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Archive : Applied Mathematics and Mathematical Medicine and Biology Seminar

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Giovanna Guidoboni, University of MissouriGiovanna Guidoboni, University of MissouriEWG336Title: Physically-based modeling for a virtual laboratory in Science and Engineering: theory and applications<br><br> Description: Physically-based models combine fundamental principles of physics, engineering, mathematics and scientific computing to provide qualitative and quantitative assessments of the mechanisms governing the behavior of complex systems. The utilization of physically-based models to study living systems helps disentangle the interaction among coexisting (often competing) factors that is not possible to single out in experimental and clinical studies. Thus, physically-based models can serve as a virtual laboratory where multiple scenarios can be simulated, conjectures can be tested and new hypotheses can be formulated. This talk will present two particular applications of physically-based models. The first application aims at characterizing changes in ocular hemodynamics due to alterations in intraocular pressure (IOP), blood pressure (BP) and vascular autoregulation (AR) of each individual. The knowledge on interacting factors gained via physically-based models can also be used as a guide for the statistical analysis of clinical data for more informative outcomes, as shown by the Singapore Epidemiology of Eye Diseases study, where our theoretical predictions on the interplay between IOP and BP have been confirmed on nearly 10,000 people. The second, more recent, application aims at elucidating the cardiovascular mechanisms giving rise to the ballistocardiogram (BCG). BCG is a signal generated by the repetitive motion of the human body due to sudden ejection of blood into the great vessels with each heartbeat. Main cardiovascular diseases, such as hypertension and congestive heart failure, have been shown to alter the BCG signal, which then yields a great potential for passive, noncontact monitoring of the cardiovascular status (e.g. through sensors positioned under the bed or on an armchair). Our work aims at standardizing BCG measurements in order to achieve a consistent clinical interpretation of the BCG signal across sensing devices. Interestingly, the need to address specific questions arising in the applied sciences calls for the theoretical study of new mathematical problems and computational methods. Examples discussed in this talk include: (i) well-posedness of partial differential equations of mixed parabolic/elliptic type with nonhomogeneous boundary conditions utilized to describe the perfusion of deformable tissues; and the (ii) energy-preserving numerical algorithms based on operator splitting to simulate multiscale problems. 12/3/2019 8:30:00 PM12/3/2019 9:30:00 PMFalse
Shawn Walker, Louisiana State UniversityShawn Walker, Louisiana State UniversityEWG336Title: The Uniaxially Constrained Q-tensor Model for Nematic Liquid Crystals<br><br> Abstract: We consider the one-constant Landau-de Gennes (LdG) model for nematic liquid crystals with traceless tensor field Q as the order parameter that seeks to minimize a Dirichlet energy plus a double well potential that confines the eigenvalues of Q (examples/applications will be described). Moreover, we constrain Q to be uniaxial, which involves a rank-1 constraint. Building on similarities with the one-constant Ericksen energy, we propose a structure-preserving finite element method for the computation of equilibrium configurations. We prove stability and consistency of the method without regularization, and $\Gamma$-convergence of the discrete energies towards the continuous one as the mesh size goes to zero. We also give a monotone gradient flow scheme to find minimizers. We illustrate the method's capabilities with several numerical simulations in two and three dimensions including non-orientable line fields. In addition, we do a direct comparison between the standard LdG model, and the uniaxially constrained model.11/19/2019 8:30:00 PM11/19/2019 9:30:00 PMFalse
Daniela Egas, EPFLDaniela Egas, EPFLEWG336Title: Topology and neuroscience<br><br> Abstract: I will broadly present some of the applications of topology and topological data analysis to neuroscience through an exploration of the collaboration between the applied topology group at EPFL and the Blue Brain Project. In particular, I will describe how we are using topology to further understand brain architectures, learning and neuroimaging techniques. 11/18/2019 8:30:00 PM11/18/2019 9:30:00 PMFalse
Shailesh ShahShailesh ShahEWG336Title: A Mathematician’s Journey </br></br> Abstract: I will provide a personal account of a forty year non-academic career spanning from mathematical modeling in a gas utility to risk modeling and management in global financial institutions. The talk will describe the transition from academia to industrial R&D to providing decision support for senior management, and discuss leveraging technical skills and building new "soft" skills to succeed in Business. Using select examples from industry (Demand Forecasting and Network Simulation) and Finance (Risk and Capital), I will provide insight into how mathematical models and related techniques such as scenario analysis and stress testing are used to guide decision making. In particular, I will touch upon their advantages, limitations and related challenges in data, models, systems and operational complexity - particularly focusing on the Great Financial Crisis and its aftermath. 11/5/2019 8:30:00 PM11/5/2019 9:30:00 PMFalse

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  • Department of Mathematical Sciences
  • University of Delaware
  • 501 Ewing Hall
  • Newark, DE 19716, USA
  • Phone: 302-831-2653