Journal of The Royal Society Interface

1Cranial sutures are important structures associated with skull growth, and it is widely known that the cranial sutures have a fractal nature. However, the measurement conditions and analytical procedures have varied among studies, making direct comparison and interpretation difficult. In addition, the mechanisms by which such fractal-like patterns arise remain incompletely understood. In this study, we established and validated a standardized box-counting protocol for quantifying the fractal dimension (FD) of cranial sutures. Using this protocol, we quantified FD in 45 digitized images of human lambda sutures and in eight structure-formation model variants designed to generate fractal-like patterns via distinct kernel designs (step, Gaussian, Mexican-hat, and time-dependent/dual-stage), spatially inhomogeneous inhibition (Fbase), low-frequency noise, and different initial conditions (including sine-curve initialization). We show that FD estimates are strongly affected by preprocessing (including skeletonization) and the selected scale range, explaining discrepancies across previous studies. Crucially, under the matched preprocessing and scale-range criteria, three of the eight model variants reproduce the FD of real sutures within predefined equivalence margins, supporting the notion that appropriate dynamics can produce the observed fractal-like suture behavior and providing testable hypotheses for how such patterns may emerge.

In insect locomotion, the transmission of energy from muscles to motion is a process within which there are many sources of dissipation. One significant but understudied source is the structural damping within the insect exoskeleton itself: the thorax and limbs. Experimental evidence suggests that exoskeletal damping shows frequency (or, rate) independence, but investigation into its nature and implications has been hampered by a lack methods for simulating the time-domain behaviour of this damping. Here, synergising and extending results across applied mathematics and seismic analysis, we provide these methods. We show that existing models of exoskeletal rate-independent damping are equivalent to an important singular integral in time: the Hilbert transform. However, these models are strongly noncausal, violating the directionality of time. We derive the unique causal analogue of these existing exoskeletal damping models, as well as an accessible approximation to them, as Hadamard finite-part integrals in time, and provide methods for simulating them. These methods are demonstrated on several current problems in insect biomechanics. Finally, we demonstrate, for the first time, that existing rate-independent damping models are not strictly dissipative: in certain circumstances they are capable of generating negative power without apparently storing energy, likely violating conservation of energy. This work resolves a key methodological impasse in the understanding of insect exoskeletal dynamics and offers new insights into the micro-structural origins of rate-independent damping as well as the directions required in order to resolve violations of causality and the conservation of energy in existing models.

Standard differentiation assays sample cell states only at discrete time points, while the underlying progression unfolds continuously and heterogeneously across cells. As a result, different combinations of proliferation, commitment, and maturation dynamics can converge to similar endpoint measurements. This many-to-one mapping between latent trajectories and observable readouts constitutes a partially observed inverse problem that limits mechanistic interpretation. Although this ambiguity is inherent to many experimental systems, it is rarely examined using models that connect cell-state dynamics to assay-level quantities. We present OsteoMin, a coarse-grained cellular automaton that links stochastic transitions between pre-osteoblast and osteoblast states to experimentally measurable readouts of alkaline phosphatase activity, collagen deposition, and mineralization. Model parameters were constrained using literature-reported kinetics and evaluated against dexamethasone and menaquinone-4 perturbations. The frame-work reproduces qualitative assay trends and enables systematic analysis of how cell-state progression, matrix maturation, and external perturbations shape differentiation outcomes. Using this framework, we quantify the identifiability limits of endpoint assays and test whether standard measurements can distinguish underlying differentiation mechanisms. Distinct perturbation families often produce similar endpoint responses (macro-F1 {approx} 0.42), indicating limited discriminative power. Incorporating temporal trajectories improves separability (macro-F1 {approx} 0.78), demonstrating that most identifiable information resides in marker dynamics rather than terminal measurements. Sobol analysis shows early markers depend on proliferation timing, whereas late mineralization is governed by nonlinear matrix maturation and parameter interactions. Together, these results show that endpoint assays constrain overall progression but do not uniquely identify underlying mechanisms. OsteoMin provides a framework linking differentiation dynamics to assay observables and a basis for assessing identifiability in endpoint-driven systems.

