A tight lower bound instance for k-means++ in constant dimension

The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial $k$ centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: Pick the first center randomly from the given points. For $i > 1$, pick a point to be the $i^{th}$ center with probability proportional to the square of the Euclidean distance of this point to the closest previously $(i-1)$ chosen centers. The k-means++ seeding algorithm is not only simple and fast but also gives an $O(\log{k})$ approximation in expectation as shown by Arthur and Vassilvitskii. There are datasets on which this seeding algorithm gives an approximation factor of $\Omega(\log{k})$ in expectation. However, it is not clear from these results if the algorithm achieves good approximation factor with reasonably high probability (say $1/poly(k)$). Brunsch and R\"{o}glin gave a dataset where the k-means++ seeding algorithm achieves an $O(\log{k})$ approximation ratio with probability that is exponentially small in $k$. However, this and all other known lower-bound examples are high dimensional. So, an open problem was to understand the behavior of the algorithm on low dimensional datasets. In this work, we give a simple two dimensional dataset on which the seeding algorithm achieves an $O(\log{k})$ approximation ratio with probability exponentially small in $k$. This solves open problems posed by Mahajan et al. and by Brunsch and R\"{o}glin.Comment: To appear in TAMC 2014. arXiv admin note: text overlap with arXiv:1306.420

Recent changes in U.S. family finances: evidence from the 1998 and 2001 Survey of Consumer Finances

Data from the Federal Reserve Board's Survey of Consumer Finances show a striking pattern of growth in family income and net worth between 1998 and 2001. Inflation-adjusted incomes of families rose broadly, although growth was fastest among the group of families whose income was higher than the median. The median value of family net worth grew faster than that of income, but as with income, the growth rates of net worth were fastest for groups above the median. The years between 1998 and 2001 also saw a rise in the proportion of families that own corporate equities either directly or indirectly (such as through mutual funds or retirement accounts); by 2001 the proportion exceeded 50 percent. The growth in the value of equity holdings helped push up financial assets as a share of total family assets despite a decline in the overall stock market that began in the second half of 2000. ; The level of debt carried by families rose over the period, but the expansion in equities and the increased values of principal residences and other assets were sufficient to reduce debt as a proportion of family assets. The typical share of family income devoted to debt repayment also fell over the period. For some groups, however--particularly those with relatively low levels of income and wealth--a concurrent rise in the frequency of late debt payments indicated that their ability to service their debts had deteriorated.Consumer behavior ; Saving and investment ; Income

New Relationships: Understanding & Supporting the Contemporary ‌: Understanding and Supporting the Contemporary Worker.

Times have changed, and both jobs and their associated 'career ladders' appear more temporary, and more elusive, than before. Yet people still seek certain fundamentals - security, community, and self-fulfilment - from their working lives. How can we still help to provide these fundamentals in a time of greater uncertainty? One answer lies in finding continuity in what we used to see as discontinuous events. People may change jobs, but retain the relationships and support systems that they had before. This paper draws on examples from a recent book The New Careers by Professor Michael Arthur and colleagues and discusses the implications of these examples for future research and practice

Invariant tensors and Casimir operators for simple compact Lie groups

The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive Casimirs equal to the rank of the underlying group. A systematic derivation is presented of a complete set of identities expressing non-primitive symmetric tensors in terms of primitive tensors. Several examples are given including an application to an exceptional Lie algebra.Comment: 11 pages, LaTeX, minor changes, version in J. Math. Phy

GPU accelerated real-time multi-functional spectral-domain optical coherence tomography system at 1300 nm.

We present a GPU accelerated multi-functional spectral domain optical coherence tomography system at 1300 nm. The system is capable of real-time processing and display of every intensity image, comprised of 512 pixels by 2048 A-lines acquired at 20 frames per second. The update rate for all four images with size of 512 pixels by 2048 A-lines simultaneously (intensity, phase retardation, flow and en face view) is approximately 10 frames per second. Additionally, we report for the first time the characterization of phase retardation and diattenuation by a sample comprised of a stacked set of polarizing film and wave plate. The calculated optic axis orientation, phase retardation and diattenuation match well with expected values. The speed of each facet of the multi-functional OCT CPU-GPU hybrid acquisition system, intensity, phase retardation, and flow, were separately demonstrated by imaging a horseshoe crab lateral compound eye, a non-uniformly heated chicken muscle, and a microfluidic device. A mouse brain with thin skull preparation was imaged in vivo and demonstrated the capability of the system for live multi-functional OCT visualization

