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Full-Text Articles in Mathematics
Sharp Inequalities Of The X-Ray Transform And The Competing Symmetries Argument, Arthur D. Dressenwall
Sharp Inequalities Of The X-Ray Transform And The Competing Symmetries Argument, Arthur D. Dressenwall
Mathematics, Statistics, and Computer Science Honors Projects
We examine the $k=1$ case of a conjecture by Baernstein and Loss pertaining to the operator norm of the $k$-plane transform from $L^p(\R^d)$ space to $L^q(\M)$ space. Previous work on this problem by Carlen and Loss, as well as by Drouot, has used an iterative technique known as the ``competing symmetries argument’’ to prove this conjecture in the $q=2$ and $q=d+1$ cases. We summarize the conjecture and this proof technique, then perform work that strongly suggest that no sufficiently ``nice” transformation exists that can be used to apply the competing symmetries argument to other cases of the conjecture.
Don’T Beep At Me: Using Google Maps Apis To Reduce Driving Anxiety, Daniel Chechelnitsky
Don’T Beep At Me: Using Google Maps Apis To Reduce Driving Anxiety, Daniel Chechelnitsky
Mathematics, Statistics, and Computer Science Honors Projects
Stress while driving is a significant issue that causes automobile incidents. Along with the physical injuries, there is often baggage and trauma associated with these accidents. Wearable health monitoring technology, like Smartwatches, has a real possibility to help people further understand the stress inducing processes of driving. Thus to help with this issue, I propose a Google Maps app extension called: "Don't Beep At Me". This project creates a map that is layered by heart rate instead of speed limit and has great potential to be useful for reducing driving anxiety.
A Comparison Of Stacking Methods To Estimate Survival Using Residual Lifetime Data From Prevalent Cohort Studies, Zhaoheng Li
A Comparison Of Stacking Methods To Estimate Survival Using Residual Lifetime Data From Prevalent Cohort Studies, Zhaoheng Li
Mathematics, Statistics, and Computer Science Honors Projects
Prevalent cohort studies are widely used for their cost-efficiency and convenience. However, in such studies, only the residual lifetime can be observed. Traditionally, researchers rely on self-reported onset times to infer the underlying survival distribution, which may introduce additional bias that confounds downstream analysis. This study compares two stacking procedures and one mixture model approach that uses only residual lifetime data while leveraging the strengths of different estimators. Our simulation results show that the two stacked estimators outperform the nonparametric maximum likelihood estimator (NPMLE) and the mixture model, allowing robust and accurate estimations for underlying survival distributions.