Applied Math Seminar

Academic Year 2023-2024 

Time and Place: Fridays at 3:30PM-4:30PM in the French Hall 4206

March 8, 2024

Professor Won Chang (UC)

Title: Ice model calibration using semicontinuous spatial data

Abstract: Rapid changes in Earth’s cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets. However, these models are typically subject to large parametric uncertainties, due to poorly constrained model input parameters that govern the behavior of simulated ice sheets. Computer model calibration provides a formal statistical framework to infer parameters, using observational data, and to quantify the uncertainty in projections due to the uncertainty in these parameters. Calibration of ice sheet models is often challenging because the relevant model output and observational data take the form of semicontinuous spatial data with a point mass at zero and a right-skewed continuous distribution for positive values. Current calibration approaches cannot handle such data. Here, we introduce a hierarchical latent variable model that handles binary spatial patterns and positive continuous spatial patterns as separate components. To overcome challenges due to high dimensionality, we use likelihood-based generalized principal component analysis to impose low-dimensional structures on the latent variables for spatial dependence. We apply our methodology to calibrate a physical model for the Antarctic ice sheet and demonstrate that we can overcome the aforementioned modeling and computational challenges. As a result of our calibration, we obtain improved future ice-volume change projections.

March 29, 2024

Professor Sabrina Sreipert (University of Pittsburgh)

TBA

April 5, 2024

Professor Tongli Zhang (UCCOM)

TBA

April 12, 2024

Professor Deniz Bilman (UC)

TBA

Aprile 19, 2024

Professor Donald French (UC)

TBA

September 1, 2023: App Math Seminar 

Prof. Greg Buzzard (Purdue University)

Title: Plug-and-Play Unplugged:  Implicit Priors in Inverse Imaging

Abstract: Image estimation problems arise in many fields such as X-ray CT scanning, ultrasound imaging, laser range finding, etc. The Bayesian approach to such problems describes them in terms of a sum of two cost functions, a forward model that promotes a good fit to data and a prior model that promotes images that aren’t excessively noisy. However, this cost function approach is inherently limited and precludes the use of neural networks and other implicitly encoded prior information. Until recently, Bayesian image estimation was also focused on finding a single "best" result rather than sampling from the set of likely results.  

In this talk I’ll describe the Plug-and-Play method, which extends Bayesian methods to incorporate implicit prior information like neural networks and give examples of Generative Plug-and-Play to sample from a distribution.  I'll also describe Multi-Agent Consensus Equilibrium (MACE), which generalizes the idea of optimization to explain the formulation behind Plug-and-Play.

September 15, 2023: MathBio Journal Club  

Graduate Student: Lora Newman

Article:  Gao et al, A mathematical model to assess the impact of testing and isolation compliance on the transmission of COVID-19, Infect. Dis. Model. 8(2):427-444 (2023) 

(https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10116127/)

September 22, 2023: App Math Seminar: Cancelled 

September 28 (Thur), 2023: Colloquium (4-5pm. Room 220, 60W Charlton)

Prof. Adrian Lam (Ohio State University)

Title: The nonlocal selection of spreading speed in shifting environments

October 13, 2023: App Math Seminar 

Assistant Prof. Sameh Eisa (Aerospace Engineering and Engineering Mechanics Department, UC)

Title: The use of differential geometric and extremum seeking methods to decode and emulate in real-time the optimized flight of soaring birds

