Papers

Sociology emerged from Comte's ambition to study society as a form of "social physics" and was later refined by Durkheim's concept of the social fact a collective regularity that cannot be reduced to any single individual's behavior. This essay argues that a structurally similar problem is now emerging in a new domain: interactions among artificial intelligence agents. Drawing on recent empirical work showing that populations of large language model agents can spontaneously develop shared conventions and collective biases through repeated interaction, the essay proposes a new field of inquiry the Sociology of Artificial Agents dedicated to studying the relational, normative, cultural, and organizational patterns that emerge among AI agents themselves, independent of direct human involvement. It introduces the concept of the "artificial social fact" as an analytical bridge between classical sociology and this new research terrain, while cautioning against anthropomorphizing AI systems. The claim is not that artificial agents form societies in the human sense, but that their interactions already produce measurable collective patterns worthy of systematic sociological study.

Achieving universal health coverage, as set out in Sustainable Development Goal 3.8, requires closing persistent geographic and socioeconomic gaps in healthcare access, especially in under-resourced settings across Africa. Healthcare-access inequality is shaped not only by poor local access, but also by limited connectivity to city- and regional-level services and opportunities. Conventional accessibility analysis can identify where poor access occurs, but not whether poorly served places form structurally disconnected pockets across scales. This paper therefore builds on and extends the percolation divergence tree framework to develop a connectivity-based multiscale approach for examining healthcare-access inequality in Ghana. It combines street-level accessibility mapping with the hierarchical structure of the road network to identify the scales at which inequality coincides with connectivity breaks. The results first show substantial inequality: around one quarter of the population lives more than 5 km from the nearest healthcare facility. Multiscale analysis further reveals distinct structural forms of poor access. In relatively well-connected, monocentric regions, local poor-access pockets emerge around metropolitan fringes despite overall regional advantage. In less well-connected, polycentric regions, poor access extends across larger subsystems, with local pockets nested within broader poorly served areas. These findings show that healthcare-access inequality reflects both local conditions and the hierarchical connectivity of the wider spatial system, which may also constrain marginalised communities' access to other key resources and services. The framework can inform targeted local interventions and policy coordination across local and regional scales.

Social networks shape how individuals make decisions and how opportunities are distributed. However, the mechanisms that generate these networks often reflect pre-existing inequalities, and technologies that rely on network-derived signals risk further amplifying such disparities. Algorithmic fairness research largely treats networks as a fixed background, grounding analysis almost exclusively in distributive justice and overlooking how network structures systematically bias decision-making. In this Perspective, we identify ten network effects and trace how they create structural biases in the relationship between what we intend to measure and what we observe. Using academic hiring as an example, we show that network biases are not inherently harmful or beneficial. Determining their legitimacy requires examining the entire decision-making process through the lenses of both distributive and procedural justice while engaging all affected stakeholders. We therefore call for a holistic, networked approach to fairness that moves beyond static group categories and recognizes the dynamic, relational, and structural nature of inequality.

Urban street networks are modeled as spatial graphs whose geometry reflects planning, history, and physical constraints. Global orientation measures describe the overall order of a city but do not reveal how street directions form coherent neighborhoods. Here we introduce bearings communities—spatially connected domains whose streets share a common orientation—and analyze them using concepts from the physics of polycrystalline materials. Across $1025$ large cities worldwide, these domains are almost perfectly ordered: their mean coherence is $0.964$ and varies by only $1.4\%$ from one city to the next, far above the value expected for randomly oriented streets. Every city is therefore a mosaic of well-ordered orientational grains, differing only in their number, size, and mutual alignment. Because the grains are equally regular everywhere, a city's global order is set mainly by how many of them it averages over: a city appears ordered because it is built from a few large grains, not because its fabric is locally more regular. A null model in which grain orientations are randomized confirms this grain-counting mechanism. Finally, the interface fraction $\gamma$ measures how strongly domains interlock, yielding a morphology diagram that organizes cities continuously between grid-like, polycrystalline, and fragmented limits.

