SLIDE 1
S P H E R A
Controlling networks while maintaining resilience
Baruch Barzel
1
Challenges
5.5 ร 107 People affected 102 Fatalities 6 ร 109 USD in damages
2
S P H E R A Controlling networks while maintaining resilience - - PowerPoint PPT Presentation
S P H E R A Controlling networks while maintaining resilience - - PowerPoint PPT Presentation
S P H E R A Controlling networks while maintaining resilience Baruch Barzel 1 Challenges 5.5 10 7 People affected 10 2 Fatalities 6 10 9 USD in damages 2 Structure vs. dynamics Structural perturbation (component failure) Dynamic
SLIDE 2
SLIDE 3
Structure vs. dynamics
Can we predict the point of Resilience loss? Structural perturbation (component failure) Dynamic outcome (Resilience loss)
SLIDE 4
Dynamic framework
๐๐ฆ๐ ๐๐ข = ๐บ ๐ฆ๐ ๐ข , ๐๐ + เท
๐=1 ๐
๐ต๐๐๐ ๐ฆ๐ ๐ข , ๐ฆ๐ ๐ข , ๐๐๐
4
๐๐ ๐ State of a system component (node)
- Concentration of a protein/metabolite
- Probability of infection of an individual
- Load on power/communications component
SLIDE 5
Dynamic framework
๐๐ฆ๐ ๐๐ข = ๐บ๐ ๐ฆ๐ ๐ข , ๐๐ + เท
๐=1 ๐
๐ต๐๐๐ ๐๐ ๐ฆ๐ ๐ข , ๐ฆ๐ ๐ข , ๐๐๐ ๐บ ๐ ๐๐, ๐๐๐ Self dynamics Interaction mechanisms Distributed parameters
๐๐ฆ๐ ๐๐ข = โ๐ท๐๐ฆ๐
๐พ๐ + เท ๐=1 ๐
๐ต๐๐ ๐ฆ๐
๐ฝ๐๐
๐๐๐ + ๐ฆ๐
๐ฝ๐๐
Interaction mechanisms
5
SLIDE 6
Dynamic framework
๐ฉ๐๐
Network structure
๐๐ฆ๐ ๐๐ข = ๐ฆ๐ 1 โ ๐ฆ๐ ๐ท๐ + เท
๐=1 ๐
๐ต๐๐ ๐ฆ๐๐ฆ๐
๐ฝ๐๐
๐๐๐ + ๐ฆ๐๐ฆ๐
๐ฝ๐๐
Interaction mechanisms
6
๐๐ฆ๐ ๐๐ข = ๐บ ๐ฆ๐ ๐ข , ๐๐ + เท
๐=1 ๐
๐ต๐๐๐ ๐ฆ๐ ๐ข , ๐ฆ๐ ๐ข , ๐๐๐
Example: population dynamics
SLIDE 7
๐๐ฆ๐ ๐๐ข = ๐บ ๐ฆ๐ ๐ข , ๐๐ + เท
๐=1 ๐
๐ต๐๐๐ ๐ฆ๐ ๐ข , ๐ฆ๐ ๐ข , ๐๐๐
๐ฉ๐๐
Network structure Interaction mechanisms
- Nonlinear
- Multi-parametric (๐๐, ๐๐๐)
- Black-box: ๐บ
๐, ๐ ๐๐ sometimes unknown
Weighted Heterogeneous (Scale-free)
7
Dynamic framework
SLIDE 8
Diverse and unpredictable
Universal resilience patterns in complex networks. Nature 530, 307 (2016)
8
Diverse & unpredictable
State State State Can we predict the point of Resilience loss?
SLIDE 9
A physicists nightmare
Current nonlinear dynamics theory:
- Low dimensional
- Symmetric structures (lattice or lattice-like)
Where real networks are:
- Disordered and weighted
- Extremely heterogeneous
- Scale free: ๐ ๐ โผ ๐โ๐ฟ
๐ spans
- rders of
magnitude
9
Each node has ๐ = 6 nearest neighbors
SLIDE 10
Symmetry
Zero order symmetry
All nodes identical
๐-order symmetry
All environments identical
10
Each node has ๐ = 6 nearest neighbors
SLIDE 11
Activity Activity ๐ธ๐๐ ๐ ๐ธ๐๐ ๐ ๐ธ๐๐ ๐ Activity Universal
State State State
๐ธ๐๐ ๐ = ๐โค๐ฉ๐๐ ๐โค๐ฉ๐
Universal parameter ๐พeff universally predicts the critical transition points of resilience loss
Universal resilience patterns in complex networks. Nature 530, 307 (2016)
11
Diverse & unpredictable
State State State Can we predict the point of Resilience loss?
