Papers

We introduce a technological capability scale that ranks civilizations by the control operations they can perform per second. A control operation is defined as setting one binary degree of freedom of matter to a specified value, whatever its previous state. Building on constructor theory, we sort them into construction and its special cases on information media, namely processing, storage and transfer. The index $\Xi = K + B$ adds to the Kardashev index $K$ an efficiency index $B$ of energy per operation, measured from the thermal floor at the microwave background temperature. The Kardashev scale gives the ceiling for resets of thermally random bits with heat radiated into the present sky, and the Barrow scale gives the floor, which for such a reset is the thermal floor at the heat-rejection temperature at every level. Since 1950 the energy per logic operation has fallen 11.7 orders of magnitude, around 5 through miniaturization. Humanity, at $K = 0.73$, computes with CMOS logic gates at $B = -0.78$ in primary energy. We describe the ultimate technology, at $\Xi = 7.58$, which would dissipate the conjectured largest power $c^5/4G$ into an uncharged, non-rotating black hole near its largest mass in de Sitter space.

Mass gathering events like concerts, sports matches, and festivals bring many people into close contact within a short period, creating localized bursts of infection that can shape epidemic outcomes across an entire city. To evaluate how these transient transmission events translate into broader urban impacts, we developed a simulation model linking event-scale contact dynamics with citywide commuting networks. Using Madrid, Spain, as a case study, we compared several types of gatherings and examined how their effects changed under different levels of disease transmissibility. We found that mass gatherings consistently amplified outbreak magnitude, accelerated progression, advanced district-level arrival times, and synchronized spatial spread. Remarkably, while the initial seed size generated at the event accounted for much of this acceleration, post-event transmission conditions provided complementary predictive signal regarding invasion timing. These findings demonstrate that mitigating transmission during mass gatherings can yield downstream public health benefits by delaying broader spatial spread. More generally, this multiscale framework offers a tool to evaluate how temporary, localized contact shifts produce longer-lasting consequences for urban populations.

Many real systems can be represented as growing networks where new nodes and links gradually emerge. The Barabási-Albert model for growing networks, and many models inspired by it, are based on the idea that nodes compete for links. However, the strength and the very presence of this competition have not been tested. We propose a robust statistical approach to quantify how strongly nodes compete for links, and apply it to data from various real systems—commenting on online news and cinema attendance data. We find a range of possible behaviors, from the perfectly elastic case, where new entrants shape network growth in a way that leaves the rest of the system unaffected, to an intermediate case where new entrants measurably affect the rest. Perfect competition is never observed. These findings have direct implications for complex systems modeling and e-commerce applications.

Motivated by biological systems and my previous studies of quorum sensing with density-enhanced motility, I study a model of density-enhanced size and motility, in which both particle size and motility increase when the local density (over a distance larger than particle diameter) exceeds the global density. The emergent structures along different size ratios are spots, holes, bands and labyrinths controlled by several distinct observations. First, the characteristic pattern length scale is controlled by the sensing radius and remains approximately independent of the size ratio. Second, the total area occupied by the particles decreases with increasing size ratio. Third, the active fraction barely depends on the size ratio. These results demonstrate how both particle size and motility can couple microscopic regulation to large-scale pattern formation. I conclude by discussing possible extensions of the model.

We develop a framework to use multiparameter persistent homology (PH) to examine access to heterogeneous-quality resources and exposure to heterogeneous-severity nuisances in a geographic region. Persistent homology, which is a type of topological data analysis {(TDA)}, has been employed previously to examine resource coverage. Unlike prior approaches, which used one-parameter PH to study resource coverage and nuisance exposure, our method accounts for heterogeneous-quality resources. Our framework, which employs a computationally-efficient approximation of multiparameter PH, allows one to study access to any resource ({or} exposure of any nuisance) using any notion of quality (or severity). Using the city of Chicago as an example region, we employ our framework to detect clusters of poor access to public parks, overexposure to landfills, and both underexposure and overexposure to pubs and bars.

