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Construction Of The Canonical Representation From A Noncanonical Representation, Yuji Hibino Mar 2022

Construction Of The Canonical Representation From A Noncanonical Representation, Yuji Hibino

Journal of Stochastic Analysis

No abstract provided.


New Limit Theorems For Increments Of Birth-And-Death Processes With Linear Rates, Alexander Ya. Kreinin, Vladimir V. Vinogradov Feb 2022

New Limit Theorems For Increments Of Birth-And-Death Processes With Linear Rates, Alexander Ya. Kreinin, Vladimir V. Vinogradov

Journal of Stochastic Analysis

No abstract provided.


Backward Stochastic Differential Equations With No Driving Martingale And Pseudo-Pdes, Adrien Barrasso, Francesco Russo Feb 2022

Backward Stochastic Differential Equations With No Driving Martingale And Pseudo-Pdes, Adrien Barrasso, Francesco Russo

Journal of Stochastic Analysis

No abstract provided.


Strict Lyapunov Functions And Feedback Controls For Sir Models With Quarantine And Vaccination, Hiroshi Ito, Michael Malisoff, Frederic Mazenc Feb 2022

Strict Lyapunov Functions And Feedback Controls For Sir Models With Quarantine And Vaccination, Hiroshi Ito, Michael Malisoff, Frederic Mazenc

Faculty Publications

We provide a new global strict Lyapunov function construction for a susceptible, infected, and recovered (or SIR) disease dynamics that includes quarantine of infected individuals and mass vaccination. We use the Lyapunov function to design feedback controls to asymptotically stabilize a desired endemic equilibrium, and to prove input-to-state stability for the dynamics with a suitable restriction on the disturbances. Our simulations illustrate the potential of our feedback controls to reduce peak levels of infected individuals.


A Bayesian Phase I/Ii Biomarker-Based Design For Identifying Subgroup-Specific Optimal Dose For Immunotherapy, Beibei Guo, Yong Zang Feb 2022

A Bayesian Phase I/Ii Biomarker-Based Design For Identifying Subgroup-Specific Optimal Dose For Immunotherapy, Beibei Guo, Yong Zang

Faculty Publications

Immunotherapy is an innovative treatment that enlists the patient's immune system to battle tumors. The optimal dose for treating patients with an immunotherapeutic agent may differ according to their biomarker status. In this article, we propose a biomarker-based phase I/II dose-finding design for identifying subgroup-specific optimal dose for immunotherapy (BSOI) that jointly models the immune response, toxicity, and efficacy outcomes. We propose parsimonious yet flexible models to borrow information across different types of outcomes and subgroups. We quantify the desirability of the dose using a utility function and adopt a two-stage dose-finding algorithm to find the optimal dose for each …


A New Matroid Lift Construction And An Application To Group-Labeled Graphs, Zach Walsh Jan 2022

A New Matroid Lift Construction And An Application To Group-Labeled Graphs, Zach Walsh

Faculty Publications

A well-known result of Brylawski constructs an elementary lift of a matroid M from a linear class of circuits of M. We generalize this result by constructing a rank-k lift of M from a rank-k matroid on the set of circuits of M. We conjecture that every lift of M arises via this construction. We then apply this result to group-labeled graphs, generalizing a construction of Zaslavsky. Given a graph G with edges labeled by a group, Zaslavsky's lift matroid K is an elementary lift of the graphic matroid M(G) that respects the group-labeling; specifically, the cycles of G that …


Dynamic Correlation Estimators For Bivariate Brownian And Geometric Brownian Motions, Majnu John, Yihren Wu Jan 2022

Dynamic Correlation Estimators For Bivariate Brownian And Geometric Brownian Motions, Majnu John, Yihren Wu

Journal of Stochastic Analysis

No abstract provided.


The Zagreb Index Of Several Random Models, Panpan Zhang Jan 2022

The Zagreb Index Of Several Random Models, Panpan Zhang

Journal of Stochastic Analysis

No abstract provided.