Cities are commonly characterized through population density, infrastructure, and mobility flows. These quantities describe where people are and how they move, but movement does not uniquely determine where populations repeatedly encounter one another or whether different locations participate in the same social environments. Here, we construct co-presence overlap networks across 13 Brazilian cities to distinguish these dimensions of urban organization. We introduce two complementary measures: colocation, which quantifies recurrent co-presence activity within individual locations, and co-connectedness, which measures the extent to which locations share the same co-present pairs. We find that the spatial concentration of colocation differs substantially from that of mobility, producing social centers that can differ in both number and location from mobility centers. At the network level, co-connectedness exhibits a non-random hierarchical organization in which locations preferentially share recurrent pairs with locations of similar activity. This hierarchy is systematically weaker and substantially more variable across cities than the corresponding mobility hierarchy, demonstrating that cities with similar mobility organization can differ in how recurrent social overlap is organized across locations. Finally, we show that the spatial proximity of colocation activity to social centers relative to residential centers provides a complementary spatial dimension of urban organization. Together, these results separate three features that are conflated when cities are characterized through mobility alone: movement between locations, local opportunities for social interaction, and the organization of recurrent social overlap across locations.

Global estimates of access to health care treat every facility alike. Drive time was routed on the OpenStreetMap network from all 217,841 of its hospitals and 15-, 30- and 60-minute isochrones dissolved for nested capability tiers, weighted with GHS-POP 2025. 96.2% of the world's population lives within an hour's drive of a hospital, 78.5% of a hospital with a documented emergency department, and 40.3% of one with a helipad or university name marking tertiary care. The 1.45 billion people within an hour of a hospital but not of an emergency hospital live mainly in South and East Asia and Nigeria; the 312 million beyond an hour of any hospital lie in a belt from the Sahel to Madagascar. Defining the tertiary tier by helipad alone leaves its estimate unchanged, and the isochrone construction shifts the 60-minute figures by a few percent. Counting every facility as equivalent overstates access to time-critical care.

Simulated societies of large language model agents are used to study online polarization, and separately to study collective intelligence, but the two are rarely measured in the same system. It is therefore difficult to say whether a society's personality composition shapes both, or whether reducing polarization costs collective competence. We present TraitMix, an experimental design in which the Big Five composition of a simulated social network, both trait levels and trait heterogeneity, is a controlled experimental variable, and in which polarization and collective performance are measured in the same runs. Across 991 simulations of hundred-agent societies, spanning six contested topics and six language models, trait heterogeneity has the largest measured effects, acting in opposite directions on two faces of polarization: varied societies hold more dispersed opinions while being less segregated into camps, so homogeneous societies are not moderate but consensual echo chambers. Trait effects are not additive, as Agreeableness determines the sign of Openness, an interaction that replicates across models although the primary model's estimate is influence-driven. Contrary to the trade-off the study was designed to measure, no polarization measure predicts poorer collective performance, and cross-cutting interaction is the only one of four whose association with collective accuracy survives partialling on the aggregation identity. We report ablations removing two potential measurement circularities, an induction gate applied to every model, and the measures that failed them.

Network motifs, recurrent local patterns of interactions in graphs, provide fundamental insights on the interplay between structure and functionality in complex systems. Many real-world systems are not well represented by traditional static pairwise networks, as interactions may involve groups of nodes, occur over time, or encode directionality. In this paper, we introduce temporal motifs for hypergraphs and directed hypergraphs, extending motif analysis to timestamped many-body interactions. We formalize the corresponding mining problem, study the combinatorial structure of these motifs, and develop exact algorithms for their enumeration. In particular, we propose a dynamic programming algorithm that substantially reduces the computational cost of motif mining, achieving orders of magnitude speedups on empirical datasets. We also introduce a null model for temporal hypergraphs to assess the statistical over- and under-expression of motifs. Applying the proposed framework to real-world datasets from different domains, including face-to-face contacts, scientific collaborations, e-mail exchanges, and Bitcoin transactions, we show that temporal hypergraph motifs reveal distinct forms of local organization across systems. Finally, we demonstrate their use as an exploratory tool through focused case studies on persistent patterns in scientific collaborations and e-mail communications.

