Chaos, Solitons & Fractals

Violent conflicts increasingly involve multiple armed actors competing for influence over shared civilian populations, creating complex dynamics that challenge conventional security analysis and policy design. We present a framework that adapts epidemiological methods informed by the conflict landscape in Nigeria to model multi-actor violent conflict as an epidemic process. We derive a basic insecurity reproduction number ($R_0$), identify violence-free and persistent-violence equilibria, and introduce a novel Civilian Harm Index (CHI) to quantify humanitarian impact. Sensitivity analyses identify recruitment, ideological support from civilian populations, and abduction as the key drivers of conflict persistence and civilian harm. The framework reveals several counterintuitive findings. Interventions that most effectively suppress violence transmission are not necessarily those that minimise civilian harm, demonstrating that epidemic control and humanitarian protection may require distinct optimisation criteria. Likewise, interventions effective against one armed actor may be ineffective, or even counterproductive, when applied uniformly across groups. In addition, prisoner exchange and ransom payments increase violence persistence and civilian harm. Although developed as an illustrative rather than predictive framework, our results show that epidemiological methods provide quantitative metrics for evaluating intervention priorities and trade-offs in complex multi-actor conflicts.

A novel mathematical framework to define the threshold of action potentials in excitable cells is presented. Unlike previously applied methods that rely on approximations or bifurcations, the approach focuses on the geometry of membrane potential trajectories. The changes in concavity during the upstroke of an action potential can be directly obtained from a time series of voltages. The concavity criterion is then extended to models based on autonomous dynamical systems where the changes in concavity can be obtained analytically from a curve of inflection points in phase space. The inflection point manifold defines a region required for excitability: all the orbits that cross it contain action potentials, and all the trajectories that contain action potentials are in it. This analytical principle can then be used to define excitability in a dynamical system, and also a measure of excitability that enables quantification and comparisons of excitability across dynamical system. The measure provides a way to compare the excitabilities of systems that model neurons with different electrophysiological phenotypes and consider different stimulus conditions. The traditionally vague physiological concept of electrical excitability is transformed into a rigorous analytical description by considering the time-dependent curvature of the membrane potential. The criterion is robust across smooth, single compartment models of electrical excitability and can be can be extended to single compartment models in higher dimensions, and multicompartment models as well.

Human Papillomavirus (HPV) infection among men who have sex with men (MSM) has become a significant public health concern, particularly in countries where male vaccination is unavailable. Given the high susceptibility of MSM to HPV and anal cancer, and the unavailability of HPV vaccination for males in low- and middle-income countries (LMICs), there is a need to identify alternative interventions for reducing disease transmission and burden in this population. The novel mathematical model presented in this article couples smoking behavior dynamics with HPV transmission and anal cancer progression among MSM. Smoking reduction is introduced as an intervention to assess its effects on disease transmission and burden. The basic reproduction number (R0) is derived using the next-generation matrix method, and a global sensitivity analysis is performed using partial rank correlation coefficients (PRCC) to identify the influence of model parameters on RR0. Further, the theoretical analysis of the model reveals a backward bifurcation, implying that RR0 < 1 is necessary but not sufficient to eradicate the disease. The study finds that smoking reduction among MSM reduces HPV infection and anal cancer burden relative to baseline projections without intervention. The joint effect of smoking reduction and vaccination shows that the critical vaccination coverage needed to achieve RR0 <1 decreases as the level of smoking reduction increases. A similar outcome is observed for contact reduction. These findings highlight the importance of concurrent interventions, which can significantly curtail the spread of HPV and reduce disease burden in both the high-risk group and the general population.

This paper introduces a sensorimotor learning framework for a corticocerebellar network, grounded in the perspective of population dynamics. Using an optimal control theory approach, the cerebellum model enhances preparatory activity through premotor input, allowing the motor cortex to reach the desired initial conditions for movement more efficiently. Unlike traditional motor learning approaches that focus on acquiring new skills, this paradigm emphasizes automatization of already executable behaviors through repetition driven by intrinsic motivation. The proposed model is evaluated using a center-out reaching task, demonstrating that the role of the cerebellum is to shorten the preparatory period required for the successful execution of the movement. These findings suggest that corticocerebellar interactions play a crucial role in optimizing motor preparation, offering insight into the neural mechanisms underlying movement efficiency.