The ecological and evolutionary benefits of collective behaviours are rooted in the physical principles and physiological mechanisms underpinning animal locomotion. We propose a turbulence sheltering hypothesis that collective movements of fish schools in turbulent flow can reduce the total energetic cost of locomotion by shielding individuals from the perturbation of chaotic turbulent eddies. We test this hypothesis by quantifying energetics and kinematics in schools of giant danio (Devario aequipinnatus) compared to solitary individuals swimming under control and turbulent conditions over a wide speed range. We discovered that, when swimming at high speeds and high turbulence levels, fish schools reduced their total energy expenditure (TEE, both aerobic and anaerobic energy) by 63-79% compared to solitary fish. Solitary individuals spend [~]25% more kinematic effort (tail beat amplitude*frequency) to swim in turbulence at higher speeds than in control conditions. However, fish schools swimming in turbulence reduced their three-dimensional group volume by 41-68% (at higher speeds) and did not alter their kinematic effort compared to control conditions. This substantial energy saving highlighted a [~]261% higher TEE when fish swimming alone in turbulence are compared to swimming in a school. Schooling behaviour could mitigate turbulent disturbances by sheltering fish within schools from the eddies of sufficient kinetic energy that can disrupt the locomotor gaits. Providing a more desirable internal hydrodynamic environment could be one of the ecological drivers underlying collective behaviours in a dense fluid environment. One-Sentence SummaryThe collective movement of fish schools substantially reduces the energetic cost of locomotion in turbulence compared to that of swimming alone.

Movement is integral to animal life, and most animal movement is actuated by the same engine: skeletal muscle. Muscle input is typically mediated by skeletal elements, resulting in musculoskeletal systems that are "geared": at any instant, the muscle force and velocity are related to the output force and velocity only via a proportionality constant G, the "mechanical advantage". The functional analysis of such "simple machines" has traditionally centred around this instantaneous interpretation, such that a small vs large G is thought to reflect a fast vs forceful system, respectively. But evidence is mounting that a complete analysis ought to also consider the mechanical energy output of a complete contraction. Here, we approach this task systematically, and use the theory of physiological similarity to study how gearing affects the flow of mechanical energy in a minimalist model of a musculoskeletal system. Gearing influences the flow of mechanical energy in two key ways: it can curtail muscle work output, because it determines the ratio between the characteristic muscle work and kinetic energy capacity; and it defines how each unit of muscle work is partitioned into different system energies, i. e. into kinetic vs. "parasitic" energy such as heat. As a consequence of both effects, delivering maximum work in minimum time and with maximum transmission efficiency generally requires a mechanical advantage of intermediate magnitude. This optimality condition can be expressed in terms of two dimensionless numbers, which reflect the key geometric, physiological, and physical properties of the interrogated musculoskeletal system, and the environment in which the contraction takes place. Illustrative application to exemplar musculoskeletal systems predicts plausible mechanical advantages in disparate biomechanical scenarios; yields a speculative explanation for why gearing is typically used to attenuate the instantaneous force output (Gopt < 1); and predicts how G needs to vary systematically with animal size to optimise the delivery of mechanical energy, in superficial agreement with empirical observations. A many-to-one-mapping from musculoskeletal geometry to mechanical performance is identified, such that differences in G alone do not provide a reliable indicator for specialisation for force vs speed--neither instantaneously, nor in terms of mechanical energy output. The energy framework presented here can be used to estimate an optimal mechanical advantage across variable muscle physiology, anatomy, mechanical environment and animal size, and so facilitates investigation of the extent to which selection has made efficient use of gearing as degree of freedom in musculoskeletal "design".

Mathematical models of infectious disease dynamics are routinely fitted to surveillance data to estimate epidemiological parameters and inform public health decisions. Such data are typically discrete and noisy, but before attempting estimation, it is essential to ask whether the model structure itself permits unique parameter identification at least under perfect (continuous, noise-free) observations. This mathematical property of a model with respect to observation(s), known as structural identifiability, serves as a necessary precondition for reliable inference, since a model that fails this test cannot yield unique parameter estimates even from perfect data. In this study, we systematically investigate structural identifiability in various classes of compartmental epidemic models and establish two main findings. First, we present and deploy a methodology for assessing structural identifiability of epidemiological quantities of interest and demonstrate that the basic reproduction number exhibits identifiability across diverse model structures--including models with multiple transmission pathways and host-vector dynamics--even when individual parameters are not uniquely identifiable. These findings challenge the assumption that complete model identifiability is necessary for reliable epidemiological inference and suggest reformulating the central question from "is the model identifiable?" to "are the quantities that matter for the decision-making identifiable?" Second, we prove that incorporating minimal complementary data, as little as a single time-point measurement from an additional state variable, can make otherwise nonidentifiable models globally identifiable. This result has direct implications for surveillance design: rather than putting limited resources into frequent monitoring of multiple data streams or relying on external parameter estimates that may be uncertain or context-dependent, public health systems can strategically prioritize collecting high-quality complementary measurements.