In July 2026, Josh Kerr broke the 26-year-old mile world record, the latest in an unusual concentration of recent middle-distance records that has led to widespread speculation about the role of advancing shoe and other technologies. However, like almost every other recent record-breaking performance, Kerr's race featured a split-staggered start – an often overlooked, relatively novel start configuration that places a subset of athletes in a front group in the outside lanes, reducing the geometric burden associated with accelerating on tight turns while also avoiding the bulk of the extra distance associated with outside positioning in a traditional distance race. Here, these advantages are quantified using empirical lane-performance data, OMEGA measurements of realized race distance, video reconstruction, and a force-based model of curved running. Applying the resulting corrections to record-breaking performances from 2026, estimated advantages range from approximately 0.1 seconds to more than 1 second, depending on the event, race configuration, and model assumptions. Although small in absolute terms, these advantages demonstrate that start configuration represents a meaningful and previously overlooked source of performance advantage in modern middle-distance racing – large enough to make the difference between a world record and an otherwise great performance.

Urban rail transit (URT) faces increasing flood risk while relying on traction power systems whose failures can trigger cascading disruption. Existing studies on URT flood resilience often oversimplify power dependency by overlooking traction power redundancy and rarely consider flood-conditioned cascading impacts, providing limited insight into how flood-induced traction power failures propagate through operations and affect system resilience. This study marks the first quantitative assessment of flood-conditioned power dependency of URT and its effects on system resilience. The methodology integrates a double-layer URT network model, spatial flood exposure assessment, service disruption simulation, a flood-conditioned power dependency index, and a journey-based performance metric that captures resilience properties of robustness and redundancy. It is applied to the London rail transit network under surface water flood scenarios across current and RCP8.5 climate conditions, two traction power feeding mechanisms, and four substation flood-failure thresholds. Results show that traction power redundancy fundamentally shapes the severity of cascading impacts. Under double-end feeding, power-attributable performance loss remains minimal, whereas single-end feeding leads to substantially greater loss and is highly sensitive to substation failure thresholds. The proposed dependency index is strongly correlated with dependency-related performance loss, supporting its use as a proxy for dependency-induced additional consequences in strategic planning.

Urban rail transit systems (URTSs) are increasingly exposed to extreme floods following heavy precipitation, yet passenger travel impacts are often assessed through delay-based indicators that overlook infeasible journeys under large-scale disruptions. This study develops a passenger-oriented, resilience-informed framework for assessing flood impacts on URTS journeys from disruption onset to recovery completion. The framework presents a novel six-category classification of journey impacts, explicitly considering rerouting, alternative station use, and a delay threshold. It is demonstrated through hourly dynamic simulations of 15 London URTS lines under 30-year, 100-year, and 1,000-year flood risk scenarios. Results indicate that severe flood disruptions lead to substantial unsatisfied demand, driven primarily by unavailable routes rather than unacceptable delays. Compared with finer behaviour adjustments, rerouting dominates travel impacts. These findings highlight the significance of moving beyond delay-based assessment and provide valuable evidence on essential behavioural mechanisms for strategic-level stress testing intended to inform URTS flood resilience intervention planning.

Temporal-network models attribute memory in contact data to either node self-excitation (branching ratio n_node) or tie reinforcement (kappa), carrying major consequences for epidemic spreading. We prove that when event initiators are observed, the two mechanisms are orthogonal: the Fisher information is block-diagonal and neither trades off against the other. In undirected proximity data, where initiators are unobserved, marginalising over them couples the mechanisms into a structural confound that survives posterior smoothing. On empirical proximity, messaging, and email records, however, a cruder failure dominates: fitted node memory is pinned to the inter-event marginal law and remains virtually invariant across latent label posterior samples (coefficient of variation below 1%). An inter-event-order shuffle test and burstiness-memory diagnostics reveal that exponential-Hawkes node memory is recovered from none, while tie reinforcement remains identifiable throughout. This near-unidentifiability is intrinsic, not an artefact of the exponential kernel: refitting flexible scale-free (sum-of-exponentials) kernels on synthetic power-law self-exciting processes fails to distinguish genuine node memory from memoryless renewal controls, with identical collapses recurring on algorithmic networks (edit bots, cloud microservices) and cortical spiking. Downstream epidemic consequences are quantitative: simulations fitted to empirical contact records under-predict outbreak sizes by up to a factor of 2.5 and shift the epidemic threshold. We conclude that observational temporal networks face a two-fold identifiability boundary: contact directionality is essential to decouple tie reinforcement, whereas heavy-tailed node self-excitation is intrinsically unidentifiable from contact timings alone.

