Knot Tightening By Constrained Gradient Descent

We present new computations of approximately length-minimizing polygons with fixed thickness. These curves model the centerlines of "tight" knotted tubes with minimal length and fixed circular cross-section. Our curves approximately minimize the ropelength (or quotient of length and thickness) for polygons in their knot types. While previous authors have minimized ropelength for polygons using simulated annealing, the new idea in our code is to minimize length over the set of polygons of thickness at least one using a version of constrained gradient descent. We rewrite the problem in terms of minimizing the length of the polygon subject to an infinite family of differentiable constraint functions. We prove that the polyhedral cone of variations of a polygon of thickness one which do not decrease thickness to first order is finitely generated, and give an explicit set of generators. Using this cone we give a first-order minimization procedure and a Karush-Kuhn-Tucker criterion for polygonal ropelength criticality. Our main numerical contribution is a set of 379 almost-critical prime knots and links, covering all prime knots with no more than 10 crossings and all prime links with no more than 9 crossings. For links, these are the first published ropelength figures, and for knots they improve on existing figures. We give new maps of the self-contacts of these knots and links, and discover some highly symmetric tight knots with particularly simple looking self-contact maps.Comment: 45 pages, 16 figures, includes table of data with upper bounds on ropelength for all prime knots with no more than 10 crossings and all prime links with no more than 9 crossing

Sampling migrants from their social networks: The demography and social organization of Chinese migrants in Dar es Salaam, Tanzania

The streams of Chinese migration to Africa are growing in tandem with rising Chinese investments and trade flows in and to the African continent. In spite of the high profile of this phenomenon in the media, there are few rich and broad descriptions of Chinese communities in Africa. Reasons for this include the rarity of official statistics on foreign-born populations in African censuses, the absence of predefined sampling frames required to draw representative samples with conventional survey methods and difficulties to reach certain segments of this population. Here, we use a novel network-based approach, Network Sampling with Memory, which overcomes the challenges of sampling ‘hidden’ populations in the absence of a sampling frame, to recruit a sample of recent Chinese immigrants in Dar es Salaam, Tanzania and collect information on the demographic characteristics, migration histories and social ties of members of this sample. These data reveal a heterogeneous Chinese community composed of “state-led” migrants who come to Africa to work on projects undertaken by large Chinese state-owned enterprises and “independent” migrants who come on their own accord to engage in various types of business ventures. They offer a rich description of the demographic profile and social organization of this community, highlight key differences between the two categories of migrants and map the structure of the social ties linking them. We highlight needs for future research on inter-group differences in individual motivations for migration, economic activities, migration outcomes, expectations about future residence in Africa, social integration and relations with local communities

Prospectus, September 18, 2013

PYGMALION MUSIC FESTIVAL 2013 PREVIEW; The benefits of being a Parkland student; International Student Award recipient: Nguyen Anh; Why your waiter hasn\u27t gotten a raise in 22 years; The on-campus effect of off-campus threats; Sign-Painters: The Movie; Meet the Pros: Doug Burgett; Cobra golf teeing up for fall seasonhttps://spark.parkland.edu/prospectus_2013/1013/thumbnail.jp

Prospectus, October 23, 2013

SEMINAR HIGHLIGHTS ART PROGRAM; Trick-or-treating trending for college students; Seminar coverage continued; Why you may have a fear of missing out; Public safety on domestic violence awareness; Discover the epidemic of overtreatment; The rise of chairs covered in chewing gum!!!; Myths and origins of Halloween; Parkland athletics help the community; Fall outings: From stargazing parties to wildlife-watching adventures, these four day trips have become cherished autumn traditionshttps://spark.parkland.edu/prospectus_2013/1018/thumbnail.jp

Network Sampling with Memory: A Proposal for More Efficient Sampling from Social Networks

Techniques for sampling from networks have grown into an important area of research across several fields. For sociologists, the possibility of sampling from a network is appealing for two reasons: (1) A network sample can yield substantively interesting data about network structures and social interactions, and (2) it is useful in situations where study populations are difficult or impossible to survey with traditional sampling approaches because of the lack of a sampling frame. Despite its appeal, methodological concerns about the precision and accuracy of network-based sampling methods remain. In particular, recent research has shown that sampling from a network using a random walk based approach such as Respondent Driven Sampling (RDS) can result in high design effects (DE)—the ratio of the sampling variance to the sampling variance of simple random sampling (SRS). A high design effect means that more cases must be collected to achieve the same level of precision as SRS. In this paper we propose an alternative strategy, Network Sampling with Memory (NSM), which collects network data from respondents in order to reduce design effects and, correspondingly, the number of interviews needed to achieve a given level of statistical power. NSM combines a “List” mode, where all individuals on the revealed network list are sampled with the same cumulative probability, with a “Search” mode, which gives priority to bridge nodes connecting the current sample to unexplored parts of the network. We test the relative efficiency of NSM compared to RDS and SRS on 162 school and university networks from Add Health and Facebook that range in size from 110 to 16,278 nodes. The results show that the average design effect for NSM on these 162 networks is 1.16, which is very close to the efficiency of a simple random sample (DE=1), and 98.5% lower than the average DE we observed for RDS

Prospectus, September 25, 2013

PROFESSOR STARS IN INDIE FILM; Access Success features Kerris Lee; International Student Award recipient: Jeongwon Yoon; The beginner\u27s guide to budgeting; Tips for students who plan on transferring after Parkland; Using reality TV to reveal your personality; GOP\u27s misguided attack on food stamps; Cobra women\u27s soccer heats up; Tips for gaming on a budgethttps://spark.parkland.edu/prospectus_2013/1014/thumbnail.jp

Transferring learning to work : making learning real for natural resource leaders and their employers

Investing in leadership development for natural resource professionals increasingly means linking learning for participants to performance for their employer. We were challenged to develop meaningful learning outcomes and their assessment, which included making the learning ‘real’ for the participants and their employer. Working collaboratively with the Ontario Ministry of Natural Resources, we combined an outcomes-based approach with problem-based learning in an 8-day Ecological Sustainability Leadership Program for foresters, biologists, and other public service professionals. An important element of the curriculum was the transfer-to-work action plan. For participants, their plan results from reflection, discerning priorities, and making commitments to take action. From the employers view, their action plan encourages and promotes explicit transfer of learning outcomes to work. From an educator’s perspective, their plan allows assessment of the suitability of the learning outcomes and our success in helping participants acquire them. Our presentation overviews this leadership program, key elements of curriculum design, along with assessment, giving particular attention to the transfer to work online tools.Keywords: online tools, transfer learning to work, natural resource leadership program, Professional developmen