Papers

Electricity demand from data centers is expected to grow from roughly 5% of U.S. consumption in 2025 to between 9% and 17% by 2030, and corporate artificial intelligence (AI) use is following a similar trajectory, spanning employee productivity assistants, direct access to large language models (LLMs), and AI features embedded in enterprise software. AI emissions today are a small share of footprints for many enterprises, but that share is unlikely to remain small for long. Without reasonable estimates, companies cannot set reduction targets or identify effective decarbonization levers as emissions grow. Companies, regulators, and auditors are asking for emissions estimates that withstand scrutiny, but no widely accepted methodology exists today. Published per-query estimates can differ by several orders of magnitude depending on what is counted, which provider is measured, and what assumptions are made about electricity use and the grid mix. This white paper proposes a standardized framework for corporate-level AI emissions accounting. The framework is designed to be defensible with current data constraints, tiered to meet companies where their data are, transparent about its assumptions, updatable as provider disclosure matures, and built for action rather than disclosure alone. Since AI emissions accounting is still nascent, it has the opportunity to design for actionability from the outset, so that measurement incentivizes responsible choices during AI's rapid buildout.

The transition to automated transportation introduces mixed-autonomy traffic where human drivers may strategically exploit the risk-averse behavior of Connected and Automated Vehicles (CAVs). While microscopic models capture these dyadic interactions, their aggregate impact on network-level stability remains unquantified due to the scale gap between agent-based and continuum models. This study bridges this analytical divide by integrating a game-theoretic friction term directly into the macroscopic kinematic wave framework. We model the cut-in maneuver as a Stackelberg game, identifying a distinct "exploitation window" where human drivers leverage CAV defensiveness to execute aggressive merges. By deriving a closed-form micro-macro bridge, we translate these discrete strategic outcomes into a continuous friction parameter that endogenously modifies the traffic conservation law. Theoretical analysis and numerical simulations confirm that this behavioral asymmetry functions as a deterministic destabilizer, generating perturbation source terms that trigger phantom jams and strictly reduce road capacity. Crucially, we reveal a convex relationship between CAV penetration and system efficiency, identifying a critical instability regime at intermediate penetration rates (approximately 45 percent) where the frequency of exploitable interactions is maximized. These findings demonstrate that without socially aware control policies, the defensive nature of early-deployment CAVs may paradoxically degrade traffic flow stability.

Anticipating tipping points in complex systems is difficult because many early warning signals require long time series, which are often unavailable in practice. Spatial early warning signals offer an alternative by using a single snapshot across many interacting elements, or nodes. However, their performance in heterogeneous systems is often inconsistent because raw node states reflect both dynamical changes associated with an approaching transition and static heterogeneity induced by network structure. Here, we propose a baseline-referenced framework for spatial early warning signals. The method compares each node's state with its own baseline far from the tipping point before computing a spatial statistic, thus reducing network-structure-induced variation. We evaluate baseline-referenced variants of five classical spatial early warning signals across diverse tipping scenarios and networks, and find that baseline referencing markedly improves variance-based spatial signals. The best variants increase consistently and progressively toward tipping points across different scenarios, outperform a single-node temporal variance that requires long time series, and retain high performance even when up to 80% of nodes are omitted from observation. These results provide a practical route for using spatial early warning signals in heterogeneous networked systems when dense temporal monitoring or complete network-wide observation is infeasible, as is often the case in real applications.

Capturing the strategic decision-making inherent in competitive human driving is critical for autonomous vehicle safety and traffic simulation. This study demonstrates that game-theoretic Inverse Reinforcement Learning (IRL) provides a robust framework for this challenge. We present a comprehensive analysis comparing data-driven IRL models against an established physics-based game-theoretic approach for predicting aggressive, safety-critical cut-in lane changes. Using the high-fidelity highD dataset, we systematically develop and evaluate a series of IRL models with increasing feature complexity. Our results reveal significant advantages: the best-performing IRL models achieve an overall prediction accuracy exceeding 75 percent while maintaining a Cut-In precision up to 51 percent and recall up to 49 percent. This represents a significant improvement over the established physics-based benchmark, which achieved only 4.4 percent precision in these high-stakes scenarios. The analysis reveals a clear trade-off: incorporating granular, instantaneous features yields higher precision, while adding temporal consistency features maximizes recall. These findings suggest that IRL-based models can effectively bridge the gap between microscopic driver intent and macroscopic safety outcomes, providing a more reliable foundation for modeling interactions in mixed-autonomy environments.

