Constructor of linear decay functions

The `linearDecay()` constructor either creates a decay function or returns a `ggplot` object for visualizing the decay model. It is a utility function used internally by circularProjection and polarProjection.

Usage

linearDecay(decay = 0.001, pdist = 0.15, plot = FALSE, demo.signal = 1)

Arguments

decay: A decay factor (in [0,1]). This term indicates how much a signal decreases as a function of distance in pathway space. For example, at a specific distance defined by the pdist parameter, the signal intensity will be the initial signal multiplied by decay.
pdist: A distance normalization term (in (0, 1]) at which the signal reaches `signal * decay`. This parameter is used to anchor the decay to a meaningful distance (see `details`). Also, when pdist = 1, it will represent the diameter of the inscribed circle within the coordinate space of a `PathwaySpace` object.
plot: A logical value indicating whether to return a `ggplot` object.
demo.signal: A numeric value in `[-Inf, Inf]`, only passed when plot = TRUE to visualize the decay curve with a specific signal intensity. The value is ignored by the function constructor, as the decay function itself is returned without using an initial signal.

Value

Returns either a function of the form function(x, signal) { ... } or, if plot = TRUE, a `ggplot` object illustrating the decay model.

Details

The `linearDecay()` constructor creates a simple linear decay model. It describes how a signal decreases proportionally with distance.

The decay function is defined as: $$y = signal \times \left(1 - (1 - decay) \times \frac{x}{pdist}\right)$$

where $signal$ represents the initial intensity, $decay$ defines the relative signal level at $pdist$, and $x$ is a vector of normalized distances. The signal decreases uniformly from its initial value to $pdist$, which is a reference distance that anchors the model such that:

$y = signal$ when $x = 0$
$y = signal \times decay$ when $x = pdist$

This makes the linear form consistent with the exponential and Weibull decay functions, both of which also reach $signal \times decay$ at the reference distance.

Author

Sysbiolab Team

Examples

# Return a decay function
decay_fun <- linearDecay(decay = 0.5, pdist = 0.25)

# Plot decay model parameters
# linearDecay(decay = 0.5, pdist = 0.25, plot = TRUE)