(a.k.a. mathematical methods you were never taught) Find below collected wisdom from 4+2 years of attempting problem sets.

FOLLOW THIS OFFICIAL INSTRUCTION TO SWITCH FROM PANDOC TO LATEXML BACKEND. Now I have a conditional equation: $$ {{\partial \Phi } \over {\partial {X_{}}}} = - 78.9 {X_{}} < 0.34,\\ - 628.3 {X_{}} \ge 0.34 $$ Can this equation be displayed correctly in LaTeXML? I also want to reference Eq. ([eq:comp]). INTERESTING. IN AN EQUATION, IF I PLACE “\%" INSIDE “", IT’S STILL “\%", I.E., I CANNOT GET RID OF THE ANTI-BACKLASH! Directional quotation mark: “one" and “two".

Noise induced excitability is studied in type I and II Morris--Lecar neurons subject to constant sub threshold input, where fluctuations arise from sodium and potassium ion channels. Ion channels open and close randomly, creating current fluctuations that can induce spontaneous firing of action potentials. Both noise sources are assumed to be weak so that spontaneous action potentials occur on a longer timescale than ion channel fluctuations. Asymptotic approximations of the stationary density function and most probable paths are developed to understand the role of channel noise in spontaneous excitability. Even though the deterministic dynamical behavior of type I and II action potentials differ, results show that a single mechanism explains how ion channel noise generates spontaneous action potentials.