{"title":"Distributed elasticity: a high-reward, moderate-risk strategy for efficient control modulation in insect flight.","authors":"Liang Wang, Congxiao Zhang, Najmeh Asadimoghaddam, Arion Pons","doi":"10.1098/rsif.2026.0304","DOIUrl":"https://doi.org/10.1098/rsif.2026.0304","url":null,"abstract":"<p><p>The environments inhabited by flying insects demand a balance between flight efficiency and flight manoeuvrability. In structural oscillators such as the insect indirect flight motor, efficiency (arising from resonance) and manoeuvrability (arising from kinematic modulation) are typically quid pro quo, with modulation incurring penalties to efficiency. Band-type resonance is a phenomenon that offers, in theory, a strategy to lessen these penalties via careful navigation through a band of efficient kinematic states. However, identifying this band is challenging: no methods exist to identify the complete band in realistic motor models, involving elasticity distributed across thorax and wing. Nor are the effects of elasticity distribution on the band known. In this work, we address both open topics. We present a suite of numerical methods for identifying the complete resonance band in general systems. Applying them to models of the insect flight motor with distributed elasticity-thoracic and wing flexion-reveals that distributed elasticity is moderate-risk, but high-reward, morphological feature. Well-tuned distributions expand the resonance band over fourfold, whereas poorly tuned distributions completely extinguish the resonance band. These results indicate that distributing elasticity across the insect flight motor can have an adaptive value, and they motivate broader work identifying distributions across species.</p>","PeriodicalId":17488,"journal":{"name":"Journal of The Royal Society Interface","volume":"23 244","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149322616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrea Di Pietro, Francesca Di Puccio, Luca Modenese
{"title":"OpenGRF: prediction of ground reaction forces and moments during activities of daily living using OpenSim.","authors":"Andrea Di Pietro, Francesca Di Puccio, Luca Modenese","doi":"10.1098/rsif.2026.0264","DOIUrl":"https://doi.org/10.1098/rsif.2026.0264","url":null,"abstract":"<p><p>OpenGRF is a new OpenSim-based tool that estimates ground reaction forces and moments (GRF&Ms) and centre of pressure (CoP) directly from joint kinematics, addressing an existing limitation of current OpenSim workflows. The approach combines calibrated foot-ground contact probes with an optimization framework derived from static optimization, and computes CoP by accounting for both kinematic and dynamic contributions. Its performance was validated against force-plate measurements. Validation involved 126 marker-based trials from seven healthy adults, each performing six trials of level walking, stair ascent and stair descent. Results showed the highest accuracy for vertical GRF, with normalized root mean square error (nRMSE) ≤ 1.5% and Pearson's correlation coefficient (ρ) ≥ 0.94, particularly during level walking. Anterior-posterior GRF was also satisfactorily predicted (nRMSE 4.4%-6.1%, ρ = 0.81-0.91). By contrast, medial-lateral GRF was less reliable, especially in stair tasks, with errors up to 11.2% and correlations as low as 0.48. Free moments were the hardest variable to estimate (nRMSE up to 28%), whereas ankle moments showed excellent agreement with force-plate data (nRMSE ≈ 1.7%, ρ ≈ 0.98). Median CoP error was 21-23 mm, with the largest discrepancies during double support. Overall, OpenGRF enables physics-consistent estimation of GRF-related variables, particularly the vertical component, from kinematics alone, although generalizability is limited by the tested sample.</p>","PeriodicalId":17488,"journal":{"name":"Journal of The Royal Society Interface","volume":"23 244","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149322620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marie Dorchain, S Nirmala Jenifer, Timoteo Carletti
{"title":"Turing patterns on adaptive networks.","authors":"Marie Dorchain, S Nirmala Jenifer, Timoteo Carletti","doi":"10.1098/rsif.2025.0941","DOIUrl":"https://doi.org/10.1098/rsif.2025.0941","url":null,"abstract":"<p><p>We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In the presence of diffusive-like coupling, Turing theory has been largely applied to explain the formation of such self-organized motifs on networked systems, where reactions occur in the nodes and the available links are used for species to diffuse. In many relevant applications, those links do not have static weights, as very often assumed, but evolve in time, and more importantly, they adapt their weights as functions of the states of the nodes. In this work, we make one step forward, and we provide a general theory to prove the validity of the Turing idea in the case of adaptive symmetric networks with positive weights. The conditions for the emergence of Turing instability rely on the spectral property of the Laplacian matrix and the model parameters, thus strengthening the interplay between dynamics and network topology. A rich variety of patterns are presented by using two prototype models of nonlinear dynamical systems, the Brusselator and the FitzHugh-Nagumo model. Because many empirical networks adapt to changes in the system states, our results pave the way for a thorough understanding of self-organization in real-world systems.