Papers

Large language models (LLMs) exhibit us-vs.-them bias: A behavioral asymmetry in which prompts framed around an ingroup (“we”/“us”) receive systematically more positive continuations than matched prompts framed around an outgroup (“they”/“them”). Using Edge Attribution Patching (EAP), we localize this behavior to directed circuits in GPT-2 Small, GPT-2 Large, Llama-2 7B, and Llama-3 8B. Across models, high-attribution edges are sparse and concentrated primarily in middle-to-late layers, while ingroup- and outgroup-related pathways are only partially overlapping and reorganize under fine-tuning. Behavioral comparisons and 30-token generations show that the measured asymmetry extends beyond next-token evaluation. Targeted patching of EAP-ranked edges reduces the bias score more than equal-cardinality random-edge controls, but also substantially degrades performance on CoLA, HellaSwag, and WikiText-2, suggesting that bias-relevant pathways are functionally entangled with broader language capabilities. Overall, our findings characterize us-vs.-them bias as a sparse, context-dependent, and functionally entangled computational phenomenon whose internal organization varies across the models examined.

Energy landscapes of non-convex optimization problems are high-dimensional surfaces that are difficult to reveal, visualize, or analyze. Message-passing algorithms, or equivalently cavity approaches in statistical physics, may fail to identify local minima as messages do not converge owing to the ruggedness of the energy landscapes. Here we aim to reveal the characteristics of these complex energy landscapes by limiting the amount of information passed in local messages, improving the convergence of messages for local minima. By studying a routing optimization problem with its convexity governed by a single parameter, we introduce a cavity message-passing algorithm with a trust region, and sample ensembles of converged local minima of rugged energy landscapes across many independent realizations of the same problem instances. We observe three regimes with different characteristics of the energy landscapes: (1) a maximally rugged regime with a peak in the diversity of low-energy minima; (2) an intermediate regime with a hierarchical multi-cluster organization of low-energy solutions; and (3) a smooth regime dominated by a single minimum. Additional tests show that the converged energies are largely insensitive to the size of the trust region if the size is small or moderate, demonstrating the robustness of the proposed approach in identifying characteristics of rugged energy landscapes.

The spatial distribution of waiting pedestrians has two primary drivers: environmental preference and interaction with other pedestrians. Spatial point processes naturally capture both spatial heterogeneity and repulsive interaction. In previous work (Sickert Karam et al., arXiv:2606.14532, 2026), we proposed a Gibbs model with inhomogeneous intensity and a modified Diggle-Gates-Stibbard interaction function, which reproduces many phenomena in replicated patterns of pedestrians waiting at a train station. Its single interaction function acts as an effective interaction, averaging over behavioral regimes such as interactions within social groups and among strangers. In this article, we show how groups affect distance-based summary statistics and take first steps towards accounting for them. We detect groups from pairwise distances and contact durations, replace each group by a “macro-pedestrian” at its average position, and refit the model. This yields a larger interaction range and better agreement in nearest-neighbor statistics than the original model, although the two fits concern different datasets and centroid-based distances likely overstate repulsion. This first attempt thus resolves some discrepancies but falls short of a fully adequate solution, opening avenues for further research.

Cooperative behavior can improve environmental quality, whereas selfish defection can degrade shared resources. In a recent agent-based study of the Aksum civilization (Vasellini et al., 2025), a population of agents moving over a reconstructed landscape and playing a local Public Goods Game grew faster and peaked higher when the game was enabled, but settled, in the long run, at the same population level as when it was not. Here we show that this behavior does not depend on the many rules of that model. We develop a theoretical ecological model of three coupled discrete-time equations, in which two sub-populations grow logistically and share a carrying capacity that rises when cooperators are sufficiently numerous and decays otherwise. Without fitting any parameter to the simulation, the equations reproduce its qualitative behavior: an initial boom, damped oscillations, and stabilization; a higher peak when the cooperative mechanism is active; and a final equilibrium that does not depend on it. Cooperation can be self-sustained for a transient period, but in the absence of measures that mitigate free-riding it collapses, and the environmental gains it produced are lost with it.

