Methods for coarse-graining systems to different levels of spatial analysis.
MacroNetwork(macro_network, macro_phi, micro_network, micro_phi, partition, grouping)¶
A coarse-grained network of nodes.
See the Emergence (Macro/Micro) example in the documentation for more information.
Network – The network object of the macro-system.
float – The \(\Phi\) of the network’s main complex.
Network – The network object of the corresponding micro system.
float – The \(\Phi\) of the main complex of the corresponding micro-system.
list – The partition which defines macro-elements in terms of micro-elements.
list(list – The correspondence between micro-states and macro-states.
float – The difference between the \(\Phi\) of the macro- and the micro-system.
Return a list of all possible coarse grains of a network.
Parameters: network (Network) – The physical system to act as the ‘micro’ level. Returns: partitions –
- A list of possible partitions. Each
- element of the list is a list of micro-elements which correspong to macro-elements.
Return type: ``list(list
Return all possible groupings of states for a particular coarse graining (partition) of a network.
- network (Network) – The physical system on the micro level.
- partitions (list(list) – The partition of micro-elements into macro elements.
- A list of all possible
correspondences between micro-states and macro-states for the partition.
Return a mapping from micro-state to the macro-states based on the partition of elements and grouping of states.
- partition (list(list) – A partition of micro-elements into macro elements.
- grouping (list(list(list) – For each macro-element, a list of micro states which set it to ON or OFF.
mapping – A mapping from micro-states to macro-states.
Create the macro TPM for a given mapping from micro to macro-states.
- micro_tpm (nd.array) – The TPM of the micro-system.
- mapping (nd.array) – A mapping from micro-states to macro-states.
macro_tpm – The TPM of the macro-system.
make_macro_network(network, state, mapping)¶
Create the macro-network for a given mapping from micro to macro-states.
Noneif the macro TPM does not satisfy the conditional independence assumption.
- micro_tpm (nd.array) – TPM of the micro-system.
- mapping (nd.array) – Mapping from micro-states to macro-states.
Network): Network of the macro-system, or
Check for emergence of a macro-system into a macro-system.
Checks all possible partitions and groupings of the micro-system to find the spatial scale with maximum integrated information.
Parameters: network (Network) – The network of the micro-system under investigation. Returns: macro_network –
- The maximal coarse-graining of the
Return the effective information of the given network.
This is equivalent to the average of the
effect_info()(with the entire network as the mechanism and purview) over all posisble states of the network. It can be interpreted as the “noise in the network’s TPM,” weighted by the size of its state space.
config.VALIDATE_SUBSYSTEM_STATESis enabled, then unreachable states are omitted from the average.
For details, see:
Hoel, Erik P., Larissa Albantakis, and Giulio Tononi. “Quantifying causal emergence shows that macro can beat micro.” Proceedings of the National Academy of Sciences 110.49 (2013): 19790-19795.
Available online: doi: 10.1073/pnas.1314922110.