Torus Knots

We have compiled here many interesting results concerning a particular collection of knots called torus knots. Torus knots are merely simple closed curves imbedded in an unknotted torus T2 in E3. We show that the fundamental groups of T2, π(T2), is the direct product of the additive group of integers with itself. The ordered pair (p, q) in Z x Z determines an equivalence class of loops on the torus, and we show in Section II that the class [(p, q)] contains a loop whose image is a simple closed curve if and only if p and q are relatively prime. A torus knot in the loop class [(p, q)] is denoted Kp, q. It is natural to ask which of the knots Kp, q are equivalently imbedded in E3. One means of answering this question is to observe the algebraic structures of the corresponding know groups π(E3 - Kp, q) and π(E3 - Kr,s) are not isomorphic, then it follows that E3 - Kp,q and E3 - Kr,s are not homeomorphic; consequently Kp,q and Kr,s are not equivalent knots. The definition and general properties of the fundamental group of a topological space are discussed in Section I of this report. In Section IV the fundamental group of E3 - Kp,q is shown to have the group presentation {a,b I ap = bq}. We will show that these groups are determined by the integers p and q, from which it follows that there are infinitely many non-equivalent torus knots. Illustrations are use extensively to aid the reader, and an entire section is devoted to the development of an algorithm for picturing torus knots. This algorithm, Section III, provides us with an intuitive feeling for the significance of p and q in determining Kp,q. Finally, in Section V, a second knot type invariant, called the genus of the knot, is developed. The genus of a knot is a nonnegative integer assigned to the knot in a particular way. We will show that there exist torus knots of arbitrary genus and construct an infinite collection of knots, all having genus 1, none of which is a torus knot. The material in this report comes from many sources. In many cases the proofs and illustrations were created by the author. We do not know of any similar compilation of facts relating to a specific class of knots and we hope that this report might be of use to other students of knot theory

Developing a systems and informatics based approach to lifestyle monitoring within eHealth:part I - technology and data management

Lifestyle monitoring forms a subset of telecare in which data derived from sensors located in the home is used to identify variations in behaviour which are indicative of a change in care needs. Key to this is the performance of the sensors themselves and the way in which the information from multiple sources is integrated within the decision making process. The paper therefore considers the functions of the key sensors currently deployed and places their operation within the context of a proposed multi-level system structure which takes due cognisance of the requisite informatics framework

Electricity load profile classification using Fuzzy C-Means method

This paper presents the Fuzzy C-Means (FCM) clustering method. The FCM technique assigns a degree of membership for each data set to several clusters, thus offering the opportunity to deal with load profiles that could belong to more than one group at the same time. The FCM algorithm is based on minimising a c-means objective function to determine an optimal classification. The simulation of FCM was carried out using actual sample data from Indonesia and the results are presented. Some validity index measurements was carried out to estimate the compactness of the resulting clusters or to find the optimal number of clusters for a data set

Assessing Feeding Damage from Two Leaffooted Bugs, Leptoglossus clypealis Heidemann and Leptoglossus zonatus (Dallas) (Hemiptera: Coreidae), on Four Almond Varieties.

Leaffooted bugs (Leptoglossus spp; Hemiptera: Coreidae) are phytophagous insects native to the Western Hemisphere. In California, Leptoglossus clypealis and Leptoglossus zonatus are occasional pests on almonds. Early season feeding by L. clypealis and L. zonatus leads to almond drop, while late season feeding results in strikes on kernels, kernel necrosis, and shriveled kernels. A field cage study was conducted to assess feeding damage associated with L. clypealis and L. zonatus on four almond varieties, Nonpareil, Fritz, Monterey, and Carmel. The objectives were to determine whether leaffooted bugs caused significant almond drop, to pinpoint when the almond was vulnerable, and to determine the final damage at harvest. Branches with ~20 almonds were caged and used to compare almond drop and final damage in four treatments: (1) control branches, (2) mechanically punctured almonds, (3) adult Leptoglossus clypealis, and (4) adult Leptoglossus zonatus. Replicates were set up for eight weeks during two seasons. Early season feeding resulted in higher almond drop than late season, and L. zonatus resulted in greater drop than L. clypealis. The almond hull width of the four varieties in the study did not influence susceptibility to feeding damage. The final damage assessment at harvest found significant levels of kernel strikes, kernel necrosis, and shriveled almonds in bug feeding cages, with higher levels attributed to L. zonatus than L. clypealis. Further research is warranted to develop an Integrated Pest Management program with reduced risk controls for L. zonatus

N<i>e</i>XOS – the design, development and evaluation of a rehabilitation system for the lower limbs

Recent years have seen the development of a number of automated and semi-automated systems to support for physiotherapy and rehabilitation. These deploy a range of technologies from highly complex purpose built systems to approaches based around the use of industrial robots operating either individually or in combination for applications ranging from stroke to mobility enhancement. The NeXOS project set out to investigate an approach to the rehabilitation of the lower limbs in a way which brought together expertise in engineering design and mechatronics with specilists in rehabilitation and physiotherapy. The resulting system has resulted in a prototype of a system which is capable in operating in a number of modes from fully independent to providing direct support to a physiotherapist during manipulation of the limb. Designed around a low cost approach for an implementation ultimately capable of use in a patients home using web-baased strategies for communication with their support team, the prototype NeXOS system has validated the adoption of an integrated approach to its development. The paper considers this design and development process and provides the results from the initial tests with physiotherapists to establish the operational basis for clinical implementation