</p>","PeriodicalId":17488,"journal":{"name":"Journal of The Royal Society Interface","volume":"23 244","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149322622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"From data-driven differential equations to mechanistic forecasting with machine learning.","authors":"Amit K Chakraborty, Hao Wang, Pouria Ramazi","doi":"10.1098/rsif.2026.0240","DOIUrl":"https://doi.org/10.1098/rsif.2026.0240","url":null,"abstract":"<p><p>The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from time-series data using a library of functions constructed from the measured variables. However, these methods typically assume time-invariant coefficients, which limits their ability to capture evolving system dynamics. To overcome this limitation, we allow some of the parameters to vary over time, learn their temporal evolution directly from data and infer a system of equations that incorporates both constant and time-varying parameters. We then transform this framework into a forecasting model by predicting the time-varying parameters and substituting these predictions into the learned equations. The model is validated on simulated susceptible-infected-recovered and consumer-resource systems, as well as on real-world greenhouse gas concentration and cyanobacteria cell count datasets. By dynamically adapting to temporal shifts, our proposed model achieved a mean absolute error below 3% for learning a time series and below 6% for forecasting up to a month ahead. We additionally compare forecasting performance against convolutional neural network-long short-term memory and gradient boosting machine, and show that our model outperforms these methods across most datasets. Our findings demonstrate that integrating time-varying parameters into data-driven discovery of differential equations improves both modelling accuracy and forecasting performance.</p>","PeriodicalId":17488,"journal":{"name":"Journal of The Royal Society Interface","volume":"23 244","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149322617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A harmonic mean theorem for optimal branching exponents in transport networks.","authors":"Himanshu Mishra, Harmesh Kumar, Neeta Lohani","doi":"10.1098/rsif.2026.0331","DOIUrl":"https://doi.org/10.1098/rsif.2026.0331","url":null,"abstract":"<p><p>Optimal branching in transport networks has been analysed mechanism by mechanism since Murray's law (branching exponent x=3), but no combining rule exists when several dissipation mechanisms coexist. We prove that the optimal exponent is the weighted harmonic mean of the single-mechanism exponents, weighted by each mechanism's share of the dissipation budget. The result holds for any smooth dissipation function and any smooth convex structural cost. A bounding consequence establishes a strict floor x>5/2 for any Poiseuille-plus-pulsatility combination at every finite Womersley number, providing a parameter-free test that distinguishes dissipation-based from impedance-based optimization of biological networks. The predictions are robust to wall compliance and physiological flow variability; the latter preferentially amplifies entrance losses, yielding a testable prediction that vascular beds with high flow variability should exhibit systematically lower branching exponents. Read inversely, the theorem predicts that roughly half of coronary pumping power is dissipated by entrance effects. An order-by-order analysis of the human pulmonary arterial tree predicts the observed transition from x≈2.1 to x≈3, in quantitative agreement with cross-species morphometric data. The same entrance-driven mechanism reproduces the two-regime architecture of allometric scaling theory as asymptotic limits of a single cost function.