Classical neuronal cable theory relies on quasi-static electric field approximations and neglects magnetic induction, Lorentz force coupling, and transient electromagnetic currents, limiting its ability to fully characterize action potential propagation within geometrically branched axons and dendrites. This work develops a coupled Maxwell-electromagnetic cable framework by integrating finite-difference time-domain (FDTD) solutions of Maxwells equations with extended Hodgkin-Huxley and Fitzhugh-Nagumo membrane dynamics, incorporating magnetic gating perturbations, electromagnetic trans-membrane currents IEM, and nanoscale quantum corrections for thin neural segments. Controlled propagation experiments are designed to quantify deviations from standard cable predictions across asymmetric and symmetric axonal bifurcation geometries. Numerical results demonstrate that inductive magnetic effects lower the critical branch radius for junction conduction failure and break symmetric action potential invasion in geometrically identical child branches under external transverse magnetic fields. An electromagnetic corrected geometric ratio GREM is proposed to revise impedance-matching conditions at branch points, accounting for size-dependent axial current imbalance induced by magnetic and displacement currents. Parent axon conduction velocity deviates substantially from the canonical [Formula] scaling law when electromagnetic feedback and quantum charge distributions are included, triggering early signal blockage at large cable diameters. Collectively, this study establishes that quasi-static cable models underestimate electromagnetic corrections to propagation speed, waveform shape, and bifurcation transmission fidelity; the coupled Maxwell-cable framework provides a comprehensive multi-physics tool for modeling electrodynamic signal behavior in complex neuronal architectures.

A fundamental biological process of transcription occurs in the cell nucleus, which is a complex medium that also contains multiple heterogeneous structures known as biomolecular condensates. Interestingly, some of these condensates contain mRNA molecules in addition to proteins, suggesting an important cellular role in transcription that is not yet well understood. In this work, we develop a minimal theoretical framework for quantitative investigation of the role of reversible mRNA condensation in transcription. Our discrete-state stochastic approach accounts for the most relevant processes, allowing us to explicitly evaluate the properties of the system and clarify the effects of condensation. Analytical calculations supported by computer simulations suggest that reversible mRNA condensation influences the transcription processes by maintaining a constant level of free mRNA in the nucleoplasm while lowering the degree of stochastic noise and increasing the robustness against external perturbations. Physicochemical arguments are presented to explain these observations. The proposed theoretical framework elucidates important microscopic aspects of transcription, providing a convenient quantitative tool for investigating complex biological phenomena.

Beta-band (13-30 Hz) oscillations are increasingly understood to occur as transient "bursts" rather than sustained rhythms, with altered burst dynamics, specifically increased duration and power alongside reduced burst rates, in patients with Parkinsons disease (PD). In this study, we utilise resting state magnetoencephalography (MEG) data from healthy adults to quantify the temporal fluctuations in the beta-band, and examine the distributions of burst statistics. We then fit a stochastic next-generation neural mass model to these empirical statistics using a Genetic Algorithm. Systematic parameter sweeps reveal that reducing background drive to excitatory and inhibitory neuronal populations reproduces the altered burst statistics observed in PD. Crucially, we show that strengthening synaptic coupling can counteract these deficits and restore healthy bursting dynamics. Together, this work establishes a computational framework linking cellular-level mechanisms to macroscale burst statistics, and highlights potential targets for therapeutic neuromodulation in movement disorders. Author summaryBrain activity is comprised of rhythmic electrical patterns called "brain waves." Traditionally, these waves were viewed as smooth and continuous, but recent evidence reveals that they actually occur in brief, intense bursts. In conditions such as Parkinsons disease, these bursts become altered--lasting longer, growing stronger, and occurring less frequently. In this study, we developed a mathematical model of brain tissue to understand what drives these burst patterns. Using real brain scans from healthy human volunteers, we tuned our model with an optimisation algorithm until its simulated bursts closely matched real human brain activity. We then systematically varied the models settings to investigate how abnormal bursting arises in disease. We discovered that reducing the background signals to the brain cells reproduces the burst alterations seen in Parkinsons disease. Importantly, our simulations showed that strengthening the connections between brain cells can counteract this deficit, restoring healthy burst patterns. By connecting microscopic cell properties to whole-brain rhythms, our work offers new insights into how movement disorders disrupt brain networks and highlights potential cellular targets to guide future brain stimulation therapies or medications.

