Papers

The worldwide cocaine market is undergoing an extraordinary surge. Insights on how cocaine is trafficked from production countries to consumer markets are limited, and often based on observed trafficking routes (e.g., seizures) alone. In this paper, we introduce a network-based model of actual transnational cocaine flows, beyond flows seized. In this model, cocaine is routed through an international transportation network of land and sea connections, where each link is assigned an interception risk metric for containerized transport. This interception risk metric combines features related to law enforcement inspections, containerized trade, and transport connectivity into three key driving components of interception risk using Principal Component Analysis (PCA). The interception risk metric on each link is then constructed from these driving components, where the importance of each component is characterized by a strength parameter. Given a set of strength parameters, cocaine is assumed to be routed from production countries to consumption countries via routes that minimize the total risk of interception, subject to country-specific supply and demand constraints. In the end, the strength parameters are calibrated by comparing the corresponding flow outcomes with known trafficking activity. From these final trafficking flows associated with the calibrated parameters, we are able to identify `blind spots' (e.g., nonzero flows on links with small or none observed trafficking activity) and provide more evidence of the waterbed effect (e.g., changing routes as a result of increased interdiction efforts by law enforcement).

The Hirsch index (introduced in 2005) has been a very successful scientometric author-level measure for the publication impact inequalities among the authors. However, it does not have any upper bound and statistically it grows in proportion to the square root of the number of publications by the author. Social scientists, on the other hand, measure the economic performance of different countries (having different wealth amounts and populations etc.) using inequality indices like the Gini index (since 1912) etc., which are normalized quantities (independent of the country's total wealth or the population size). We show here that a normalized fractional Hirsch index, giving the fraction of total citations earned by fraction of those successful papers published by the author, can even indicate that typically about $14\%$ of the top cited papers earn about $86\%$ of citations for very successful scientists (like the 95 Nobel Laureates considered here). This is similar to Pareto's 80-20 law (since 1896) and agrees more precisely with those observed for self-organized sandpile models, where typically $86\%$ of the avalanche masses are dissipated through $14\%$ of the largest avalanches as the piles approach their respective self-organized critical points.

Why do political parties polarise when most voters remain in the centre? Moving beyond conventional point-based models, we address this classic puzzle by developing a spatial voting framework that conceptualises political parties as continuous ideological distributions. Operating under endogenous turnout, these parties adapt their positioning to maximise a combination of total votes and parliamentary representation. We demonstrate that this theoretical formulation reveals a distinct phase transition in multiparty competition, moving from centripetal convergence to centrifugal separation. These dual objectives do not necessarily reward the same directional party movement as voters only cast ballots for ideologically acceptable parties. The numerical results map the precise boundaries of this transition: a higher party count destabilises the centrist equilibrium and expands the zone of divergence, whereas pronounced internal party dispersion and a stronger emphasis on representation contract it. Furthermore, electoral institutions critically govern this divergence: when voter preferences vary across geographic districts, the same national electorate can trigger entirely different phase transitions depending on how votes are converted into seats. Together, our results show how party differentiation emerges endogenously from the dynamics of electoral competition itself. Whether small initial differences grow or decay is not merely a reflection of voter preferences, but an outcome dictated by party goals, competitor count, internal party breadth, and vote-to-seat conversion rules.

Conflict events in Middle Eastern countries exhibit complex temporal fluctuations. As a simple baseline, we examine whether their conflict-frequency time series contain measurable linear temporal structure using the autoregressive integrated moving average (ARIMA) framework, which assumes linear dependence on past observations and errors. Despite this simple linear assumption, the temporal dependence is largely captured for most countries by ARIMA. Predictions based on the selected ARIMA models reproduce the overall temporal behavior to some extent, although abrupt changes remain difficult to predict. We further examine the short-term persistence of changes in conflict activity using the first zero-crossing point $k^*$, which characterizes the duration of the initial positive temporal correlation, and the integrated correlation time $\tau_{\mathrm{int}}$, which additionally reflects its strength and decay. The resulting $k^*$ values are approximately 2–6 days, while $\tau_{\mathrm{int}}$ ranges from approximately 0.6 to 1.7 days. The significant negative association of $\tau_{\mathrm{int}}$ with mean GDP per capita suggests a possible relation between short-term conflict persistence and broader socioeconomic conditions. These results reveal measurable linear temporal structure and country-dependent short-term persistence in the temporal patterns of conflict activity across the Middle East.

