finding

active

finding:in-hierarchical-systems-with-independent-cliques-there-exist-parameter-regimes-where-individual-cliques-maintain-uniform-magnetisation-while-others-flip

In hierarchical systems with independent cliques, there exist parameter regimes where individual cliques maintain uniform magnetisation while others flip.

Shows how hierarchical topology enables local order within global flexibility; explains biological multiscale organization

Source paper

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Topological constraints on self-organisation in locally interacting systems

(2025) · Francesco Sacco · Dalton A R Sakthivadivel · Michael Levin

Neighborhood — ranked by edge-count

Claims (1)

claim

Hierarchical structure in interaction topology enables complex multiscale patterns that cannot exist in flat networks.
supports
Explains why biological systems achieve organization across scales while language models struggle; grounds in free energy scaling

Communities (4)

community

Causal emergence in biological systems
members_of
Examines how macro-scale causal power exceeds micro-scale in living and learning systems.
Hierarchical structure and multiscale coherence in physical systems
members_of
How graph topology and hierarchical interaction patterns enable or prevent phase transitions and ordered states, from statistical mechanics to biological organization.
Hierarchical network ordering & thermodynamics
members_of
Statistical mechanics of clique-structured graphs linking domain walls, free energy, and biological multiscale coherence.
Hierarchical network topology and emergent dynamics
members_of
How nested, clique-based structures enable multiscale pattern formation and selective state transitions unavailable in flat networks.

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

For a graph with independent cliques, individual cliques may flip magnetisation while remaining uniformly magnetised if intra-clique coupling > (T/2) log n_i (Theorem 4)finding0.842
Condition for hierarchical order with locally coherent but globally varying phases
Hierarchical clique-structured networks can maintain multiscale coherence; biology evolved hierarchy and stigmergy as coherence solutions.claim0.793
Free-energy scaling under domain-wall formation in Potts, autoregressive, and hierarchical networks shows that combinatorics of interactions on a graph prevent or allow spontaneous ordering.finding0.788
Core result demonstrating topological constraints on self-organization
Hierarchical structures in biological systems enable local order while globally disordered, explaining complex patterning.claim0.781
Claim that multiscale organisation produces complex patterns via clique-based local coherence
The results generalise readily to non-equilibrium systems where scaling relationships remain similar (e.g., dynamic or localised scaling).claim0.772
Claim about broader applicability of the scaling argument
Purely local-interaction systems on 1D topologies cannot maintain long-range order at finite temperature.claim0.769
In buildings, especially, the success of the process will be judged by the extent to which these middle-range entities appear with their own distinct symmetries, with their own definite and distinct force as strong centers.claim0.766
Proposes middle-range entity quality as the criterion for judging the success of a building process
There exists a non-empty critical temperature range of hierarchical behaviour (Proposition 3)finding0.759
Proof that the conditions of Theorem 4 are realisable in a range of temperatures