Blood Plasma Viscosity (PV) is an established biomarker for numerous diseases. While PV colloquially refers to the shear viscosity, there is a second viscosity component--the bulk viscosity--that describes the irreversible fluid compressibility on short time scales. The bulk viscosity is acutely sensitive to solid-like suspensions, and obtainable via the longitudinal viscosity from acoustic attenuation measurements. Whether it has diagnostic value remains unexplored yet may be pertinent given the association of diverse pathologies with the formation of plasma suspensions, such as fibrin-microstructures in COVID-19 and long-COVID. Here we show that the longitudinal PV measured using Brillouin Light Scattering (BLS) can serve as a proxy for the shear PV of blood plasma, and exhibits a temperature dependence consistent with increased suspension concentrations in severe COVID-patient plasma. Our results open a new avenue for PV diagnostics based on the longitudinal PV, and show that BLS can provide a means for its clinical implementation.

The preferred stride ratio (PSR), defined as the ratio of step length to cadence, is approximately invariant across a wide range of walking speeds in healthy adults but breaks down at slow speeds. The lower speed boundary at which this constancy is broken was estimated by Murakami and Otaka (2017) to be approximately 62 m min-1 ({approx} 1.03 m s-1) on the basis of unstandardised K-means cluster analysis applied to data from 21 healthy adults at five speed conditions. The present report re-examines this estimate using the digitised individual-level scatter of Fig. 1-A and the published group-level statistics of Table 1 of that study, applying three breakpoint estimators in parallel: (i) unstandardised K-means (replicating the original method), (ii) a Gaussian mean-and-variance changepoint estimator, and (iii) a piecewise-linear regression on PSR. Applied directly to the digitised scatter (n = 84 resolved markers from a total of 105; 44 of 44 slow-walk markers, 40 of 61 normal-walk markers), the unstandardised K-means estimator returned 62.0 m min-1, matching the originally reported value to the reported precision; the mean-and-variance changepoint estimator returned 55 m min-1; and the piecewise-linear estimator was numerically unstable on the raw heteroscedastic data. To quantify uncertainty, 5 000 Monte Carlo realisations of synthetic individual-level data were generated from a bivariate truncated-normal model conditioned on the published condition means and standard deviations and on the published within-cluster speed-PSR correlations. The Monte Carlo distributions gave median estimates of 61 m min-1 (95 % MC interval 55-67) for unstandardised K-means, 39 m min-1 (29-53) for the mean-and-variance changepoint estimator, and 35 m min-1 (19-49) for piecewise-linear regression. Under a log-normal sensitivity model the corresponding intervals were 60 [55, 66], 34 [20, 58], and 19 [5, 42] m min-1. The likelihood-based estimator placed the central tendency substantially below 62 m min-1, and its Monte Carlo intervals did not include the original boundary under either marginal-distribution model. An additional robust heteroscedastic segmented profile-likelihood analysis on log-PSR yielded lower Monte Carlo median breakpoints across all model specifications, although the full-variance intervals overlapped the original K-means boundary. The qualitative finding of Murakami and Otaka -- that PSR constancy breaks down at slow walking speeds -- is supported by the present reanalysis. The original 62 m min-1 boundary is reproduced under the unstandardised K-means estimator, where it reflects the location of the largest density gap in the published five-condition speed sampling rather than a formally estimated changepoint; estimators formally designed for changepoint detection localise the joint PSR mean-and-variance transition substantially below this value. O_FIG O_LINKSMALLFIG WIDTH=162 HEIGHT=200 SRC="FIGDIR/small/720900v2_fig1.gif" ALT="Figure 1"> View larger version (41K): org.highwire.dtl.DTLVardef@2bb53dorg.highwire.dtl.DTLVardef@187d9bborg.highwire.dtl.DTLVardef@1e7a6a0org.highwire.dtl.DTLVardef@16c587b_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 1.C_FLOATNO Reproduction and likelihood-based extension of the boundary reported in Murakami and Otaka [5]. (A) Digitised individual-level scatter from Fig. 1-A of [5] (n = 84 resolved markers from a total of 105: 44 of 44 slow-walk markers and 40 of 61 normal-walk markers). The dashed vertical line marks the value 62.4 m min-1 as drawn in the original figure. (B) PSR variance amplification across the five speed conditions, expressed as Var(PSR)/Var(PSR)Preferred, on a logarithmic vertical axis. (C) Distributions of the breakpoint estimates over N = 5 000 Monte Carlo realisations under the bivariate truncated-normal model with cluster-specific within-cluster correlations: unstandardised K-means (median 61 m min-1), the Gaussian mean-and-variance changepoint estimator (median 39 m min-1), and piecewise-linear regression on PSR (median 35 m min-1). The dashed vertical line marks 62.4 m min-1. (D) Sensitivity of each estimator to the choice of marginal-distribution model (truncated normal vs. log-normal); error bars are 95 % Monte Carlo simulation intervals. (E) PSR mean {+/-} SD across the five speed conditions (Table 1 of [5], height-adjusted). C_FIG O_TBL View this table: org.highwire.dtl.DTLVardef@24fe39org.highwire.dtl.DTLVardef@ae8fdborg.highwire.dtl.DTLVardef@66a473org.highwire.dtl.DTLVardef@b6ad84org.highwire.dtl.DTLVardef@139bca7_HPS_FORMAT_FIGEXP M_TBL O_FLOATNOTable 1.C_FLOATNO O_TABLECAPTIONSource data reproduced from Murakami and Otaka [5], height-adjusted, n = 21 per condition. C_TABLECAPTION C_TBL

