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 outcome Can we predict the (Resilience loss) point of Resilience loss?

Dynamic framework 𝑂 𝑒𝑦 𝑗 𝑒𝑢 = 𝐺 𝑦 𝑗 𝑢 , 𝛘 𝑗 + ෍ 𝐵 𝑗𝑘 𝑅 𝑦 𝑗 𝑢 , 𝑦 𝑘 𝑢 , 𝛊 𝑗𝑘 𝑘=1 𝒚 𝒋 𝒖 State of a system component (node) • Concentration of a protein/metabolite • Probability of infection of an individual 4 • Load on power/communications component

Dynamic framework 𝑂 𝑒𝑦 𝑗 𝑒𝑢 = 𝐺 𝑗 𝑦 𝑗 𝑢 , 𝛘 𝑗 + ෍ 𝐵 𝑗𝑘 𝑅 𝑗𝑘 𝑦 𝑗 𝑢 , 𝑦 𝑘 𝑢 , 𝛊 𝑗𝑘 𝑘=1 Interaction mechanisms Self dynamics 𝐺 Interaction mechanisms 𝑅 Distributed parameters 𝛘 𝑗 , 𝛊 𝑗𝑘 𝛽 𝑗𝑘 𝑂 𝑦 𝑘 𝑒𝑦 𝑗 𝛾 𝑗 + ෍ 𝑒𝑢 = −𝐷 𝑗 𝑦 𝑗 𝐵 𝑗𝑘 𝛽 𝑗𝑘 𝑙 𝑗𝑘 + 𝑦 𝑘 𝑘=1 5

Dynamic framework 𝑂 𝑒𝑦 𝑗 𝑒𝑢 = 𝐺 𝑦 𝑗 𝑢 , 𝛘 𝑗 + ෍ 𝐵 𝑗𝑘 𝑅 𝑦 𝑗 𝑢 , 𝑦 𝑘 𝑢 , 𝛊 𝑗𝑘 𝑘=1 Interaction mechanisms Network structure Example: population dynamics 𝑩 𝒋𝒌 𝛽 𝑗𝑘 𝑂 𝑦 𝑗 𝑦 𝑘 𝑒𝑦 𝑗 1 − 𝑦 𝑗 𝑒𝑢 = 𝑦 𝑗 + ෍ 𝐵 𝑗𝑘 𝛽 𝑗𝑘 𝐷 𝑗 𝑙 𝑗𝑘 + 𝑦 𝑗 𝑦 𝑘 𝑘=1 6

Dynamic framework 𝑂 𝑒𝑦 𝑗 𝑒𝑢 = 𝐺 𝑦 𝑗 𝑢 , 𝛘 𝑗 + ෍ 𝐵 𝑗𝑘 𝑅 𝑦 𝑗 𝑢 , 𝑦 𝑘 𝑢 , 𝛊 𝑗𝑘 𝑘=1 Interaction mechanisms Network structure 𝑩 𝒋𝒌 • Nonlinear Weighted • Multi-parametric ( 𝛘 𝑗 , 𝛊 𝑗𝑘 ) Heterogeneous (Scale-free) • Black-box: 𝐺 𝑗 , 𝑅 𝑗𝑘 sometimes unknown 7

Diverse and unpredictable Diverse & unpredictable State Can we predict the point of Resilience State loss? State Universal resilience patterns in complex networks. Nature 530 , 307 (2016) 8

A physicists nightmare Current nonlinear dynamics theory: Where real networks are: 𝑙 spans Each node has 𝑙 = 6 nearest orders of magnitude neighbors • Disordered and weighted • Low dimensional • Extremely heterogeneous • Symmetric structures (lattice or lattice-like) • Scale free: 𝑄 𝑙 ∼ 𝑙 −𝛿 9

Symmetry Zero order symmetry 𝒐 -order symmetry Each node has 𝑙 = 6 nearest neighbors All nodes identical All environments identical 10

Global control parameter Diverse & unpredictable Universal Activity State State Universal parameter 𝛾 eff universally predicts the critical transition points of 𝜸 𝐟𝐠𝐠 Can we predict the resilience loss point of Resilience Activity State 𝜸 𝐟𝐠𝐠 = 𝟐 ⊤ 𝑩 𝟑 𝟐 State loss? 𝟐 ⊤ 𝑩𝟐 𝜸 𝐟𝐠𝐠 Activity State State 𝜸 𝐟𝐠𝐠 Universal resilience patterns in complex networks. Nature 530 , 307 (2016) 11

Global control parameter Structure 𝑩 𝒋𝒌 Well mapped Control parameter Our prediction 𝜸 𝐟𝐠𝐠 = 𝟐 ⊤ 𝑩 𝟑 𝟐 𝟐 ⊤ 𝑩𝟐 Translating Structure into Dynamic observables of interest Example : Using the Structure of the power network to determine its Dynamic resilience against Resilience local failures or load perturbations A Dynamic observable of the system that we seek to predict, understand and influence Universal resilience patterns in complex networks. Nature 530 , 307 (2016) 12

Top-down - Global control parameter 𝑂 𝑒𝑦 𝑗 𝑒𝑢 = 𝐺 𝑦 𝑗 𝑢 , 𝛘 𝑗 + ෍ 𝐵 𝑗𝑘 𝑅 𝑦 𝑗 𝑢 , 𝑦 𝑘 𝑢 , 𝛊 𝑗𝑘 𝑘=1 𝒚 𝟐 𝜸 𝒅 𝟑 𝜸 𝒅 Bridges between Topology and Dynamics Sets guidelines for 𝜸 intervention Universal resilience patterns in complex networks. Nature 530 , 307 (2016) 13

Bottom-up - Intervention 𝑂 𝑒𝑦 𝑗 𝑒𝑢 = 𝐺 𝑗 𝑦 𝑗 𝑢 , 𝛘 𝑗 + ෍ 𝐵 𝑗𝑘 𝑅 𝑗𝑘 𝑦 𝑗 𝑢 , 𝑦 𝑘 𝑢 , 𝛊 𝑗𝑘 + 𝐶 𝑗𝑘 𝑇 𝑘 𝑢 𝑘=1 Structural interventions Dynamic interventions 𝑻 𝒌 (𝒖) Removing External signals nodes, adding 𝑻 𝒌 (𝒖) to selected links, changing nodes weights Functional interventions Manipulating 𝑮 𝒋 and 𝑹 𝒋𝒌 or their parameters 14

Spatio-temporal spreading patterns Diverse & unpredictable Universal Control parameter 𝜾 𝑩 𝒋𝒌 Individual node response time 𝜾 𝝊 𝒋 ∼ 𝒍 𝒋 𝐺 𝑗 𝑦 𝑗 , 𝛘 𝑗 𝑅 𝑗𝑘 (𝑦 𝑗 , 𝑦 𝑘 , 𝛊 𝑗𝑘 ) Time Time 15 Predicting the spatio-temporal propagation of signals in complex networks. Nature Physics. Hopefully soon

Soft stability 𝜾 < 𝟏 𝜾 = 𝟏 𝜾 > 𝟏 Beyond stability How much time do we have before an undesired transition occurs 16

Optimizing functionality vs. resilience Beyond stability How much time do we have before an undesired transition occurs 17

Open threads Top-down Identify macroscopic control parameters ( 𝛾, 𝜄 ) 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

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. 19

Can we identify general principles for the bottom-up control of socio- economic or ecological systems? How can driver nodes be identified based on 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? 20