With the rapid spread of news on social media, understanding the propagation of misinformation is becoming increasingly important. One factor that affects individuals' vulnerability to false information is their ideological predisposition. Despite the large number of agent-based models that focus on social influence as a driver of the spread of false claims, they often fail to explicitly integrate personal ideological biases into belief formation. In this work, we explore how misinformation spreads through the interaction between individuals' ideological biases and social influence. Our model accounts for both the strength of individuals' ideological biases and the extent to which a false claim aligns with their ideology. Social influence modifies the effects of ideological intensity and false claim alignment through network interactions. Notably, the influence of neighbours' ideological intensity on belief is strongly affected by how well those neighbours are connected to one another. These results highlight the importance of considering both network structure and personal ideological biases when modelling misinformation propagation.

We present a comprehensive description of the network of Italian Business-to-Business commercial relationships, based on the universe of electronic invoices collected by the Italian Tax Office. The firm-to-firm detail of the data is exploited to describe the distribution of the numbers of buyers (customers) and sellers (suppliers) per firm, the centrality of each firm in the production network, and the average distance between firms. We characterize for the first time the firm-to-firm network describing the Italian production system, and present its geographic and sectoral breakdown. The analysis reveals heavy tailed distributions for the numbers of buyers and sellers per firm, implying a scale-free structure of the network. The distributions of centrality values display heavy tails as well, indicating a strong concentration of importance in a relatively small number of firms. We estimate the tail exponents for all these distributions, finding in all cases lower exponents for downstream (buyer-side) distributions than for the upstream (seller-side) ones.

The integration of new energy forms into existing energy infrastructure has emerged as a critical challenge in the context of the pursuit of a sustainable energy transition. One of the main challenges is understanding how this integration takes place not only from the introduction, but also as energy follows existing paths or creates new ones through which it is transformed and used by different activities. Here we introduce techniques from network science to analyse this process for the case of 29 European countries between 1992 and 2021. We study how new energy forms increase or decrease the variety (heterogeneity) of paths through the system of each country by establishing new ones and replacing or phasing out existing ones. We find that the transition to systems based on renewable energy is characterised by an initial increase in the variety of paths while the heterogeneity of paths decreases at the end of the transition, when the proportion of non-renewables in the system tends to zero. We then demonstrate that greater heterogeneity (complexity) is associated with larger annual fluctuations in the proportion of non-renewable sources in the system, establishing a direct relationship between the progress of the transition and the complexity of the energy system in which it occurs. This contributes to the understanding of general properties of the dynamics of the energy transition and effects that accelerate or deter it.

Generative artificial intelligence (AI) tools are increasingly accessible and have the potential to improve efficiency across clinical workflows. However, clinicians may also use non-institutional AI tools that are not provided, managed, or governed by their healthcare institutions, creating potential concerns related to privacy, security, accuracy, and clinician-AI interaction. Little is known about how clinicians currently use these tools for work-related tasks. We conducted a descriptive survey of clinicians recruited from the University of Arizona College of Medicine-Tucson and Banner University Medical Center-Tucson between May 20 and June 26, 2026. Participants reported their use of AI tool categories and the frequency with which they used AI for specific tasks across five workload categories: administrative work, clinical work, research, studying/continued education, and teaching. Forty-four respondents completed the survey. Forty-three respondents reported using AI for at least one work-related task during the preceding 6 months. Conversational AI and clinical decision support/diagnostic AI were the most used tool categories, each reported by 28 respondents. Administrative and clinical tasks demonstrated the most frequent use. AI was also used for higher-risk activities, including diagnostic assistance and clinical decision support. Non-institutional AI use was common among surveyed clinicians and extended across a broad range of work-related activities, including tasks with potential implications for clinical reasoning and patient care. Further research is needed to characterize how clinicians use these tools, how they evaluate AI-generated outputs, and how AI can be safely and effectively integrated into clinical workflows.

How cultural repertoires maintain diversity under selection is a fundamental question in cultural evolution. We address this using thirteen years of weekly popularity data for approximately 20,000 Irish traditional tunes, fitting ecological birth-process models under neutral, frequency-dependent, and per-tune selection hypotheses. We find strong evidence that tunes differ in intrinsic fitness - some are systematically more likely to be learned than others. We find that 29% of the variance in fitness can be explained by a mixture of social and melodic features. Some tunes appear to be carried along via linkage due to the tradition of playing tunes in sets, analogous to selective sweeps in genetics. By measuring changes in fitness over time and comparing this with recordings we precisely identify the mechanism by which a long-dormant tune can become fit through a popular recording. Despite the directional selection, repertoire diversity increases, driven by the continual arrival of new compositions. These results demonstrate that selection and diversity can coexist in a cultural ecosystem, and establish Irish traditional music as a quantitatively tractable system for studying the evolution of cultural variants and understanding what makes a tune stand out.

