This Week in Mathematics


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Today:

Colloquium Tea
Time: 3:00 pm Room: 204 LOV

Machine Learning Seminar [url]
StyleGAN-www.thispersondoesnotexist.com
- Emmanuel Hartman, FSU
Time: 1:25pm Room: LOV 102

Mathematics Colloquium [url]
Building, Analyzing and Calibrating Multi-Scale Models in 2D and 3D: Tuberculosis as a Case Study
- Denise Kirschner, University of Michigan
Time: 3:35 Room: Lov 101
Abstract/Desc: Multi-scale models (MSM) are increasingly being used to study complex biological processes. Multi-scale models span a range of both spatial and temporal scales and can also encompass multiple physiological compartments. MSMs are growing more complex and cumbersome and it is necessary to coarse grain model aspects when appropriate. A new approach that we call tuneable resolution can provide that flexibility. Tuneable resolution involves fine- or coarse-graining existing multi-scale models at the user’s discretion, allowing adjustment of the level of resolution specific to a question, an experiment, or a scale of interest. Tuneable resolution expands options for revising and validating mechanistic multi-scale models, can extend the longevity of multi-scale models, and may increase computational efficiency. The tuneable resolution approach can be applied to many model types, including differential equation, agent-based, and hybrid models and can be automated. Additionally, analyses of MSMs can be difficult, and we have fine-tuned a global uncertainty and sensitivity analysis approach that can be applied to all MSM types performing both inter- and intra-scale analyses. Finally, we have been exploring optimization, for example of drug treatment regimens, in the context of MSMs and have identified protocols that are computationally efficient.

Entries for this week: 7

Wednesday February 19, 2020

Departmental Tea Time
C is for cookie, and shorthand for C[0,1] w/the sup norm
Time: 3: Room: 204 LOV

Geometry, Topology and Data
Asymptotic expansion of the heat kernel on Riemannian manifold
- Haibin Hang, FSU
Time: 3:35 pm Room: 102 LOV

Thursday February 20, 2020

Financial Mathematics Seminar [url]
Delivering Multi-Specialty Care via Online Telemedicine Platforms
- Lingjiong Zhu, Florida State University
Time: 3:35pm-4:25pm Room: LOV 201
Abstract/Desc: The online telemedicine platforms represent a rapidly growing segment of healthcare delivery markets. In this paper, we develop a model of telemedicine platform operations that focuses on managing multi-specialty online-based care in the presence of general/specialty demand interaction. While such demand interaction is common in practice, its impact on platform and physician decisions has not received sufficient attention in the operations literature. Our paper focuses on providing guidance on managing multi-specialty telemedicine platforms. We formulate a queueing model of online service with multiple interacting demand and supply types. In our model, the platform sets the patient fees and physician compensation levels, and physicians, anticipating equilibrium patient demand response, follow by deciding whether to join the platform, and how much of their capacity to allocate to the platform. We derive closed-form expressions for the optimal physician and platform policies in the presence of demand interaction between the general and specialist demand streams. Moreover, we quantify the impact of policies that explicitly account for demand interaction on the platform profitability. Our analysis describes optimal management policies for multi-specialty telemedicine platforms and provides a foundation for the study of the role of telemedicine platforms within broader patient-centric healthcare ecosystems. This is based on the joint work with Sergei Savin and Yuqian Xu.

Algebra and Its Applications
The modular number, congruence number, and multiplicity one
- Amod Agashe, Florida State University
Time: 3:35pm Room: LOV 104
Abstract/Desc: The modular number and congruence number are certain invariants associated to modular abelian varieties (e.g., elliptic curves), and in joint work with K. Ribet, we proved a relation between them. Multiplicity one is a technical condition in Arithmetic geometry that came up in our work. In two talks, I plan to discuss as much of our work as possible. In the first talk, I shall go over the background material needed, define all the terms that we shall need, and state some results. In the second talk, I shall give the proofs of some of these results.

Friday February 21, 2020

Colloquium Tea
Time: 3:00 pm Room: 204 LOV

Machine Learning Seminar [url]
StyleGAN-www.thispersondoesnotexist.com
- Emmanuel Hartman, FSU
Time: 1:25pm Room: LOV 102

Mathematics Colloquium [url]
Building, Analyzing and Calibrating Multi-Scale Models in 2D and 3D: Tuberculosis as a Case Study
- Denise Kirschner, University of Michigan
Time: 3:35 Room: Lov 101
Abstract/Desc: Multi-scale models (MSM) are increasingly being used to study complex biological processes. Multi-scale models span a range of both spatial and temporal scales and can also encompass multiple physiological compartments. MSMs are growing more complex and cumbersome and it is necessary to coarse grain model aspects when appropriate. A new approach that we call tuneable resolution can provide that flexibility. Tuneable resolution involves fine- or coarse-graining existing multi-scale models at the user’s discretion, allowing adjustment of the level of resolution specific to a question, an experiment, or a scale of interest. Tuneable resolution expands options for revising and validating mechanistic multi-scale models, can extend the longevity of multi-scale models, and may increase computational efficiency. The tuneable resolution approach can be applied to many model types, including differential equation, agent-based, and hybrid models and can be automated. Additionally, analyses of MSMs can be difficult, and we have fine-tuned a global uncertainty and sensitivity analysis approach that can be applied to all MSM types performing both inter- and intra-scale analyses. Finally, we have been exploring optimization, for example of drug treatment regimens, in the context of MSMs and have identified protocols that are computationally efficient.

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Department of Mathematics

This Week in Mathematics