Papers

Anticipating the onset of collective synchronization is important in many networked systems, yet observing every oscillator is often impractical. We investigate whether synchronization transitions can be detected from a small set of monitored, or sentinel, nodes. Using a stochastic Kuramoto model on networks, we numerically compare three early warning signals: the local order parameter, its temporal variance, and the variance of individual oscillator phases after removing their mean rotational trends. We also compare sentinel-selection strategies based on node dynamics, degree, and random sampling. We show that, under partial observation, the local order parameter and the variance of detrended phases provide substantially stronger warning signals than the variance of the local order parameter. Selecting nodes according to their dynamical behavior near the transition consistently improves performance over other sentinel-selection methods. With only $\lfloor\ln N\rfloor$ dynamically selected sentinels, two success indicators approach the performance obtained by observing all $N$ nodes. These results demonstrate that synchronization transitions can be anticipated from sparse observations when the warning signal and monitored nodes are chosen appropriately.

Populations of large language model agents are increasingly used as experimental societies. Three doubts shadow every such result: whether the agents behave like the humans they stand in for, whether a finding survives changes to the apparatus that leave the rules untouched, and whether apparent social dynamics are interaction at all rather than the reproduction of experiments the models have read. This article introduces SILICA, an open instrument that tests all three. Five environments carry published human anchors, each paired with perturbations that re-render the same rules and with variants whose payoffs point away from the memorised result. Twelve open-weight models were run through it on a single consumer graphics card. Agreement with human data is confined to starting points: first-round public-goods contributions fall inside the equivalence margin for eight of eleven models, while no model matches end-state contributions or the human corridor of cooperation. Merely swapping the order in which two actions are listed costs one model 58 points of cooperation. Presenting responders with a fixed schedule of offers shows that only one model, the sole reasoning-trained one, places its acceptance threshold where the incentive requires; two move theirs part of the way, two move them the wrong way, and three never acquire one. Conventions form through a shared prior over the names rather than through negotiation, though negotiation reappears once that prior is disrupted. On the certification ladder defined here, current silicon societies support exploratory claims and no more.

China has become the world's largest producer of scientific publications, yet concerns persist that this growth is inflated by excessive domestic citation practices. In this study, we analyze a citation network of over 45 million publications from Web of Science (1980-2025) to investigate China's home citation bias and research impact. Using a network reshuffling null model to control for the structural effect of publication volume, we find that China's home citation bias is less pronounced than commonly assumed and has been steadily declining over the past two decades. Chinese researchers do not exhibit a significantly stronger home citation preference than other major countries, indicating increasing internationalization rather than insularity. Furthermore, using the persistent disruption framework, we show that Chinese papers are converging toward American papers in their capacity to produce paradigm-shifting work. These findings challenge prevailing narratives about Chinese scientific home bias and suggest that China's advances in research impact.

The Anthropocene mode of development is driving civilization toward a "singularity crisis": artificial intelligence (AI) is rapidly approaching general intelligence (AGI) with escalating risks of losing control, while unrestrained economic growth generates super-exponential growth of entropy production that pushes the Earth system toward its tipping points. This paper proposes the "Save 2050" initiative: a distributed planetary-scale collective prediction system that aggregates judgments about the future from humans and AI through open registration, crowdsourcing, and incentive mechanisms, and integrates them via large-scale simulation into inspectable "predicted worlds," enabling humanity to systematically see the future for the first time. We argue for the initiative's feasibility along four dimensions—the maturation of AI forecasting, human collective intelligence and the institutional environment, supporting progress in related fields, and societal demand. We then identify three key enabling technologies: long-horizon automated resolution, simulation-based prediction aggregation, and reflexivity governance. We analyze potential risks—including reflexivity, cognitive monoculture, narrative capture, and regulatory and ethical concerns—together with mitigation strategies, and we outline a phased roadmap with open problems. The initiative's primary goal is not to intervene in the future, but to make the future visible, discussable, and co-writable.

