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Full-Text Articles in Mathematics
A Stochastic Model For Microbial Fermentation Process Under Gaussian White Noise Environment, Yanping Ma
A Stochastic Model For Microbial Fermentation Process Under Gaussian White Noise Environment, Yanping Ma
Mathematics Faculty Works
In this paper, we propose a stochastic model for the microbial fermentation process under the framework of white noise analysis, where Gaussian white noises are used to model the environmental noises and the specific growth rate is driven by Gaussian white noises. In order to keep the regularity of the terminal time, the adjustment factors are added in the volatility coefficients of the stochastic model. Then we prove some fundamental properties of the stochastic model: the regularity of the terminal time, the existence and uniqueness of a solution and the continuous dependence of the solution on the initial values.
Solving The Ko Labyrinth, Alissa Crans, Robert J. Rovetti
Solving The Ko Labyrinth, Alissa Crans, Robert J. Rovetti
Mathematics Faculty Works
The KO Labyrinth is a colorful spherical puzzle with 26 chambers, some of which can be connected via holes through which a small ball can pass when the chambers are aligned correctly. The puzzle can be realigned by performing physical rotations of the sphere in the same way one manipulates a Rubik’s Cube, which alters the configuration of the puzzle. The goal is to navigate the ball from the entrance chamber to the exit chamber. We find the shortest path through the puzzle using Dijkstra’s algorithm and explore questions related to connectivity of puzzle with the adjacency matrix, distance matrix, …
The Forbidden Number Of A Knot, Alissa S. Crans, Blake Mellor, Sandy Ganzell
The Forbidden Number Of A Knot, Alissa S. Crans, Blake Mellor, Sandy Ganzell
Mathematics Faculty Works
Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbid- den number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.
Enhanced Lasso Recovery On Graph, Xavier Bresson, Thomas Laurent, James Von Brecht
Enhanced Lasso Recovery On Graph, Xavier Bresson, Thomas Laurent, James Von Brecht
Mathematics Faculty Works
This work aims at recovering signals that are sparse on graphs. Compressed sensing offers techniques for signal recovery from a few linear measurements and graph Fourier analysis provides a signal representation on graph. In this paper, we leverage these two frameworks to introduce a new Lasso recovery algorithm on graphs. More precisely, we present a non-convex, non-smooth algorithm that outperforms the standard convex Lasso technique. We carry out numerical experiments on three benchmark graph datasets.