Phylogenetics-Identifiability

JCNetworkParameterization is a Macaulay2 package that can find the parameterization of a given network

Documentation

To build documentation, go to M2/JCNetworkParameterization.m2, open Macaulay2, and then run the code in the section "BUILD DOCUMENTATION" at the end of the file. (This will open a browser with documentation).

Data Types

A Network N contains informations of edges, leaves, reticulation edges, and level of the network

A Model M contains information of the nuclotide sequence and transformation table for the Fourier coordinates k

Key Method Functions

Function computeParameterization of this package can be used to compute the parameterization of given network under a given model

The usage of computeParameterization is computeParameterization(M,N,includeQs), and the output is a list of polynomials as the parameterizations of the network N under the model M

includeQs is an optional input as a Boolean

• If includeQs => true then the Fourier coodinates are included in the parameterization
• If includeQs => false then the Fourier coodinates are not included in the parameterization

Function addNetworkEdges provides a faster way to construct a network

One usage of addNetworkEdges is addNetworkEdges(N,edgesToDivide,vertexInNewReticulation), and the output is a new network that has level +1

• N is a Network object, e.g. a network with edges ${e_{1,8},e_{2,7},e_{3,6},e_{4,5},e_{5,6},e_{6,7},e_{7,8},e_{5,8}}$
• edgesToDivide is a list that contains a pair of edges, e.g. {{1,8},{7,2}}
• vertexInNewReticulation is an integer representing a vertex's index, e.g. 7
• example: edges $e_{1,8}$ and $e_{2,7}$ will be subdivide to create new vertices $9$ and $10$. This will create new edges $e_{1,9},e_{8,9},e_{2,10},e_{7,10}$, and $e_{9,10}$. The edge $e_{9,10}$ will be chosen to be one of the new reticulation edges, and since vertexInNewReticulation is assigned to be $7$, the other edge in the new reticulation pair will be $e_{7,10}$

addNetworkEdges is override with another usage of addNetworkEdge(N,listOfEdgesToDivide,listOfVerticesInNewReticulation)

• listOfEdgesToDivide is a list of edges to divide in order, e.g. {{{1,8},{7,2}},{{3,6},{4,5}}}
• listOfVerticesInNewReticulation is a list of vertex indices indicating the edge in the new reticulation pairs, e.g. {7,3}

This usage of this methods is able to add multiple reticulations one by one with one call of the function

Other

OSCAR-NetworkParametrization/ -- this code not working yet

Todo

• Change "Model" datatype to name "FourierIndices", and change the "NucleotideSequence" datatype to "FourierEquivalenceClasses" (or something to this effect). Also need to change the functions getNucleotideSequence, getModel, etc.
• Update the function computeDimensionNumerically in Parameterization-Generation.m2 (add to examples, add documentation)
• change "nucleotideSeq" to "equivclass" or something in iMap
• we need to figure out why we have different dimensions in the half-ziggurat case /M2/JCNetworkParameterization/EXPERIMENTS/Paper_Examples/
• we need to rerun our computations with the new code
• add examples to documentation
• read through algorithm section in paper
• add pictures to documentation (couldn't find a way to embed this, but may be possible to add a link to the image)
• not urgent: writing tests
• add roadmap to readme.
• fix the function addEdge so that it splits edges properly when reticulations are added