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- ANGULAR CUTOFF (1)
- Boltzmann-Enskog equation (1)
- CONVERGENCE (1)
- Epidemic models (1)
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- GLOBAL STABILITY (1)
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- Immunotherapy (1)
- Lyapunov functions (1)
- Quarantine (1)
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- Stability (1)
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- Subgroupsbiomarkerphase III trialdose findingimmune responserisk-benefit tradeoffBayesian adaptive design (1)
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Articles 1 - 4 of 4
Full-Text Articles in Entire DC Network
On Uniqueness And Stability For The Boltzmann-Enskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar
On Uniqueness And Stability For The Boltzmann-Enskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar
Faculty Publications
The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Boltzmann-Enskog equation. Based on a McKean-Vlasov equation with jumps, the associated stochastic process was recently constructed by modified Picard iterations with the mean-field interactions, and more generally, by a system of interacting particles. By the introduction of a shifted distance that exactly compensates for the free transport term that accrues in the spatially inhomogeneous setting, we prove in this work an inequality on the Wasserstein distance for any two measure-valued solutions to the Boltzmann-Enskog equation. As a …
Strict Lyapunov Functions And Feedback Controls For Sir Models With Quarantine And Vaccination, Hiroshi Ito, Michael Malisoff, Frederic Mazenc
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
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
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 …