In social dilemmas, individuals need to forgo short-term temptations to achieve synergistic collective outcomes through cooperation. Previous work has examined mechanisms through which cooperation can evolve, including direct reciprocity, indirect reciprocity, environmental stochasticity, network reciprocity, and demographic stochasticity. These mechanisms have largely been studied under natural selection or social learning, where strategies with higher payoffs are more likely to spread. It is equally important to study cooperation under self-learning, where individuals adapt through their own experiences. Here, we focus on multi-agent reinforcement learning and derive analytical conditions under which these mechanisms stabilize cooperation under learning dynamics across scales. We find that reinforcement learning can steer self-interested individuals toward cooperation when they value the future over short-term temptation. Our work provides a unified approach to identifying the determinants of learning to cooperate in a changing world, thereby paving the way for the advancement of cooperative artificial intelligence.

The African School of Fundamental Physics and Applications, also known as the African School of Physics (ASP), was initiated in 2010, as a three-week biennial event, to offer additional training in fundamental and applied physics to African students with a minimum of three-year university education. Since its inception, ASP has grown to be much more than a school. ASP has become a series of activities and events to support academic development of African students, teachers, high school pupils (learners) and faculties. We report on the ninth African School of Physics, ASP2026, organized in Kenya, on July 5–19, 2026. ASP2026 included programs for university students, high school teachers and learners.

Groups differing in social and economic circumstances often differ markedly in depressive symptom levels, yet their estimated symptom networks show few clear differences. Such null results are often read as evidence that the groups' symptom systems are the same, but they only show that no difference was detected in how symptoms interact. How readily symptoms become present, and how this depends on the contextual conditions under which they are observed, is rarely compared. Building on a slow-fast perspective, we treat depressive symptoms as a relatively fast-changing system embedded in more persistent social, economic, psychosocial, health, and lifestyle conditions that shape symptom activation. Using a cohort of 23,689 adults from Amsterdam, we illustrate this with PHQ-9 depressive symptoms and a composite index of persistent socioeconomic, psychosocial, and health-related conditions, which we call Slow Risk Load (SRL). Participants with high SRL had substantially higher symptom levels than those with low SRL. A standard Network Comparison Test detected no overall difference in network structure, although global strength was modestly higher in the high-SRL group. Ising models, which separate how symptoms co-occur from how readily each becomes present, indicate higher activation under high SRL for eight of nine symptoms, and model comparison consistently favored group-specific activation over group-specific interactions. The slow-fast perspective reframes group network comparisons as a multiple-timescale problem in which network structure, symptom activation, and context should be considered jointly. It places symptom-focused and context-focused interventions at different layers of the same coupled system rather than in competition.

Success-driven imitation is a fundamental aspect of social learning, yet group interactions beyond pairwise require more subtle imitating rules since success can be observed at either the group or individual level. How such heuristic imitating rules based on these distinct levels of social information compete and coevolve with collective behavior, particularly cooperation, remains poorly understood. Here, we address this issue by studying the coevolutionary dynamics of cooperation in public goods games and individual- and group-based imitating rules on hypergraphs. We distinguish three rules according to whether payoff-biased imitation operates at the individual level, the group level, or both. Our results identify a mutual reinforcement between cooperation and group-biased imitation: preferentially learning from successful groups promotes cooperation, while cooperators in turn favor group-biased imitation. We confirm this synergy between cooperation and group-biased imitation across diverse synthetic and empirical higher-order network populations. We further show that the subtle scale and organization of group interactions critically shape this coevolution, with intermediate group sizes providing the greatest advantage for cooperation. Our results reveal how learning whom to imitate can jointly evolve to shape collective cooperation.

