Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm

Over the past five decades, k-means has become the clustering algorithm of choice in many application domains primarily due to its simplicity, time/space efficiency, and invariance to the ordering of the data points. Unfortunately, the algorithm's sensitivity to the initial selection of the cluster centers remains to be its most serious drawback. Numerous initialization methods have been proposed to address this drawback. Many of these methods, however, have time complexity superlinear in the number of data points, which makes them impractical for large data sets. On the other hand, linear methods are often random and/or sensitive to the ordering of the data points. These methods are generally unreliable in that the quality of their results is unpredictable. Therefore, it is common practice to perform multiple runs of such methods and take the output of the run that produces the best results. Such a practice, however, greatly increases the computational requirements of the otherwise highly efficient k-means algorithm. In this chapter, we investigate the empirical performance of six linear, deterministic (non-random), and order-invariant k-means initialization methods on a large and diverse collection of data sets from the UCI Machine Learning Repository. The results demonstrate that two relatively unknown hierarchical initialization methods due to Su and Dy outperform the remaining four methods with respect to two objective effectiveness criteria. In addition, a recent method due to Erisoglu et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms (Springer, 2014). arXiv admin note: substantial text overlap with arXiv:1304.7465, arXiv:1209.196

Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions II - The deconfined phase

We present a non-perturbative study of the equation of state in the deconfined phase of Yang-Mills theories in D=2+1 dimensions. We introduce a holographic model, based on the improved holographic QCD model, from which we derive a non-trivial relation between the order of the deconfinement phase transition and the behavior of the trace of the energy-momentum tensor as a function of the temperature T. We compare the theoretical predictions of this holographic model with a new set of high-precision numerical results from lattice simulations of SU(N) theories with N=2, 3, 4, 5 and 6 colors. The latter reveal that, similarly to the D=3+1 case, the bulk equilibrium thermodynamic quantities (pressure, trace of the energy-momentum tensor, energy density and entropy density) exhibit nearly perfect proportionality to the number of gluons, and can be successfully compared with the holographic predictions in a broad range of temperatures. Finally, we also show that, again similarly to the D=3+1 case, the trace of the energy-momentum tensor appears to be proportional to T^2 in a wide temperature range, starting from approximately 1.2 T_c, where T_c denotes the critical deconfinement temperature.Comment: 2+36 pages, 10 figures; v2: comments added, curves showing the holographic predictions included in the plots of the pressure and energy and entropy densities, typos corrected: version published in JHE

Patient-reported outcome after rheumatoid arthritis-related surgery in the lower extremities: A report from the Swedish National Register of Rheuma Surgery (RAKIR)

Background and purpose Although decreasing with the development of effective pharmacological regimes, joint surgery has improved the function and quality of life of patients with rheumatoid arthritis (RA). Few studies have assessed patient-reported outcomes after RA surgery to the lower extremities. Here we report patient-relevant outcome after RA-related surgery based on the first data from the Swedish National Register of Rheuma Surgery (RAKIR). Patients and methods 258 RA patients (212 women) who had joint surgery performed at the Department of Orthopaedics, Spenshult Hospital between September 2007 and June 2009 were included. Mean age at surgery was 64 (20-86) years. The patients completed the SF-36 and HAQ questionnaires preoperatively and 6 months postoperatively, and 165 patients completed them after 12 months. Results Improvement was seen as early as at 6 months. At 12 months, 165 patients (141 women)-including hip (n = 15), knee (n = 27), foot (n = 102), and ankle (n = 21) patients-reported statistically significant improvements from preoperatively to 12 months postoperatively in HAQ (mean change: -0.11) and SF-36 subscales physical function (11), role physical (12), bodily pain (13), social functioning (6.4), and role emotional (9.4). Hip and knee patients reported the greatest improvements. Interpretation Orthopedic RA-related surgery of the lower extremities has a strong effect on pain and physical function. Improvement is evident as early as 6 months postoperatively and remains after 12 months

Molecular and cellular mechanisms underlying the evolution of form and function in the amniote jaw.

