Samuel Pastva
Phase portrait
Oscillating attractor
Continuous dynamical systems
Topological equivalence of continuous trajectories
Partitioning of parameter space into equivalence classes
Behavioural features: Attractors, repellers, saddle points, ...
Modes of behaviour: stability, oscillation, chaos/disorder, ...
Discrete state-transition systems
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"We show that although the two approaches are based on equivalent information, the resulting qualitative dynamics are different." [1]
[1] Jamshidi, Shahrad, Heike Siebert, and Alexander Bockmayr. "Preservation of dynamic properties in qualitative modeling frameworks for gene regulatory networks." Biosystems 112.2 (2013)
This is not a bug!
Anchor set: The smallest set of states that partitions every run into finite segments.
Continuous autonomous dynamical system
Autonomous system of discrete runs
Phase portrait
Anchor set diagram
Topological equivalence
Anchor set isomorphism
Bifurcation diagram
Bifurcation decision tree
Network variables
Logical parameter(s)
"Coloured" asynchronous state-transition graph
Different colours may lead to qualitatively different outcomes
In a fair system, the anchor set corresponds to bottom SCCs only
SCC closed = If x is in the set, the whole SCC of x is in the set as well.
F = FWD(set) is SCC closed.
B = BWD(set) is SCC closed.
Intersection of F and B is SCC closed.
set
FWD(set)
BWD(set)
If set = {x}, then this intersection is exactly the SCC of x.
If (FWD(set) ∖ set) is empty, then the SCC is a BSCC
In the coloured paradigm, this is happening for all colours simultaneously.
Even if BSCC is small, BWD is still limited by graph diameter.
Now we can continue reducing based on the remaining update functions...
* Coloured approach gives at least a 10-100x speedup compared to parameter scanning.
** Running on ~150 real-world networks, a benchmark set collected as part of this project.
Uninterpreted functions
generalise unknown behaviour beyond logical parameters
Fully featured interactive editor with static analysis