Higher-order networks take group interactions as given. I ask what happens when a group interaction is made by pairwise dynamics on a graph, and follow it through the transition that decides whether it matters at large scale, Anderson localisation. An emergent hyperedge is a $k$-body bound state of a Hamiltonian whose terms live on the vertices and edges of the graph, Borromean when none of its $(k-1)$-body faces is bound, detected on a finite graph by a $k$-fold coincidence that survives the thermodynamic limit while the $(k-1)$-fold ones vanish. Sparse random graphs produce one from the simplest pairwise dynamics: three distinguishable particles with on-site attraction $U$ and hopping $t$ bind into a trimer before any pair binds. The thresholds are obtained on the Bethe lattice, in closed form for the pair, in both sectors that an expander graph has and a lattice lacks, the one a condensate sees and the one a Fermi liquid sees. On a disordered graph the emergent hyperedges nucleate on rare deep sites and localise before their parts: the compact trimer, with a narrow band and a threefold sensitivity to site energies, undergoes the Anderson transition at a disorder of $1.6t$, against $17t$ for a single particle and $4t$ for a pair, and the Fermi liquid of trimers is a glass above a line between $1.5t$ and $1.7t$, where a liquid of single particles at the same density needs $15t$ to $16t$. The transition is the single-particle cavity transition with the composite's hopping and effective disorder. A group interaction made by pairwise dynamics is an order of magnitude more fragile to heterogeneity than the network that makes it.

Geospatial simulation of infrastructure interventions requires mobility generators that respond directly to edited maps, yet many data-driven generators do not expose the map as an editable condition. We formulate this task as map-conditioned autoregressive generation of human mobility: a road raster conditions a decoder that emits nominal 31.25 m mesh-cell tokens at one-minute intervals. The mesh-local vocabulary supports held-out and locally edited maps without retraining or vocabulary changes. We instantiate a ResNet-50 visual-prefix configuration and a Vision Transformer (ViT) cross-attention configuration, trained from scratch on 87,400 smartphone-derived trajectories from 874 meshes in Ishikawa Prefecture, Japan; 219 meshes are held out. We evaluate map sensitivity by comparing correct-map and within-split shuffled-map generations with held-out real trajectories. On the 110-mesh test split, for the ResNet-50 configuration, correct-map generations are closer than shuffled-map generations on 60% of meshes under Hausdorff-based energy distance (p = 0.021), while DTW is directional but inconclusive (57%, p = 0.074); correlation with real density is 0.38 with the correct map versus 0.01 with shuffled maps. The ViT configuration shows weaker trajectory-level sensitivity and smaller density gains. An illustrative bridge-removal edit changes generated continuations without retraining. Together, these results support the feasibility of editable-map human-mobility simulation.

The FCC's projected average electricity consumption is 1.3 TWh per year. If supplied entirely by nuclear power, this would represent about 10% of the annual output of a large third-generation nuclear reactor, together with a corresponding share of its radioactive waste. By 2050, however, renewable sources could provide up to 80% of this electricity on a substantially decarbonised European grid, supported by long-term power-purchase agreements and flexible operation. This could reduce the residual nuclear requirement, and its associated waste, by up to a factor of five. This essay asks whether hydrogen could help bridge the remaining periods of low wind and solar generation. It examines production from renewable electricity, transport as hydrogen or ammonia, storage and conversion back into electricity, together with their efficiency losses and carbon footprints. It then considers the still uncertain prospect of naturally occurring hydrogen. None of these routes offers a ready-made solution. But the decades before the FCC begins operation leave time to develop one–and CERN could help accelerate that development by becoming a credible long-term customer.