The debate over pairwise and higher-order models is often framed as a contest of expressive power. This framing is misleading. A graph with arbitrary multivariate node functions can reproduce the node-level dynamics of many hypergraph models, but the hypergraph's grouping information does not thereby disappear: it may simply move from the structure to the rule. We separate four notions frequently conflated here: structural representation, functional representability, statistical identifiability, and mechanistic adequacy. We then prove that interaction order, the number of variables that must act jointly in some term of any additive decomposition of a node's update, is the same in every exact representation: no change of structural language can lower it. As a description-length problem, at the unrestricted algorithmic level a fixed compiler redistributes information between structure and rule at constant overhead, so expressiveness alone cannot privilege either language. Preferences arise only relative to explicit model classes, code families, and data. This yields an operational minimum-description-length criterion combining structural cost, conditional rule cost, and imperfect fit. Within it, for $M$ disjoint groups of size $k$, the clique projection's edge list is asymptotically $k-1$ times longer than the hyperedge list it replaces: the projection encodes the same grouping at higher cost. Examples from diffusion, Boolean dynamics, ecology, and ambiguous projections give graph-preferred, hypergraph-preferred, and unresolved cases; for bipartite and multilayer lifts, cost, fit, and identifiability tie, and the choice turns on which entities are posited as primitive. The position is symmetric: higher-order structure should not be inferred from phenomenology alone, nor does a graph's ability to emulate a system make it the most parsimonious or adequate description.

The idea that emotions in biological systems are analogous to intrinsic colored noise is advanced and justified. A model describing the dynamics of operation of biological networks under the influence of colored noise is suggested. The agents of a biological network can be represented either by biological species, such as humans and animals, or by neurons of the brain, or by the nodes of a neural network. Operational actions, or decisions, in a biological noisy network are based not only on the evaluation of utility of alternatives, but also on the agents emotions. The model is probabilistic, with the choice of alternatives characterized by the related probabilities. At the initial step, the agents make decisions individually and then start exchanging information with each other and imitating the actions of other agents, thus forming a biological network of interacting agents. Numerical simulations are accomplished for a heterogeneous society consisting of three groups of agents, one group possessing long-range memory, the other group, short-range memory, and the third group of super-rational agents acting strictly on the basis of utility, being deprived of emotions. Dynamics of opinions in different groups can be smooth, oscillatory, or chaotic. Altogether, eight types of operation are found, depending on the dynamics of group decisions. Under strong imitation effect, there appears chaotic motion in the evolution of decision choice. It is shown how the Ellsberg paradox can be resolved and how the exchange of information influences the dynamics of this paradox.

We propose that instructional effectiveness may depend on an interaction between two design dimensions: dosage—the total duration of student-centered active learning allocated to a topic—and precision—the degree to which an intervention targets a specific, documented cognitive bottleneck with a mechanism-matched representational tool. This paper formalizes the framework, anchors it in cognitive load theory, derives its falsifiable predictions, and clarifies its incremental contribution relative to existing instructional-design literature. The central theoretical move is to decompose precision into three components—targeting ($P_t$), representational match ($P_r$), and scope restriction ($P_s$)—and to argue that only representational match acts directly on extraneous load. This decomposition yields a compact model in which the effective dosage is $D_{\mathrm{eff}}=D P_s$, the germane processing is $G=D P_s\eta(P_r)$ with $\eta$ the representational efficiency, and learning is $E=g(G)$ with $g$ increasing and concave \rev{(here $E$ is the cumulative learning outcome on the target construct, not a rate)}. The framework's core proposition (P3)—that precision can compensate for dosage—then becomes a quantifiable substitutability claim, $\mathrm{d}D/\mathrm{d}P_r=-\eta/\eta'$, rather than a mere existence statement; its scope is bounded by a precision ceiling and a minimum dosage threshold. We distinguish the framework from Carroll's classic time-needed model by the directional character of precision and by the estimability of the substitution rate, and from the ICAP framework by distinguishing “matching of participation content to the bottleneck” from “mode of participation.” As an illustrative case (not a test of the framework),