Random selection is widely used in resource allocation and auditing, making reliable implementation essential for AI-agent systems. Behavioural tests across six reasoning models uncovered threshold and divisibility rules used in identifier-based choices. For threshold-following GPT-6 Sol and Gemini 3.8 Flash, single-agent measurements prospectively predicted correlated participation under shared identifiers and biased participation under distinct identifiers with common timestamp bits. Changing dates, formats and identifier labels revealed when these predictions held. Explicit instructions to randomize independently reduced but did not eliminate shared-input correlation. To test implications for oversight, we asked four models to select customer requests randomly for human review. GPT-6 Sol approached the target rate while selecting predictably from identifiers; the others rarely selected requests. All four closely followed supplied random draws. These findings expose collective and audit vulnerabilities that selection rates alone miss, making input-dependent bias, correlation and predictability central targets for agent evaluation.

From cells to cities, ecosystems to economies, complex networks exhibit peak intensities that define their empirical limit. Estimating these limits traditionally requires domain-specific knowledge. We demonstrate that a wide range of complex networks share a capacity frontier that constrains these maxima. We formalize this regularity by proposing Structural Capacity Theory for Network Substrate Structured Systems. These systems couple a fixed network substrate with an observable dynamical process. The frontier is learned from a vector representation of the network substrate and modulated log-additively by a vector representation of the dynamical process. Frontiers trained on one set of domains reliably bound empirical maxima of entirely different ones without observing their peak intensities or simulating their dynamics. Independent learning paradigms converge on consistent upper bounds. Frontier performance is stable under perturbation, yet degrades under deliberate falsification, with no performance gain under ablation. These findings support the capacity frontier as a generalizable constraint that describes how network structure bounds dynamical processes across otherwise unrelated systems.

The Search for Extraterrestrial Intelligence programme aims to find evidence of extraterrestrial intelligence. SETI scientists pursue this objective by searching for technosignatures primarily in the radio or optical spectrum. The IAA SETI Committee has been developing protocols to offer guidelines in case of an actual extraterrestrial signal reception. These protocols establish procedures to confirm the authenticity of the signal and its actual extraterrestrial nature, as well as the committee's role in managing the discovery in relation to the scientific community and the general public, targeting scientific queries in relation to the management and development of equipment and methodologies employed in current SETI search. The project A Sign in Space part 2 aims to actively engage the global SETI community and the global telescope network, with scientific facilities responding and coordinating themselves to confirm the extraterrestrial nature of the received signal. The project develops some of the societal, scientific and technological methodologies already employed in the interdisciplinary work A Sign in Space. Here, we established a global collaboration between SETI scientists, radio observatories and the European Space Agency to test the communication and technological pipeline and protocols leading to the reception of a simulated extraterrestrial signal by a network of radio telescopes across the globe. We also employed an ESA spacecraft for system validation. A Sign in Space part 2 aims to further implement deep space technologies in SETI search through a structured and sustained programme, in collaboration with ESA, the SETI Institute and the Italian Institute for Astrophysics. The project will aim to stage and test the entire Post Detection procedure, implementing the protocol as envisioned by the IAA SETI committee.

A combination of remote sensing techniques, open space data and field testing was developed to derive astronomical and meteorological parameters and assess Dark Sky brightness of the hitherto unstudied Schist Villages region in the mountainous Interior Center of Portugal. This study covered the period 2012-2017 and established the methodology for regular light pollution and sky brightness studies in the region using satellite imagery to reduce cost and time and increase accuracy of the final analysis. Long-term Artificial Light At Night (ALAN) data from VIIRS instrument aboard the Suomi-NPP satellite along with cloud cover inferred from MODUS/AQUA satellite data and orographic data, were analyzed in a Geographical Information Systems (GIS) environment. The derived ALAN values were consistent with a preliminary site survey selection, confirming the accuracy of the identified dark sky spots in the region. The analyzed region area spans 1624 Km$^2$ and the darkest site within it showed a sky brightness of 21.4 mag/arcsec$^2$. Ground-based SQM photometer observations of the Night Sky Brightness (NSB) at the zenith validated the satellite derived ALAN data. The devised field testing is itself a low cost solution that can be used by teams in developing countries to easily assess dark sky potential prior to the development of local observatories and astro-tourism activities. This study supported the initial certification of this region as a Dark Sky Starlight Tourist Destination since 2018, an important milestone for dark sky protection in central Portugal.