This study addresses a theoretical model regarding equity and accessibility challenges in designing shared transportation systems (such as micro-mobility networks) by applying graph-vertex domination setting. The work focuses on identifying dominating forced vertices, that represent nodes belonging to every dominating set of a graph of the smallest possible cardinality, and which correspond to critical, non-negotiable station locations essential for maintaining system efficiency and coverage. From a theoretical perspective, in the paper it is first demonstrated that determining whether a given vertex is a dominating forced vertex is co-NP-hard, establishing the computational infeasibility of exact identification in large networks. To analyze graph structures, sharp theoretical bounds on the maximum number of dominating forced vertices are established, proving that their count is bounded above by one-third of the order of the graph, and provide complete structural characterizations for graphs achieving this bound, as well as, trees with no dominating forced vertices. To overcome computational limits in practical urban settings, the study uses an iterated greedy metaheuristic framework to generate minimal dominating sets and approximate critical forced nodes based on their appearance frequency across iterations. The methodology is validated on strong grid graphs and applied to real-world road network models of Algeciras and La Línea de la Concepción, two cities in the area of Campo de Gibraltar, Spain, which successfully pinpoints candidate location points for scooter-sharing stations across both cities.

Epidemic spread and collective opinion formation are tightly coupled processes: individual beliefs about the severity of an outbreak and the value of protective measures shape behavior, while the evolving epidemic itself reshapes public sentiment through risk perception. We propose an agent-based framework that couples opinion dynamics with a compartmental epidemic model, in which each agent carries both a health status and a continuous opinion variable describing adherence to protective measures. Opinion evolution is driven by binary interactions among agents and by an exogenous background field that reflects the current state of the epidemic, while the disease transmission rate depends explicitly on the opinions of interacting agents. Using methods of statistical mechanics, we characterize the resulting macroscopic system for the compartmental mass fractions and mean opinions in both far-from-equilibrium and close-to-equilibrium regimes. The calibration shows that incorporating behavioral opinion dynamics substantially improves the interpretation of epidemic evolution. In particular, the inferred risk perception function evolves consistently with the observed epidemic burden, indicating that behavioral adaptation can explain part of the temporal variation that would otherwise be absorbed into time-dependent transmission parameters. Our results illustrate how integrating opinion heterogeneity in kinetic epidemic models offers quantitative insights into the feedback between behavior and disease spread.

Stochastic processes underpin dynamics across biology, physics, epidemiology, and finance, yet accurately simulating them remains a major challenge. Classical approaches such as the Gillespie algorithm are exact for Markovian, time-independent systems, where propensities depend only on the current state and agents of a given type are statistically identical. While efficient, this framework misses a defining feature of many real systems: heterogeneity and memory at the level of individual agents. Cells may divide or differentiate on distinct intrinsic timescales, individuals may preferentially interact with specific partners, and inter-event-time distributions can deviate strongly from the exponential. We introduce MOSAIC (Modeling of Stochastic Agents with Individual Complexity), a general and scalable framework that embeds agent-specific properties directly into the dynamics. MOSAIC unifies heterogeneous rates, dynamic interaction preferences, and both Markovian and non-Markovian waiting-time distributions within a single stochastic formalism, while retaining Gillespie-like computational cost.

Routing and search respond in opposite ways to rapid network expansion. Short graph distances make a known destination easy to reach, while the neighborhood accessible within a few hops can be vastly larger than any finite inspection budget. We show that this tension imposes an algorithm-independent constraint on sparse search. If $m_q$ relevant nodes are placed without structural information among $N$ nodes and at most $M$ nodes can be inspected, any target-blind exploration protocol has success probability at most $Mm_q/N$, irrespective of correlations between successive inspections, of revisits, and of any structural preference the exploration rule may have. Geometry determines when this constraint becomes relevant: a target becomes accessible with order-one probability when the graph-distance ball volume satisfies $V(R_c)\sim N/m_q$. At this scale, any inspection mechanism achieving a fixed success probability $\delta>0$ must enrich the probability of inspecting relevant nodes by at least order $N/(Mm_q)$ relative to the neutral target density. For uniformly searched candidate sets, this entails a vanishing visible fraction of the accessible region. Thus rapidly expanding networks can make rare targets geometrically close while target-blind search remains ineffective. Numerical results on Krioukov hyperbolic random graphs and two-dimensional lattices show that this separation can arise within only a few hops in the rapidly expanding case, while the lattice accessibility radius grows algebraically.