A recent article explores some respective contributions of the initial velocity and effective mass of a striking implement to the ultimately induced, post-collision velocity of a stationary strike target, in a combat sports context. Therein, it was found that multiplicative increases in the effective mass associated with a punch to the human body can have a greater quantitative effect on target velocity than that of its initial, pre-collision speed. Given that fold-increases in effective mass may be limited to low-integer multiples of a modest, literature-supported value that spans martial arts styles – and the fact that increases in the strike velocity are likely bounded by a factor of two, even for trained fighters – translating the aforementioned findings into incremental changes in either variable may be of more benefit to coaches who intend to apply the theoretical physics of fighting to develop practical training programs. Here, we build on previous work, studying the effects of marginal increases in effective mass on target velocity, and relating them to equivalent, single-unit changes in strike speed.

As generative AI agents are deployed at scale, safety will depend not only on technical safeguards and individual model design, but also on collective equilibria that determine how agent populations process information, prioritize actions, and respond to uncertainty. Yet the same equilibria that enable agents to coordinate also create a social attack surface. The standard framework to assess this vulnerability is critical mass dynamics: the minimum fraction of adversarial agents required to overturn an equilibrium through direct competition. Here, we show that this approach risks underestimating system vulnerability by reducing the problem to the identification of singular tipping points, and ignoring indirect but potentially more efficient routes through which collective behavior can be redirected. Through experiments with populations of LLM agents and an analytic framework that captures their collective dynamics at scale, we map critical-mass thresholds that define a directed, weighted topology over the space of coordination equilibria, and treat this topology as a navigable landscape. We show that indirect tipping through intermediate stepping-stone equilibria can reduce the committed minority required to reach an alternative state, bypass majority requirements, and make possible transitions inaccessible through direct challenges. The diversity of available alternatives and timing of the attack further reshape this landscape, creating opportunities for control as well as risks of unintended destabilization. These results show that an equilibrium's resistance to committed intervention is not an intrinsic property but a structural feature of its competitive relations with alternative states. Securing populations of interacting AI agents therefore requires mapping this social landscape alongside individual agent capabilities and the technical channels through which they interact.

Language change may be studied by tracking linguistic variant frequencies through space and time. Observed frequencies may be viewed as realisations of a statistical field. We first set out an efficient cross validated method for inferring the empirical field — the variant frequency distribution estimated directly from data — in our case, high resolution surveys from 20th century USA. We then derive a model of the statistical field, assuming that individuals diffuse locally, periodically migrate, and copy one another based on a form of replicator dynamics involving both bias and linguistic accommodation. We infer model parameters by comparing changes in model and empirical fields. Our inferences demonstrate that spatial linguistic patterns can be rapidly destroyed by migration but that accommodation can create them, protect them, and in combination with diffusion, produce partially predictable pattern dynamics. The results provide the strongest evidence yet for surface tension driven phase ordering in human dialects. We quantify the model's forecasting ability up to a time horizon of twenty five years using the Kullback-Leibler divergence between forecasts and observations.