The United States allots USD 15 billion for lead service line replacement in proportion to documented lead, the largest of a growing class of environmental-indicator transfers. Reconstructed exactly, the rule prices looking below zero. Resolving an unknown pipe lowers a state's expected allotment in three of the eight jurisdictions we can measure above the statutory floor, and raises it in none. Below it the allotment cannot move. Systems filing nothing are scored lead-free. We prove no fixed formula on self-reported inventories can pay for need without punishing its measurement, so we made an audited one. The unique additive repair credits unknowns at a rate no filing can move, and is strategy-proof. Discovery is repriced from a median loss of USD 48.63 per line per year to zero. Allocation swings fall from 16.5% of the pool to 0.8%, for an audit costing 1.23% of annual funds. The formula's tilt toward vulnerable systems survives.

Identifying the smallest set of elements whose removal dismantle a complex network, known as the network dismantling problem, is a fundamental task with many practical applications. Whereas network dismantling has been extensively studied over the past decade, most work has focused on developing efficient algorithms for large but finite networks. By contrast, the physics of the network dismantling process, namely how the network structural connectivity is affected by the removal of nodes or edges, remains largely unexplored in the thermodynamic limit. Here, we shed light on this understudied aspect of network dismantling by introducing an adaptive biased percolation process able to optimally dismantle a network. Through a systematic analysis of synthetic network models, we find that the proposed percolation process displays a universal phase transition, characterized by the abrupt and simultaneous disappearance of both the giant connected component and the largest 2-core, across networks with markedly different degree distributions. Simulations on real networks further support this universality, indicating that the physics of network dismantling is insensitive to a broad range of topological properties. Together, these results suggest that a topology-agnostic theory could be developed to explain the critical behavior of network dismantling.

Traditional frameworks of political communication operate under linear, event-driven assumptions that treat voter persuasion as a static, transactional function. This paper introduces Dynamic Consent Engineering (DCE), a novel interdisciplinary paradigm that synthesizes Edward Bernays' foundational principles of public relations with the S-E-E-D (Snowball, Equilibrium, Elasticity, Dominance) framework of system dynamics. By expanding Bernaysian operational constraints into a four-dimensional resource matrix (incorporating algorithmic media infrastructure alongside manpower, mindpower, and capital), we mathematically formalize how democratic institutions construct, optimize, and sustain political dominance. We map Bernays' classic eight-step engineering workflow directly onto non-linear feedback loops, information time lags, and demographic carrying capacities. Through rigorous modeling of systemic feedback structures, we isolate the dynamic root causes of political elasticity, policy resistance plateaus, and threshold-triggered trust collapses. Finally, we establish a four-step diagnostic pipeline and validate the framework via historical reference mode verification, demonstrating that long-term political stability depends not on ephemeral rhetoric, but on the structural synchronization of policy execution and dynamic feedback calibration.

Threshold-driven activation governs a wide range of collective phenomena, yet the microscopic origins of its phase transitions in spatial systems remain unresolved. Here, we show that spatial activation systems undergo multiple distinct routes to phase transitions, controlled by a single parameter—the interaction range. We uncover a unified phase diagram featuring continuous, first-order, and mixed-order transitions, and demonstrate that the two abrupt transitions arise from fundamentally different mechanisms: nucleation-driven front propagation and critical branching. These routes exhibit distinct dynamical scaling, establishing a direct link between microscopic activation dynamics and macroscopic critical behavior. We further identify a metastable phase in which global activation cannot be achieved by random activation alone, but can be triggered by localized seeds. In this regime, the critical activation nucleus remains finite and independent of system size, implying that arbitrarily large systems can remain stable under random perturbations yet highly vulnerable to localized triggers. The onset of this phase is abrupt, revealing an extreme sensitivity of collective dynamics to small parameter changes. These results establish a mechanistic framework for phase transitions in spatial activation systems and reveal how microscopic perturbations can trigger macroscopic cascades.