AI agents built on a few shared models increasingly act for many people. A shared forecast about others can align their choices and change how scarce capacity is allocated. We tested this feedback in a two-road congestion game. Adding one sentence warning that others might follow a routing tip made populations of 50 GPT agents crowd one road while avoiding the nearly empty alternative. Average travel time rose from 64 to 95 min, although any crowded-road agent could have saved 69 min by switching alone. The warning discouraged the very move it predicted. The pattern persisted for 100 rounds. Two other model families shifted the same way without locking onto one road. Twelve all-human groups (240 participants) stayed near balance under numerical reports or the tip and warning. In 24 mixed groups with a further 240 participants, imbalance grew with the share of agents in the registered analysis, while people increasingly took the road the agents avoided. Collective costs stayed below the allagent reference, but with 15 agents and 5 humans, agent seats averaged 80 min, compared with 44 min for human seats. Shared forecasts can thus sustain collective inefficiency among similar agents. A better group average can also hide an unequal burden. Evaluations of AI agents that share resources should test populations, treat messages as interventions and report who bears the costs.

Cities differ in built form, land cover and development history, complicating comparison across places and time. Satellite foundation models map Earth's surface onto common numerical representations. Yet the tasks and targets used to shape them typically do not focus on cities: globally consistent labels for urban function do not exist, and many datasets - especially land cover and land use classifications - collapse the built environment into few classes. Here we audit the representation, focusing on AlphaEarth but with broader applicability to other Earth embeddings, by probing the geometry and geography of embeddings for 1,000 urban areas in 162 countries. We find that cities occupy a shifted but overlapping region on the hypersphere, 62.7{\deg} from the global mean direction, and continent and climate predict 24.3% of variation among the mean directions of urban centres in excluded countries. Inside cities, degrees of urbanisation carry 8.9% of the variation, and what they leave holds shared directions whose local orientation varies, not one universal axis of urbanisation. Retained variation is itself unequal: dispersion within urban centres is 14.1% greater per standard deviation of national development, even after adjusting for population, land area and continent. Further controls suggest cities in developing countries present less contrast in vegetation and texture, and dispersion follows that contrast: full adjustment for it leaves at most 6.4% of the gradient. Annually, a city's representation moves nearly eight times more than redrawing its own pixels explains, and contracts where the 2022 loss of Sentinel-1B removed a pass direction. AlphaEarth's representations therefore support comparison across regions, while the differences between its annual layers are not yet validated for comparison over time.

Could a collider become the symbol of everything that must be abandoned to save the climate? In the summer of 2026, this question ran through discussions within the Particles and Fields Division of the French Physical Society. An unacceptable carbon footprint, two EPR nuclear reactors, five hundred deaths, billions to be reallocated and, to top it all, unclear scientific objectives: the objections to CERN's Future Circular Collider (FCC) appeared to form an overwhelming indictment. This essay examines each charge in turn. Grounded in a clear and compelling scientific vision, it confronts emotionally charged imagery with orders of magnitude, distinguishes a project's footprint from its full balance sheet, considers the costs of postponing or abandoning it, and explores ways of reducing its impacts-including the still uncertain prospect of natural hydrogen. The climate alone does not decide the future of the FCC; it requires us to judge the available choices by their real consequences. Developed for the public debate organised by France's National Commission for Public Debate (CNDP) and for the Swiss consultation, this essay is intended for the broadest possible readership, well beyond particle physics and the scientific community. It frames the FCC debate as a choice about the kind of society we want to build: should we organise society around renunciation and ever-shrinking horizons, or transform how we produce and choose a future worth wanting?

