Quantum information and computation is an active area of research in physics, computer science, and electrical engineering. The mathematical model of game theory is applied to quantum systems for better computation. We explore basic game theory, coordinatization of quantum states, the difference between quantized games and gaming the quantum and how the ideas of quantized games are utilized in quantum information theory.

Precision oncology aims to improve outcomes in cancer patients by targeting therapies to the specific genetic background of each patient. In my PhD work at OHSU, I’m using data obtained from large screening experiments that measure the growth of cancer cell lines in the presence of various drugs at several doses. This response data is stored as a three-dimensional tensor (cell lines × drugs × doses), which is decomposed into latent factor matrices for each dimension and linked to predictors via sparse projection matrices. Values in these latent and projection matrices are inferred using a Bayesian statistical inference technique called variational inference. The trained model highlights relationships present in the data and can be used to predict responses for new cell lines and drugs.

Partial differential equations (PDE) arise in virtually every description of physical phenomena and enjoy widespread applications to engineering and physics! It is of great interest to researchers in applied mathematics and engineering to find novel techniques for approximating the solutions to these equations numerically using a computer. One recent method involves the use of the SBP finite difference operators. Both the motivation for and the implementation of this method for the solution of commonly encountered PDE, such as the heat equation and wave equation, will be discussed along with an introduction to the concepts of well-posedness, numerical stability, and weak enforcement of boundary conditions. Only a background in calculus and linear algebra is assumed.

Modeling fluid-solid interactions is important in diverse fields. It aids in studying: brain aneurysms, the stresses on airplane wings, subduction zone tsunamis, and volcanic eruptions. We want to model this interaction by coupling fluid equations to a solid. To model the fluid, we solve the linearized Euler equations, which are a set of hyperbolic PDEs that represent conservation of mass, and balance of momentum and energy.

We will discuss one numerical method to solve the linearized Euler equations. Boundary conditions that make this a well-posed problem will be derived using the energy method and then the problem will be solved numerically.

There will be some discussion of future directions woven through the talk. Only a background in calculus and basic linear algebra will be needed.