The transition from clinical latency to active HIV infection is a stochastic process. Traditional deterministic models based on ordinary differential equations (ODEs) fail to capture the extinction boundary and the subsequent rebound of the virus because they neglect demographic noise in the small-population limit. We map the resulting Master Equation onto a coherent-state path integral using the Doi-Peliti second-quantization formalism and verify that the stochastic Hamiltonian reproduces the correct mean-field ODEs on the classical manifold $\bar{\phi}_i = 1$. In the semiclassical (large system-size) limit we derive eight coupled Hamilton-Jacobi equations, identify the virus-free and endemic fixed points, and obtain the basic reproduction number $R_0$ for the four-species network. For the analytically tractable case of single-virion bursting ($n=1$) we show that the stochastic Hamiltonian factorizes into two bilinear terms, exposing a non-trivial zero-energy surface that constitutes the instanton trajectory. A quasi-steady-state reduction then yields a first-order linear ODE whose closed-form solution gives the instanton action $S_{\rm inst}$ in terms of biological parameters. Calibrating to clinical data—infected-cell half-life $\delta_I^{-1}\approx 2\,\rm d$, viral burst size $N\approx 10^3$, clearance rate $\delta_V\approx 23\,\rm d^{-1}$, reactivation rate $\eta\approx 10^{-3}\,\rm d^{-1}$, and latent reservoir size $L_0\approx 10^6$ cells—we obtain a mean first-passage time (MFPT) to viral rebound of $\approx 6$ months for a typical patient, with a range of days to years depending on reservoir size. These predictions are qualitatively consistent with observed post-interruption rebound timescales.

Material and energy flows underpin sociotechnical metabolism. However, despite growing sustainability concerns over expanding material stocks and declining stock productivity, the link between material use and energy consumption remains poorly understood. This gap reflects a limited distinction between structures and the activity they enable, and the lack of quantification of the installed power of energy consuming structures. Here we reconstruct the long-term growth dynamics of U.S. road vehicles, distinguishing professional and consumer assets. We show that installed power, mass, and fuel energy use follow divergent patterns within and across vehicle categories. By introducing the usage factor as a metric linking structure to activity, we quantify decoupling mechanisms such as engine oversizing and fleet redundancy, which drive up material immobilization. As electrification requires large-scale fleet replacement, our findings highlight that avoiding power oversized vehicles could reduce material demand, emphasizing the need to account for structure-activity decoupling in energy transition policies.

Compact surrogates could reduce the cost of simulating large language model societies, but must reproduce collective behavior. We compare individual predictions and collective forecasts using 9,455 published trajectories and new experiments on opinion dynamics. Neighbor information improves individual prediction in all 16 public-data settings and pooled collective forecasts on held-out questions, although collective gains depend on transfer conditions. Tests on 24 new statements do not confirm earlier contrasting history effects in forecasts from the initial state. Qwen benefits from history after three observed rounds. These findings motivate direct collective validation, explicit limits on available observations, and comparisons with simple baselines.

Complex networks balance metric wiring costs against functional routing demands, rarely conforming to idealized dichotomies of pure planar grids or unconstrained topologies. Yet, existing latent-space models remain computationally bottlenecked by stochastic sampling on small, unweighted graphs. Here, we formulate a scalable generative framework to solve the inverse problem of spatio-functional inference in weighted networks. By coupling explicit metric spaces with an unobserved latent geometry, we jointly reconstruct hidden coordinates and infer a coupling parameter $\lambda \in [0, 1]$, quantifying the connectivity propensity explained by functional affinity conditioned on metric distance decay. Our deterministic pipeline pairs a physics-informed spectral residual initialization with hybrid first- and quasi-Newton optimization. Across diverse empirical systems, the framework reveals a continuous spatio-functional spectrum. In the Drosophila melanogaster whole-brain connectome, it resolves an architectural progression from metric-constrained sensory circuits to specialized associative and chemo-affinity neuropils. In the continental European power grid, line pruning preserves a strictly metric baseline ($\hat{\lambda} \approx 0$), whereas topological rewiring drives a sharp surge in $\hat{\lambda}$, demonstrating that macroscopic component connectivity can mask spatial degradation. Finally, tracking global aviation throughout the COVID-19 pandemic captures dynamic regime shifts toward localized metric connectivity, establishing a unified diagnostic to probe structural organization and resilience in spatially embedded networks.

Two-round legislative elections are decided not only by first-round vote shares, but by how voters whose preferred party did not advance redistribute their votes among the surviving candidates. We develop a principled model of this transfer process, grounded in multi-dimensional ideological embeddings derived from the Chapel Hill Expert Survey, and apply it to French legislative elections. Calibrated on the 2017 and 2022 elections, the model is evaluated on the unusually complex 2024 contest, in which three ideologically distinct blocs reached the second round simultaneously, achieving 90.34 percent constituency-level accuracy. We show that ideological proximity alone explains the large majority of vote transfers, that a simple left-right axis is insufficient to capture the relevant distances, and that the structural configuration of the 2024 electorate was far less favorable to the far right than pre-election forecasts suggested.

