Predicting Fluid Intelligence of Children using T1-weighted MR Images and a StackNet

In this work, we utilize T1-weighted MR images and StackNet to predict fluid intelligence in adolescents. Our framework includes feature extraction, feature normalization, feature denoising, feature selection, training a StackNet, and predicting fluid intelligence. The extracted feature is the distribution of different brain tissues in different brain parcellation regions. The proposed StackNet consists of three layers and 11 models. Each layer uses the predictions from all previous layers including the input layer. The proposed StackNet is tested on a public benchmark Adolescent Brain Cognitive Development Neurocognitive Prediction Challenge 2019 and achieves a mean squared error of 82.42 on the combined training and validation set with 10-fold cross-validation. In addition, the proposed StackNet also achieves a mean squared error of 94.25 on the testing data. The source code is available on GitHub.Comment: 8 pages, 2 figures, 3 tables, Accepted by MICCAI ABCD-NP Challenge 2019; Added ND

Unbiased estimators for spatial distribution functions of classical fluids

We use a statistical-mechanical identity closely related to the familiar virial theorem, to derive unbiased estimators for spatial distribution functions of classical fluids. In particular, we obtain estimators for both the fluid density rho(r) in the vicinity of a fixed solute, and for the pair correlation g(r) of a homogeneous classical fluid. We illustrate the utility of our estimators with numerical examples, which reveal advantages over traditional histogram-based methods of computing such distributions.Comment: 15 pages, includes 3 color figure

Error Estimates for Measurements of Cosmic Shear

In the very near future, weak lensing surveys will map the projected density of the universe in an unbiased way over large regions of the sky. In order to interpret the results of studies it is helpful to develop an understanding of the errors associated with quantities extracted from the observations. In a generalization of one of our earlier works, we present estimators of the cumulants and cumulant correlators of the weak lensing convergence field, and compute the variance associated with these estimators. By restricting ourselves to so-called compensated filters we are able to derive quite simple expressions for the errors on these estimates. We also separate contributions from cosmic variance, shot noise and intrinsic ellipticity of the source galaxies.Comment: 12 pages, including 5 figures, uses mn.sty. Substantially revised version accepted by MNRA