Peixoto et al. (arXiv:2602.16937v2) stress that graph-based formulations can express any interaction model, a point the literature on higher-order networks (HONs) has often overlooked. We agree with much of their critique. We argue that expressiveness, however, might not be the main reason hypergraphs are often preferred. A network is read from a model rather than assumed, and to properly study the role of structure-one of the most basic questions in complex systems research-one needs a representation that keeps that structure separate from the functional form of the interactions. We show that such representation is in general a directed hypergraph (equivalently, a directed factor graph), with one hyperarc per interaction term, recovering a (directed) graph for pairwise interactions, and an undirected hypergraph for symmetric, higher-order ones. Most of the HONs literature has focused so far on symmetric interactions, which, in light of what established here, might explain why there (undirected) hypergraphs are regularly presented as the natural representation for systems with higher-order interactions.

In September 2026 the U.S. Department of War released an infrared video recorded from a military aircraft over the Middle East, with a mission report describing six small spherical objects moving at an estimated 480 miles per hour. We measure the brightness of each object in every frame. All six brighten and dim steadily at 7.1-7.9 times per second, each at its own rate and out of step with the others. Tests with planted constant-brightness objects show that neither compression nor the sensor produces this flicker. The same analysis, applied to the Galileo Project's ground-based infrared cameras near Las Vegas, finds flying animals beating steadily at 3.4-10.0 times per second, within the range of bird wingbeats. A nearly stationary object at 60-80% of the aircraft's height would produce the reported ground-projected speed of 480 miles per hour. The six objects are best explained as a small flock of birds flying nearer to the aircraft than the crew assumed. The same analysis also finds seven objects with similar beats, at 3.0-11.0 times per second, in four other released military videos. More broadly, this work shows that even heavily redacted videos of unidentified anomalous phenomena can be analyzed using reproducible, quantitative methods to test specific hypotheses. Releasing the redacted sensor and platform data would provide information that could refute these hypotheses.

The development of national policy and legal outputs toward space resource utilization across several countries accelerated after the introduction of the Artemis Accords in 2020. The announcement also further intensified the debate about the necessity of specifying a regime for using space resources on the international level. In 2021 the Legal Subcommittee of the UN Committee on the Peaceful Uses of Outer Space finally approved the establishment of its Working Group on Legal Aspects of Space Resource Activities. Therefore, this chapter builds on diplomacy under conditions of polycentric governance and aims to map the diversity of actors' ideas and interests about governance for space resource utilization on the level of the Working Group. The research process follows qualitative analysis methodology and assigns the results into the matrix of prospective alternatives for governing space resources. The available materials of the Working Group including reports and recordings, constitute the core empirical data used in the analysis.

Scientific productivity and collaboration are closely related, yet the causal direction between these two dimensions of academic careers remains unclear. Here we analyze the careers of 26,876 Brazilian researchers holding a nationally prestigious fellowship across multiple disciplines to test whether productivity shapes collaboration or the reverse. Focusing on total publications and distinct coauthors, we assess their directional relationship using a causal discovery framework based on asymmetries in conditional and distributional structure to determine the more plausible generative direction. Collaboration conditioned on productivity exhibits a highly regular mean-variance relation consistent with a geometric model, whereas the reverse conditioning yields a much less coherent pattern. Consistently, publication counts follow a lognormal distribution, whereas the coauthor distribution is reproduced by a geometric-lognormal mixture where productivity determines the expected number of collaborators. Surrogate tests indicate that the data are considerably more compatible with productivity shaping collaboration than with the reverse. The two quantities also accumulate asymmetrically: publication inequality rises steadily with career age, whereas coauthor inequality does not, indicating that advantage compounds more in output than in network breadth. Area-resolved analyses reveal a more nuanced picture, and although the direction where collaboration shapes productivity is never favored, the two directions are most clearly distinguished in areas more organized around laboratory and research-group models, where productivity inequality also grows most clearly. Among this cohort of prominent scientists, larger collaboration networks are thus more likely to reflect cumulative advantage in productivity than to independently generate greater output.

