k is the Magic Number -- Inferring the Number of Clusters Through Nonparametric Concentration Inequalities

Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically unfounded, such as searching for an elbow in the curve of a given cost measure. In contrast, statistically founded methods often make strict assumptions over the data distribution or come with their own optimization scheme for the clustering objective. This limits either the set of applicable datasets or clustering algorithms. In this paper, we strive to determine the number of clusters by answering a simple question: given two clusters, is it likely that they jointly stem from a single distribution? To this end, we propose a bound on the probability that two clusters originate from the distribution of the unified cluster, specified only by the sample mean and variance. Our method is applicable as a simple wrapper to the result of any clustering method minimizing the objective of $k$-means, which includes Gaussian mixtures and Spectral Clustering. We focus in our experimental evaluation on an application for nonconvex clustering and demonstrate the suitability of our theoretical results. Our \textsc{SpecialK} clustering algorithm automatically determines the appropriate value for $k$, without requiring any data transformation or projection, and without assumptions on the data distribution. Additionally, it is capable to decide that the data consists of only a single cluster, which many existing algorithms cannot

Requirements modelling and formal analysis using graph operations

The increasing complexity of enterprise systems requires a more advanced analysis of the representation of services expected than is currently possible. Consequently, the specification stage, which could be facilitated by formal verification, becomes very important to the system life-cycle. This paper presents a formal modelling approach, which may be used in order to better represent the reality of the system and to verify the awaited or existing system’s properties, taking into account the environmental characteristics. For that, we firstly propose a formalization process based upon properties specification, and secondly we use Conceptual Graphs operations to develop reasoning mechanisms of verifying requirements statements. The graphic visualization of these reasoning enables us to correctly capture the system specifications by making it easier to determine if desired properties hold. It is applied to the field of Enterprise modelling

Clinical course, costs and predictive factors for response to treatment in carpal tunnel syndrome: The PALMS study protocol

Background Carpal tunnel syndrome (CTS) is the most common neuropathy of the upper limb and a significant contributor to hand functional impairment and disability. Effective treatment options include conservative and surgical interventions, however it is not possible at present to predict the outcome of treatment. The primary aim of this study is to identify which baseline clinical factors predict a good outcome from conservative treatment (by injection) or surgery in patients diagnosed with carpal tunnel syndrome. Secondary aims are to describe the clinical course and progression of CTS, and to describe and predict the UK cost of CTS to the individual, National Health Service (NHS) and society over a two year period. Methods/Design In this prospective observational cohort study patients presenting with clinical signs and symptoms typical of CTS and in whom the diagnosis is confirmed by nerve conduction studies are invited to participate. Data on putative predictive factors are collected at baseline and follow-up through patient questionnaires and include standardised measures of symptom severity, hand function, psychological and physical health, comorbidity and quality of life. Resource use and cost over the 2 year period such as prescribed medications, NHS and private healthcare contacts are also collected through patient self-report at 6, 12, 18 and 24 months. The primary outcome used to classify treatment success or failures will be a 5-point global assessment of change. Secondary outcomes include changes in clinical symptoms, functioning, psychological health, quality of life and resource use. A multivariable model of factors which predict outcome and cost will be developed. Discussion This prospective cohort study will provide important data on the clinical course and UK costs of CTS over a two-year period and begin to identify predictive factors for treatment success from conservative and surgical interventions

Negative pressure characteristics of an evaporating meniscus at nanoscale

This study aims at understanding the characteristics of negative liquid pressures at the nanoscale using molecular dynamics simulation. A nano-meniscus is formed by placing liquid argon on a platinum wall between two nano-channels filled with the same liquid. Evaporation is simulated in the meniscus by increasing the temperature of the platinum wall for two different cases. Non-evaporating films are obtained at the center of the meniscus. The liquid film in the non-evaporating and adjacent regions is found to be under high absolute negative pressures. Cavitation cannot occur in these regions as the capillary height is smaller than the critical cavitation radius. Factors which determine the critical film thickness for rupture are discussed. Thus, high negative liquid pressures can be stable at the nanoscale, and utilized to create passive pumping devices as well as significantly enhance heat transfer rates

Improving SNR and reducing training time of classifiers in large datasets via kernel averaging

Kernel methods are of growing importance in neuroscience research. As an elegant extension of linear methods, they are able to model complex non-linear relationships. However, since the kernel matrix grows with data size, the training of classifiers is computationally demanding in large datasets. Here, a technique developed for linear classifiers is extended to kernel methods: In linearly separable data, replacing sets of instances by their averages improves signal-to-noise ratio (SNR) and reduces data size. In kernel methods, data is linearly non-separable in input space, but linearly separable in the high-dimensional feature space that kernel methods implicitly operate in. It is shown that a classifier can be efficiently trained on instances averaged in feature space by averaging entries in the kernel matrix. Using artificial and publicly available data, it is shown that kernel averaging improves classification performance substantially and reduces training time, even in non-linearly separable data

Search for CP violation in D0 and D+ decays

A high statistics sample of photoproduced charm particles from the FOCUS (E831) experiment at Fermilab has been used to search for CP violation in the Cabibbo suppressed decay modes D+ to K-K+pi+, D0 to K-K+ and D0 to pi-pi+. We have measured the following CP asymmetry parameters: A_CP(K-K+pi+) = +0.006 +/- 0.011 +/- 0.005, A_CP(K-K+) = -0.001 +/- 0.022 +/- 0.015 and A_CP(pi-pi+) = +0.048 +/- 0.039 +/- 0.025 where the first error is statistical and the second error is systematic. These asymmetries are consistent with zero with smaller errors than previous measurements.Comment: 12 pages, 4 figure

Quality Measures for the Diagnosis and Non-Operative Management of Carpal Tunnel Syndrome in Occupational Settings

Introduction: Providing higher quality medical care to workers with occupationally associated carpal tunnel syndrome (CTS) may reduce disability, facilitate return to work, and lower the associated costs. Although many workers’ compensation systems have adopted treatment guidelines to reduce the overuse of unnecessary care, limited attention has been paid to ensuring that the care workers do receive is high quality. Further, guidelines are not designed to enable objective assessments of quality of care. This study sought to develop quality measures for the diagnostic evaluation and non-operative management of CTS, including managing occupational activities and functional limitations. Methods: Using a variation of the well-established RAND/UCLA Appropriateness Method, we developed draft quality measures using guidelines and literature reviews. Next, in a two-round modified-Delphi process, a multidisciplinary panel of 11 U.S. experts in CTS rated the measures on validity and feasibility. Results: Of 40 draft measures, experts rated 31 (78%) valid and feasible. Nine measures pertained to diagnostic evaluation, such as assessing symptoms, signs, and risk factors. Eleven pertain to non-operative treatments, such as the use of splints, steroid injections, and medications. Eleven others address assessing the association between symptoms and work, managing occupational activities, and accommodating functional limitations. Conclusions: These measures will complement existing treatment guidelines by enabling providers, payers, policymakers, and researchers to assess quality of care for CTS in an objective, structured manner. Given the characteristics of previous measures developed with these methods, greater adherence to these measures will probably lead to improved patient outcomes at a population level