Many idle insects exhibit discontinuous gas exchange cycles (DCGs). During DCGs, CO2 is released in discrete bursts, followed by periods of negligible gas exchange. The standard metabolic rate (SMR) is thus determined to first order by the product between cycle frequency (fc) and burst volume (Vb, SMR {approx} fc{middle dot} Vb). The evolutionary allometry of these parameters is well studied, but it remains unclear if their static allometry, measured in individuals of the same species, sharing the same ontogenetic stage, follows the same patterns. To address this question, we investigate the static allometry of DCGs in Atta cephalotes leaf-cutter ants workers varying by two orders of magnitude in body mass. The SMR allometry significantly exceeded the standard prediction from the nutrient supply network model, and differed from the SMR allometry observed across insects. This disproportional increase was exclusively achieved by an increase in Vb, perhaps because fc is stabilised by neural and mechanical constraints. It may be necessitated by the positive allometry of the largest muscle in Atta--the mandible closer muscle--which increases with a virtually identical allometric coefficient, providing further evidence that the principles of symmorphosis may be upheld in insects.

Human mobility plays a critical role in the transmission dynamics of infectious diseases, influencing both their spread and the effectiveness of control measures. In the process of quantifying the real-time situation of an epidemic, the instantaneous reproduction number Rt appears to be one of the useful metrics widely used by public health researchers, officials, and policy makers. Since individuals can contract infections both within their region of origin and in other regions they visit, ignoring human mobility in the estimation process overlooks its impact on transmission dynamics and can lead to biased estimates of Rt, potentially misrepresenting the true epidemic situation. Our study explicitly integrates human mobility into a renewal-equation based disease transmission model to capture the mobility-driven effect on transmission. By incorporating pathogen-specific generation-time distribution, observational delay, the framework is epidemiologically informed and flexible to a wide range of diseases. We primarily validate the approach using simulated data, and demonstrate the limitations of estimating Rt without considering mobility. We then apply it to two real-world mobility settings using SARS-CoV-2 mortality data: the regions of England and the LTLAs of North East region of England, and uncover the mobility driven effect on transmission at different spatial resolutions. This framework uses non-identifiable and widely accessible publicly available datasets, demonstrating its practical applicability and supporting better-informed and more targeted public health measures. Author summaryThe real-time or instantaneous reproduction number Rt is a key metric for assessing the state of an epidemic at any given time. When estimating these numbers across multiple connected regions, human mobility plays a crucial role, as movement patterns significantly influence disease transmission. Traditional epidemic models often assume homogeneous mixing, which does not reflect real-world interactions. On the other hand, individual-based models incorporate heterogeneous mixing at individual level but demands an extremely refined data and substantial computational support. To address these challenges, we employ a renewal equation-based transmission framework, particularly useful for its effectiveness in real-time epidemic analysis, by incorporating heterogeneous mobility flows at a chosen spatial resolution. This yields the estimates of spatially connected instantaneous reproduction number for each region. This improved understanding enables better assessment of the impact of mobility on disease transmission spread, and provides valuable insights for designing targeted epidemic control and intervention strategies.