Kinetic Ising models are widely used to describe binary opinion dynamics, but their microscopic validity has rarely been tested empirically. Here, we infer the transition probabilities governing opinion updates from a year-long online social network and show that they are accurately described by an Ising heat-bath dynamics. The inferred parameters admit a direct sociological interpretation: the external field quantifies intrinsic bias, the coupling strength measures social influence, and a persistence term captures temporal inertia. We further show that persistence is positively correlated with node degree, while both persistence and interaction strength are strongly correlated with global network heterogeneity and clustering. Using the inferred time-dependent parameters in Monte Carlo simulations on the empirical temporal networks, we accurately reproduce the observed response functions, flip probabilities, and macroscopic opinion dynamics. Within the Twitter climate debate, our results provide direct empirical support for a kinetic Ising description of online opinion formation and establish a quantitative link between microscopic social behavior and evolving network topology.

Social influence can preserve errors that individuals would correct on their own. We study this possibility by representing opinions as directions in a semantic space. The formulation connects established models of personal preference, social agreement, and external influence. A common factual signal pulls every opinion toward a reference direction, individuals remain attached to their initial preferences, and connected individuals imitate one another. When the factual signal exceeds the preference strength, each isolated individual corrects, apart from an exactly opposite initial opinion. We prove that every finite undirected network then has a unique state of minimum total energy in which all opinions favor the factual direction. This state is the best overall compromise between factual alignment, personal preferences, and agreement with neighbors. Yet on a ring with planar opinions, sufficiently strong imitation can trap the same individuals in a different stable state that retains misinformation. We prove convergence to that state from the specified initial opinions. We also derive a network spectral condition that excludes competing stable states, and show how an additional semantic direction can destabilize the constructed planar pattern. Numerical maps reveal persistent error, history dependence, and coexisting outcomes, while comparisons across networks show differences that a single spectral scale does not remove. These results distinguish individual correctability from collective correction and identify how attractive social influence can obstruct the latter.

Many models of collective behavior write headings, beliefs, and meanings in one experimenter-defined frame. Organisms do not live there: each represents the world in a private space, and comparison requires translation. Consensus becomes an existence problem before it becomes a dynamical one. Reciprocal pairwise translations need not compose consistently around a loop. This return transformation (the holonomy) can expose a mismatch no isolated reciprocal pair can carry. We develop a gauge-covariant theory in which physical predictions are invariant under private relabeling. For reciprocal unitary translations, the kernel of the connection Laplacian is isomorphic to the joint fixed space of loop holonomies: a collective can hold in common exactly what all its loops leave unchanged. A blind-subgroup criterion identifies invisible defects. Common-frame comparison, such as in traditional models of collective behaviour, occupies the flat sector. For independent uniform translations from a finite group $G$, a connected graph with $E$ relations among $N$ individuals is flat with probability $|G|^{-(E-N+1)}$. Exact cycle spectra determine persistence under linear relaxation. The consequence is operational as well as structural. For unrecorded routes under a specified model with isotropic Gaussian source and readout noise, we derive the smallest mean-squared error achievable by any decoder. At fixed signal-to-noise ratio, the jointly preserved feature fraction fixes its long-route limit. Networks with identical loop angles can differ in recoverable content when their preserved axes differ. The relational geometry of a collective sets both the states it can share and the content it can recover.

This paper investigates the role of quantum grassroots organizations in The Association of South-east Asian Nations (ASEAN), the challenges they face, and how these organizations can be better supported by other players in the ecosystem of quantum technologies. We look into the goals and strategies of ASEAN grassroots organizations and their potential impacts and investigate the obstacles and challenges currently faced by these groups. We propose providing mentors with specialized knowledge to assist in the refinement of technical content and organizational management, building connections between grassroots and key stakeholders in the quantum space, and creating opportunities to obtain stable funding. These can help to mitigate the aforementioned challenges and ensure its longevity, sustainability, and impact on the wider quantum community.