With 302 neurons and a rigorously characterized connectome, the nematode Caenorhabditis elegans represents a powerful model organism to study the fundamental roles of neuronal circuits in behavior. However, despite the breadth of research, many questions remain unanswered regarding how these organisms are able to successfully navigate their environment. Here, we present a biologically grounded dynamical circuit model for the investigation of sensory-guided behavior during C. elegans chemotaxis. Our mathematical model consists of the chemosensory neuron AWA, interneurons RIM and RIA, motor neurons, including SMDs and RMDs, and body wall muscles that provide proprioceptive feedback through stretch receptors. After optimization with an evolutionary algorithm, the model locomotes effectively toward a chemical attractant, realistically capturing nematode chemotactic behavior. Chemotaxis is ensured by sharp turns, which resemble the omega turns of living nematodes, as a key emergent property of the model. The sharp turning behavior is triggered by decreases in the concentration of the attractant. These result in reduced AWA activity, which in turn triggers disinhibition of RIM and subsequent changes in RIA oscillations. The ensuing coordinated changes in downstream motor neurons activity patterns produce sharp turns, which correct the nematodes path, so that the model worm heads toward the attractant, and remains at its proximity, after it reaches the gradient peak. The proposed framework, along with its emergent dynamics, provides new insights into the minimum requirements for C. elegans circuitry to display major features of its chemotactic behavior, including omega turns. In parallel, it generates experimentally testable hypotheses with respect to the participating neuronal elements.

In the two-process model of sleep-wake regulation, circadian-modulated thresholds time every sleep onset and awakening, yet they remain free parameters rather than quantities derived from neuronal dynamics. This limitation leaves the framework unable to predict how sleep patterns change when neuromodulatory drive is altered, as in aging and narcolepsy. Here we close that gap by deriving closed-form, circadian-modulated threshold expressions from the Phillips-Robinson model with explicit orexinergic excitation of the wake-promoting population. Within this single threshold geometry, aging and narcolepsy appear as opposite deformations along the orexinergic axis: age-related hyperexcitability of orexin neurons elevates the sleep-onset boundary and creates a fragility regime in which minor nocturnal disturbances trigger premature awakenings, whereas orexin loss depresses the same boundary toward the wake-onset threshold and produces the rapid state fragmentation of narcolepsy. Concurrently, reduced circadian amplitude compresses the inter-threshold corridor, advancing sleep onset and shortening sleep duration. These results convert the classical two-process thresholds from descriptive conveniences into mechanistic organizers of sleep-wake dynamics across healthy aging and orexin deficiency. Author summaryThe classical two-process model of sleep relies on a pair of switching thresholds that have been imposed by hand rather than derived from the neurons that actually stabilize sleep and wakefulness. Here we remove this limitation: starting from a biophysical mean-field model of the sleep- and wake-promoting populations, and adding the orexin system that stabilizes arousal, we derive the sleep-onset and awakening thresholds analytically from the bifurcation geometry of the underlying dynamical system. These closed-form thresholds depend explicitly on circadian phase, homeostatic state, and orexinergic tone, revealing that aging and narcolepsy are opposite deformations of a single threshold corridor along one orexinergic axis. In aging, orexin hyperexcitability raises the sleep-onset barrier past a sharp "arousal fragility boundary," beyond which a minor disturbance triggers irreversible awakening; in narcolepsy, orexin loss collapses the same barrier and fragments sleep while paradoxically preserving total sleep time. We further find, contrary to common assumption, that orexin sustains wakefulness chiefly by raising the barrier to falling asleep rather than by resisting awakening. This work turns phenomenological sleep thresholds into physics-derived organizers of behavior, providing a mechanistic bridge from neuronal circuitry to whole-organism sleep dynamics.

Structural network representations of metastatic dissemination typically focus on static topology without resolving transport dynamics, relaxation timescales, or steady-state behaviour. Here, we formulate a discrete Markovian transport model on a directed higher-order network with transition rates derived from qualitative clinical affinity classes. By constructing a non-Hermitian row-stochastic transfer operator, we characterise the relaxation dynamics through its spectral decomposition. The system exhibits a fast-mixing regime characterised by a spectral gap of {gamma} {approx} 0.67, corresponding to a characteristic relaxation timescale of {tau} {approx} 1.49 discrete steps, with the influence of the primary tumour origin progressively attenuated during dissemination. Convergence towards a non-equilibrium steady state (NESS) is accompanied by a reduction in Shannon entropy, concentrating probability mass within specific topological sinks. This spectral relaxation delineates two distinct dynamical regimes: early transient dissemination (n < {tau}), dominated by local organ-specific transition probabilities (organotropism), and the asymptotic regime (n > {tau}), determined increasingly by the global transport architecture of the network. Comparison with independent clinical and autopsy observations across 21 primary tumours and 23 target organs indicates that the predicted stationary distribution is consistent with the observed hierarchy of metastatic organ involvement.