We investigate random recursive simplicial complexes growing by adding, at each step, a vertex together with a simplex formed by joining the new vertex with a randomly chosen existing simplex. We also add all faces of the new simplex to ensure that the resulting object remains a simplicial complex. If the choice of an existing simplex is uniform among simplices of dimension $<m$, the number $S_d$ of simplices of any admissible dimension $d\leq m$ is an asymptotically self-averaging random variable. This feature allows us to determine the asymptotic growth law of the average of $S_d$ when the number of vertices diverges. We also probe the degree distribution, examine the probabilities of various extreme outcomes, and analyze the characteristics of the first vertex.

Complex hypergraphs (chygraphs) contain graphs, hypergraphs, multiplex and interacting networks as special cases, and the percolation threshold of all of them follows from one symbolic calculation: the spectrum of a tensor $A$ built from four matrices of first moments. That calculation stops at the threshold. Here I show that $A$ is the Jacobian, at its trivial fixed point, of a non-linear self-consistency map whose non-trivial fixed point is the giant component fraction, so threshold and order parameter are two orders of one object on one index set. Carrying the expansion one order further gives the critical amplitude $B$ in $S=B\Lambda+O(\Lambda^2)$ in closed form, and exposes a hierarchy: first moments fix the threshold, second moments the amplitude, and only the generating functions themselves the order parameter away from it. Dropping the assumption that a complex's participation in different layers is independent generalises the tensor again, replacing unconditional first moments by inclusion-biased second moments: distributions with identical marginals have different thresholds and different order parameters. Six constructions from the literature are then solved by substitution, among them AND- against OR-logic hypergraph percolation, which share a chygraph and differ in one generating function, and SIR epidemics with two levels of mixing, whose household reproduction number falls out of the tensor. A reported failure of mean-field theory on strongly clustered graphs is shown to be a failure of applying it to the wrong object: mapped onto the treelike backbone rather than the clustered graph, the same calculation reproduces the exact threshold, order parameter and critical exponents. Everything is implemented in one class, in which a chygraph is specified once by its generating functions and then returns all three, and validated against Monte Carlo simulation.

We propose a formal account of how structured, shared knowledge about social relationships shapes action interpretation. The model represents relationships as constraints in a social environment, analogous to boundaries or obstacles in a physical environment and operating within the same generative model, but exerting distinct constraints on action. As an initial test of this framework, we draw on research across the social sciences to capture in the models how one dimension of relationships – formality versus intimacy – shapes how people interpret interpersonally vulnerable behavior. We test this account in stories of naturalistic everyday situations, extending structured models of action understanding to open-ended contexts. Across six preregistered experiments (N = 1,554), the model captures people's inferences about desires, physical environments, and social relationships. This work formalizes how relationships can constrain – and be revealed through – everyday action.

Urban food environments may reflect broader socioeconomic inequalities, but district-level evidence remains limited in Brazilian cities. This study examined whether indicators of food retail and street-market availability discriminate between levels of social vulnerability across the 96 districts of São Paulo. We conducted an exploratory cross-sectional ecological analysis integrating the São Paulo Social Vulnerability Index (IPVS), establishment records from the Relação Anual de Informações Sociais (RAIS), and street-market data from CAISAN. Census-sector information was aggregated at the district level. Twenty districts without an IPVS classification were excluded, resulting in 76 observations. The outcome distinguished districts classified as IPVS level 1 from those classified as levels 2–7. Predictors described the densities of healthy and unhealthy food establishments, the number of street markets, and the availability of establishments selling fresh or in natura food. Eight conventional machine-learning classifiers were evaluated using leave-one-out cross-validation. Reported mean F-scores ranged from 0.62 to 0.75, with XGBoost obtaining the highest value. In the Random Forest model, the densities of healthy and unhealthy food establishments jointly accounted for approximately 60% of the total impurity-based feature importance. These findings indicate that publicly available food-environment indicators contain information associated with the district-level distribution of social vulnerability. However, the small ecological sample, class imbalance, outcome binarization, and cross-sectional design limit predictive generalization and preclude causal or household-level interpretations.

