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Infers the maximum growth rate from time-series absorbance data using non-parametric spline smoothing with cross-validation.

Method

Unlike parametric models (e.g., logistic curves), this approach:

• Makes no assumptions about the growth curve shape
• Uses univariate splines to smooth the data
• Optimizes the smoothing parameter s via K-Fold cross-validation
• Computes growth rate as the maximum of the spline's first derivative

Process

1. For each well, tests multiple smoothing parameters
2. Performs K-Fold CV to find optimal smoothing (minimizing MSE)
3. Fits best spline on full data
4. Computes derivative (instantaneous growth rate)
5. Extracts maximum growth rate and corresponding time

Inputs

• table: Time-series data with time in first column, wells in subsequent columns

Outputs

• parameters: Table with inferred parameters (Best_S, Max_Growth_Rate, Max_Growth_Time)
• growth_curves_plot: Plot showing original data, smoothed curves, and derivative
• growth_rate_comparison: Bar chart comparing maximum growth rates across wells

Configuration

• n_splits: Number of K-Fold cross-validation splits (default: 5)
• s_min: Minimum smoothing parameter to test (default: 0.01)
• s_max: Maximum smoothing parameter to test (default: 100.0)
• n_s_values: Number of smoothing values to test (default: 500)

Advantages

• Flexible for non-standard growth patterns
• No parametric assumptions
• Robust to noise via optimized smoothing

Notes

This method is complementary to logistic fitting. Use when:

• Growth curves don't follow logistic pattern
• You need only growth rate (not full curve parameters)
• Data has complex or multi-phase growth