Global control parameter
SLIDE 12
Example: Using the Structure of the power network to determine its Dynamic resilience against local failures or load perturbations
Global control parameter
12
Structure ๐ฉ๐๐
Well mapped
Resilience
A Dynamic observable of the system that we seek to predict, understand and influence
Our prediction
๐ธ๐๐ ๐ = ๐โค๐ฉ๐๐ ๐โค๐ฉ๐ Translating Structure into Dynamic observables of interest
Control parameter
Universal resilience patterns in complex networks. Nature 530, 307 (2016)
SLIDE 13
Top-down - Global control parameter
13
Universal resilience patterns in complex networks. Nature 530, 307 (2016)
๐ธ ๐
๐ธ๐
๐
๐ธ๐
๐
๐๐ฆ๐ ๐๐ข = ๐บ ๐ฆ๐ ๐ข , ๐๐ + เท
๐=1 ๐
๐ต๐๐๐ ๐ฆ๐ ๐ข , ๐ฆ๐ ๐ข , ๐๐๐
Bridges between Topology and Dynamics Sets guidelines for intervention
SLIDE 14
๐๐ฆ๐ ๐๐ข = ๐บ๐ ๐ฆ๐ ๐ข , ๐๐ + เท
๐=1 ๐
๐ต๐๐๐ ๐๐ ๐ฆ๐ ๐ข , ๐ฆ๐ ๐ข , ๐๐๐ + ๐ถ๐๐๐
๐ ๐ข
๐ป๐(๐)
Dynamic interventions External signals ๐ป๐(๐) to selected nodes Structural interventions Removing nodes, adding links, changing weights
14
Bottom-up - Intervention
Functional interventions Manipulating ๐ฎ๐ and ๐น๐๐ or their parameters
SLIDE 15
Spatio-temporal spreading patterns
Time
๐บ
๐ ๐ฆ๐, ๐๐
๐ ๐๐(๐ฆ๐, ๐ฆ๐, ๐๐๐)
Time
๐ฉ๐๐
15
Predicting the spatio-temporal propagation of signals in complex networks. Nature Physics. Hopefully soon
Control parameter ๐พ
Individual node response time
๐๐ โผ ๐๐
๐พ
Diverse & unpredictable Universal
SLIDE 16
Beyond stability
How much time do we have before an undesired transition
- ccurs
16
Soft stability
๐พ < ๐ ๐พ > ๐ ๐พ = ๐
SLIDE 17
Beyond stability
How much time do we have before an undesired transition
- ccurs
17
Optimizing functionality vs. resilience
SLIDE 18
Top-down Identify macroscopic control parameters (๐พ, ๐) Bottom-up Selecting nodes for intervention (real-time mitigation) Stability vs. resilience Enriching the discussion on stability Functionality vs. resilience Can we introduce balanced incentives
18
Open threads
SLIDE 19
19
In the top-down approach systems are influenced by means of global control
- parameters. Quite often these act as boundary conditions for the system
- dynamics. To identify such control parameters is a challenge on its own. Often
they can be derived from the known macroscopic, or system dynamics. As a major conceptual drawback, control parameters usually reflect limitations of stability, rather than of resilience.
- In the bottom-up approach systems are influenced by specifically targeting
some of the system elements, e.g. agents in an agent-based model or nodes in a network representation. Again, two different possibilities exist: (i) the agents can be controlled in their internal dynamics, or (ii) the agent interactions can be controlled.
SLIDE 20
20
Can we identify general principles for the bottom-up control of socio- economic or ecological systems? How can driver nodes be identified based
- n data-driven methods?
Can we explain the breakdown of resilience in social organizations as a misallocation of resources? What is the relation between resilience and the natural tendency of systems to maximize their performance?