The amniote jaw complex is a remarkable amalgamation of derivatives from distinct embryonic cell lineages. During development, the cells in these lineages experience concerted movements, migrations, and signaling interactions that take them from their initial origins to their final destinations and imbue their derivatives with aspects of form including their axial orientation, anatomical identity, size, and shape. Perturbations along the way can produce defects and disease, but also generate the variation necessary for jaw evolution and adaptation. We focus on molecular and cellular mechanisms that regulate form in the amniote jaw complex, and that enable structural and functional integration. Special emphasis is placed on the role of cranial neural crest mesenchyme (NCM) during the species-specific patterning of bone, cartilage, tendon, muscle, and other jaw tissues. We also address the effects of biomechanical forces during jaw development and discuss ways in which certain molecular and cellular responses add adaptive and evolutionary plasticity to jaw morphology. Overall, we highlight how variation in molecular and cellular programs can promote the phenomenal diversity and functional morphology achieved during amniote jaw evolution or lead to the range of jaw defects and disease that affect the human condition

Inapparent infections and cholera dynamics

In many infectious diseases, an unknown fraction of infections produce symptoms mild enough to go unrecorded, a fact that can seriously compromise the interpretation of epidemiological records. This is true for cholera, a pandemic bacterial disease, where estimates of the ratio of asymptomatic to symptomatic infections have ranged from 3 to 100 (refs 1-5). In the absence of direct evidence, understanding of fundamental aspects of cholera transmission, immunology and control has been based on assumptions about this ratio and about the immunological consequences of inapparent infections. Here we show that a model incorporating high asymptomatic ratio and rapidly waning immunity, with infection both from human and environmental sources, explains 50 yr of mortality data from 26 districts of Bengal, the pathogen's endemic home. We find that the asymptomatic ratio in cholera is far higher than had been previously supposed and that the immunity derived from mild infections wanes much more rapidly than earlier analyses have indicated. We find, too, that the environmental reservoir(5,6) (free-living pathogen) is directly responsible for relatively few infections but that it may be critical to the disease's endemicity. Our results demonstrate that inapparent infections can hold the key to interpreting the patterns of disease outbreaks. New statistical methods(7), which allow rigorous maximum likelihood inference based on dynamical models incorporating multiple sources and outcomes of infection, seasonality, process noise, hidden variables and measurement error, make it possible to test more precise hypotheses and obtain unexpected results. Our experience suggests that the confrontation of time-series data with mechanistic models is likely to revise our understanding of the ecology of many infectious diseases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62519/1/nature07084.pd

Use of Self-Selected Postures to Regulate Multi-Joint Stiffness During Unconstrained Tasks

The human motor system is highly redundant, having more kinematic degrees of freedom than necessary to complete a given task. Understanding how kinematic redundancies are utilized in different tasks remains a fundamental question in motor control. One possibility is that they can be used to tune the mechanical properties of a limb to the specific requirements of a task. For example, many tasks such as tool usage compromise arm stability along specific directions. These tasks only can be completed if the nervous system adapts the mechanical properties of the arm such that the arm, coupled to the tool, remains stable. The purpose of this study was to determine if posture selection is a critical component of endpoint stiffness regulation during unconstrained tasks.Three-dimensional (3D) estimates of endpoint stiffness were used to quantify limb mechanics. Most previous studies examining endpoint stiffness adaptation were completed in 2D using constrained postures to maintain a non-redundant mapping between joint angles and hand location. Our hypothesis was that during unconstrained conditions, subjects would select arm postures that matched endpoint stiffness to the functional requirements of the task. The hypothesis was tested during endpoint tracking tasks in which subjects interacted with unstable haptic environments, simulated using a 3D robotic manipulator. We found that arm posture had a significant effect on endpoint tracking accuracy and that subjects selected postures that improved tracking performance. For environments in which arm posture had a large effect on tracking accuracy, the self-selected postures oriented the direction of maximal endpoint stiffness towards the direction of the unstable haptic environment.These results demonstrate how changes in arm posture can have a dramatic effect on task performance and suggest that postural selection is a fundamental mechanism by which kinematic redundancies can be exploited to regulate arm stiffness in unconstrained tasks

Identification of women with an increased risk of developing radiation-induced breast cancer: a case only study

Introduction: Radiation exposure at a young age is one of the strongest risk factors for breast cancer. Germline mutations in genes involved in the DNA-damage repair pathway (DDRP) may render women more susceptible to radiation-induced breast cancer. Methods: We evaluated the contribution of germline mutations in the DDRP genes BRCA1, BRCA2, CHEK2 and ATM to the risk of radiation-induced contralateral breast cancer (CBC). The germline mutation frequency was assessed, in a case-only study, in women who developed a CBC after they had a first breast cancer diagnosed before the age of 50 years, and who were (n = 169) or were not (n = 78) treated with radiotherapy for their first breast tumour. Results: We identified 27 BRCA1, 5 BRCA2, 15 CHEK2 and 4 truncating ATM germline mutation carriers among all CBC patients tested (21%). The mutation frequency was 24.3% among CBC patients with a history of radiotherapy, and 12.8% among patients not irradiated for the first breast tumour (odds ratio 2.18 (95% confidence interval 1.03 to 4.62); p = 0.043). The association between DDRP germline mutation carriers and risk of radiation-induced CBC seemed to be strongest in women who developed their second primary breast tumour at least 5 years after radiotherapy. Th