As generative AI gains traction, researchers are investigating its potential to serve as proxies for humans. From undergoing cognitive psychology experiments to experiencing an epidemic, generative agents, agents powered by generative AI models, produce realistic human behavior when prompted. This study explores the sensitivity of these generative agents' behavior to prompt modifications and varied persona names of the agents. To assess this sensitivity, we use a generative agent epidemic model, wherein each agent is prompted daily on whether it wants to isolate or commingle with other agents. We found that using synonymous prompts results in negligible changes to the model's outcomes. However, minor variations in prompts, as well as contextual changes, do influence the model's results. Lastly, our data indicates that different persona names assigned to generative agents, specifically those imbued with personas, do not significantly impact epidemic outcomes.

Strongly connected components (SCCs) characterize modular structure in directed networks but are fragile to single node failures. We study strongly biconnected components (SBCs), which are the set of nodes in which every node pair remains mutually reachable after the removal of any single node, as a more robust notion of connectivity. Using a generating function formalism, we derive the size of the giant SBC and analyze its percolation behavior under random node and link removal. We show that the giant SBC emerges at the same threshold as the giant SCC but grows more slowly due to stricter connectivity requirements. We also applied our theoretical framework to real-world biological networks including gene regulatory networks and neural connectome. Our framework provides insight into the interplay between connectivity, redundancy, and robustness in complex directed systems.

Hypergraphs describe higher-order interactions that involve more than a pair of nodes. A characteristic feature of hypergraphs is that their robustness can be strongly affected by the different roles of the nodes. Indeed, some nodes might be essential for a hyperedge's function, while others might not be. The loss of a single essential node completely destroys the hyperedge it belongs to, while the loss of a non-essential node has a buffering effect, inducing the hyperedge to simply reduce its size. In order to capture this phenomenology, we formulate a comprehensive theoretical framework for $(k,n)$-core percolation models on hypergraphs, where each node of a hyperedge is an anchor with probability $\theta$, and a hyperedge fails if an anchor node fails. Hypergraph $(k,n)$-core percolation problems can be classified as first-neighbor and second-neighbor problems, indicating that in the pruning process the connectivity is ensured only by the state of the first neighbors or the second neighbors, respectively. We derive self-consistency equations for first-neighbor and second-neighbor (node- and hyperedge-based) pruning processes, and obtain the size of the giant $(k,n)$-core. We obtain the phase diagram, including continuous and discontinuous transitions, and confirm our theory on random hypergraphs using numerical simulations. The results show how the heterogeneity of the nodes' functional roles and the extended range of the interactions affect the robustness of higher-order networks.

Sparsifying large road-network graphs by removing a fraction of their edges is a common way to reduce storage and accelerate spatial queries, but the choice of which edges to remove can quietly degrade the network that remains. We compare three edge-importance criteria for deciding what to prune, namely uniform random removal, low edge-betweenness removal, and low-effective-resistance removal, on 27 urban road networks drawn from OpenStreetMap that span a wide range of sizes and street-network morphologies. At edge-removal ratios from five to thirty percent we evaluate each criterion along three complementary axes: length-weighted routing utility, a topology-only measure given by the retention of the second-smallest eigenvalue of the normalized Laplacian of the largest connected component, and the fraction of an externally defined arterial backbone, taken from OpenStreetMap road classes, that each criterion destroys. The criteria disagree. Low-effective-resistance ranking, which targets electrically redundant edges, preserves connectivity well only below ten percent removal; beyond this level, retention falls below that of random removal in a growing majority of cities, and by thirty percent the method removes a larger share of the arterial backbone than random deletion does. Betweenness removal is consistently the best of the three on all three axes, at every removal ratio. Resistance-based redundancy is therefore not a safe proxy for routing importance when compressing real road networks, and a routing-oriented criterion is the more dependable choice.

