Multilayer and dynamic networks

Transcription

1 OHBM 2016 Multilayer and dynamic networks Danielle S. Bassett University of Pennsylvania Department of Bioengineering

2 Outline Statement of the problem Statement of a solution: Multilayer Modeling Utility for dynamic network data Metrics for dynamic networks Null models for dynamic networks Example applications and natural extensions

3 Kivelä et al J Complex Networks Statement of the Problem Observation: Nodes connected by different types of edges.

4 Domenico et al. 2015, J Complex Networks Statement of the Problem Electrical Junction Mono Synaptic Poly Synaptic Aggregate Observation: Nodes connected by different types of edges.

5 Muldoon & Bassett 2016 Philasophy of Science A frequent observation Nodes: Brain regions Edges: Structural FA, number of streamlines, etc. Functional Different frequency bands Different measures of association Morphological Across Subjects Across Time Across Tasks or Conditions Pymnet

6 An observation or a problem? Option 1: Treat each edge type as forming a separate graph or network Assumes independence of information Neglects the potential for information to be transmitted or shared across edge types Problem!

7 An observation or a problem? Option 2: Treat the set of graphs as an ensemble, and describe ensemble properties Closer! Still ignores the dependency that nodes in one graph are the same as nodes in the other graph.

8 An observation or a problem? Option 3: Develop an explicit modeling framework that accounts for dependencies between graphs

9 Kivelä et al J Complex Networks Solution: Multilayer Modeling Transforms a matrix into a tensor Multilayer modeling defines new edges between nodes to hard-code the fact that their identity remains constant. Identity links Are all dependencies now acknowledged?

10 Mucha et al Science Ordinal or Categorical? If the graphs are ordered Age Time Feature Symptom etc. What happens if graphs are categorical?

11 Mucha et al Science Categorical Coupling Ordinal coupling Categorical coupling Gender, Race, Hair Color, Eye Color, Imaging modality, Task

12 Binary or Weighted? How might one weight identity links? Most common: Choose a single value (ω=1) Other options: Choose based on a priori knowledge Choose based on data-driven parameter optimization

13 Bassett et al. 2013, Chaos A data-driven choice of ω Maximize the difference between a statistic and its expected value in a null model, over choices of ω ω Modularity, Q Where is this particularly useful?

14 Utility for dynamic network data Fast time-scale network reconfigurations Slow time-scale network reconfigurations 0 Temporal resolution parameter, ω What is most changeable across the graphs? What is most consistent across the graphs?

15 Kivelä et al J Complex Networks Metrics for dynamic networks Degree Walks, paths, distances Clustering coefficient, transitivity, triangles Centrality measures Community structure (including modularity) Core-periphery structure (generalization of rich-clubs) Diffusion, spreading, percolation

16 Khambhati et al In Prep Example: Modularity Statement of the problem:

17 Mucha et al Science Solution: Multilayer Modularity Multilayer modularity: estimate community structure in temporal networks. Resolution Parameter For Module Size Adjacenc y Matrix For i and j in same communit y Communit y i in time slice l Mason Porter Null Model Adjacenc y Matrix Resolution Parameter for Module Dynamics Communit y j in time slice r Large ω gives community structure consistent across time. Small ω gives community structure that varies across time. Peter Mucha

18 Bassett et al PNAS Null models For temporal multilayer networks: Connection Null Model Nodal Null Model Temporal Null Model

19 Muldoon & Bassett 2016 Philosophy of Science Example applications Multimodal studies Multigroup studies Multitask studies Temporal networks (across many time scales): Lifespan, development, longitudinal, withintask, frequency bands

20 Temporal Networks in Brains

21 Metrics and Considerations Flexibility: fraction of layer that a node changes module allegiance over time (Bassett et al PNAS) Promiscuity: number of different communities a node allies with over time (Papadopoulos et al Phys Rev E in Revision) Choice of time window(telesford et al Neuroimage) Longer time windows provide more regional variation in dynamics Shorter time windows are more sensitive to individual variation

22 Betzel et al arxiv Example: Over the lifespan Functional brain modules reconfigure at multiple scales across the human lifespan At a coarse scale, modules become progressively more segregated, while at finer scales, they become more integrated.

23 Domenico et al arxiv Brookes et al Neuroimage Example: Over Frequencies Hubs in the multiplex are different from those in the nonmultiplex. Multiplex hubs provide greater power in distinguishing healthy from schizophrenia.

24 Bassett et al PNAS, 2013 PLoS CB, 2013 Chaos, 2014 Chaos, 2015 Nature Neuroscience; Mantzaris et al PLoS CB Example: As we learn Modular structure of functional brain networks changes slowly during many hours of learning in the scanner. Recruitment: Module allegiance within communities Integration: Module allegiance between communities

25 Bassett et al Nature Neuroscience A growing autonomy Between motor and visual modules with task practice

26 Example: Multi-task Cole et al Neuron Mattar et al PLoS CB Telesford et al Neuroimage Either observe what is consistent across tasks Or the dynamic roles that modules play across tasks Recruitment Integration

27 Other topics and natural extensions Other Topics: Language processing (Doron et al PNAS), working memory (Braun et al PNAS), behavior (Wymbs et al Neuron), positive mood (Betzel et al arxiv) Natural Extensions: Multilayer along several aspects (time and modality, subject and task, etc.)

28 Open Methodological Questions Metric development: different sorts of reconfiguration statistics Network normalization: within and across layers Parameter choices: particularly in weights of inter-layer links

29 Summary Statement of the problem Solution: Multilayer Modeling Utility for dynamic networks Metrics Null models Applications and extensions