In this study, we propose a kinetic trap–diffusion model to describe the emergence of Pareto distributions in money-exchange systems. Using kinetic Monte Carlo simulations, we show that the Pareto exponent depends explicitly on temperature and takes values in the range $0.5 \leq \nu(T) \leq 1.5$. In the present framework, the temperature $T$ acts as a control parameter that regulates the exchange dynamics through thermally activated diffusion. Unlike conventional kinetic exchange models, where the Pareto exponent is fixed by microscopic rules, the proposed model generates a range of Pareto exponents as a function of $T$. The temperature-dependent Pareto exponent constitutes the central novelty of the proposed kinetic trap–diffusion framework. This feature provides a natural explanation for the empirically observed variations in Pareto exponents across different countries and economic conditions. In addition, the fraction of zero-wealth agents and the Gini index exhibit a non-monotonic dependence on temperature, revealing distinct dynamical regimes arising from the competition between trapping and money mobility. The persistence of the Pareto-like stationary distribution under strongly nonuniform initial conditions further supports the robustness of the proposed mechanism. These results show that different Pareto-tail and inequality regimes can emerge from the same trap–diffusion dynamics through changes in a single control parameter

Social Physics seeks quantitative, empirically testable explanations of collective human behavior. Its name has a long and contested history, but its contemporary program is neither the claim that society is literally a physical system nor an attempt to replace the social sciences with physics. It is an interdisciplinary practice: observation and experimentation, model construction, mathematical and computational analysis, and repeated confrontation with data. The field has been transformed by analyzing digital traces, network science, agent-based modeling, large-scale experiments, and the capacity to study coupled dynamics across economic, social, technological, biological, and physical layers. We review advances in financial analysis and modeling; economic complexity; the structure and evolution of social networks; spreading, opinion, and information dynamics; inequality, cooperation, conflict, mobility, cities, culture, science, and collective behavior; and the emerging study of human-AI ecosystems. Across these domains, common features recur - heterogeneity, interaction, feedback, adaptation, non-equilibrium dynamics, multiscale organization, and emergent collective outcomes. We also confront the limitations that have arisen in this field: convenience samples, platform dependence, weak causal identification, over-universal claims, insufficient engagement with meaning and institutions, privacy risks, and the danger that predictive models become instruments of manipulation. We propose a future Social Physics organized around theory - data reciprocity; causal and generative explanation; measurement validity and cross-context generalization; responsible, participatory data governance; genuinely interdisciplinary collaboration; and reflexive study of interventions and algorithms that alter the systems being observed.

We give a unified analytic account of a finite bid–ask spread in a two-field reaction–diffusion order book. The model retains separate bid and ask densities in operational time, with diffusion, cancellation, reaction and external order creation. On the symmetric equal-coefficient branch, the imbalance field determines the reaction price, while the total standing density carries the spread geometry. A market-making source is introduced by withholding order placement over a finite interval around the reaction boundary, representing round-trip replenishment displaced from the quote. Under a separated, quasistationary and weak-overlap approximation, transport penetrates inward from the placement edges over the cancellation length, giving the quoted spread as the sub-threshold core of the placement-source-free interval. Market orders remove standing density at the observed quote, whereas replenishment is delivered outside it and must diffuse back across the penetration depth. We derive the resulting delayed and attenuated quote-level response in operational time. On that branch, finite spread and price impact arise from distinct response sectors, while their calendar-time appearance requires a separate observation clock.

In this work, we investigate three modified versions of the classic Hegselmann-Krause opinion dynamics model, incorporating features that are typical of many real-world systems, such as uncertainty in the selection of interacting agents and a weighted evaluation of the relevance of their opinions in the influence function to enhance confirmation bias. Through extensive simulations across different network topologies, ranging from stylized network models (Barabási-Albert, Erdős-Rényi, and Watts-Strogatz networks) to empirical networks with community structure, we identify the influence of each modification on opinion evolution and convergence. Our findings reveal that they exert opposite effects on the bounded confidence threshold required for consensus. We further explore an extension based on a data-driven opinion initialization on the empirical networks, where initial opinions are drawn from Gaussian distributions specific to each detected community. While the qualitative effects of the three modified models remain consistent, this new initialization strategy reveals distinct dynamics within the network communities. These insights provide a new and comprehensive perspective on how realistic variations of the Hegselmann-Krause model, in terms of both interaction rules and initial opinion distributions, affect opinion dynamics and shed light on the mechanisms of consensus formation within structured communities.

Modern science has moved decisively toward larger and more collaborative research teams. Yet an influential 2019 study reported that small teams are more disruptive than large teams, a conclusion difficult to reconcile with both the well-known trend toward increasing collaboration and the disproportionately large teams behind widely recognized disruptive research, such as work that has been awarded Nobel Prizes. Here we show that the reported disruptive advantage of small teams is largely an artifact of measurement rather than a fact about teams. Analyzing about 60 million scientific publications, we find that larger teams cite more references and that the standard disruption index declines mechanically as reference lists lengthen. Equalizing reference-count distributions across team sizes reverses the negative gradient within the index's own framework. Evaluating each paper against one reference at a time yields a reference-robust measure that distinguishes recognized breakthroughs from ordinary papers more sharply and more consistently than the standard disruption index across six independently curated benchmarks, including the Nobel Prize. Under this validated measurement, scientific disruption increases with team size across four scientific domains and in every decade from the 1970s to the 2010s. For scientific publications, we conclude that larger teams are more, not less, disruptive.