Human walking is often considered an inverted pendulum during single support, suggesting conservative dynamics. Gait consists of discrete steps connected by mechanically costly transitions. We examine how step length, walking speed, and work capacity jointly constrain walking mechanics. Using a powered simple walking model, minimum speed required to complete a step of given length is derived based on gravitational work; below this threshold, forward progression becomes mechanically infeasible, and the next heel-strike occurs early, producing shorter steps. Comparisons with empirical step length-speed relationships show that humans walk at higher speeds and require greater push-off work, indicating energy dissipation. We extend pendular dynamics by incorporating hip torque, a linearized axial force model, and muscle intervention. This framework reproduces key GRF features, including the M-shaped profile, without prescribing force trajectories a priori. Fitted parameters suggest reduced average loading (CBaseline < 1), active mid-stance unloading (Am < 0), and narrowly timed muscle action (small{sigma} m). Parameter studies show that increasing step length or speed increases transition work and peak forces, while hip torque timing indicates mechanical cost is minimized when energy modulation occurs after mid-stance. These findings indicate that preferred walking speed emerges from feasibility and work-capacity constraints, not energetic optimality alone.

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 adaptive value, and motivate broader work identifying distributions across species.

A key theoretical challenge posed by single-molecule studies is the inverse problem of deducing the underlying molecular dynamics from the time evolution of low-dimensional experimental observables. Toward this goal, a variety of low-dimensional models have been proposed as descriptions of single-molecule signals, including random walks with or without conformational memory and/or with static or dynamics disorder. Differentiating among different models presents a challenge, as many distinct physical scenarios lead to similar experimentally observable behaviors such as anomalous diffusion and nonexponential relaxation. Here we show that information-theory-based analysis of single-molecule time series, inspired by Shannons work studying the information content of printed English, can differentiate between Markov (memoryless) and non-Markov single-molecule signals and between static and dynamic disorder. In particular, non-Markov time series are more predictable and thus can be compressed and transmitted within shorter messages (i.e. have a lower entropy rate) than appropriately constructed Markov approximations, and we demonstrate that in practice the LZMA compression algorithm reliably differentiates between these entropy rates across several simulated dynamical models.

Organisms and machines must use measured sensory cues to estimate unknown information about themselves or their environment. Cleverly applied sensor motion can be exploited to enrich the quality of sensory data and improve estimation. However, a major barrier to modeling such active sensing problems is the lack of empirical, yet rigorous, tools for quantifying the relationship between movement and estimation performance. Here, we introduce "BOUNDS: Bounding Observability for Uncertain Nonlinear Dynamic Systems". BOUNDS can discover patterns of sensor motion that increase information and reduce uncertainty in either real or simulated data. Crucially, it is suitable for high dimensional and partially observable nonlinear systems with sensor noise. We demonstrate BOUNDS through a case study on how flying insects estimate wind properties, showing that specific active sensing motifs improve estimation. Additionally, we present a framework to refine sporadic estimates from active sensing. When combined with an artificial neural network, we show that the information gained via active sensing in real Drosophila flight trajectories is suitable for precise wind direction estimation. Collectively, our work will help decode active sensing in organisms and inform the design of estimation algorithms for machines.