A latent space network model places the nodes in a metric space and lets the probability of a tie decrease with distance. In a space of constant curvature, pairwise distances determine the positions up to an isometry. In the products and in the three remaining three-dimensional model geometries they do not. We study the three geometries that are neither of constant curvature nor products: the Heisenberg group, the solvable group and the universal cover of the unit tangent bundle of the hyperbolic plane. We ask what one network identifies about positions in them and when their geometry is detectable. Two anchors remove the isometry ambiguity. Small configurations are not determined by their distances, and generic local identification holds beyond a finite threshold, certified in the Heisenberg group. We derive the posterior on the quotient by the isometry group. For small configurations, the divergence to the nearest product or constant-curvature competitor is the stress component of the curvature difference and vanishes at high order in the scale; undirected ties therefore detect the geometry only in large networks with large enclosed areas. Directed ties expose it at first order: in the two twisted geometries, asymmetric preferences circulate around triangles in proportion to enclosed area, which no additive ranking produces. On dense competitive-game counter networks, the coupled model beats rankings on every geometry, degree-corrected rankings and free antisymmetric terms. A Euclidean model with the same coupled term matches it, so the gain is the coupling of similarity and circulation through shared coordinates. An additive-and-multiplicative-effects model predicts better still.

Can asymmetry between two interacting networks fundamentally change how they synchronize? We identify double explosive transitions in the forward direction, backward direction, or a combination thereof, with single or double hysteresis loops in an adaptive bilayer multiplex network of Kuramoto oscillators with pairwise and three-body interactions and asymmetric phase lags. Using the Ott-Antonsen reduction, we derive a low-dimensional system and perform a stability analysis. The reduced model accurately captures the full microscopic dynamics and enables analytical expressions for the bifurcation points. Systematic mapping across multiple parameter planes reveals eight distinct synchronization regimes. The relative ordering of saddle-node and pitchfork bifurcation points—controlled by phase-lag asymmetry, cross-layer adaptation, and the higher-order interaction strength—creates two distinct coherent branches (weak and strong), giving rise to double explosive transitions. Crucially, phase-lag asymmetry acts as a robust control knob: while symmetric phase lags suppress explosive transitions, layer-specific differences promote multistability and double explosive transitions. The higher-order interaction strength $K_2$ and adaptation strengths $q$, $p$, and $h$ further modulate these transitions in a complex, parameter-dependent manner. Excellent agreement between analytical predictions and numerical simulations confirms the robustness of our reduced description.

Many models across the sciences require global distance-decay interactions on large sparse networks. Gravity models, accessibility measures, spatial economic models, and network influence processes all evaluate distance-weighted potential fields: each location accumulates contributions from every other location, weighted by a decaying function of the shortest-path travel cost between them. Computed directly, such aggregate fields require the dense matrix of all pairwise network costs, which scales quadratically in time and memory. Common approximations either discard long-range contributions or fail when interaction is governed by network distances rather than geometric proximity. We introduce HierX, a hierarchical sparse-plus-correction operator for distance-decay potential fields on networks. HierX constructs multi-scale representative layers with explicit correction terms ensuring each location pair contributes exactly once at the finest available resolution. Under bounded-growth assumptions common in spatially embedded networks, applying HierX scales as O(n log n). Systematic benchmarks confirm quasi-linear scaling to 100,000 nodes. In head-to-head comparison with distance cutoff truncation and Nystrom low-rank approximation on 25,000-zone networks, HierX achieves 5-9% RMSE at a fraction of the computational work; Nystrom degrades severely on steep decay kernels. Case studies compute population-weighted accessibility on the 2.58-million-node Great Britain driving network and the 1.77-million-node London pedestrian network: a one-time hierarchy construction (~1 hour) yields a compact reusable operator that then evaluates each national-scale accessibility field in under one second (~700 ms for Great Britain, ~150 ms for London). Open-source code and worked examples are provided.

