Analysis of the contour structural irregularity of skin lesions using wavelet decomposition

The boundary irregularity of skin lesions is of clinical significance for the early detection of malignant melanomas and to distinguish them from other lesions such as benign moles. The structural components of the contour are of particular importance. To extract the structure from the contour, wavelet decomposition was used as these components tend to locate in the lower frequency sub-bands. Lesion contours were modeled as signatures with scale normalization to give position and frequency resolution invariance. Energy distributions among different wavelet sub-bands were then analyzed to extract those with significant levels and differences to enable maximum discrimination. Based on the coefficients in the significant sub-bands, structural components from the original contours were modeled, and a set of statistical and geometric irregularity descriptors researched that were applied at each of the significant sub-bands. The effectiveness of the descriptors was measured using the Hausdorff distance between sets of data from melanoma and mole contours. The best descriptor outputs were input to a back projection neural network to construct a combined classifier system. Experimental results showed that thirteen features from four sub-bands produced the best discrimination between sets of melanomas and moles, and that a small training set of nine melanomas and nine moles was optimum

Unit roots in moving averages beyond first order

The asymptotic theory of various estimators based on Gaussian likelihood has been developed for the unit root and near unit root cases of a first-order moving average model. Previous studies of the MA(1) unit root problem rely on the special autocovariance structure of the MA(1) process, in which case, the eigenvalues and eigenvectors of the covariance matrix of the data vector have known analytical forms. In this paper, we take a different approach to first consider the joint likelihood by including an augmented initial value as a parameter and then recover the exact likelihood by integrating out the initial value. This approach by-passes the difficulty of computing an explicit decomposition of the covariance matrix and can be used to study unit root behavior in moving averages beyond first order. The asymptotics of the generalized likelihood ratio (GLR) statistic for testing unit roots are also studied. The GLR test has operating characteristics that are competitive with the locally best invariant unbiased (LBIU) test of Tanaka for some local alternatives and dominates for all other alternatives.Comment: Published in at http://dx.doi.org/10.1214/11-AOS935 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Refined Asymptotics of the Finite-Size Magnetization via a New Conditional Limit Theorem for the Spin

We study the fluctuations of the spin per site around the thermodynamic magnetization in the mean-field Blume-Capel model. Our main theorem generalizes the main result in a previous paper (Ellis, Machta, and Otto) in which the first rigorous confirmation of the statistical mechanical theory of finite-size scaling for a mean-field model is given. In that paper our goal is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume-Capel model. The main result is that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter $\alpha$ governing the speed at which the sequence approaches criticality is below a certain threshold $\alpha_0$. Our main theorem in the present paper on the fluctuations of the spin per site around the thermodynamic magnetization is based on a new conditional limit theorem for the spin, which is closely related to a new conditional central limit theorem for the spin.Comment: 78 pages, 2 figure

Star cluster disruption in the starburst galaxy Messier 82

Using high-resolution, multiple-passband Hubble Space Telescope images spanning the entire optical/near-infrared wavelength range, we obtained a statistically complete sample, $U$-band selected sample of 846 extended star clusters across the disk of the nearby starburst galaxy M82. Based on careful analysis of their spectral energy distributions, we determined their galaxy-wide age and mass distributions. The M82 clusters exhibit three clear peaks in their age distribution, thus defining a relatively young, log(t/yr) < 7.5, an intermediate-age, log(t/yr) $\in$ [7.5, 8.5], and an old sample, log(t/yr) > 8.5. Comparison of the completeness-corrected mass distributions offers a firm handle on the galaxy's star cluster disruption history. The most massive star clusters in the young and old samples are (almost) all concentrated in the most densely populated central region, while the intermediate-age sample's most massive clusters are more spatially dispersed, which may reflect the distribution of the highest-density gas throughout the galaxy's evolutionary history, combined with the solid-body nature of the galaxy's central region.Comment: 10 pages, 6 figures, 2 online-only data tables; ApJS, in pres

Exploring Privacy Preservation in Outsourced K-Nearest Neighbors with Multiple Data Owners

The k-nearest neighbors (k-NN) algorithm is a popular and effective classification algorithm. Due to its large storage and computational requirements, it is suitable for cloud outsourcing. However, k-NN is often run on sensitive data such as medical records, user images, or personal information. It is important to protect the privacy of data in an outsourced k-NN system. Prior works have all assumed the data owners (who submit data to the outsourced k-NN system) are a single trusted party. However, we observe that in many practical scenarios, there may be multiple mutually distrusting data owners. In this work, we present the first framing and exploration of privacy preservation in an outsourced k-NN system with multiple data owners. We consider the various threat models introduced by this modification. We discover that under a particularly practical threat model that covers numerous scenarios, there exists a set of adaptive attacks that breach the data privacy of any exact k-NN system. The vulnerability is a result of the mathematical properties of k-NN and its output. Thus, we propose a privacy-preserving alternative system supporting kernel density estimation using a Gaussian kernel, a classification algorithm from the same family as k-NN. In many applications, this similar algorithm serves as a good substitute for k-NN. We additionally investigate solutions for other threat models, often through extensions on prior single data owner systems