We study the relationship between exposure to immigrants and right-wing votes used as a proxy for anti-immigrant sentiment in the Netherlands. Exposure to immigrants is measured using a novel indicator, adapted from the residential segregation literature, applied to grid data available for the entire country at the aggregate level. Using the proxy of election results, we are able to study the entire voting population instead of a limited subset of panel respondents. In our cross-sectional study of the 2023 national election, we find that municipalities and neighbourhoods with greater exposure have less anti-immigrant sentiment. However, looking at the increase in right-wing vote share from the 2021 to the 2023 national elections, we find evidence of an “overexposure effect”, as this relationship reverses, and the areas that saw significant increases in migrants subsequently experienced an increase in right-wing votes. Furthermore, we see that at high levels of exposure, wealth (and inequality) plays an important role in the voting dynamics, indicating that relative deprivation theory may play a role.

Parliamentary systems pass more bills than presidential systems at baseline, but collapse to near-zero passage under party-system fragmentation. The literature offers three competing micro-explanations: coalition-formation failure, party discipline, and committee gatekeeping. These operate simultaneously in any real legislature, so observational studies struggle to separate their contributions. We present an agent-based model that compares four democratic institutions: pure parliamentary, pure republican/presidential, premier-presidential (France), and president-parliamentary (Russia). Across four scenarios and N=200 seeds per cell we report bootstrap confidence intervals, Morris screening, Sobol variance decomposition, mechanism ablations, and a hung-parliament variant comparison. Three findings emerge. First, government formation failure alone does not halt legislation: when a fragmented parliament reverts to personal voting, parliamentary passage (46.4%) is statistically indistinguishable from the presidential benchmark (44.8%); collapse requires cohesive opposition obstruction, which drives passage to 0.05%. Second, disabling discipline restores fragmented passage to 46.7%, and the rescue magnitude is monotone across the four institutions in a pattern that survives varying the common discipline level. Third, the passage-representation tradeoff is a single spectrum: parliamentary maximises throughput at the cost of representational fidelity; republican maximises fidelity via the presidential veto; semi-presidential variants split the difference.

Gravity models describe bike-sharing origin-destination (OD) flows as increasing with origin and destination activity and decreasing with distance. Yet how these relationships change within a day and across observation areas remains unclear. We examine temporal and spatial variation in origin, destination and distance exponents $\alpha$, $\beta$, and $\gamma$, together with $R^2$ and mean absolute error (MAE), across eight bike-sharing systems. Temporal modeling uses sliding windows, while spatial modeling expands a circular area and separates intra-zonal, cross-zonal outflow, cross-zonal inflow and extra-zonal trips. We find recurring patterns across cities: morning and evening peaks differ in origin and destination dependence, while cross-zonal outflow and inflow across the same boundary show opposite changes in their relative origin and destination dependence as radius increases. Model performance and distance dependence also vary with time and radius. A full-day, citywide fit therefore combines time periods and flow types with different gravity relationships.

For nearly two decades, human mobility has been read as scale free. Displacement distributions follow heavy tails that look like truncated power laws, traced to individual Lévy flights. A rival account holds that movement within each spatial container is lognormal, and the aggregate power law is an artifact of mixing containers of different sizes. The two fit the same aggregate data, so the debate has been hard to settle. We use the COVID-19 lockdowns as a natural experiment that removes long-distance travel and leaves local travel intact. We analyze 2.1 billion displacements from 4.4 million mobile-phone users across three distinct periods. The aggregate exponent increases under lockdown, from 1.66 to 1.74. Resampling the pre-lockdown traveling population to match the lockdown population reproduces that shift on its own, so we must look at the individual level to decides the question. Lognormal classification is a stable attractor (81% retained) while the power-law classification is fragile (32% retained), and the users who switch are the ones whose travel range collapsed the most. Matching the sample size we find that single users' tails reject the power law and pooled mixtures of equal size pass, so the heavy tail behavior originates in the aggregate behavior and not on the individual. Tail tests find no power-law threshold at full sample size, and the apparent power law disappears above ten thousand points. A level mixture rebuilds the aggregate ($R^2$ up to 0.98), the radius-of-gyration collapse fails and worsens under lockdown (CV $= 0.62$ to $0.76$), and the steepening concentrates in wide-ranging users ($P = 0.0003$). The power law of human travel is a feature of aggregation, not of individual movement.