Using a fuzzy inference system to control a pumped storage hydro plant

The paper discusses the development of a fuzzy inference system (FIS) based governor control for a pumped storage hydroelectric plant. The First Hydro Company's plant at Dinorwig in North Wales is the largest of its kind in Europe and is mainly used for frequency control of the UK electrical grid. In previous investigations, a detailed model of the plant was developed using MATLAB(R)/SIMULINK(R) and this is now being used to compare FIS governor operation with the proportional-integral-derivative (PID) controller currently used. The paper describes the development of an FIS governor, and shows that its response to a step increase in load is superior to the PID under certain conditions of load. The paper proceeds to discuss the implications of these results in view of the possible practical application of an FIS governor at the Dinorwig plant

Timelords & Timelines: Four Web Apps for Storytelling in Libraries

From online embeds to interactive displays, timelines can serve many purposes and tell powerful stories. In this panel librarians discuss collaboration and how to bring history to life through displays, events and online platforms for engaging students and preserving community milestones. Four of our favorite tools for creating digital timelines and gathering content will be shared including Prezi, TikiToki, TimeToast, and Piktochart. Comparisons will be given based on cost, technical limitations, and general ease of use. Specific examples will also be shared and discussed

Time Lords & Timelines Panel

From self-guided online embeds to immersive live displays, timelines can serve many purposes and tell powerful stories. In this panel three members of UGA\u27s Law Library shared how they bring history to life, engage students, and preserve the scholarly and institutional milestones of the Law School with timelines by enhancing guide and repository collections, complimenting physical item displays and interacting with patrons at special events using multimedia. A variety of tools for creating digital timelines and gathering content were discussed including our four favorite applications: Prezi, TimeToast, Tiki-Toki, and Piktochart. Comparisons were given based on cost, technical limitations, collaborative potential, and general ease of use. Handouts were provided and the session was followed with an opportunity to ask questions of panelists

Mice expressing HLA-DQ6α8β transgenes develop polychondritis spontaneously

Relapsing polychondritis (RP) is a human autoimmune disease of unknown etiology in which cartilaginous sites are destroyed by cyclic inflammatory episodes beginning, most commonly, during the fourth or fifth decade of life. We have previously described collagen-induced polychondritis that closely mirrors RP occurring in young (6–8 weeks old) HLA-DQ6αβ8αβ transgenic Aβ0 mice, following immunization with heterologous type II collagen (CII). We present evidence here that transgenic strains expressing the DQ6α8β transgene develop spontaneous polychondritis (SP) at the mouse equivalent of human middle age (4.5–6 months and 40–50 years old, respectively) and display polyarthritis, auricular chondritis and nasal chondritis – three of the most common sites affected in RP. Auricular chondritis in SP, like RP but unlike CII-induced polychondritis, exhibited a relapsing/remitting phenotype, requiring several inflammatory cycles before the cartilage is destroyed. Elevated serum levels of total IgG corresponded with the onset of disease in SP, as in RP and CII-induced polychondritis. No CII-specific immune response was detected in SP, however – more closely mirroring RP, in which as few as 30% of RP patients have been reported to have CII-specific IgG. CII-induced polychondritis displays a strong CII-specific immune response. SP also demonstrated a strong female preponderance, as some workers have reported in RP but has not observed in CII-induced polychondritis. These characteristics of SP allow for the examination of the immunopathogenesis of polychondritis in the absence of an overwhelming CII-specific immune response and the strong adjuvant-induced immunostimulatory influence in CII-induced polychondritis. This spontaneous model of polychondritis provides a new and unique tool to investigate both the initiatory events as well as the immunopathogenic mechanisms occurring at cartilaginous sites during the cyclic inflammatory assaults of polychondritis

Consumer Purchases of Biotech Sweet Corn: Results from a Market Experiment

In the increasingly consumer-driven food system, consumer preferences toward agricultural biotechnology have the potential to influence decisions about development and adoption of biotech crop varieties. Current knowledge about consumer attitudes toward biotech foods is largely based on a number of consumer surveys and a growing body of experimental auctions. This paper reports results of a market experiment designed to isolate the effect of the use of biotechnology on consumer choices between two otherwise identical products. Two related varieties of fresh-market sweet corn were grown, labeled, and sold side-by-side in nine participating grocery stores in the Philadelphia area. Sales data indicate a market share of biotech corn of about 45 percent, with store-specific shares varying between 10 and 80 percent. Over 700 surveys were collected in stores. Surprisingly, only 65 percent of respondents noticed that there were two types of corn for sale despite the labeling and merchandising, and 87 percent of the sample spent one minute or less choosing their corn. About half of the respondents had heard of biotechnology before, and 16 percent volunteered the biotechnology trait as an influence on their purchase decision. Approximately 40 percent of the sample purchased some of the biotech variety, with several respondents purchasing some of each.Institutional and Behavioral Economics,