Scent detection work is a form of interspecies cooperation. Dogs sample odors that handlers cannot perceive, and handlers decide where the team searches and which of the dogs' responses counts as a find. However, detection performance is predominantly measured by outcomes and dog characteristics. To better observe the search process itself, we collected data at two judged detection events (109 searches of 37 professional narcotics teams). All searches were video-recorded and included an outdoor area, a vehicle, and a building search, each with two targets and food and currency distractors. We synchronized computer-vision tracking of dogs and handlers with continuous behavioral coding. We observed variation across teams and in total 42% of targets were found. Finds were rarely missed because dogs never came close to a target or because handlers did not call an indication. Rather, most were missed at the encounter itself, as dogs came within 1~m of nearly every target but indicated on only about one in six of these passes. Handlers did not behave differently near targets than near distractors before their dogs responded. Finding targets was moderately consistent within teams, whereas false calls depended on the individual search and on specific items. Observing the search process suggests that success is a result of the dog's response, the handler's decision, and their coordination.

Preferential centrality (Hellervik, Nilsson and Andersson, 2019) models spatial activity through feedback between activity and attraction. We extend it with a density penalty. The local response depends on activity per unit of capacity and scales with capacity. A correction that is uniform per unit of capacity preserves total activity, and for a chosen response function and penalty strength, conservation determines this correction. We provide prefcent, an open-source reference implementation with convergence and feasibility checks and records of each run's inputs and settings. It reproduces the 200-iteration outputs of a companion Porto Alegre study across all 65,357 network segments, with median relative differences of order $10^{-14}$. In a strong-feedback example, the penalty reduces concentration and reaches the stopping tolerance in fewer iterations. Other synthetic examples show how penalty strength changes the relative prominence of centers and how their number varies with transport costs. A further example reaches different numerical equilibria from different initial states on the same network and capacity landscape. In multi-start sweeps on three synthetic two-dimensional landscapes, distinct converged states occur over a range of parameter values: at 172 of 420 points of a grid in feedback strength and transport cost, including 75 where the states differ in their number of centers. The note provides a model specification and a reproducible computational basis for further theoretical and empirical work.

Stochasticity shapes evolutionary dynamics in finite populations beyond the reach of infinite-population theories. Using a stochastic birth–death framework on random regular networks, we establish evolutionary stability criteria for finite structured populations playing three-strategy games and identify critical degree thresholds governing invasion dynamics. Our framework goes beyond two-strategy evolutionary games to reveal that the initial composition of multi-type mutants, together with population structure and stochasticity, shapes the evolutionary fate of the resident population.

Groups of individuals can solve collective problems more accurately than any single member, by aggregating their opinions. Recent theoretical work has identified individual-level reward schemes that allow uninformed individuals to evolve collective intelligence from the bottom up, through social learning. Yet these results are restricted to linear prediction problems and simple averaging, while the decision tasks that real groups confront are often non-linear, and the institutions that aggregate opinions are seldom single-layer averages: districts elect representatives who in turn vote on policy, referees advise editors who decide on publication. Here we develop a framework for the evolution of collective intelligence in multi-layer voting populations, where individuals observe limited information and groups recursively aggregate their opinions by majority rule. We prove that single-layer voting cannot solve non-linear classification problems under any individual reward scheme. We then identify a "marginal feedback" payoff structure, which rewards individuals only when their opinion is pivotal in their group, and at every layer above them. This reward scheme induces a layered population to evolve accurate collective solutions to complex, non-linear decision tasks through individual-level peer imitation alone. The collective behavior that emerges is equivalent to a multi-layer perceptron in machine learning. Our results provide a naturalistic account of hierarchical institutions, in which the outsize importance of swing voters is the incentive that sustains collective accuracy; and they identify the credit-assignment rule in machine learning as not just an engineered solution but a natural evolutionary outcome.