The COVID-19 pandemic triggered an unprecedented volume of real-time discourse on social media platforms, with Twitter serving as a global forum for public reactions, fears, and evolving narratives. Traditional sentiment analysis approaches treat tweets as independent, static samples, failing to capture the temporal evolution and geographic heterogeneity of public opinion. This paper presents a comprehensive spatio-temporal framework that integrates fine-grained sentiment classification using COVID-Twitter-BERT with dynamic topic modeling via BERTopic to automatically discover and track evolving narratives. Using a corpus of 2.4 million geolocated tweets collected between January 2020 and June 2022, our analysis reveals distinct pandemic phases: early fear-driven narratives about mask shortages (Q1 2020), vaccine optimism followed by polarization (2021), and pandemic fatigue (2022). Regional comparisons show significant differences, with US discourse dominated by freedom-versus-mandate debates while European discussions emphasized collective solidarity. Our framework achieved 76% F1-score in sentiment classification and successfully identified 50 distinct narratives with high coherence scores. This work provides a powerful methodology for real-time epidemiological narrative surveillance and crisis communication monitoring.

This study presents improvements to the Hodgkin-Huxley (HH) models of ionic conductance and action potential generation. Sodium and potassium conductances are expressed by a single analytical formula describing the impulse response of a convolution of exponential distributions within a short-memory integration space. Treating transmembrane ion transit duration as a random variable, conductance profiles are interpreted as realizations of the probability density functions governing ionic movements. Applying the central limit theorem, the lognormal distribution emerges as the asymptotic profile of ionic conductances, constituting a fundamental primitive for such biosignals. A temporal state-transition paradigm describes the action potential waveform through four successive membrane potential transitions. Applied to electrophysiological recordings from lamprey reticulospinal neurons, this framework enables indirect estimation of key physiological quantities, including depolarization threshold, Nernst potentials, and net ion fluxes across the membrane. These advances open new perspectives for parameter estimation from experimental data and neuronal network simulation.

Time compaction theory is a general framework explaining how a brain can efficiently deal with dynamic situations occurring in, e.g., sports games. It involves a geometric representation of the time dimension, which enables effective learning and strategic action planning. The theory has recently received experimental support in humans. However, its current computational model has an important limitation: it does not account for deliberate waiting and speed modulation, behaviors ubiquitous in natural environments. This work substantially extends the original model formulation by a dimensional lifting of an n-D workspace into (n + 1)-D mental space, where time remains geometrically embedded. The proposed biologically inspired computational model can generate adaptive behavior across increasingly complex situations, from navigation in everyday social environments to competitive sports. Furthermore, by actively conditioning the expected responses of other agents and stabilizing future predictions, we introduce the concept of uncertainty points in sequences of generalized cognitive maps to support the generation of adaptive strategies in interactive environments, where future prediction has a limited time horizon. Thus, we provide a mechanism for chaining short-term solutions into long-term strategies, which is illustrated by simulating the behavior of a player in a real football game. Author summaryHumans often anticipate future interactions in dynamic environments. Many behaviors, such as avoiding other pedestrians, letting someone pass through a narrow corridor, or reproducing the kind of dribbling maneuvers performed by elite football players, require deciding not only where to move but also when to move. Existing theories suggest that the brain simplifies such situations by representing future interactions as static spatial maps, making them easier to learn and recall. However, current computational models cannot naturally account for common behaviors such as waiting, slowing down, or modulating speed. Here we show that these behaviors readily emerge if the model space is extended by an additional virtual coordinate that encodes accumulated waiting rather than physical time. The proposed model simultaneously admits a wide variety of behaviors, including speed modulation, multigoal decisions, and compound actions, while preserving the principles of time compaction. We illustrate the model in everyday situations and by reproducing two real football plays, comparing the observed behaviors with model simulations. Our results suggest computational principles through which the human brain may efficiently represent, memorize, and exploit dynamic situations.