This research establishes a connection between macroscopic urban commuting flows and thermal equilibrium. Using mobility data from around 30 million records across six Japanese cities over one year, we introduce the Gravity-based Home Swapping Model (GHSM). This model applies Metropolis dynamics to urban commuting by treating individuals as interacting particles. Within this framework, total commuting time dictates the system energy, and temperature controls how strongly mobility responds to cost savings. Consequently, urban commuting can be analyzed through an evaluable free energy and simulated similarly to physical systems of matter. The maximumentropy doubly constrained gravity model serves as the stationary state. We find that the residential dynamics exhibit glassy characteristics. Through calibration to observed data, we reveal that the system demonstrates signatures of kinetically constrained models, specifically ageing, hysteresis, and freezing near equilibrium. Simulations initialized from arbitrary states converge to empirical origin-destination matrices. This demonstrates that minimal physical mechanisms can reconstruct complex urban realities.

Identifying the minimal set of nodes whose removal breaks a complex network apart, also referred as the network dismantling problem, is a highly non-trivial task with applications in multiple domains. Whereas network dismantling has been extensively studied over the past decade, research has primarily focused on the formulations of the optimization problem for single-layer networks, neglecting that many, if not all, real networks display multiple layers of interdependent interactions. In such networks, the optimization problem is fundamentally different as the effect of removing nodes propagates within and across layers in a way that can not be predicted using a single-layer perspective. Here, we propose a dismantling algorithm named MultiDismantler, which leverages multiplex network representation and deep reinforcement learning to optimally dismantle multi-layer interdependent networks. MultiDismantler is trained on small synthetic multiplex graphs; when applied to large, real and synthetic networks, it displays exceptional dismantling performance, clearly outperforming all existing methods that rely on a single-layer approach to network dismantling. We show that MultiDismantler is effective in guiding strategies for the containment of diseases in social networks characterized by multiple layers of social interactions. Also, we show that MultiDismantler is useful in the design of protocols aimed at delaying the onset of cascading failures in interdependent critical infrastructures.

Societies worldwide are described as increasingly polarized, yet issue polarization – how divided a society is over political positions – has been measured almost entirely on a single left-right axis developed in Western democracies. Whether that axis describes political division elsewhere is largely untested, because no survey measures political attitudes on multiple dimensions across many countries. Here, we harmonize 1,299 items from nine cross-national survey programs and 23 national election studies to place 1.14 million people from 141 countries on four dimensions: social liberalism, economic left-right, democratic commitment, and anti-elite sentiment. A single left-right axis does not describe political division in most of the world. The median within-country correlation between a person's social and economic positions is -0.015. Societies differ instead in what they are divided about, and they do so by region. European countries divide most often over social liberalism, East Asian and Arab countries over democratic commitment, Latin American countries over economic left-right, and African countries over anti-elite sentiment. Of the 81 countries measured on all four dimensions, 39 are most divided on a dimension no left-right scale would capture. Most political disagreement lies within countries rather than between them, at 58 to 88 percent of the variance. Ideological constraint, long treated as a property of mass publics, holds in nineteen of the eighty-three we can test, most strongly in the United States at +0.70, and there it is concentrated among the politically attentive. Understanding political conflict therefore requires asking not how polarized a society is but what it is polarized about. Our released item bank and fitted parameters place respondents from any future survey on the same scale without re-estimation, once that survey's items are harmonized to the bank.

This work introduces a spectral transfer formalism for nonlinear synchronisation dynamics to resolve how internal dynamical activity redistributes across network scales, moving beyond traditional global observables like the Kuramoto order parameter. By projecting Kuramoto phase dynamics onto the eigenbasis of the graph Laplacian, we construct a time-dependent transfer matrix and derive novel network metrics, including the spectral flux, which quantifies directional redistribution between structural dynamical scales rather than physical transport across nodes. Numerical simulations on modular and hierarchical networks reveal highly structured, intermittent spectral transfer episodes characterised by forward and inverse spectral cascades, directional reversals, and complex interaction geometries. Crucially, we demonstrate a clear separation between macroscopic coherence and microscopic spectral interactions, showing that highly organised, fluctuating internal redistribution dynamics persist even beneath nearly stationary and featureless global synchronisation states. This framework extends conventional synchronisation analysis and establishes a multiscale approach for interpreting network dynamics as an evolving process of spectral reorganisation.

