Browsing Applied mathematics by Subject "Mathematics"
Now showing items 16 of 6

Closing the Loop: Optimal Stimulation of Neuronal Networks via Adaptive Control Algorithms
The Caenorhabditis elegans (C. elegans) worm is a wellstudied biological organism model. The nervous system of C. elegans is particularly appealing to study, since it is a tractable fully functional neuronal network for ... 
Interface Problems using the Fokas Method
Interface problems for partial differential equations are initial boundary value problems for which the solution of an equation in one domain prescribes boundary conditions for the equations in adjacent domains. These ... 
RiemannHilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions
(20131114)The computation of special functions has important implications throughout engineering and the physical sciences. Nonlinear special functions include the solutions of integrable partial differential equations and the ... 
Some BoundaryValue Problems for Water Waves
(20120913)Euler's equations describe the evolution of waves on the surface of an ideal incompressible fluid. In this dissertation, I discuss some boundaryvalue problems associated with Euler's equations. My approach is motivated ... 
Stochastic Dynamics: Markov Chains, Random Transformations and Applications
Stochastic dynamical systems, as a rapidly growing area in applied mathematics, has been a successful modeling framework for biology, chemistry and data science. Depending upon the origin of uncertainties in an application ... 
This Brain Is a Mess: Inference, Random Graphs, and Biophysics to Disentangle Neuronal Networks
At first glance, the neuronal network seems like a tangled web in many areas throughout the nervous system. Often, our best guess is that such “messy” connections are close to random, while obeying certain statistical ...