A major index for matchings and set partitions

We introduce a statistic \pmaj on partitions of $[n]=\{1,2,..., n\}$, and show that it is equidistributed with the number of 2-crossings over partitions of $[n]$ with given sets of minimal block elements and maximal block elements. This generalizes the classical result of equidistribution for the permutation statistics inversion number and major index.Comment: 17 pages, 9 figure

Chemical Abundances of the Damped Lya Systems at z>1.5

We present chemical abundance measurements for 19 damped lya systems observed with HIRES on the 10m W.M. Keck Telescope. Our principal goal is to investigate the abundance patterns of the damped systems and thereby determine the underlying physical processes which dominate their chemical evolution. We place particular emphasis on gauging the relative importance of two complementary effects often invoked to explain the damped lya abundances: (1) nucleosynthetic enrichment from Type II supernovae and (2) an ISM-like dust depletion pattern. Similar to the principal results of Lu et al. (1996), our observations lend support both for dust depletion and Type II SN enrichment. Specifically, the observed overabundance of Zn/Fe and underabundance of Ni/Fe relative to solar abundances suggest significant dust depletion within the damped lya systems. Meanwhile, the relative abundances of Al, Si, and Cr vs. Fe are consistent with both dust depletion and Type II supernova enrichment. Our measurements of Ti/Fe and the Mn/Fe measurements from Lu et al. (1996), however, cannot be explained by dust depletion and indicate an underlying Type II SN pattern. Finally, the observed values of [S/Fe] are inconsistent with the combined effects of dust depletion and the nucleosynthetic yields expected for Type II supernovae. This last result emphasizes the need for another physical process to explain the damped lya abundance patterns. We also examine the metallicity of the damped lya systems both with respect to Zn/H and Fe/H. Our results confirm previous surveys by Pettini and collaborators, i.e., [] = -1.15 +/- 0.15 dex. [abridged]Comment: 18 pages, 4 embedded figures, 20 additional figures. Accepted to the Astrophysical Journal 10/20/98. Uses Latex2e, emualteapj.sty, and onecolfloat.st

Self-organized Networks of Competing Boolean Agents

A model of Boolean agents competing in a market is presented where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority. After a long time interval, the poorest player's strategy is changed randomly, and the process is repeated. Eventually the network evolves to a stationary but intermittent state where random mutation of the worst strategy can change the behavior of the entire network, often causing a switch in the dynamics between attractors of vastly different lengths.Comment: 4 pages, 3 included figures. Some text revision and one new figure added. To appear in PR

Prehabilitation Before Total Knee Arthroplasty Increases Strength and Function in Older Adults With Severe Osteoarthritis

Preparing for the stress of total knee arthroplasty (TKA) surgery by exercise training (prehabilitation) may improve strength and function before surgery and, if effective, has the potential to contribute to postoperative recovery. Subjects with severe osteoarthritis (OA), pain intractable to medicine and scheduled for TKA were randomized into a usual care (UC) group (n = 36) or usual care and exercise (UC + EX) group (n = 35). The UC group maintained normal daily activities before their TKA. The UC + EX group performed a comprehensive prehabilitation program that included resistance training using bands, flexibility, and step training at least 3 times per week for 4-8 weeks before their TKA in addition to UC. Leg strength (isokinetic peak torque for knee extension and flexion) and ability to perform functional tasks (6-minute walk, 30 second sit-to-stand repetitions, and the time to ascend and descend 2 flights of stairs) were assessed before randomization at baseline (T1) and 1 week before the subject\u27s TKA (T2). Repeated-measures analysis of variance indicated a significant group by time interaction (p \u3c 0.05) for the 30-second sit-to-stand repetitions, time to ascend the first flight of stairs, and peak torque for knee extension in the surgical knee. Prehabilitation increased leg strength and the ability to perform functional tasks for UC + EX when compared to UC before TKA. Short term (4-8 weeks) of prehabilitation was effective for increasing strength and function for individuals with severe OA. The program studied is easily transferred to a home environment, and clinicians working with this population should consider prehabilitation before TKA. [PUBLICATION ABSTRACT

TB132: An Annotated Bibliography of Predator Research in Maine, 1974-1988

From 1974 to 1988, graduate students (13 M.S. and 5 Ph.D.) and faculty members from the University of Maine conducted a series of studies regarding the ecology of coyotes, red foxes, bobcats, pine martens, fishers, otters, and their prey. This research was reported in 67 theses, journal articles, or other reports, which are abstracted here. An introductory section summarizes the major findings.https://digitalcommons.library.umaine.edu/aes_techbulletin/1068/thumbnail.jp