weibullDecay

The <code>weibullDecay</code> function is used by
PathwaySpace's methods for signal convolution and projection.

For a given graph containing vertices, edges, and a signal associated with the vertices, the 'PathwaySpace' package performs a convolution operation, which involves a weighted combination of neighboring vertices and their associated signals. The package then uses a decay function to project these signals, creating geodesic paths on a 2D-image space. 'PathwaySpace' could have various applications, such as visualizing and analyzing network data in a graphical format that highlights the relationships and signal strengths between vertices. It can be particularly useful for understanding the influence of signals through complex networks. By combining graph theory, signal processing, and visualization, the 'PathwaySpace' package provides a novel way of representing and analyzing graph data.

Mauro Castro

PathwaySpace

Spatial Projection of Network Signals along Geodesic Paths

Vinicius Chagas

Victor Apolonio

weibullDecay function

<dl><dt>x</dt>
<dd>A numeric vector of distances (in [0,1]).</dd>
<dt>signal</dt>
<dd>A single numeric value representing a signal.</dd>
<dt>decay</dt>
<dd>The rate (in [0,1]) at which the signal decays.
This term indicates how much the <code>signal</code> decreases at a certain
distance in <code>x</code>. At the distance defined by the <code>pdist</code> term
(see <code>circularProjection</code>), the signal's value will
correspond to the initial signal multiplied by <code>1 - decay</code>.</dd>
<dt>shape</dt>
<dd>A parameter (&gt;=1) of a Weibull function. When <code>shape=1</code>
the Weibull decay follows an exponential decay. When <code>shape&gt;1</code>
the function is first convex, then concave with an inflection point.</dd></dl>

Arguments

Vinicius Chagas, Victor Apolonio, and
Mauro Castro (<a href="/link/mauro.castro%40ufpr.br?package=PathwaySpace&version=0.99.4" data-mini-rdoc="PathwaySpace::mauro.castro@ufpr.br">mauro.castro@ufpr.br</a>)

Author

Weibull decay function. — weibullDecay

<dl>

<dt>x</dt>
<dd>A numeric vector of distances (in [0,1]).</dd>


<dt>signal</dt>
<dd>A single numeric value representing a signal.</dd>


<dt>decay</dt>
<dd>The rate (in [0,1]) at which the signal decays.
This term indicates how much the <code>signal</code> decreases at a certain
distance in <code>x</code>. At the distance defined by the <code>pdist</code> term
(see <code>circularProjection</code>), the signal's value will
correspond to the initial signal multiplied by <code>1 - decay</code>.</dd>


<dt>shape</dt>
<dd>A parameter (&gt;=1) of a Weibull function. When <code>shape=1</code>
the Weibull decay follows an exponential decay. When <code>shape&gt;1</code>
the function is first convex, then concave with an inflection point.</dd>

</dl>

Vinicius Chagas, Victor Apolonio, and
Mauro Castro (<a href='mailto:mauro.castro@ufpr.br'>mauro.castro@ufpr.br</a>)

weibullDecay: Weibull decay function.

Description

Usage

Value

Arguments

Author

See Also

Examples