Lipschitz extensions of maps between Heisenberg groups

Let $\H^n$ be the Heisenberg group of topological dimension 2n+1 . We prove that if n is odd, the pair of metric spaces $(\H^n, \H^n)$ does not have the Lipschitz extension property.

Enhanced Knowledge Management by Synchronizing Mind Maps and Fuzzy Cognitive Maps

This paper presents a conceptual approach to enhance knowledge management by synchronizing mind maps and fuzzy cognitive maps. The use of mind maps allows taking advantage of human creativity, while the application of fuzzy cognitive maps enables to store information expressed in natural language. By applying cognitive computing, it makes possible to gather and extract relevant information out of a data pool. Therefore, this approach is supposed to give a framework that enhances knowledge management. To demonstrate the potential of this framework, a use case concerning the development of a smart city app is presented.

LOGITCPRPLOT: Stata module to graph component-plus-residual plot for logistic regression

logitcprplot can be used after logistic regression for graphing a component-plus-residual plot (a.k.a. partial residual plot) for a given predictor, including a lowess, local polynomial, restricted cubic spline, fractional polynomial, penalized spline, regression spline, running line, or adaptive variable span running line smooth

RRLOGIT: Stata module to estimate logistic regression for randomized response data

rrlogit fits a maximum-likelihood logistic regression for randomized response data.

Radiomic Texture Analysis Mapping Predicts Areas of True Functional MRI Activity.

Individual analysis of functional Magnetic Resonance Imaging (fMRI) scans requires user-adjustment of the statistical threshold in order to maximize true functional activity and eliminate false positives. In this study, we propose a novel technique that uses radiomic texture analysis (TA) features associated with heterogeneity to predict areas of true functional activity. Scans of 15 right-handed healthy volunteers were analyzed using SPM8. The resulting functional maps were thresholded to optimize visualization of language areas, resulting in 116 regions of interests (ROIs). A board-certified neuroradiologist classified different ROIs into Expected (E) and Non-Expected (NE) based on their anatomical locations. TA was performed using the mean Echo-Planner Imaging (EPI) volume, and 20 rotation-invariant texture features were obtained for each ROI. Using forward stepwise logistic regression, we built a predictive model that discriminated between E and NE areas of functional activity, with a cross-validation AUC and success rate of 79.84% and 80.19% respectively (specificity/sensitivity of 78.34%/82.61%). This study found that radiomic TA of fMRI scans may allow for determination of areas of true functional activity, and thus eliminate clinician bias.

Grain coarsening maps: A new tool to predict microfabric evolution of polymineralic rocks

Polymineralic rocks undergo grain coarsening with increasing temperature in both static and deformational environments, as long as no mineral reactions occur. The grain coarsening in such rocks is complex because the different phases influence each other, and it is this interaction that controls the rate of grain coarsening of the entire aggregate. We present a mathematical approach to investigate coupled grain coarsening using a set of microstructural parameters, including grain size and volume fraction of both second phases and matrix mineral in combination with temperature information. Based on samples from polymineralic carbonate mylonites that were deformed at different temperatures, we demonstrate how the mathematical relation can be calibrated for this natural system. Using such data sets for other lithologies, grain coarsening maps can be generated, which allow the prediction of microstructural evolution in polymineralic rocks. Such predictions are crucial for all subdisciplines in the earth sciences that require fundamental knowledge about microstructural changes and rheology of an orogen at different depths, such as structural geology, geophysics, geodynamics, and metamorphic petrology.