This paper explores some optimization methods such as the gradient descent method, Gauss-Newton method, and stochastic gradient method. Some examples of minimizing objective functions are given to validate the theories. Then we introduce a simple example of artificial neural networks, define its structure, and apply the optimization methods to it....
Spreadsheet language programs, which include commercial spreadsheets, are among the most common form of software in use today. Unlike more "traditional" forms of software however, spreadsheet language programs are created and maintained by end-users with little or no programming experience. As a result, a high percentage of these programs contain...
Numerical model and assimilation experiments were conducted in the tropical Pacific Ocean to obtain a better understanding of the processes that control the cold tongue surface mixed layer temperature balance during August 1999 to July 2004. The numerical model was first applied to test two hypotheses (asymmetric background currents and...
Living in the Pacific Northwest, we are acutely aware of the dangers posed by wildfires. Largely due to the worsening effects of climate change, this danger is only increasing. Along with causing property and economic damage to those communities affected by wildfires, exposure to the smoke generated by wildfires can...
Aggregation equations have been used to model phenomena such as insect swarming and chemotaxis. Previous work on aggregation equations in the area of analysis applied to PDE has proven well-posedness of certain classes of aggregation equations in Lebesgue spaces. We will prove local existence of solutions in H^1 to an...
We present a theoretical free-space optical (FSO) transmitter that utilizes a dynamically steered and shaped laser beam to communicate with a randomly moving receiver adorned with a retroreflector. The transmitter tracks the receiver's position by repeatedly scanning the field of view (FOV), measuring reflections from the retroreflector, and estimating the...
In this work, we consider a convexity splitting scheme for a coupled phase field and energy equation, a modification of Stefan problem. The Stefan problem is a free boundary value problem that models the temperature in a homogeneous multiphase medium. Each phase is modeled using a heat diffusion parabolic partial...
Most of the work so far in the subfield of Gender HCI has followed a theory-driven approach. Established theories, however, do not take into account specific issues that arise in end-user debugging. We suspected that there may be important information that we were overlooking. We therefore employed a methodology change:...
Proper orthogonal decomposition (POD) in conjunction with the Galerkin projection has been used as a model reduction technique for the tractable real-time control of high-dimensional systems. While POD based model reduction may improve the tractability of high-dimensional models, the nonlinear POD based model may be impractical for control due to...
In this paper we develop an upscaling technique for non-Darcy flow in porous media. Non-Darcy model of flow applies to flow in porous media when large velocities occur. The well-posedness results for theory of quasilinear elliptic partial differential equations. To discretize the model we used lowest order Raviart-Thomas mixed finite...