The quantum model of the two-sentence liar paradox proposed by Aerts, Broekaert, and Smets is an early example of the use of quantum formalism to describe cognitive dynamics. Our reconstruction is primarily pedagogical in intent, but it also leads to a number of clarifications, and to some new observations, concerning the structure of the model. Rewriting the model in Dirac notation, we make explicit the distinction between truth values originating from a decision and from semantic inference, and show that the associated enlargement of the one-sentence state space corresponds to a factorization with respect to which the non-paradoxical configurations are separable while the genuine liar state is entangled. We also derive the Hamiltonian generating the four-state cyclic evolution, express it in compact operator form, and give the resulting transition probabilities in closed form. We emphasize that the liar cycle admits a unitarily equivalent representation in the four-dimensional truth-only space, where the unmeasured liar state is separable, so the dimensional enlargement is not required by the unitary part of the dynamics; it is required, however, by the measurement structure. The enlargement is also required by the dynamics as soon as revision processes are admitted, in which states with identical truth content but different origins have different successors, the origin degree of freedom then acting as a minimal form of cognitive memory. We conclude by discussing the possible relationship between the model and more general deliberative processes.

We introduce a probability-wave framework for modeling the collective behavior of interacting adaptive agents, deriving testable eigenmodes through a generalized behavioral intelligence (GBI) nonlocal probability-wave equation. This framework captures a broad range of human intelligence behaviors with analytical mechanisms and offers an indirect method to examine the Liu-Chen-Ao (LCA) hypothesis of nonlocal entangled nerve fibers in the brain through collective trader behaviors. Our empirical analysis of Chinese intraday stock market data demonstrates that adaptive entangled game modes explain 82-94% (89% overall) of observed decision patterns, a sharp contrast to the predictions of neoclassical finance based on independent rational agents. Moreover, 2-12% of behaviors show adaption to intraday news, events, and environments, characterized by dual equilibrium states and abrupt reference point shifts, while purely independent modes occur in less than 5% of cases. These findings empirically support the LCA hypothesis, as observable trading behaviors reflect underlying brain mechanisms and internal intelligence decision-making in behavioral psychology. Our results highlight the necessity of incorporating adaptive entangled game modules into artificial general intelligence (AGI) architectures, addressing the limitations of conventional artificial neural network (ANN)-based AI, which relies on trillions of opaque parameters. By integrating ANN-based AI with probability-wave-based entangled-brain simulations, machine learning can enrich AGI foundation models (FMs) and facilitate the development of human-like processing units (HPUs) that leverage brain-inspired mechanisms. Such HPUs may ultimately create more compact, efficient, and robust AGI systems, particularly for embodied intelligence and robotics.

Higher-order structures offer a natural representation of complex systems that involve interactions between groups of different sizes. A widespread feature of their higher-order structure is nestedness, whereby interactions involving smaller groups are contained within larger ones. Yet, why interactions of different orders organise into nested structures remains largely unexplained. Here, we introduce an analytically tractable geometric model of higher-order networks in which a single latent geometric space couples interactions across orders, leading to the spontaneous emergence of nestedness. We show analytically and numerically that nestedness undergoes a transition between a nested geometric regime, where it remains finite in the thermodynamic limit, and a regime where it vanishes with system size. In this regime, we uncover a weakly geometric range characterized by an anomalously slow finite-size decay, allowing substantial nestedness to persist in finite systems even when its asymptotic value vanishes. Finally, with a single geometric coupling parameter, the model reproduces the nestedness profiles observed in real-world hypergraphs across different domains. Our results reveal latent geometry as a simple organising principle underlying the nested organisation of higher-order interactions.

