Complexities

This study investigated the impact of post-activation performance enhancement (PAPE) on the parameters of the 3 min all-out test (3MT) in non-motorized tethered running, applying the concept of complex networks for integrative analysis. Ten recreational runners underwent anthropometric assessments, a one-repetition maximum test (1RM), a running ramp test, and 3MT trials under both PAPE and CONTROL conditions across five separate sessions. The conditioning activity consisted of two sets of six back squats at 60% 1RM. For each scenario, complex network graphs were constructed and analyzed using Degree, Eigenvector, PageRank, and Betweenness centrality metrics. In the PAPE condition, anthropometric parameters and parameters related to aerobic efficiency exhibited greater centrality, ranking among the top five nodes. Paired Student’s t-tests (p ≤ 0.05) revealed significant differences between conditions for end power (EP-W) (CONTROL: 407.83 ± 119.30 vs. PAPE: 539.33 ± 177.10 (effect size d = −0.84)) and end power relativized by body mass (rEP-W·kg⁻¹) (CONTROL: 5.38 ± 1.70 vs. PAPE: 6.91 ± 2.00 (effect size d = −0.76)), as well as for the absolute and relative values of peak output power, mean output power, peak force, and mean force. These findings suggest that PAPE alters the configuration of complex networks, increasing network density, and may enhance neuromuscular function and running economy. Moreover, PAPE appears to modulate both aerobic and anaerobic contributions to performance. These results highlight the importance of network-based approaches for advancing exercise science and providing individualized strategies for training and performance optimization.

Hypergraphs, a generalisation of traditional graphs in which hyperedges may connect more than two vertices, provide a natural framework for modeling higher-order interactions in complex biological systems. In the context of protein complexes, hypergraphs capture relationships in which a single protein may participate in multiple complexes simultaneously. A fundamental question is how such protein complex hypergraphs evolve over time. Motivated by duplication–divergence–deletion models often used for protein–protein interaction networks, we propose a novel Duplication–Divergence Hypergraph (DDH) model for the evolutionary dynamics of protein complex hypergraphs. To evaluate network resilience, we simulate targeted attack strategies analogous to drug treatments or genetic knockouts that remove selected proteins and their associated hyperedges. We measure the resulting structural changes using hypergraph-based efficiency metrics, comparing synthetic networks generated by the DDH model with empirical E. coli protein complex data. This framework demonstrates closer alignment with empirical observations than standard pairwise duplication–divergence models, suggesting that hypergraphs provide a more realistic representation of protein interactions.

This review traces the historical evolution, conceptual foundations, and contemporary applications of the term homeodynamics across biological, ecological, cognitive, and social systems. Initially coined in the 19th century but largely forgotten, the term re-emerged in the second half of the 20th century as scholars sought to describe dynamic stability in open, self-organizing systems. From Yates’s theoretical formalization in biology to Rattan’s work in biogerontology and recent applications in psychology and organizational theory, homeodynamics has progressively evolved from a synonym of homeostasis to a distinct systems concept. It now denotes the capacity of complex systems to sustain coherence through transitions between multiple temporary equilibria, integrating feedbacks, bifurcations, and adaptive reconfigurations. By revisiting the term’s lineage, this review clarifies its epistemological scope and proposes its use as a heuristic and modeling framework for understanding dynamic stability and regime shifts in living and social systems.