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# Archive: Applied Mathematics and Mathematical Medicine and Biology Seminar

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 Dr. Pavol Bokes, Department of Applied Mathematics and Statistics, Comenius University, Slovakia Dr. Pavol Bokes, Department of Applied Mathematics and Statistics, Comenius University, Slovakia EWG336 Title: Controlling gene-expression noise with negative feedback in burst size

Abstract: Burst-like synthesis of protein is a significant source of cell-to-cell variability in protein levels. Negative feedback is a common example of a regulatory mechanism by which such stochasticity can be controlled. Here we consider a specific kind of negative feedback, which makes bursts smaller in the excess of protein. Increasing the strength of the feedback may lead to dramatically different outcomes depending on a key parameter, the noise load, which is defined as the squared coefficient of variation the protein exhibits in the absence of feedback. Combining stochastic simulation with asymptotic analysis, we identify a critical value of noise load: for noise loads smaller than critical, the coefficient of variation remains bounded with increasing feedback strength; contrastingly, if the noise load is larger than critical, the coefficient of variation diverges to infinity in the limit of ever greater feedback strengths. Interestingly, feedbacks with lower cooperativities have higher critical noise loads, suggesting that they can be preferable for controlling noisy proteins. 10/4/2018 7:30:00 PM 10/4/2018 8:30:00 PM False Shawn Walker, Department of Mathematics, Louisiana State University Shawn Walker, Department of Mathematics, Louisiana State University Ewing 336 Conference Room Title: A Numerical Scheme for the Generalized Ericksen Model of Liquid Crystals, With Applications to Virus DNA Packing

Abstract: We consider the generalized Ericksen model of liquid crystals, which is an energy with 8 independent elastic'' constants that depends on two order parameters $\mathbf{n}$ (director) and $s$ (variable degree of orientation). In addition, we present a new finite element discretization for this energy, that can handle the degenerate elliptic part without regularization, is stable and it $\Gamma$-converges to the continuous energy. Moreover, it does not require the mesh to be weakly acute (which was an important assumption in our previous work). A minimization scheme for computing discrete minimizers will also be discussed. Furthermore, we include other effects such as weak anchoring (normal and tangential), as well as fully coupled electro-statics with flexo-electric and order-electric effects. We also present several simulations (in 2-D and 3-D) illustrating the effects of the different elastic constants and electric field parameters. Lastly, we show how this model can be used to simulate the packing of DNA inside viral capsids. This part is joint with Carme Calderer (UMN). 9/10/2018 3:15:00 PM 9/10/2018 4:15:00 PM False Dr. Ben Bagozzi, UD Department of Political Science Pt. II Dr. Ben Bagozzi, UD Department of Political Science Pt. II Ewing 336 Title: Modeling Political Event Data: Opportunities and Challenges Part II

Abstract: Political event data measure "who did what to whom (and where/when)" for a wide number of actors (e.g., diplomats, police, military members, civilians, or NGOs) and actions (e.g., verbal threats, expressions of intents to cooperate, bombings, or atrocities). These data are typically machine coded from international newswires reports, and now encompass millions of (daily, geo-located) events arising both between and within all countries of the world. This talk will introduce political event data, their structure, and their most common uses. The talk will then detail a series of methodological challenges that arise in efforts to model and predict political event data. Here, special attention will be given to the (spatio-temporal and network) structure of event data, the inherent rarity of most events of interest (e.g., political violence), underlying measurement error issues, and the discrete (mixture) properties of many commonly analyzed event data variables. A selection of proposed modeling solutions to these challenges will then be presented in finer detail. 4/25/2018 3:15:00 PM 4/25/2018 4:15:00 PM False Seth Cowall, Dept of Mathematical Sciences, UD Seth Cowall, Dept of Mathematical Sciences, UD Ewing 336 Title: Data-Driven Modeling of Phytoplankton Blooms in the Ocean

Abstract: Phytoplankton are the base of the marine food web. They are also responsible for almost half of the oxygen we breathe and they remove carbon dioxide from the atmosphere. A macroscale plankton ecology model is constructed consisting of coupled, nonlinear reaction-diffusion equations with spatially and temporally changing coefficients. An example of an NPZ model, this model simulates biological interactions between nutrients, phytoplankton and zooplankton. It also incorporates seasonally varying, physically driven forces that affect the phytoplankton growth: solar radiation and depth of the ocean’s upper mixed layer. The model’s predictions are dependent on the parametric functional behavior of the model. The model is analyzed using seasonal oceanic data with the goals of understanding the model’s dependence on its parameters and of understanding seasonal changes in plankton biomass. The model is tested on different regions of the world’s oceans so that appropriate choices can be made for parameters that correspond to physical/biological quantities in those regions. A study of varying parameter values and the resulting effects on the solutions, stability, and the timing of blooms is carried out. This modeling effort can be helpful for understanding the ecological structure of plankton communities and the timing of seasonal phytoplankton blooms, which are debated topics in oceanography. 4/18/2018 3:15:00 PM 4/18/2018 4:15:00 PM False

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