Laws from physics to social science rest on a small, enumerable number of factors explaining variation in the systems they describe. While the orthodoxy of economics, physics and chemistry relies on a small number of analytically interpretable laws, large data models pursuing universality throw in all available data. Both fail in their extremes through the same flaw, an incorrect basis: too few orthogonal variables to describe system variation, or an explosion of dimensionality around fundamentally low dimensional but unknown dynamics. We propose and validate a framework that extracts an interpretable, mathematically sound, low dimensional and dynamically informed basis directly from arbitrary timeseries. Combining Takens' Delay Embedding Theorem, dimensionality reduction and optimal transport, we produce a phase space of phase spaces (PSoPS) on which all interrelated dynamical series exist: barycenters formed from many phase spaces, together with the families of transport plans between individual phase spaces and the barycenter, yield a basis describing the relational geometry of each timeseries and the topology of economic relationships. The macroeconomic PSoPS built from 281,536 series is a single connected object of effective dimension 7.3 +/- 0.2, into which the canonical laws (Phillips, Okun, Solow) embed as roughly 2-dimensional looped sub-attractors. The coupling between concept barycenters is directed, with the price of money and productivity as net sources and credit and output as sinks, recovering monetary transmission from geometry alone. IAAFT phase-randomized surrogates destroy 36-43% of the dimension across the three laws and 38% on the full corpus, so the basis is irreducibly nonlinear. We close with proposed extensions to fields whose dynamics share attractor geometries and to systems that are intrinsically low dimensional yet hard to navigate in raw coordinates.

Infectious diseases may interact by competing for the same hosts or by facilitating subsequent infections. Understanding the dynamics of such multi-pathogen systems, particularly those subject to endemic seasonality and mitigation, is essential for designing robust public health interventions. We propose a three-stage modeling framework to disentangle the interplay between seasonality and behavioral feedback as a way of mitigation. First, we analyze a coupled susceptible-infectious-recovered-susceptible (SIRS) system without external forcing and show that the abrupt transition between the disease-free and endemic equilibria arises from a backward bifurcation-induced first-order phase transition. Second, we independently examine seasonality and behavioral feedback, characterizing where and when oscillatory behavior is induced near critical tipping points. Third, we demonstrate that their combination generates complex multi-annual wave patterns, with high-incidence cycles driven by seasonality and low-incidence intervals driven by behavioral feedback. By mapping stability as a function of seasonal forcing, mitigation strength, and cooperativity, we identify distinct period-doubling cascades with chaotic signatures arising from different mechanisms: the interplay between seasonality and behavior, and inter-pathogen cooperativity with the backward bifurcation it induces. We then analyze how these mechanisms interact across parameter ranges. Altogether, we show that cooperation fundamentally expands the spectrum of possible epidemic patterns, highlighting the importance of considering multi-pathogen interactions in epidemic modeling and control strategies.

We test whether the Kuramoto model quantitatively describes spatial synchronization in regional epidemic waves, using daily COVID-19 incidence for 400 German Kreise (2021–2023) and weekly ILI rates for 12 European countries (ECDC, 2021–2026). Bandpass filtering and Hilbert-transform phase extraction yield high global order parameters ($\langle r\rangle\approx0.87$ for Germany; $\langle r\rangle\approx0.97$ for Europe), yet both are dominated by a common-mode driver rather than pairwise local coupling. Removing the common mode reveals genuine short-range synchronization: an exponentially decaying residual local order with correlation length $\xi=152\pm6$~km in Germany, and a significant neighbor-vs.-non-neighbor contrast (Mann–Whitney $p=0.005$) in the European panel. We interpret this convergent pattern across two diseases and two spatial scales as a universal two-scale structure: a long-range common-mode field superimposed on shorter-range diffusive coupling. Cross-validation against a companion gauge-mediated Doi–Peliti framework shows that district-level effective screening mass $m_R$ is uncorrelated with local~$r$ (null result), the national $(m_R,r)$ phase portrait independently reproduces a previously reported hysteresis loop, and pairwise phase lags quantitatively match fractional-calculus predictions. A frequency–degree correlation provides the structural signature of explosive synchronization; excess synchronization between districts sharing the same Bundesland implicates shared school-holiday calendars and state-level policy as local coupling drivers.

A physical learning network is read at a few accessible nodes. Every task and learning rule that uses only the steady voltages and currents there, at a fixed operating point, acts through the boundary response map. Changes in the kernel of its Jacobian are blind to first order. A walk along one fiber ran to a 600-step cap, one edge then at 15.2 times its start. A decomposition theorem splits the response Jacobian over the hidden components. The blind dimension adds over components whose surviving slots are disjoint. A boundary-to-boundary edge adds one parameter and deletes one slot. Exposing a hidden node changes only its component. For one hidden node the contribution counts the bipartite components of the non-adjacency graph of its neighbors. For a pocket of h hidden nodes a factor-analysis bound caps what outside electrodes can expose. It is attained when every pocket node meets every neighbor and no edge joins two of those neighbors, so past a threshold further electrodes outside such a pocket expose nothing. An electrode inside such a pocket, when its hidden nodes form a clique, is worth h-1 directions where one outside is worth none. Read as vector displacements rather than potentials, the same nodes left no deficit beyond counting in all 90 spring networks tested, each a pocket fully joined to five or more accessible nodes, and nothing blind in 88. What limits the reading is the quantity measured as much as the number of contacts. Maximum-weight spanning forests give a proved upper bound on the blind dimension. The matching equality is proved for one hidden node and conjectured beyond. It holds in all 5,343 components whose maximum could be attained and certified, and the forest count matched the certified blind dimension in 1,448 of 1,500 held-out networks, where the maximum must be searched. A self-learning circuit shows the split on hardware.

