The genus Mycobacteria comprises a multitude of species known to cause serious disease in humans, including Mycobacterium tuberculosis and M. leprae, the responsible agents for tuberculosis and leprosy, respectively. In addition, there is a worldwide spike in the number of infections caused by a mixed group of species such as the M. avium, M. abscessus and M. ulcerans complexes, collectively called nontuberculous mycobacteria (NTMs). The situation is forecasted to worsen because, like tuberculosis, NTMs either naturally possess or are developing high resistance against conventional antibiotics. It is, therefore, important to implement and develop models that allow us to effectively examine the fundamental questions of NTM virulence, as well as to apply them for the discovery of new and improved therapies. This literature review will focus on the known molecular mechanisms behind drug resistance in NTM and the current models that may be used to test new effective antimicrobial therapies.

Wavenumber selection in pattern forming systems remains a long standing puzzle in physics. Previous studies have shown that external noise is a possible mechanism for wavenumber selection. We conduct an extensive numerical study of the noisy stabilized Kuramoto-Sivashinsky equation. We use a fast spectral method of integration, which enables us to investigate long time behavior for large system sizes that could not be investigated by earlier work. We find that a state with a unique wavenumber has the highest probability of occurring at very long times. We also find that this state is independent of the strength of the noise and initial conditions, thus making a convincing case for the role of noise as a mechanism of state selection.

We use direct statistical simulation to find the low-order statistics of the well-known dynamical system, the Lorenz63 model. Instead of accumulating statistics from numerical simulation of the dynamical system or solving the Fokker–Planck equation for the full probability distribution of the dynamical system, we directly solve the equations of motion for the low-order statistics after closing them by making several different choices for the truncation. Fixed points of the statistics are obtained either by time evolving or by iterative methods. The stability and statistical realizability of the fixed points of the statistics are analyzed, and the statistics so obtained are compared to those found by the traditional approach. Low-order statistics of the chaotic Lorenz63 system can be obtained from cumulant expansions more efficiently than by accumulation via direct numerical simulation or by solution of the Fokker–Planck equation.