This paper provides a detailed account of the origins, objectives, design, and implementation of the Milestone-Based Fusion Development Program, a public-private-partnership (PPP) program launched by the U.S. Department of Energy's Office of Science in September 2022. The purpose of this program is multi-faceted, with policy, scientific and technological (S&T), and commercialization objectives. Tactically, the program supports privately funded fusion companies in closing S&T gaps toward delivering preliminary engineering designs of their demonstration fusion plants (aka "fusion pilot plants"). The program is a key element of a shift in U.S. fusion strategy, initiated in 2022, to accelerate fusion commercialization by leveraging PPPs. The design of the Milestone Program was underpinned by its authorizing legislation and the U.S. National Academies report Bringing Fusion to the U.S. Grid (2021), and drew inspiration from other PPP programs discussed in this paper. Finally, the paper provides the authors' perspectives and reflections on the strengths/weaknesses of the program as implemented, implementation barriers, and lessons learned, with the intent to inform future PPP programs in fusion and other energy/technology disciplines.

We examine the interchangeability between two duplex systems with opinion dynamics: one characterized by different dynamics parameters $a_1$ and $a_2$ on each layer and full node overlap, and the second with the same parameter $a_1$ on both layers but only partial node overlap $r$. We introduce a general framework for identifying the critical line between the ordered and disordered phases, thereby translating one system into another. The description is supported by several examples of opinion dynamics models and a rigorous measure of the distance between the stationary solutions of the rate equations in both settings. Our results show that even large values of $r$ are sufficient to obtain very good correspondence between the two settings.

The danger of collective risk in a public goods game could provide an effective escape route from the tragedy of the commons. Existing studies usually embed risk mitigation in the contribution itself, whereas many real systems rely on a separate costly and non-excludable protective activity that requires a participation quorum. Whether such protection can evolve and persist remains unclear. Here, we formulate an $N$-player public-goods game with ordinary cooperators, defectors, and protective cooperators. Defectors endogenously increase a saturating probability of collective failure, whereas protective cooperators incur an additional cost and reduce this risk for all group members once their number reaches the quorum. Replicator analysis and numerical bifurcation calculations yield three main findings. First, protective cooperation gains an advantage when the focal participant completes the quorum and the resulting expected loss reduction exceeds its additional cost. This advantage varies non-monotonically with group composition. Second, when a single protective cooperator cannot activate protection, protection effectiveness does not enter its first-order invasion fitness at full defection; greater effectiveness cannot overcome the rare-invasion barrier when full defection is locally asymptotically stable. Third, a boundary saddle–node bifurcation creates a saddle and a locally asymptotically stable coexistence equilibrium of defectors and protective cooperators. When full cooperation and full defection are also locally asymptotically stable, three attractors coexist, and the numerically observed evolutionary outcome depends on the initial population composition. These results distinguish the effectiveness of activated protection from its ability to become established from rarity.

