Small refactor of engine #5. Typos in #4

README.md

@@ -1,7 +1,7 @@
 von Foerster Hazards
 ====================
 
-In this project I implement a model of age dependent communicable diseases using a mysterious and magical alchemy of von Foerster dynamics, Gompertz processes - biologically endogenous ageing modeled by Poisson processes subordinated by integrated geometric Brownian motion, Makeham processes - biologically exogenous casualties of serialized interactions, accelerated failure time models, and phase type distributions, while incanting the theory of stochastic processes and their infinitesimal generators: the all mighty hazard rate.
+In this project I implement a model of age dependent communicable diseases using a mysterious and magical alchemy of von Foerster dynamics, Gompertz processes - biologically endogenous ageing modeled by Poisson processes subordinated by integrated geometric Brownian motion, Makeham processes - biologically exogenous casualties of serialized interactions, accelerated failure time models, phase type distributions, and the Lie algebra of hazard rates, while incanting the theory of stochastic processes.
 
 Citing
 ------

docs/GompertzProcesses.tex

@@ -277,7 +277,7 @@
 
   \section{Hazard Rate}
   Consider the first passage stopping time $T_1$ of the Gompertz process $G_t$, its 
-  cumulative distribution is the characteristic functions of $Y_t$:
+  cumulative distribution is the characteristic function of $Y_t$:
   \begin{IEEEeqnarray}{rCl}
     \operatorname{\mathbb{P}}\left[ T_1 \ge t\right]
     & = &
@@ -327,7 +327,7 @@
     & $h = \lambda$ &
     $\displaystyle\left[\frac{\partial}{\partial\mu}\cdot + \frac{\partial}{\partial\sigma}\cdot\right]\left(f_{\mu, \sigma}\left( \lambda \operatorname{\mathbb{E}}\left[Y_t\right] \right)\right)$\\\\
     $\sigma = 0$
-    & $h = \lambda \mu e^{\mu t}$ &
+    & $h = \lambda e^{\mu t}$ &
     $\displaystyle\frac{\partial}{\partial\sigma} f_{\mu, \sigma}\left( \lambda \operatorname{\mathbb{E}}\left[Y_t\right] \right)$\\\\
   \end{longtable}
 \end{document}

src/vonFoersterHazards.ipynb

@@ -923,7 +923,7 @@
     "\\end{array}\n",
     "$$\n",
     "\n",
-    "Likewise, early in advancing the cutoff the logarithm will be constant. To determine $c_t$ we then simply need to read off the graph of the cumulative effectively available population $F\\left(c_t\\right)$ the point at which the following solution holds:\n",
+    "Likewise, $\\hat{\\omega}$ can be roughly estimated as the ratio of the entire population to those not currently infected. To determine $c_t$ we then simply need to read off the graph of the cumulative effectively available population $F\\left(c_t\\right)$ the point at which the following solution holds:\n",
     "\n",
     "$$\n",
     "\\begin{array}{rcl}\n",

src/vonFoersterHazards.jl

@@ -59,10 +59,10 @@ function Base.iterate(E::evolve, step::Int64)
     else
 
         # One time computation of the extensize birth rate
-        b = birthrate(E.ages, E.population)
+        b = birthrate(E)
 
         # One time computation of the extensive hazard rate
-        H = hazardrate(E.ages, E.population)
+        H = hazardrate(E)
 
         # Curried transition function
         t(a, n) = conservesum!(randomtruncate.(exp(-E.size * hazardrate(a, H)) * n), sum(n))
@@ -74,7 +74,7 @@ function Base.iterate(E::evolve, step::Int64)
 
         # Youngest cohort is less than 1 year old, add births to youngest cohort
         if E.ages[end] < 1.0 then
-            @inbounds E.population[end] = E.population[end] + b
+            E.population[end] = E.population[end] + b
 
         # Youngest cohort is more than 1 year old, generate a new youngest cohort
         else
@@ -86,20 +86,20 @@ function Base.iterate(E::evolve, step::Int64)
 end
 
 """
-    birthrate(a, n)
+    birthrate(E)
 
 Stub function to be overloaded in implementation. Compute the extensive
-birth rate vector from the ages a and occupancy n of the population.
+birth rate vector from the population E.
 """
-function birthrate(a::AbstractVector{Float64}, n::AbstractVector{T})::T where T<:AbstractVector{Int64} end
+function birthrate(E::evolve)::T where T<:AbstractVector{Int64} end
 
 """
-    hazardrate(a, n)
+    hazardrate(E)
 
 Stub function to be overloaded in implementation. Compute the extensive
-hazard rate matrix from the ages a and occupancy n of the population.
+hazard rate matrix from the population E.
 """
-function hazardrate(a::AbstractVector{Float64}, n::AbstractVector{T} where T<:AbstractVector{Int64})::AbstractMatrix{Float64} end
+function hazardrate(E::evolve)::T where T<:AbstractMatrix{Float64} end
 
 """
     hazardrate(a, H)