</p>","PeriodicalId":17488,"journal":{"name":"Journal of The Royal Society Interface","volume":"23 244","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149322615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Incorporating authority perception, economic status and behavioural response in infectious disease control.","authors":"Huaning Liu, Junke Yang, Soren Larsen, Pamela Martinez, Gokce Dayanikli","doi":"10.1098/rsif.2026.0281","DOIUrl":"https://doi.org/10.1098/rsif.2026.0281","url":null,"abstract":"<p><p>We introduce a multi-population mean field game framework to examine how economic status and authority perception shape vaccination and social distancing decisions under different epidemic control policies. We conducted a survey to inform our model and stratify the population into six groups by income and perception of authority, capturing behavioural heterogeneity. Individuals choose socialization and vaccination levels to optimize objectives such as minimizing treatment costs, complying with social distancing guidelines if they are authority-followers, or reducing losses from decreased social interactions if they are authority-indifferents, alongside economic costs. Public health authorities influence behaviour through social distancing guidelines and vaccination costs. We characterize the Nash equilibrium via a forward-backward differential equation system, provide its mathematical analysis and numerically solve it. Our findings reveal a trade-off between social distancing and vaccination. Under stricter guidelines that target both susceptible and infected individuals, followers reduce both socialization and vaccination levels, while indifferents increase socialization owing to followers' preventative measures. Adaptive guidelines targeting infected individuals effectively reduce infections and narrow the gap between low- and high-income groups, while lower vaccination costs incentivize vaccination among low-income groups. Trust-building remains critical in epidemic mitigation, underscoring the importance of data-informed, game-theoretical models for understanding complex human responses to mitigation policies.</p>","PeriodicalId":17488,"journal":{"name":"Journal of The Royal Society Interface","volume":"23 244","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149322618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Saeed Farjami, Karen Camargo Sosa, Jonathan H P Dawes, Robert N Kelsh, Andrea Rocco
{"title":"Intrinsic noise reduces fluctuation frequencies in a cross-repressilator model motivated by stem cell differentiation.","authors":"Saeed Farjami, Karen Camargo Sosa, Jonathan H P Dawes, Robert N Kelsh, Andrea Rocco","doi":"10.1098/rsif.2026.0013","DOIUrl":"https://doi.org/10.1098/rsif.2026.0013","url":null,"abstract":"<p><p>The dynamical effects of intrinsic noise in gene regulatory networks (GRNs) can be significant when the number of molecules is low. In previous work, we proposed a new conceptual model, comprising a network of three transcription factors (TFs) that mutually inhibit each other (i.e. a 'cross-repressilator', also referred to as a 'toggle triad'), that offers a route to reconcile the direct fate restriction (DFR) and progressive fate restriction (PFR) hypotheses for stem cell fate choice. In the deterministic case, the cross-repressilator model generically displays three kinds of dynamics. Between the multipotent and fate-specified regimes there exists a third, initially unanticipated, intermediate oscillatory regime that provides a mechanism for environmental signals to influence fate choice. Here, we analyse in detail a stochastic version of the cross-repressilator model. Our findings reveal that, as the system size reduces, intrinsic noise systematically lowers the characteristic frequencies associated with fluctuations both in the multipotent state and in the oscillatory regime. Hence, while the cross-repressilator conceptual model points to a possible resolution of the DFR/PFR dichotomy, the effect of noise is to reduce the number of oscillatory cycles that would be present and thus to accelerate movement of the cell state towards differentiation during the fate specification process.</p>","PeriodicalId":17488,"journal":{"name":"Journal of The Royal Society Interface","volume":"23 244","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149322619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Passive ankle exoskeleton assistance selectively modulates triceps surae neural control during balance.","authors":"Raphaël Hamard, François Hug, Taylor J M Dick","doi":"10.1098/rsif.2025.1305","DOIUrl":"10.1098/rsif.2025.1305","url":null,"abstract":"<p><p>Wearable assistive devices have potential to improve human balance, but their effectiveness remains limited by an incomplete understanding of how mechanical assistance influences neuromuscular control. This study aimed to determine the neural adaptations in the control of lower leg muscles in response to passive ankle exoskeleton assistance during standing balance tasks with varying levels of difficulty. Lower limb kinematics and kinetics were recorded to assess changes in joint dynamics and balance performance. Neural drive to the muscles was assessed by decomposing high-density electromyography signals into motor unit spike trains. Ankle exoskeleton assistance, provided by a simple spring-loaded passive device, did not alter or improve balance performance and had minimal effects on lower limb kinematics. However, exoskeleton assistance affected triceps surae neural control, but only in the soleus, by reducing neural drive, while the gastrocnemii showed no detectable changes in neural control. Together, these results demonstrate that passive exoskeleton assistance alters neural control of the triceps surae in a muscle-specific manner during balance. Understanding muscle-specific adaptations can support more effective exoskeleton design and the development of their control strategies informed by myoelectrical signals.