Within the studies of stochastic gene expression, apart from the variability of copy number of gene products, the problems of threshold crossing of those products are biologically important as they often lead to terminal cellular events. Here, we study the threshold crossing problem of the messenger ribonucleic acid (mRNA) and present an exact probability distribution of first passage times in Laplace space. The function furnishes moments of any order and also predicts the characteristic time of the exponential tail of the distribution, which we match against Gillespie simulations. We find that all the measures of relative fluctuations of the threshold crossing times show U-shapes within this simple model of mRNA, as was found earlier in more mathematically involved models of threshold crossing time statistics of proteins. Furthermore, we extend the exact formula to include the phenomenon of DNA duplication and the corresponding doubling of transcription rate. As expected, the distribution varies considerably depending on the onset of the duplication stage within the cell cycle.

The study of tissue dynamics has been stimulated during the last decades thanks to the use of quantitative descriptions, with the development of several theoretical and computational frameworks, many of them revolving around the notion of reaction-diffusion systems, eventually with additional structure variables beyond time and space. The use of structure variables can accommodate phenotypic traits. In this work, we study a family of competition models, where a given population depends on a resource (e.g. oxygen) and several populations are competing for it. Our quantitative description incorporates phenotypic traits and heterogeneity at the level of cell cycle variations, which influence replication rates via oxygen consumption. This enables us to replicate the fitness of specific subpopulations to environmental conditions (e.g. oxygen shortage or external influences). Using numerical simulations, we show that such models display dynamical pattern formation in the form of coupled travelling wave profiles that expand or retreat at the same wave speed. The full theoretical analysis of such dynamics is quite involved; to circumvent this difficulty, we introduce a quasi-stationary approximation for the resource dynamics. We find that this approximation can reproduce the overall behaviour very accurately, with the additional benefit of allowing theoretical treatment of the reduced model. In this way, we provide estimates on the wave speed which are numerically shown to be robust across a wide range of macroscopic parameters of the full model. The wave speeds are thus found to depend strongly on the proliferation rate of the fittest population, resembling a winner-takes-all dynamics.

The global market concentrates extractive pressure on lands held by Indigenous peoples, including peoples living in isolation, for whom free, prior and informed consent cannot be obtained and protection must therefore rest on territorial instruments. Halmahera, Indonesia, holds some of the worlds largest lateritic nickel reserves beneath a lowland rainforest inhabited by the Hongana Manyawa, yet the trajectory of land use and cover change across the island has not been quantified. We characterised land use and cover change over the 17,437 km2 island between 2014 and 2024 using MapBiomas time series, and projected a business-as-usual scenario to 2054 with a stochastic cellular-automata model implemented in Dinamica EGO, calibrated with weights of evidence on eight variables describing mining and logging concessions, transport infrastructure, settlements and previous clearing. Forest covered 83.0% of the island in 2014 and 82.1% in 2024; under unchanged policy it falls to 73.7% by 2054, a net loss of 162 thousand ha, or 11.2% of the 2014 baseline, at gross rates of 47,000-51,000 ha per decade. Deforestation probability is highest within 500 m of previous clearing and declines with distance from settlements, cities and mining sites, while proximity to national parks carries a negative weight of evidence. The frontier is self-propagating and spatially predictable, and legally designated territory retains forest within it. Protecting the Hongana Manyawa consequently depends on excluding extractive licensing from the interior forest ahead of the frontier rather than behind it.

Purpose Prevention and early detection of osteoporosis remains a global challenge, more so in regions like the Philippines where screening barriers exist. Chest x-rays meanwhile are relatively inexpensive, and more frequently done, and therefore can be used for opportunistic screening. This study aimed to develop a deep learning model for osteoporosis detection from chest x-rays using DXA as the gold standard. Methods A convolutional neural network called Osteo-AI was developed using 406 pairs of chest x-rays and DXA scans of Filipino patients aged 50 and above. With data augmentation, the training set expanded to 6,300 pairs. Gradient-weighted class activation mapping technique was applied to localize and identify patterns and areas in the chest x-ray images correlating with osteoporosis. Results Training data consisted of 369 female patients and 37 males. Ages of the patients ranged from 50 to 89 with a mean age of 63 years old. Initial testing yielded promising results, with Osteo-AI achieving a diagnostic accuracy of 85.71%, easily outperforming a benchmark of 33.33% Conclusion Our findings suggest the potential of Osteo-AI to enhance osteoporosis screening accessibility, aiding in early intervention to prevent fragility fractures. Further research involving larger datasets is warranted to refine and optimize the model, potentially improving detection accuracy and expanding its utility in global healthcare settings.