Abstract: In this seminar, we explain further and, in more detail, our recent radical results in decoding the flight physics of soaring birds, which have been highlighted in the news by the Society for Industrial and Applied Mathematics (SIAM): https://sinews.siam.org/Details-Page/albatross-optimized-flight-physics-a-natural-extremum-seeking-system. The mystery of soaring birds, such as albatrosses and eagles, has intrigued biologists, physicists, aeronautical/control engineers, and applied mathematicians for centuries. These fascinating avian organisms are able to fly for long durations while expending little to no energy, utilizing wind to gain lift. This flight technique/maneuver is called dynamic soaring (DS). For biologists and physicists, the DS phenomenon is nothing but a wonder of the very elegant ability of these birds to interact with nature and use its physical ether in an optimal way for better survival and energy efficiency. For the engineering community, the DS phenomenon is a source of inspiration and an unequivocal opportunity for biomimicking. Mathematical characterization of the DS phenomenon in the literature has been limited to optimal control configurations that utilized developments in numerical optimization algorithms along with control methods to identify the optimal DS trajectory taken (or to be taken) by the bird/mimicking system. Unfortunately, all of these methods are highly complex and non-real-time. Hence, the mathematical characterization of the DS problem, we believe, appears to be at odds with the phenomenon/behavior. In this paper, we provide a novel two-layered mathematical approach to characterize, model, mimic, and control DS in a simple real-time implementation, which we believe more effectively decodes the biological behavior of soaring birds. First, we present a differential geometric control formulation and analysis of the DS problem, which allow us to introduce a control system that is simple yet controllable. Second, we establish a link between the DS philosophy and a class of dynamical control systems known as extremum seeking systems. This linkage provides the control input that makes DS a real-time reality. We believe our framework accurately describes the biological behavior of soaring birds and opens the door for geometric control theory and extremum seeking systems to be utilized in biological systems and natural phenomena. Simulation results are provided along with comparisons to powerful optimal control solvers, illustrating the advantages of the introduced method.

October 20, 2023: MathBio Journal Club  

Graduate Student: Jenny Niemantsverdriet

Article: Yao et al, Mathematical analysis of robustness of oscillations in models of the mammalian circadian clock, PLoS Comput biol 18(3):e1008340 (2022)

(https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008340)

October 27, 2023: App Math Seminar 

Prof. Wanda Strychalski (Case Western University)

Title: Computational modeling of adhesion-independent confined cell migration 

Abstract: Cell migration is critical for many vital processes, such as embryogenesis and tissue repair, as well as harmful processes, such as cancer cell metastasis. Recent experiments highlight the diversity in migration strategies employed by cells in physiologically relevant environments. In 3D fibrous matrices and confinement between two surfaces, some cells migrate using round membrane protrusions, called blebs. In bleb-based migration, the role of substrate adhesion is thought to be minimal, and it remains unclear if a cell can migrate without any adhesion complexes. We present a 2D computational fluid-structure model of a cell using cycles of bleb expansion and retraction in a channel with several geometries. The cell model consists of a plasma membrane, an underlying actin cortex, and viscous cytoplasm. Cellular structures are immersed in viscous fluid which permeates them, and the fluid equations are solved using the method of regularized Stokeslets. Simulations show that the cell cannot effectively migrate when the actin cortex is modeled as a purely elastic material. We find that cells are able to migrate in rigid channels if actin turnover is included with a viscoelastic description for the cortex. Results also show that even with actin turnover, a cell can become lodged when the channel geometry height varies. Our study highlights the non-trivial relationship between cell rheology and its external environment during migration with cytoplasmic streaming.

November 3, 2023: MathBio Journal Club  

Graduate Student: Kevin Schmitt

F. Ihlenburg et al. Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM

https://www.sciencedirect.com/science/article/pii/089812219500144N

November 17, 2023: App Math Seminar 

Prof. Don French (UC)

Title: A Partial Differential Equation reinterpretation of Scheling's Model of Segregation

Abstract: TBA

December 1, 2023: App Math Seminar 

Prof. Chris Hong (Pharmacology & Systems Biology, UC)

Title: Interconnected network of circadian rhythms, cell cycle, and DNA damage response

Abstract: 

Circadian rhythms coordinate temporal organization of cellular processes including cell cycle and DNA damage response (DDR) optimizing fitness and survival of organisms. Previously, it was demonstrated that DNA damage resets circadian rhythms in Neurosora crassa via DNA damage-activated checkpoint kinase, PRD-4, triggering phosphorylation and degradation of the core negative element, FRQ. It was also shown that the expression of prd-4 is clock-controlled. However, detailed mechanisms regulating this bidirectional link remain largely unknown. In this work, we utilized mathematical modeling and experimental validations investigating interconnected networks of circadian rhythms, DNA damage response (DDR), and cell cycle where the circadian clock coordinates short- and long-term responses of DDR and cell cycle.