Across biological and social complex systems, models of epidemics or contagions incorporate complexity through network correlations, adaptive behavior, higher-order interactions, or co-circulating strains. Tracking these mechanisms lead to high-dimensional mathematical systems that resist analytical treatment. We show that a broad class of models admits a systematic reduction via fast-variable elimination. The central insight is that complexity can be captured by fast variables equilibrating much faster than the epidemic, leading to “emergent complex contagion” where the force of infection depends on prevalence. The epidemic transition follows a universal equation and is continuous or discontinuous whether the force of infection decays or intensifies with prevalence. Our results reveal diverse epidemic models share a common skeleton such that mechanisms that share a characteristic form can be macroscopically indistinguishable.

We propose a distribution-free metric to rate individual skill in “player-versus-environment” settings, where participants face heterogeneous tasks without direct opponents. Such settings are common in digital platforms, games, education, finance, and the benchmark evaluation of AI agents. They combine high randomness, tasks of widely varying difficulty, and unknown heterogeneity across individuals. Our metric maps each task outcome to a bounded performance score with zero population mean and variance bounded by $1/3$, regardless of the outcome distribution, so that scores are directly comparable across tasks. Aggregating these scores over tasks yields an interpretable skill score for each individual (the “Solo” rating), and a reshuffling null model tests whether that score exceeds what chance alone would produce. We validate the approach on the progression of $2\times10^5$ players in the mobile games Candy Crush Saga and Bubble Witch 3 Saga. The metric identifies high- and low-skill players with high statistical confidence, their classification persists over hundreds of subsequent levels, and a windowed version of the score tracks changes in performance along progression.

Calibrating microscopic traffic models for digital twins is an expensive black-box optimization problem: tuning car-following and lane-changing parameters requires a full simulation run, affording only a tight budget per recalibration window. Matching raw trajectories yields a rugged objective that sparse surrogates cannot learn, reducing sequential acquisition to near-random probing. We present FLAT, which couples what to optimize with where to sample next. An eight-dimensional behavioral fingerprint smooths the parameter-error landscape, making the objective learnable from a few dozen samples; annealed lower-confidence-bound (LCB) acquisition then spends each remaining run where it most reduces error. The surrogate, interchangeable among a Gaussian process (GP), random forest (RF), or multi-layer-perceptron (MLP) ensemble, plugs into the same LCB loop. Across six heterogeneous real-world scenes, FLAT-GP achieves the lowest scene-averaged behavioral error, winning 6/6 scenes against SPSA, GA, and CMA-ES and 5/6 against TPE under the matched budget. Some baselines need up to 4.4 times more simulations to match. Ablations show objective choice shifts final behavioral error by 81% on average, removing sequential LCB raises the six-scene mean by 20%, and surrogate choice shifts it by at most 4.2%, confirming gains trace to objective geometry and sequential allocation rather than surrogate capacity.

We present an analysis of active interrogation in space with the goal to verify the absence of nuclear weapons hidden in a large constellation of satellites. We propose a 16 MeV photon beam generated by advanced laser wakefield accelerators and the detection of fission neutrons using segmented organic scintillators. We use Starlink as a real-world example for the constellation and solve the inspector routing problem against this set of 7,852 satellites over a 5-year mission period. We perform detailed simulation of the nuclear and orbit physics: signal generation and detection with GEANT4 against an orbit-resolved neutron and gamma background, routes flown with Orekit including the effects from the Earth's oblateness, and detection decided by a likelihood ratio test. We identify different encounter types and fleet designs based on a range of inspector platforms. The radiation dose to target satellites from the beam can be kept to about 1% or less of the 5-year space environment dose. We find that a small number of inspection platforms, 20-70 depending on the accelerator assumptions, can serve inspections to the full constellation with a detection probability of 90% against a single deployed warhead. A 10% random sample of the whole fleet can be inspected by 2-20 platforms providing a 37% detection probability against 5 deployed warheads.