Dietary iron deficiency in the absence of anemia (IDNA) affects numerous people worldwide, with a wide range of negative effects on brain functioning and cognition. Although studies employing electroencephalography (EEG) have revealed a number of negative effects of IDNA in both the time- and frequency domains, to date there have been no attempts to characterize the effects of IDNA on the temporal dynamics of whole brain interactions. To address this issue, we applied multiscale entropy (MSE) analysis to resting-state EEG data collected from IDNA (n = 21) and iron sufficient (IS, n = 21) women. The MSE analysis on this data revealed that entropy was higher overall for the IS than the IDNA group, with significant differences appearing primarily at longer time scales and under right frontal and left and right parietal electrodes. These results suggest that IDNA may negatively affect long-distance interactions among brain regions and that this could conceivably be a source of diminished cognitive function and neural resilience in IDNA.

Accurate epigenetic age prediction from DNA methylation profiles is intrinsically high-dimensional, creating a need for parsimonious models that preserve predictive performance while reducing the number of assayed cytosine-phosphate-guanine (CpG) loci. This study introduces MOSurvivor, a population-based multi-objective search framework that jointly optimizes a weight-threshold CpG selector and eight XGBoost hyperparameters. Experiments used the GSE40279 whole-blood cohort (656 individuals profiled on the Illumina HumanMethylation450 platform). After retaining 1,000 age-correlated CpGs, five strategies were evaluated on the same 30 seeded 80:20 train/test splits: fixed-parameter XGBoost using all 1,000 CpGs, random search, a genetic algorithm, particle swarm optimization, and MOSurvivor. Internal fitness was estimated using three-fold cross-validation on each training set. Across the 30 held-out test sets, MOSurvivor achieved a mean absolute error (MAE) of 4.149 {+/-} 0.300 years, root mean squared error of 5.545 {+/-} 0.392 years, and R2 of 0.855{+/-} 0.027 while retaining 211.6 {+/-} 54.8 CpGs. Relative to full-feature XGBoost (MAE 4.095 {+/-} 0.285 years), MOSurvivor reduced the feature set by 78.8% at an MAE increase of only 0.054 years (1.3%). Paired Wilcoxon tests found no significant accuracy difference between MOSurvivor and any comparator (all unadjusted p > 0.05; all Holm-adjusted p [&ge;] 0.476). The most recurrent locus, cg16867657, appeared in 29 runs, whereas mean pairwise Jaccard similarity was 0.124, indicating a small stable core embedded in multiple near-equivalent feature subsets. MOSurvivor thus offers a competitive accuracy-parsimony trade-off rather than superior absolute accuracy. External validation and leakage-free nested feature preselection remain necessary before biological or clinical translation. Keywords: epigenetic clock, DNA methylation, feature selection, multi-objective optimization, XGBoost, metaheuristics, biological aging.

From animal societies to self-organizing multi-agent systems, collectives adapt their group structure to tasks and environments. However, how they determine appropriate group sizes and the number of subgroups to form remains unclear. We formulate the Group Size and Number Regulation Problem (GSNRP), which asks how individuals regulate group sizes and numbers using only local information. In a first step, we establish a graph-theoretic model demonstrating that simple following behavior suffices to form group structures that match theoretical expectations, but is insufficient for active regulation of group size and number. In a second step, we operationalize individual group-size preferences in a decentralized fission-fusion mechanism based on perceived group size. Through multi-agent simulations, we validate that this mechanism achieves stable convergence across three signaling regimes, from position-only sensing to continuous group-size communication. Using tracking data from wild white-nosed coatis (mammals in the raccoon family), we calibrate individual group-size preferences and show that the controller recovers selected group-size, subgroup-count, and transition statistics. This in-sample case study demonstrates descriptive consistency with natural fission-fusion dynamics without establishing the underlying behavioral mechanism. These results suggest that natural and engineered collectives may share local principles of perception, preference, and response for regulating group structure.