Prediction-market probabilities increasingly appear in news coverage, yet little is known about which market movements become news or how much trading money sits behind the numbers journalists quote. Unlike a poll, a market price can be moved by anyone willing to trade, so the cost of manufacturing a number that circulates as news bears directly on the information environment. We link 173.7 million signed Polymarket trades to news coverage from 2024-2025. From 6,990 articles mentioning prediction-market venues, an LLM-based, human-validated matcher extracts 1,582 sentences quoting market odds and attributes 918 to the specific market whose price they cite. We then detect 44,976 price dislocations, movements of at least five percentage points backed by concentrated one-sided trading, and ask whether a market is cited more often afterward. In the days after a dislocation, a market's citation rate is about 33% higher than its matched baseline (log citation-rate ratio $\tau_{\mathrm{cite}}=0.283$, permutation $p=0.001$), robust to binary and Poisson count outcomes. Yet move size is not the strongest predictor of citation: prominence dominates (standardized $\beta=0.610$ vs. $\beta=0.159$ for move size). Finally, we combine the dollar flow behind a given price change with observed citation rates into a metric we call epistemic leverage, the dollars needed to move a market five points and have the move cited. It stays near \$0.7-1.0 million across prominence quintiles, because cheaper-to-move markets are proportionally less likely to be cited. The implied threat model centers not on the long tail of cheaply moved markets but on the few prominent markets newsrooms treat as informational infrastructure, where a seven-figure price of influence sits within the budgets of actors with a large stake in the quoted number. We release aggregate event-study data and validation materials.

Fringe online message boards are often studied in the context of the extreme ideology that they produce. So far, however, not much of this research has focused on direct real-world harm in the all-too-common form of collective harassment. We directly analyze the complex dynamics of KiwiFarms, an online message board dedicated largely to the harassment of individuals from vulnerable communities. We conduct exploratory analyses of the hyperlink structure of the platform and linguistic changes over time, and prospective modeling of thread size. After establishing this broader picture of the complex traits of the system, we observe the temporal evolution of community-specific vocabulary, finding that the community's framing of their harassment targets persistently evokes more danger in the early 2020s than the late 2010s. We lastly find that early thread-growth behavior is predictive of longer-term thread virality. We discuss the implications for broader understanding of toxic online behavior and threat assessment, and make the case for studying fringe platforms as complex systems with significant societal impact.

Safety evaluations typically focus on individual agents, but interacting agents can spread harmful information and influence the environment in which later decisions are made. We study how collective failure changes with harmful-agent fraction and society size in a controlled financial agent society, where agents communicate over a social network and trade in a shared market. In the primary financial scenario, collective failure requires broad harmful diffusion together with severe price dislocation or liquidity stress. Across all tested society sizes, failure remains rare at low harmful fractions but rises sharply over a narrow range. As society size grows from N=100 to N=2000, the harmful fraction associated with a 50% failure probability decreases from 4.7% to 2.2%, while the corresponding number of harmful agents increases from approximately 5 to 44. In contrast, when the number of harmful agents is held fixed, their impact becomes weaker as the society grows. Controlled interventions further show that broader network reach shifts the collapse boundary toward lower harmful fractions, whereas stronger conformity alone has little effect. To characterize these effects, we introduce Agent Society Dynamics, a finite-size framework for relating harmful-agent fraction, society size, and interaction structure to collective failure. Overall, our results reveal a nonlinear, size-dependent collapse transition in financial agent societies, showing that collective failure depends not only on the prevalence of harmful agents but also on the size and interaction structure of the surrounding society. Code is available at https://github.com/SAIL-Research-Lab/WolfSociety.