The stability of markets hosting leveraged exchange-traded products is governed not by any single product's loop gain but by the spectral radius of a loop-gain matrix, and scalar per-product monitoring underestimates system feedback by construction. Recent work measures the self-reinforcement of a leveraged fund's daily close rebalancing through a scalar loop gain and treats cross-asset spillovers as bias. We model complexes on correlated underlyings as a coupled feedback system with matrix gain L and show that scalar monitoring has two blind spots: (i) cycle amplification, since rho(L) >= max_i l_ii for nonnegative coupling, strict under two-way coupling; and (ii) transmitted displacement, which arises already under one-way coupling and is invisible to the receiver's own gain. We give a reduced-form estimator of L requiring only prices and public fund assets – no signed order flow – via cross-asset overnight reversals, reporting its measurement-convention sensitivity explicitly. In simulation the spectral radius is recovered with RMSE 0.005 at T=250, a lead-lag confounder yields a 2% false-alarm rate, and in a calibrated blind-spot configuration the scalar monitor reports "safe" and the matrix monitor "unsafe" on 100% of paths. In the 2026 Korean single-stock LETF episode we detect transmission from the SK Hynix complex into Samsung Electronics' closing price (DiD z=-2.82; exact randomization p=0.0055 against 182 control pairs), scaling with the sender's rebalancing capital; conservatively, about 41% of Samsung's closing displacement variance is imported – invisible to its own "moderate" gain of 0.24. The same estimator returns nulls for the U.S. MSTR-Bitcoin-Coinbase complex, whose capital is comparable but whose closing venue is far deeper. Monitoring should be organized around the (complex x venue) matrix, not around products.

Cooperation is ubiquitous in both natural and human societies, yet its evolutionary basis remains a major challenge. A long-standing puzzle is whether having more information leads to better decision-making and thus a higher level of cooperation. To address this question, we adopt a recently developed reinforcement learning framework in which individuals learn through trial and error to maximize cumulative rewards - a paradigm that has successfully explained diverse emergent patterns in human behaviors. Specifically, we equip a structured population with the Q-learning algorithm and systematically vary the size of the interactive neighborhood, which serves as a proxy for perceived information. Interestingly, we observe a non-monotonic relationship between cooperation prevalence and neighborhood size in both two-dimensional square lattices and Barabasi-Albert scale-free networks. This inverted U-shaped dependence reveals that an optimal amount of information exists, yielding the highest level of cooperation. Mechanistic analyses show that a moderate neighborhood size enables individuals to strike an optimal balance between information sufficiency and decision-making tractability. This balance allows them to detect reciprocal opportunities while avoiding the deterioration of decision quality due to information overload. Our findings challenge everyday intuition, suggesting that a proper amount of information - not more - is optimal for the emergence of cooperation.

Reconstructing the state of a large networked system from measurements at only a few nodes is a challenge for monitoring, prediction, and intervention. Here we ask whether such reconstruction is possible and whether it can transfer across different nonlinear dynamics. We study this question across various networks and across $16$ nonlinear dynamics on networks from different domains. For each network, we observe only a vanishingly small fraction of sentinel nodes and train either a neural network or linear decoder. We find that accurate reconstruction is often possible, and that transferability is structured rather than universal. Eleven dynamics with adjacency-matrix-type coupling form a robust transferable class. By contrast, five diffusively coupled dynamics form isolated transfer components. Non-random sentinel selection is consistently important, and linear decoders often approach neural-network performance. These results show that sparse node observations can encode enough information to reconstruct full network equilibria across broad families of nonlinear dynamics, while also revealing sharp limits to universal transfer.