</p>","PeriodicalId":17488,"journal":{"name":"Journal of The Royal Society Interface","volume":"23 243","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13682571/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149182707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stress-correlated stereom organization in the echinoid tubercle reveals hierarchical mechanical integration.","authors":"Timon Gehrmann, Przemyslaw Gorzelak, Susanna Labisch, Jan-Henning Dirks","doi":"10.1098/rsif.2026.0592","DOIUrl":"10.1098/rsif.2026.0592","url":null,"abstract":"<p><p>Echinoid tests consist of a highly porous skeletal microstructure (stereom) optimized in terms of functional performance. One of the most mechanically demanding components of the test is the tubercle, which forms the mechanical interface between the test plates and spines and is subjected to complex loads generated by motion of the spine. However, the mechanical behaviour of tubercles under realistic loading conditions remains poorly explored. Here, we investigate the tubercle of Prionocidaris baculosa using high-resolution X-ray microscopy and finite-element analysis to simulate physiologically relevant loading, identify the main stress directions, and assess mechanical efficiency through topology optimization. By correlating experimental and numerical results, we quantify the relationship between stress distributions and stereom organization, providing new insights into the mechanical complexity of echinoid skeletons. We found a strong correlation between experimentally determined density and different stress parameters (von Mises stress, principal stress trajectories and mean normal stress), supporting the hypothesis of a functionally graded and mechanically optimized stereom architecture. These findings highlight the echinoid skeleton as a naturally optimized, load-adaptive structure with potential relevance for bioinspired design. In particular, stereom-inspired architectures could inform additive manufacturing approaches, enabling lightweight and material-efficient components with tailored mechanical performance derived from a single material.</p>","PeriodicalId":17488,"journal":{"name":"Journal of The Royal Society Interface","volume":"23 243","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13682557/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149182778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alexander Dack, Tomislav Plesa, Thomas E Ouldridge
{"title":"Recurrent neural chemical reaction networks trained to switch dynamical behaviours through learned bifurcations.","authors":"Alexander Dack, Tomislav Plesa, Thomas E Ouldridge","doi":"10.1098/rsif.2026.0169","DOIUrl":"10.1098/rsif.2026.0169","url":null,"abstract":"<p><p>Both natural and synthetic chemical systems not only exhibit a range of non-trivial dynamics, but also transition between qualitatively different dynamical behaviours as environmental parameters change. Such transitions are called bifurcations. Here, we show that recurrent neural chemical reaction networks (RNCRNs), a class of chemical reaction networks based on recurrent artificial neural networks that can be trained to reproduce a given dynamical behaviour, can also be trained to exhibit bifurcations. First, we show that RNCRNs can inherit some bifurcations defined by smooth ordinary differential equations (ODEs). Second, we demonstrate that the RNCRN can be trained to infer bifurcations that allow it to approximate different target behaviours within different regions of parameter space, without explicitly providing the bifurcation itself in the training. These behaviours can be specified using target ODEs that are discontinuous with respect to the parameters, or even simply by specifying certain desired dynamical features in certain regions of the parameter space. To achieve the latter, we introduce an ODE-free algorithm for training the RNCRN to display designer oscillations, such as a heart-shaped limit cycle or two coexisting limit cycles.</p>","PeriodicalId":17488,"journal":{"name":"Journal of The Royal Society Interface","volume":"23 243","pages":""},"PeriodicalIF":3.4,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13682565/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149182758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}