Change Detection in Stochastic Shape Dynamical Models with Application to Activity Recognition
Resilience and vulnerability from a stochastic controlled dynamical system perspective
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Transcript of Resilience and vulnerability from a stochastic controlled dynamical system perspective
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Resilience and vulnerability from a stochastic controlled dynamical system perspective
Charles Rougé, Jean-Denis Mathias and Guillaume Deffuant
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The viability framework for resilience
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Example: The case of lake eutrophication(Carpenter et al., 1999)
Lake(Phosphorus concentration P)
Inflow Outflow
Algae
Phosphorus input L
Bounded!!! (by U>0)
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Deterministic viability: single trajectories
Event
Events
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Part I
Resilience of a stochastic controlled dynamical system
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Impact of uncertainty on the viability kernel
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Multiplicity of recovery trajectories
Events
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Resilience in a stochastic dynamical system
Recovery is defined by getting back to the stochastic viability kernel
Centrality of the probability of recovery after a given date: the Probability of resilience
No longer a unique measure of recovery but possibility to derive statistics.
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Resilience statistic:expected recovery date
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Resilience statistic: maximal recovery time (99% confidence)
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Resilience statistic: probability of resilience
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Part II
Vulnerability as a measure of future harm
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Harm: a value judgement on a state
Economic harmIncreases linearly as L decreases
Eco
logi
cal h
arm
Qua
drat
ic in
crea
se w
ith P
Threshold of harm Properties
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Defining vulnerability
1) One associates harm values to a trajectory:Þ Sum of static harm values (cost criterion)Þ Crossing of a threshold (viability criterion)
2) Vulnerability is a statistic on the distribution of harm values:Þ Expected value of the costÞ Exit probability (crossing of a threshold) Þ Value-at-risk (e.g. worst 1%) of the cost
3) Interest in low-vulnerability kernels.
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Vulnerability as total costΤ=100
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Vulnerability as exit probability
Stochastic viability kernel!!!
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Part III
Towards a resilience-vulnerability framework
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Conceptual definitions
Resilience: capacity to keep or recover properties after a hazard, disturbance or change.
Probability of recovery at date t Statistic on a recovery time distribution
Vulnerability: a measure of future harm (Hinkel, 2011). Statistic on an exit probability Statistic on a cost distribution
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Combining resilience and vulnerability
Dynamic safety criterion(or property of interest)
Low-vulnerability zone
Resilience: capacity to recover
Vulnerability: harm experienced(equivalent to a restoration cost)
?
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The proposed framework
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Take home messages
Complimentarity of resilience and vulnerability
The notion of low-vulnerability kernel generalizes that of viability kernel.
Resilience is the ability to get back to this safety set after a disturbance or a change.
Vulnerability is a statistic based on the harm values associated to the possible trajectories.
Choice of the strategy dependent on the indicator.