Complex systems are often organised into hierarchies whose internal interactions are stronger or faster than interactions across levels. When markets are treated as genuinely multilevel systems it becomes natural to represent them as systems with hierarchical causality. Here we show that reflexivity can be formulated within such a discrete hierarchical causal system; but one in which a higher-level actor state restricts the lower-level transition kernels that remain admissible. Then event dynamics can be separated from calendar embeddings: a set-valued actor-conditioned correspondence can be used to define the admissible family of event kernels, while joint state and waiting-time laws can be used to determine compatible timing to then natural demonstrate reflexivity. A selected event-state law need not determine a unique calendar embedding. Locally, uniqueness of the joint event or timing specification requires uniqueness of both the admissible event kernel and its compatible timing law. Reflexivity is thus the endogenous closure of a hierarchical constraint loop, while timing and projection can generate calendar-time memory or causal ambiguity even for Markov event dynamics.

Mathematics has often been organized around an authorial subject: one person, or a small group, composing proofs through language, notation, and judgment. Large language models, proof assistants, formal libraries, and repositories now make another production unit technically credible: a human-machine assemblage. This article calls that unit a studio ecobiont and asks when it is epistemically legitimate. Its governance thesis is that human participation is substantive only when the system preserves traceable provenance, reconstructible human competence, capacity to challenge the result, effective authority to stop or withdraw it, and public responsibility. These conditions distinguish a governed studio from a degenerate studio whose human oversight is ceremonial. A comparison of Polymath, the Liquid Tensor Experiment, Danus, and the Jacobian counterexample episode shows that collaboration, formalization, technical orchestration, and epistemic governance are independent dimensions. The proposed understanding audit and contribution-authority trace are governance designs, not validated measures. No causal superiority over authorial practice is claimed.

Standard epidemiological models coupled with evolutionary game theory (e.g., vaccination games) typically rely on the free-rider dilemma inherent to infectious diseases. In this paper, we present a coupled behavior-disease model where the underlying disease is non-infectious, and transmission occurs strictly at the cultural level. We model the competition between two medical paradigms, namely evidence-based medicine ($M$) and alternative medicine ($A$), using replicator dynamics driven by treatment-specific social-amplification coefficients. We show analytically that the nonlinearity of the coupled system arises from social feedback rather than from the underlying biological dynamics. Crucially, the stability analysis reveals that the system lacks isolated fixed points; instead, it converges to a one-dimensional continuous manifold of non-hyperbolic neutral equilibria, generating persistent path dependence in the cultural composition. Furthermore, we derive an explicit constant of motion that constrains each trajectory to a distinct invariant level set. Restricting this invariant to the equilibrium manifold yields a strictly monotonic selection function, uniquely determining the equilibrium selected from any given initial state. Our findings show that derivative-based cultural feedback is sufficient to generate a continuum of coexisting health paradigms, while asymmetric social amplification modifies this selection. Because transient interventions that directly alter paradigm adoption break this invariant, they shift the system to a different level set, producing persistent changes in the long-run cultural composition. The model thus reveals how societies retain a deterministic memory of prior health and treatment states, demonstrating that both misinformation shocks and targeted public health interventions can leave lasting structural changes long after the perturbation has ended.