Understanding structural similarities across dynamical systems at different scales remains a central problem in nonlinear science [1, 3]. Here we propose a modeling framework for cross-scale morphogenetic dynamics, termed Generalized Morphogenesis Theory (GMT), based on a flow-inertia formulation: O_FD O_INLINEFIG[Formula 1]C_INLINEFIGM_FD(1)C_FD where S denotes system state, E environmental input, F (E, S) a driving function, and {micro}(S) an inertia function representing resistance to change. This formulation provides a structural representation that encompasses several classical dynamical models--including Newtonian relaxation, logistic growth, and reaction-diffusion systems [13]--under appropriate parameterizations. Non-dimensionalization reveals a small set of control parameters governing regime transitions. Empirical validation is performed across two independent scales. At the organism scale, crop growth time-series datasets from multiple species exhibit consistent multiplicative dynamics F (E, S) = f (E) {middle dot} S, statistically preferred over additive alternatives in 5 of 6 independently tested systems ({Delta}AIC ranging from +2 to +891; R2 up to 0.98). Independently estimated inertia time constants agree in two plant systems (cucumber:{tau} = 3.7 days, CV=3.3%; maize:{tau} = 36.8 days, CV=17.3%), with the 10-fold ratio consistent with structural complexity differences. At the molecular scale, publicly available perturbation transcriptomics datasets (Perturb-seq) show directional response structures consistent with the proposed flow-inertia decomposition (93% causal direction agreement across three independent datasets; p < 10-25). Across domains, recurrent dynamical motifs are organized into 12 canonical design patterns, derived from a 2 x 2 x 3 orthogonal structure (4 elementary operations x 3 temporal scales), associated with stability classes and bifurcation conditions. These results suggest that the flow-inertia formulation functions as a domain-independent structural modeling principle for dissipative morphogenesis.

Host-microbe interactions constitute dynamical systems that can be represented by mathematical formulations that determine their dynamic nature, and are categorized as deterministic, stochastic, or chaotic. Knowing the type of dynamical interaction is essential for understanding the system under study. Very little experimental work has been done to determine the dynamical characteristics of host-microbe interactions and its study poses significant challenges. The most straightforward experimental outcome involves an observation of time to death upon infection. However, in measuring this outcome, the internal parameters, and the dynamics of each particular host-microbe interaction in a population of interactions are hidden from the experimentalist. To investigate whether a time-to-death (time to event) dataset provides adequate information for searching for chaotic signatures, we first determined our ability to detect chaos in simulated data sets of time-to-event measurements and successfully distinguished the time-to-event distribution of a chaotic process from a comparable stochastic one. To do so, we introduced an inversion measure to test for a chaotic signature in time-to-event distributions. Next, we searched for chaos, in time-to-death of Caenorhabditis elegans and Drosophila melanogaster infected with Pseudomonas aeruginosa or Pseudomonas entomophila, respectively. We found suggestions of chaotic signatures in both systems, but caution that our results are preliminary and highlight the need for more fine-grained and larger data sets in determining dynamical characteristics. If validated, chaos in host-microbe interactions would have important implications for the occurrence and outcome of infectious diseases, the reproducibility of experiments in the field of microbial pathogenesis and the prediction of microbial threats. ImportanceIs microbial pathogenesis a predictable scientific field? At a time when we are dealing with Coronavirus Disease 2019 (COVID-19) there is intense interest in knowing about the epidemic potential of other microbial threats and new emerging infectious diseases. To know whether microbial pathogenesis will ever be a predictable scientific field requires knowing whether a host-microbe interaction follows deterministic, stochastic, or chaotic dynamics. If randomness and chaos are absent from virulence, there is the hope for prediction in the future regarding the outcome of microbe-host interactions. Chaotic systems are inherently unpredictable although it is possible to generate shortterm probabilistic models, as is done in applications of stochastic processes and machine learning to weather forecasting. Information on the dynamics of a system is also essential for understanding the reproducibility of experiments, a topic of great concern in biological sciences. Our study finds preliminary evidence for chaotic dynamics in infectious diseases.

AO_SCPLOWBSTRACTC_SCPLOWMedical practice in the intensive care unit is based on the supposition that physiological systems such as the human glucose-insulin system are reliabile. Reliability of dynamical systems refers to response to perturbation: A dynamical system is reliable if it behaves predictably following a perturbation. Here, we demonstrate that reliability fails for an archetypal physiological model, the Ultradian glucose-insulin model. Reliability failure arises because of the presence of delay. Using the theory of rank one maps from smooth dynamical systems, we precisely explain the nature of the resulting delay-induced uncertainty (DIU). We develop a recipe one may use to diagnose DIU in a general dynamical system. Guided by this recipe, we analyze DIU emergence first in a classical linear shear flow model and then in the Ultradian model. Our results potentially apply to a broad class of physiological systems that involve delay.

