LetQ be the unit cube in R n and H a hyperplane thru the Origin. The intersection is called Cube slice and was investigated by Henesley, Vaaler , Ball and others. We give an example of a cube slice in R 4 that is not a zonoid. This contrasts with a result in R 3 that follows from a Theorem due to Herz and Lindenstrauss where every cube slice is a zonoid. The volume of this slice is computed and used to determine the likely known result, the value of the sinc integral I 4
Alzheimer’s Disease (AD) conversion prediction from the mild cognitive impairment (MCI) stage has been a difficult challenge. This study focuses on providing an individualized MCI to AD conversion prediction using a balanced random forest model that leverages clinical data. In order to do this, 383 Early Mild Cognitive Impairment (EMCI) patients were gathered from the Alzheimer’s Disease Neuroimaging Initiative (ADNI). Of these patients, 49 would eventually convert to AD (EMCI_C), whereas the remaining 334 did not convert (EMCI_NC). All of these patients were split randomly into training and testing data sets with 95 patients reserved for testing. Nine clinical features were selected, comprised of a mix of demographic, brain volume, and cognitive testing variables. Oversampling was then performed in order to balance the initially imbalanced classes prior to training the model with 1000 estimators. Our results showed that a random forest model was effective (93.6% accuracy) at predicting the conversion of EMCI patients to AD based on these clinical features. Additionally, we focus on explainability by assessing the importance of each clinical feature. Our model could impact the clinical environment as a tool to predict the conversion to AD from a prodromal stage or to identify ideal candidates for clinical trials.
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