A composite structural index summarises a network in one number, and for a triangle-based index it is spectrally redundant: Tr(A^3) is the third moment of the adjacency spectrum. The non-redundant content sits one level down, in diag(A^3), which depends on eigenvectors and is not spectrally determined. A corollary in the theory paper predicted that the global scalar should tie sharpened spectral baselines rather than beat them, while the node-wise attribution should do better where the number of structural epicentres is unknown. We construct Omega-N by localizing each of the four factors. The direct localization is badly conditioned; two corrections from published practice fix it, a configuration-null excess per factor and a personalized-PageRank neighbourhood at several scales, giving ten interpretable features per node, with no attributes, training or embeddings. Against a recursive feature engine at five levels of recursion, Omega-N wins on three and ties on two of the six in-domain evaluations, the sixth a declared null where every arm returns chance, with ten features against its 28 to 252 before pruning. Two statistics from the graph and labels, not from performance, partition the eight benchmarks without error, and the two they exclude are the two on which it loses. The strongest application is drug-target prioritisation on protein interaction networks: +0.032 to +0.103 AUPRC over a six-feature centrality battery and +0.084 to +0.208 over the four-feature one, across three constructions, replicated on an independent AP-MS network and label source (degree-matched: +0.0723 on STRING, +0.0560 on BioPlex, p=0.00195). Adding Omega-N to centralities plus Node2Vec changes nothing. The claim is narrow and it is the point: ten named features, computed without training, match or beat hand-crafted centralities and a recursive engine, and do not touch learned representations.

We formulate planetary sustainability as a minimal nonequilibrium problem for coupled finite stocks and fluxes, using the operational language of closed life-support systems: inventories, flux balances, recycling efficiencies, processing capacities, reserve times and failure thresholds. Rather than asserting that waste is universally more limiting than resources, we propose a reserve-time principle: the binding constraint is whichever buffer becomes critical first. A nonlinear model coupling a regenerative resource stock, an accumulated waste stock and an activity variable exhibits a soft threshold, where waste suppresses growth while processing remains formally capable, and a hard threshold, where waste production exceeds maximal processing capacity. With immediate waste feedback, activity settles globally at the soft threshold; the hard threshold is crossed only transiently or under exogenous forcing. A resource-side threshold completes the picture. We extend the model to recycling and to multiple resource and waste classes, give a numerical example, situate the four-function description of life against the origin of life, viruses and aging, contrast the biosphere's two long-term failure modes, and relate the approach to Spaceship Earth, planetary boundaries, Limits to Growth, System Dynamics and stock-pollution economics.

Africa has deep and diverse traditions of astronomical knowledge, ranging from archaeological astronomy, pharaonic stellar timekeeping, and manuscript astronomy in Timbuktu and the Sahel, to ecological seasonal astronomy in southern Africa and calendrical computation in the Ethiopian tradition. These multiple epistemic traditions form part of a long intellectual history that precedes and intersects with contemporary astronomy on the continent. In the context of this long-standing intellectual heritage, an important question arises regarding the contemporary circulation of African astronomical knowledge within the global scientific system. This study therefore examines where African astronomical knowledge is produced, validated, and circulated in modern scholarly communication. Using bibliometric data from the Web of Science Core Collection, our analysis investigates publication and citation patterns in the research area Astronomy and Astrophysics between 2000 and 2025, with particular attention to the publication venues of African scholars. The findings highlight a critical paradox: while African researchers are active contributors to global astronomical discovery, the intellectual capital generated through this work is largely stored, validated, and circulated through publication systems located outside the continent. This pattern reflects broader asymmetries within global scholarly communication, where dominant publishing infrastructures shape visibility, citation impact, and authority. By applying a decolonial lens to metrics such as citation impact and ownership, the paper calls for a critical reassessment of the academic practices that sustain epistemic coloniality. It concludes that achieving scientific equity requires a strategic shift in publication choices to build and fortify a sovereign African knowledge archive.

Nonlinear dynamical systems manifest rich variety of dynamical states and transitions driven by fluctuations. To understand the pattern of fluctuations during dynamical transitions, we investigate the structural features of chaos to order transition in logistic map. We determine fluctuations as amplitude jumps and encode them onto a complex network where nodes represent amplitude levels and links represent transitions between distinct amplitude bins. We discover that global network measures identify points of period doubling, regimes of periodicity and chaos, including interior crises events. Using local network measures, we also unravel novel peculiar parabolic-shaped patterns in the orbit diagram that we show are reminiscent of the distribution of stable and unstable periodic points in the bifurcation diagram.