Types

struct ConstantRateBranchingProblem{P<:SciMLBase.AbstractDEProblem, L<:(UnivariateDistribution), O<:Union{Integer, DiscreteUnivariateDistribution, UnivariateDistribution{Discrete}, DiscreteDistribution{Univariate}}} <: BranchingProcesses.BranchingProblem

A structure to define a branching stochastic process with constant branching rate.

Fields

• prob: The SDE or jump process problem defining the single-particle dynamics of the branching process, an instance of SciMLBase.AbstractSDEProblem or SciMLBase.AbstractJumpProblem.

• lifetime: The lifetime distribution of the process, which must be a discrete or continuous univariate distribution with positive support.

• nchild: The number of children to be created for each particle, which can be a non-negative integer or a discrete distribution with non-negative support from which the number of children is sampled.

• ndim: Spatial dimension for the tissue growth algorithm (0 = no spatial, 1 = line, 2 = plane, 3 = 3D space). When set to 1, 2, or 3, spatial positions are assigned to all BranchingProcessNodes after calling solve.

struct BranchingProcessSolution{P<:BranchingProcesses.BranchingProblem, T<:SciMLBase.AbstractSciMLSolution}

A complete solution of a branching stochastic process, containing both the problem definition and the resulting tree structure.

Fields

• prob: The branching problem that was solved.

• tree: The root node of the solution tree.

• alg: Algorithm used to solve the problem (optional).

• retcode: Return code indicating success/failure.

• stats: Additional statistics or metadata (optional).

mutable struct BranchingProcessNode{T<:SciMLBase.AbstractSciMLSolution}

A tree node structure to hold individual particle solutions in a branching process.

Fields

• sol: The solution of the particle associated to this node.

• children: A vector of child nodes representing offspring particles.

• position: Spatial grid position of this particle, assigned by tissue_growth!. nothing if no spatial algorithm has been run. Stores the final position after all divisions have been processed; use tissue_position to query the position at a specific time.

• position_history: Time-indexed position history recorded by tissue_growth!. Each entry is a (time, position) pair; entries are sorted in ascending time order. nothing if tissue_growth! has not been run. Use tissue_position to query the position at a specific time.

AbstractTrees.children(node::BranchingProcessNode)

Return the children of a BranchingProcessNode.

AbstractTrees.nodevalue(node::BranchingProcessNode)

Return the value of a BranchingProcessNode, defined as its final state value.

struct ReducedBranchingProcessSolution{T, N, uType, tType, P, A, IType, TransType, RedType, OrigType, PType, SysType, NpType, CombType, NeutType} <: RecursiveArrayTools.AbstractDiffEqArray{T, N, uType}

A solution type for the output of reduce_tree. Contains the reduced time series from a branching process tree where values of all particles alive at each time point have been combined using a reduction function.

This type is a subtype of RecursiveArrayTools.AbstractDiffEqArray, which provides standard indexing, iteration, and time-series interface compatible with SciMLBase.EnsembleAnalysis.

Fields

• u: The reduced values at each time point.

• t: The time points.

• prob: The original branching problem (optional).

• alg: Algorithm information (optional).

• dense: Whether dense output is available.

• interp: Interpolation object.

• tslocation: Time series location.

• retcode: Return code.

• transform: Transformation function applied to particle values before reduction.

• reduction: Reduction method used to combine particle values ("sum", "prod", or custom function).

• original_solution: Original BranchingProcessSolution that was reduced (optional).

• p: Parameters (unused; included for RecursiveArrayTools.AbstractDiffEqArray compatibility).

• sys: Symbolic system (unused; included for RecursiveArrayTools.AbstractDiffEqArray compatibility).

• nparticles: Number of particles alive at each time point (computed during solveandreduce).

• combine: Incremental binary combine function used during on-the-fly reduction (computed during solveandreduce).

• neutral_fn: Factory function returning the neutral element for the reduction (computed during solveandreduce).

struct BootstrappedTimeSeriesSolution{T, N, uType, tType, LowerType, UpperType, StatType, SamplingType, ConfIntType} <: RecursiveArrayTools.AbstractDiffEqArray{T, N, uType}

A summary type for bootstrapped time series statistics.

Fields

• u: Bootstrapped expected values at each time point.

• t: The time points.

• lower: Lower confidence bounds at each time point.

• upper: Upper confidence bounds at each time point.

• statistic: Statistic summarized by the bootstrap output.

• sampling: Bootstrap resampling method used.

• confint_method: Confidence-interval method used.