deletions | additions       diff --git a/Theory.md b/Theory.md  index 3906067..0ae39c1 100644  --- a/Theory.md  +++ b/Theory.md 
...
Very short section on theory primarily referencing other papers.  - Digital Microstructure function - Basis selection for local states and FFT for space  - Homogenization (2-Point Statistics Equation)   - Workflow: Spatial Correlatiions -> Dimensionality Reduction -> Regression  - Localization (MKS equation) with consistent notation to the online documentation  - Assumptions/Boundary Conditions  - explain how they go together and in theory imporve materials design ## Microstructure Discretization  The first step in all of the MKS work-flows is to discretize the microstructures. In order to do this we introduce a probabilistic description of the microstructure using the continuous local state variable $h$, the local state space $H$ and the microstructure function $m(h, x)$. The local state space $H$ can be thought of as all of the thermodynamic state variables that are needed to uniquely define the material at a given location. The local state variable $h$ is one instance of the local state space, or one configuration of state variables. The microstructure function $m(h, x)$ is a probability density function of finding a local state $h$ at location $x$. For instance let $\mu(x)$ be a microstructure that we plan to discretize, then $\mu$ is the expectation of the microstructure function.  $$ \mu(x) = \int_H h m(h, x) dh $$  Now we will discretize the microstructure in space by averaging over small cubic domains in the microstructure function. The local state can be discretized using two methods one is to bin the microstructure using the primitive (or hat) basis $\Lambda$  $$ \frac{1}{\Delta x} \int_{H} \int_{s} \Lambda(h - l) m(h, x) dx dh = m[l, s] $$  the other is to using a spectral representation using some orthogonal basis function $\xi$  $$ \frac{1}{\Delta x} \int_{s} m(h, x) dx dt = \sum_{l=0}^{L-1} m[l, s] \xi_l (h) $$  In the notation above all of the round brackets are used to indicate continuous variables while the square brackets indicate discrete variables. The variables $s$ and $S$ represent a discrete position and the total volume, while $l$ and $L$ represent the discrete versions of $h$ and $H$. In PyMKS the Legendre polynomials are currently the only orthgonal basis functions available