Psychological dynamics unfold across multiple timescales: symptoms and other psychological states can change rapidly, whereas social, environmental, biological, and developmental conditions often evolve more slowly. We formulate this structure as a stochastic slow-fast system in which binary symptom states form a fast interacting network embedded within a slow contextual field. Pairwise symptom coupling governs interactions within the fast layer, while the contextual field shifts symptom-specific activation tendencies and can itself receive feedback from sustained symptom activation. Simulations show that changes in the slow field can shift the macroscopic activation state of the symptom system even when the underlying interaction matrix remains fixed. Perturbations to the field generate transient increases in symptom activation followed by recovery, while feedback between the fast and slow layers delays recovery and, when sufficiently strong, produces dependence on initial conditions. We further show that when between-person variation in the contextual field is omitted from network estimation, the inferred system exhibits stronger total coupling and nonzero couplings between symptom pairs that are uncoupled in the data-generating model. Thus, slowly varying context can alter both the dynamics and the apparent interaction structure of a fast psychological system. The framework connects psychological network models with slow-fast dynamical systems and provides a formal basis for distinguishing changes in activation from changes in coupling.

By its most visible quantitative metrics: numbers of researchers, papers, journals, and institutions, science has never looked healthier. Yet a set of subsurface indicators points the other way: the disruptiveness of the average paper and patent is falling, progress slows in the largest fields, replication is rare and often unsuccessful. Incentive systems can select for poor methods even when no one is actually cheating. Lay society shows a curious mixture of admiration and lack of trust for scientists and their work. We argue that a healthy-looking surface can coexist with, and mask, an accumulation of below-the-surface damage due to slow-acting, internally and externally driven pressures, weakening the social position of science. This process is best understood not as an acute shock but as a creeping crisis. And while the damage grows slowly, it may result in a sudden collapse of the research as social institution. To make this diagnosis tractable rather than merely alarming, we import the conceptual and mathematical apparatus of two mature research fields that already study such slow degradation and sudden collapse processes: the continuum damage mechanics of creep, fatigue, and corrosion, and the ecology of resilience, regime shifts, and critical transitions. We do not claim to resolve whether science is merely robust under strain or is approaching a tipping point; the available data are too fragmentary. This remains a question of importance and we propose what would answer it: finding measurable early-warning indicators, use of agent-based models of the coupled trust-incentive-funding feedback system, understanding adversarial attacks, and the design of resilience building and recovery interventions. The result is a research agenda, and an argument for why the health of science cannot be read off its own success reports.

We examine log-optimal portfolio allocation when the long-run price of an asset follows a power-law trajectory, $P(t)=At^\alpha$, and its instantaneous return variance decays as $\sigma^2(t)=\sigma_0^2 t^{-2\gamma}$. Under a zero risk-free-rate benchmark, the continuous-time Kelly fraction scales as $K^\ast(t)=(\alpha/\sigma_0^2)t^{2\gamma-1}$. Exact temporal invariance therefore occurs when $\gamma=1/2$, whereas deviations from this value produce systematic age dependence in the allocation. We propose a scaling hypothesis connecting growth in network participation, effective market liquidity, and declining volatility. Under a specified set of scaling assumptions, this model predicts the benchmark exponent $\gamma=1/2$. Using historical daily Bitcoin prices, we estimate the power-law price exponent and examine the sensitivity of the volatility exponent to the length of the rolling window. For windows of four to nine years, the estimated volatility exponents have an arithmetic mean of 0.53 and a cross-window standard deviation of approximately 0.03. Because these estimates are obtained from overlapping observations and the same underlying price history, this spread is interpreted as a measure of model sensitivity rather than a formal confidence interval. Finally, we show that a time-dependent multiplicative contribution to return variance generally breaks exact Kelly invariance. We illustrate this result using a scenario in which Bitcoin transaction-fee variability affects the effective variance process. The results identify the conditions under which log-optimal allocation can remain stable under non-stationary power-law asset dynamics and clarify the assumptions required when applying this result to Bitcoin.