The ability of chemotactic populations to localize and track targets in fluctuating environments depends critically on the temporal structure of environmental signals. Using a minimal agent-based framework of non-interacting run-and-tumble cells implementing an E. coli-inspired temporal sensing strategy, populations are exposed to static and moving chemoattractant fields perturbed by noise with controlled temporal structure, spanning white, pink (1/f), and correlated Ornstein-Uhlenbeck processes. Chemotactic populations are found to act as temporal filters, robustly suppressing fast fluctuations while remaining highly sensitive to slowly varying perturbations. As a consequence, chemotactic performance is governed not by noise amplitude, but by its temporal correlations. By continuously varying the noise correlation time, a critical regime emerges at{tau} c [~]{tau} run, where aggregates lose stability, tracking errors increase sharply, and spatial dispersion rises. Power spectral analysis further shows that the low-frequency power fraction of the signal provides a strong predictor of failure, outperforming total signal variance and establishing a direct link between environmental noise spectra and collective behavior. Introducing external flow reveals that advective transport amplifies noise-induced destabilization when it overlaps the chemotactic capture region, defining a combined spatiotemporal constraint on robustness. Together, these results identify temporal correlations and spectral structure as fundamental control parameters for chemotactic organization and provide a quantitative framework for predicting and designing collective behavior in fluctuating environments.

Conventional diagonal stride skiing traditionally includes a glide phase, characterised by a period of relatively passive gliding on one ski. While the glide phase may take advantage of low ski-snow friction, it does not exhibit the same whole-cycle mechanical energy fluctuations seen in running or walking on foot. A new sub-technique, known as running style, substantially reduces the glide phase and may alter the role of elastic tissues, making the movement pattern more similar to uphill running on foot in its temporal organisation. We examined knee extensor and plantar flexor muscle-tendon behaviour in eight competitive skiers performing conventional diagonal and running techniques on a treadmill inclined at 10{degrees}. Using synchronised ultrasonography, 3D kinematics, ski forces and EMG, we quantified gastrocnemius medialis and vastus lateralis fascicle and muscle-tendon unit (MTU) dynamics in both the running (RUN) and conventional (CON) styles. Shorter glide and total cycle durations during RUN shifted MTU peak length and velocity earlier during the kick phase. Fascicles in both muscles operated at similar velocities across techniques, showing MTU-fascicle decoupling. Vastus lateralis fascicles shortened at higher absolute peak velocities than gastrocnemius in both conditions, while normalised velocities were similar. RUN increased preactivation and advanced EMG timing, while integrated EMG during the kick was lower compared to CON. These findings suggest that, despite large shifts in external mechanics between glide-based and more running-like skiing, elastic tissues may help stabilise fascicle behaviour and preserve a similar contractile strategy across muscles and techniques.

Many complex natural systems undergo shifts in dynamics at particular points in time. Examples include phase transitions in gene expression during the cell cycle, introduced species affecting predator-prey interactions, and disease outbreaks responding to intervention measures. Such changepoints partition timeseries into different dynamical regimes characterized by distinct parameter sets, and inference on both the changepoints and regime-specific dynamical parameters is of primary interest. Conventional approaches to analyzing switching dynamical systems first estimate changepoints, and then estimate dynamical parameters assuming the changepoints are fixed and known. Such two-stage approaches are ad-hoc, can introduce biases in the analysis, and do not fully account for uncertainty. Here, we introduce a rigorous, simulation-based inference framework that simultaneously estimates changepoints and model parameters from noisy data while admitting full uncertainty. We use simulation studies of oscillatory predator-prey dynamics and stochastic gene expression to demonstrate that our method yields accurate estimates of changepoints and model parameters together with appropriate uncertainty bounds. We then apply our approach to a real-world case study of COVID-19 intervention effects, and show that our inferred changepoints aligned closely with the actual dates of intervention implementation. Taken together, these results suggest that our framework will have broad utility in diverse scientific domains.