserves some historical context of the cage problem by providing translations of influential works that have no known English translations

Design of a robot for gait rehabilitation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.Cataloged from PDF version of thesis.Includes bibliographical references.The ability to walk is important for independent living and when this capacity is affected by injury, gait therapy is the traditional approach to re-train the nervous system, to re-build muscle strength, to improve balance, and to re-train kinematics in order to reduce the stresses applied to bones and muscles. The importance of this problem is illustrated by the approximately 5.8 million stroke survivors alive in the US today and an estimated 700,000 strokes occurring each year. In fact, for stroke survivors with mild to moderate impairment, only 37% regain the ability to walk within one week post-stroke and 73% fall within the first six months. Falls are a leading cause of injury among Americans over 65 years old with over one third of this population experiencing a fall each year and an unsteady gait increases this risk. This growing population will require gait therapy. This thesis presents the design, development, fabrication, and proof-of-concept testing for a novel device to deliver gait therapy. While robotic devices exist, none of them take advantage of the concept of passive walkers and most focus on reproducing gait kinematics for impaired patients. Yet research has found that appropriate neural input is an important factor in efficacious therapy. For gait, this input would be the collision between the foot and the ground at heel-strike. The goal of this novel device is to allow patients to begin gait therapy before they are able to independently walk overground while maximizing the amount interface driven neural input during stepping in a safe environment.by Caitlyn Joyce Bosecker.S.M

Different strategies for recovering metals from CARON process residue

http://dx.doi.org/10.1016/j.jhazmat.2011.03.048The capacity of Acidithiobacillus thiooxidans DMS 11478 to recover the heavy metals contained in the residue obtained from the CARON process has been evaluated. Different bioreactor configurations were studied: a two-stage batch system and two semi-continuous systems (stirred-tank reactor leaching and column leaching). In the two-stage system, 46.8% Co, 36.0% Mg, 26.3% Mn and 22.3% Ni were solubilised after 6 h of contact between the residue and the bacteria-free bioacid. The results obtained with the stirred-tank reactor and the column were similar: 50% of the Mg and Co and 40% of the Mn and Ni were solubilised after thirty one days. The operation in the column reactor allowed the solid–liquid ratio to be increased and the pH to be kept at low values (<1.0). Recirculation of the leachate in the column had a positive effect on metal removal; at sixty five days (optimum time) the solubilisation levels were as follows: 86% Co, 83% Mg, 72% Mn and Ni, 62% Fe and 23% Cr. The results corroborate the feasibility of the systems studied for the leaching of metals from CARON process residue and these methodologies can be considered viable for the recovery of valuable metals

Quantitative assessment based on kinematic measures of functional impairments during upper extremity movements: a review

Quantitative measures of human movement quality are important for discriminating healthy and pathological conditions and for expressing the outcomes and clinically important changes in subjects' functional state. However the most frequently used instruments for the upper extremity functional assessment are clinical scales, that previously have been standardized and validated, but have a high subjective component depending on the observer who scores the test. But they are not enough to assess motor strategies used during movements, and their use in combination with other more objective measures is necessary. The objective of the present review is to provide an overview on objective metrics found in literature with the aim of quantifying the upper extremity performance during functional tasks, regardless of the equipment or system used for registering kinematic data

Conference Report: The Art Fair

Conference Report of the TIAMSA conference "The Art Fair", London, July 201

An Evaluation of the University of Illinois Extension Get Up & Move! Program

Get Up & Move! is a program created by University of Illinois Extension to address childhood obesity. It provides ready-to-use materials for youth leaders to promote healthy lifestyles through physical fitness and healthy eating. The impact of the program on participants’ physical activity was evaluated to see whether involvement produces an increase in physical activity to the USDA recommended 60 minutes per day. It was found that a significant increase in minutes of physical activity occurred in participants from an average of 51.88 minutes per day to an average of 58.84 minutes per day

Considerations about recovery of critical metals using bio-metallurgy

The increased requirement of critical metals due to green technologies needs, together with the geopolitical environment to ensure these metals, has entailed decisive measures to avoid current supply insecurities in each country. These metals are essential to the products and services made and used daily, and contribute to sustaining and growing the economy. Thus, sustainable approaches from technological, environmental, economic and social point of view are needed to recover these metals from different resources. By using resources more efficiently, innovating in the concept of circular economy, it can be assure re-using, re-manufacturing or recycling of valuable materials. In this paper are presented some considerations related to using the waste dumps as potential resources to obtain critical metals by bio-metallurgical processes