We construct a wind-driven forest-fire model in one dimension in which a fire can jump gaps between trees to ignite disjoint downwind forests. The size of a gap that a fire can jump depends on the fire intensity, which increases as the fire propagates through trees and diminishes as the fire jumps gaps. Trees grow on empty sites at rate $r$ and lightning strikes each site with rate $f$. When $f\ll r/L$, where $L$ is the system length, lightning is sufficiently rare that quasi-deterministic dynamics arises where all trees are consumed when a lightning-induced fire occurs. For $f\gg L^{-\mu}$ with $\mu\approx 0.8$, lightning is sufficiently frequent that a steady state is reached, but with unexpected behaviors for the forest- and gap-size distributions. Intermittency arises in between these regimes, with coexisting temporal domains of deterministic and chaotic dynamics.

Opioid overdose deaths remain a severe public health crisis in the US, with heterogeneous burden across counties that differ in epidemic trajectory, baseline resources, and local context. While harm reduction through naloxone distribution and buprenorphine treatment are both evidence-based strategies, limited information on county-level effects hinders the ability of policymakers to prioritize resources across counties. We developed a simulation model of opioid use disorder (OUD), calibrated separately to six Pennsylvania counties spanning large urban (Allegheny, Philadelphia), intermediate-sized (Erie, Dauphin), and rural (Clearfield, Columbia) settings. We projected county-specific overdose mortality trajectories under three levels of increase in buprenorphine dispensing and naloxone distribution (10%, 20%, and 30% above each county's baseline), over a five-year horizon from 2025 to 2029. A 30% increase in naloxone distribution above observed county baseline levels was projected to reduce 2029 overdose deaths by approximately 70% (95% uncertainty interval, UI: 55-81%) in Allegheny County, 11% (95% UI:4-17%) in Erie County, and 28% (95% UI:2-64%) in Clearfield County. Projected reductions in overdose deaths from increasing buprenorphine were consistently smaller (10%-23%), except that in Erie buprenorphine produced larger projected reduction by 20% vs 11% for naloxone. Heterogeneity in naloxone responsiveness was strongly associated with each county's historical naloxone dispensing variability. The same proportional increase in naloxone distribution yields substantially different projected mortality reductions across counties depending on each county's baseline distribution history, a pattern invisible from mortality statistics alone. County-level context is important for informing harm reduction and treatment prioritization at the county level.

Power law scaling relations between size and output are central to quantitative theories of cities, organisms, and other complex systems. Competing theories predict scaling exponents that differ by small fractions, but there is no existing theory for verifying whether a given dataset can even distinguish exponents at the required resolution to address such discrepancies. Here we derive a resolution limit for scaling exponents, giving the smallest exponent difference that any method of analysis can detect. We find that the Hurst exponents governing the evolution of systems' sizes and deviations from the scaling law determine how long a record of growing systems must be before it can separate competing scaling theories. Empirical results suggest that many available data panels are insufficient for reliable scaling model selection.

Global trade is more than a single network of aggregate flows. Beneath the observable exchange of products among economies lies a complex multilayer structure, formed by thousands of product-specific trade relationships that differ in their similarity, interdependence, and temporal evolution. Using the CEPII's BACI database, which records bilateral product-level trade flows between economies, we represent the global trade network from 1995 to 2024 as a temporal multilayer network, with economies as nodes and directed weighted trade flows as edges. To investigate product-level organisation and cross-layer similarity, temporal structural change, and the structural role of individual economies, we introduce a random-walk-based similarity measure that provides a unified framework for comparing weighted and directed trade layers. Our results show that the global trade network remains relatively stable over short periods but undergoes gradual structural change over longer timescales. We also find that similarity-based product communities only partially align with the official product taxonomy, indicating that products assigned to the same official category do not necessarily exhibit similar trade-network structures. Finally, we show that an economy's structural influence is not always determined by its trade volume. These results highlight the value of multilayer network analysis for revealing patterns in global trade that remain hidden at the aggregate level.