Rapid growth of data centers and artificial-intelligence services is producing computational loads at scales once associated mainly with largest power plants. Recent grid events show that a routine transmission disturbance can cause several gigawatts of data-center demand to disconnect or transfer to backup nearly at once. This article revisits the classical synchronization and transient-stability theory needed to reason about such events. We organize four lines of work—graph-based synchronization conditions, winding-number descriptions of nonlinear power flow, separable convex network optimization, and direct energy methods—into a single cycle-space certificate framework for the lossless fixed-voltage model. The static layer gives an exact strict-cohesion test within a prescribed winding cell and reveals the widely used Dörfler–Chertkov–Bullo test as a quadratic surrogate of the same convex problem. The dynamic layer converts the critical-energy calculation into a finite family of convex boundary problems. Standard MATPOWER benchmarks illustrate both what the stronger static test gains and where it gains nothing: the 118-bus case admits $16.2\%$ more loading than the sufficient screen, while the 39-bus case is bridge-limited and the thresholds coincide. A stylized $2.7$-GW 39-bus event further shows that transient margin can change by about a factor of two depending on where balancing power is supplied, even when every final balanced operating point remains statically feasible. The result is a tutorial synthesis and an extensible deterministic certificate for emerging gigawatt-scale computational-load contingencies.

Capability and efficiency are two key dimensions of reasoning in large language models (LLMs). Capability refers to the ability to solve a given problem correctly, whereas efficiency refers to the ability to do so with limited resources. When LLMs use Chain-of-Thought (CoT) reasoning to solve problems of controlled hardness, both the number of problems solved correctly and the number of tokens required to reach a correct answer depend on problem hardness and model size. However, how these factors jointly shape capability and efficiency remains poorly understood. Here, we use hierarchical Bayesian models to evaluate the capability and efficiency of LLMs from the DeepSeek-R1-Distill model family across four classes of arithmetic and algorithmic reasoning problems. At a fixed model size, the probability of correctly solving an instance decays approximately exponentially with instance size, our proxy for problem hardness. The decay scale grows sublinearly with model size, indicating that larger models are more capable, but that capability gains diminish with scale. Output length grows as a power law with instance size, which serves as a proxy for difficulty. However, the parameters of this power law do not vary systematically with model size, suggesting that larger models do not become more efficient. Together, these findings reveal potential limitations of naive scaling as a strategy for developing more capable AI systems: capability improves with diminishing returns, while efficiency shows little to no improvement.

The stochastic block model is a paradigmatic model of networks with community structure. Yet percolation in the model has been studied primarily in cases with a fixed block structure, even though in real networks, the community structure may evolve as the network grows. Here we study percolation in sequences of stochastic block models in which the numbers and sizes of communities, as well as the intra- and intercommunity connection probabilities may all change with the network size. We analyze five such sequences using two methods: linearized self-consistent equations for the locally tree-like models and a branching process at the community scale for the models with nonvanishing clustering. We find that the critical average degree is not generally equal to $1$, even in locally tree-like sequences, because the transition depends on how connections are distributed across the evolving community structure. We also show that the community-scale branching process accurately predicts the transition when intercommunity connections are sufficiently sparse, even in the presence of nonvanishing clustering, while a geometric stochastic block model sequence demonstrates the limitations of this method when correlations between intercommunity connections cannot be neglected. These results extend percolation studies in the stochastic block model to more realistic scenarios with evolving community structure, and may provide new methods to derive the upper and lower bounds for the percolation threshold in geometric long-range percolation.

Public health measures at mass gatherings work only if people follow them, and adherence depends both on how instructions are communicated and what others do. We link these behavioural factors to pathogen transmission in a local-scale, agent-based exposure model combining pedestrian dynamics with airborne transmission. Rather than fitting a parametric behavioural model, agents draw their adherence at run time from survey respondents (2,170 attendees of UK sports and music events) who reported the same context: we vary stewards' communication effectiveness and adherence of role models, as well as agents' shared social identity with each, assuming that strong shared social identity increases their influence. In a ticket-checkpoint queue of 101 agents, effective communication combined with strong shared social identity with stewards reduces the number of highly exposed agents by 82% for mask wearing. In contrast, strong shared social identity with non-adhering role models gives almost nine times as many highly exposed agents as with adhering role models. Physical distancing was not monotonically beneficial, because adherence changes how agents move: an infectious agent that kept distance moved along the edge of the queue, leading to similar results across conditions. Our pipeline transfers to any survey that includes behavioural measures and contextual variables.