A leading explanation for why humans cooperate with strangers is indirect reciprocity: when conduct is observed, individuals earn good reputations by cooperating with the deserving. Previous research has identified many "moral systems" that sustain cooperation through indirect reciprocity - each pairing a strategy for how to act with a norm for how to judge others - yet what makes them succeed, and whether that success generalizes beyond the donation game, has remained unclear. Here we evaluate all 1,048,576 moral systems whose norms condition on both players' reputations and actions, across every two-player social dilemma. We find that every highly stable, cooperative system pairs a "discriminating" strategy - one that cooperates with the good and defects against the bad when in good standing - with a "consistent" norm that deems good exactly those who act as the strategy prescribes. Such systems "practice what they preach" and preach what they practice. In the limit of small errors, only one strategy paired with a consistent norm remains stable across all social dilemmas: the "contrite discriminator", which cooperates to make amends when its standing is bad. Our results unify decades of research on indirect reciprocity, revealing moral consistency as the common ingredient of every stable, cooperative moral system.

Non-recurrent epidemics on complex networks, such as the paradigmatic susceptible-infected-recovered (SIR) model, are often studied by mapping the model to bond percolation. However, the conditions under which this identification is justified have not been fully understood, except in specific cases. Here, we systematically determine when this mapping can be applied, starting from minimal assumptions on the epidemic model and the underlying network. Specifically, we discuss the conditions for three different forms of equivalence between a general non-recurrent epidemic model and Bernoulli bond percolation: isomorphism, equality of marginal infection probabilities, and equality of expected epidemic size. We numerically demonstrate the validity of our findings and examine how epidemiological outcomes are affected when these equivalences are not upheld. Our results establish the methodological basis and limitations of a common tool for analyzing epidemic processes on networks.

Power grids are beginning to host AI data centers whose demand can change abruptly and in a correlated way, and operators and planners must decide whether existing controllers can absorb the resulting transients and where new flexibility is worth installing. We cast this as a question in stochastic control: how far from optimal is an implementable controller? For controlled diffusions with affine, state-independent actuation, additive and possibly degenerate noise and quadratic control cost, any Hamilton-Jacobi-Bellman (HJB) subsolution bounds the optimal cost from below and simulation bounds the deployed cost from above, so their gap certifies the permissible suboptimality. We construct subsolutions from path-integral control by completing the control geometry: enlarging the control Gramian until it matches the physical noise makes the problem linearly solvable, and its Feynman-Kac value is an automatic lower bound whose HJB residual is exactly the energy of the fictitious control. A dual noise-deflation construction can be tighter but requires a curvature condition. The geometry yields planning rules: price control authority in proportion to local noise variance, and use shadow values to guide sparse reinforcement. For nonlinear stochastic swing dynamics of the IEEE 118-bus system after a severe load loss, a simple generator controller is certified within 2.8% of optimal under homogeneous forcing; under heterogeneous forcing the gap is 39% with uniform prices and 1.2% once the same total authority is repriced, before any hardware is added.

When two AI agents disagree, who persuades whom? As multi-agent systems increasingly combine language models of different families and sizes, the answer can determine which judgments survive interaction. Measuring persuasion as the probabilistic shift in an agent's decision after a single exchange with a dissenting peer, we test seven open-weight models across three language understanding tasks. We find that persuasion is strong: when models disagree, receivers often abandon their initial judgment after seeing a peer's answer and explanation. Surprisingly, however, neither standalone certainty nor model scale reliably predicts persuasion dynamics. Models producing almost perfectly consistent decisions in isolation can be among the most susceptible to persuasion, and small models can match larger ones as persuaders and resist their influence just as effectively. Furthermore, we show that the size of the shift depends more on the susceptibility of the listener than on the persuasiveness of the speaker. Persuasion patterns are therefore specific to each model pairing, with heterogeneity amplifying persuasion in some combinations and suppressing it in others, allowing a dissenting agent running a small model to overturn the judgments of a much larger one. These findings show that the behavior of interacting models cannot be inferred from their individual properties but must be evaluated in the combinations in which they will operate.

We investigate the relationship between long-range degree correlations and fractality in scale-free random networks. By analyzing degree correlations in scale-free random networks at the percolation threshold, at which a giant component emerges, we derive the ball volume $\tilde{\nu}_k(l)$, defined as the average number of nodes within distance $l$ from a root node with degree $k$. The resulting expression predicts a degree-dependent structural crossover. For $l\ll k^{1/(\df-1)}$, the ball volume grows as $\tilde{\nu}_k(l)\sim kl$, whereas for $l\gg k^{1/(\df-1)}$, it crosses over to the global fractal scaling $\tilde{\nu}_k(l)\sim l^{\df}$. Here, $\df$ is the fractal dimension of critical scale-free random networks. We further show that the structural crossover can be naturally understood in terms of critical branching processes and is also observed in empirical fractal networks.