Group interactions are widespread, and higher-order extensions of familiar models display collective phenomena absent from their pairwise baselines, which are routinely offered as evidence of a distinct higher-order physics. We ask whether that claim survives the test that gives new a precise meaning in statistical physics: that of universality. Revisiting canonical higher-order models, we argue that what classifies collective behavior are the infrared ingredients that survive at long scales. Arity is not a universality label. Beyond universality, we examine two further questions: whether higher-order structure is a fact about the system or a choice of description, and what data can and cannot tell us about interaction order. Higher-order descriptions remain indispensable when they expose the organizing structure, provide a better mechanistic language, or improve prediction. We close with what should be measured before new phenomena can be claimed, and where higher-order structure already earns its place.

The great transoceanic voyages of the Age of Discovery imposed severe human costs on their crews. Long travel durations, deteriorating sanitary conditions, and finite food and water supplies made disease, exhaustion, and mortality central features of maritime expansion. We propose a minimal compartmental model describing the voyage itself as a dynamical system coupling crew health and resource depletion. The population is divided into healthy, ill, and dead individuals, while an additional variable represents the effective level of provisions on board. Illness incidence depends nonlinearly on resource availability, capturing the increasing health risk associated with deteriorating food, water, and sanitary conditions. The coupled ordinary differential equations are analyzed in the transient regime relevant to finite-duration voyages. Rather than reconstructing specific historical expeditions, the model identifies generic mechanisms linking provisioning, health deterioration, mortality, and voyage duration. Numerical results show that resource limitations can substantially reduce the healthy and operational fraction of the crew even when overall survival remains relatively high, revealing a distinction between demographic survival and operational viability. Increasing initial provisioning delays the crossover at which ill individuals become as numerous as healthy individuals and extends the period over which the crew remains predominantly operational. We also introduce a critical provisioning time, defined as the time required for resources to reach a prescribed stress threshold, and find an approximately linear dependence on the initial resource buffer. The framework provides a quantitative perspective on the internal dynamics of early transoceanic navigation and illustrates how dynamical-systems approaches can contribute to the study of historical processes.

The current debate on higher-order interactions raises a fundamental question: when can systems organized through group interactions be faithfully represented within a graph-based formalism? Recent results show that graph descriptions can reproduce higher-order dynamics exactly or preserve selected macroscopic observables. Yet reducibility does not necessarily imply simplification, as information removed from the interaction structure may reappear as complexity in the effective dynamics, while structural features such as nestedness, heterogeneity, and cross-order correlations may be obscured by the reduction. We argue that formal representability alone is insufficient as a criterion for model choice. Both "simpler" and "equivalent" are question-dependent notions: parsimony must be assessed for the complete structure-dynamics model, and adequacy must be defined relative to the observables, scales, and regimes required by the scientific question. A reduced model may therefore be fully adequate for locating a phase transition or identifying a universality class while being inadequate for reproducing microscopic trajectories, transient dynamics, or structure-function relations. When group structure carries relevant microscopic information, higher-order representations may remain the most direct, interpretable, and parsimonious description, as well as the natural framework for understanding how microscopic organization gives rise to macroscopic behavior and functionality.

GeoAI increasingly produces reusable Earth representation s, physical forecasts, multimodal systems, and reasoning a gents. Their progress exposes two distinct limitations. Geo graphic completeness asks whether the represented world ex tends beyond readily observed land surfaces and atmospher ic fields to oceans, biogeography, economies, institutions, and human agency. Geographic intelligence asks whether model outputs preserve place, scale, relations, process, un certainty, and the limits of valid inference. The first con cerns what exists in a model; the second concerns what may responsibly be claimed about it. This critical integrative review argues that geography provides the organizing gram mar that connects these dimensions. Seven structural gaps, propositions, and corresponding review questions translate the argument into testable requirements. The resulting re search agenda advances Living Geospatial Models as federat ed, continually updated systems that couple specialist Earth and human-domain models through shared geographic iden tity, support, relations, provenance, and uncertainty. The objective is not a single universal network, but geospatial intelligence that can explain connections and change, antic ipate plausible futures, and support accountable decisions across places and scales.