The physics of spreading in static networks is well understood through mappings to percolation. We show that spreading dynamics on temporal networks can analogously be mapped to reachability in temporal event graphs. This provides a theoretical and computational framework for a class of processes, such as variants of the susceptible-infected-susceptible model. Without explicit simulations, through the component analysis of event graphs, we obtain epidemic prevalence and derive epidemic thresholds for temporal networks with arbitrary degree and inter-event time distributions, with significant computational advantages as compared to explicit simulations.

Using official government data sets of USA and France we analyze the occurrence/frequency/popularity distributions of given names on a time scale of more than 100 years. These distributions are characterized through the Lorenz and Pareto curves broadly used in the analysis of wealth inequality in the world. These curves remain stable during the considered time period with the Gini coefficient remaining in the narrow range 0.85-0.95. As for the case of wealth inequality, we show that the distributions of names are well described by the Rayleigh-Jeans (RJ) thermalization and condensation phenomenon well studied in various physical systems. The RJ thermalization results from two integrals of motion being analogous to energy and probability norm conservation in physical systems with energy states corresponding to popularity levels of names. Time correlations between names are also determined showing their stability until the middle of the twentieth century and a significant change after that.

We introduce a majority-rule model in which collective reversal can be activated in highly aligned groups even when a limited number of members dissent. The dissent tolerance $d$ extends the strict-unanimity dynamics by making near-unanimous group compositions eligible for reversal. Mean-field analysis and simulations reveal that this change qualitatively alters the phase structure. Under strict unanimity, a physically accessible transition exists only for $n=3$ and $n=4$. Allowing dissent restores transitions at larger interaction sizes, replacing the fixed interaction-size threshold with an accessibility boundary in the $(n,d)$ plane. When the activation window is sufficiently broad, directional asymmetry can eliminate one of the two ordered attractors through a saddle-node bifurcation, producing a single stable collective state. In the one-sided case, increasing the dissent tolerance can shorten the transient approach to consensus but leaves its leading logarithmic dependence on population size unchanged. Activation selectivity acts as an independent control parameter for collective ordering, bistability, and consensus dynamics.

Remote work has fundamentally reshaped urban economic life, and the spatial organisation of activity across cities. However, access to flexible work is distributed unevenly across industries, income groups, and genders, creating disparities in health risks, social mixing, and economic opportunity. Understanding where workplace dependence (WPD) is concentrated is therefore important, yet its distribution across urban areas remains poorly understood. Here we pair fine-grained hourly population data with detailed company records in a large European city to examine how location, industry composition, and socio-economic characteristics shape physical workplace attendance. By comparing workplace activity during periods of low versus high COVID-19 restrictions, we identify the determinants of WPD. We find that while industry and firm productivity are key drivers, the relationship between WPD, income, and gender is highly contingent on distance from the city center. Near the centre, female-majority and income-diverse locations show the highest WPD, consistent with a residual, place-bound service workforce. These findings reveal a spatially contingent 'service trap' at the urban core, extending remote-work inequalities beyond individuals to the urban ecosystem as a whole.

Transmission through temporary groups does not necessarily preserve complete information about the group-size distribution in aggregate epidemic data. We show that, in finite-population SIS and SIR models, the group-size distribution enters the dynamics only through a finite set of moments selected by the order of the nonlinear transmission kernel. Consequently, markedly different distributions can generate identical stochastic dynamics when their relevant moments coincide. This equivalence extends to transient evolution, fluctuations, extinction-time statistics, and final outbreak sizes. In the deterministic limit, the first moment sets the invasion threshold, whereas the second controls the nature of the transition and the emergence of bistability and hysteresis. The two distributions become distinguishable only when a higher-order transmission mechanism activates their first unmatched moment; even a weak additional channel can shift the phase boundary and place the systems in different dynamical regimes. Solutions of the master equation and stochastic simulations support these analytical predictions. These results establish an intrinsic limit on epidemic inference: a single aggregate dynamical protocol can identify only an equivalence class of group-size distributions, rather than uniquely reconstructing the full distribution.

We propose a mathematical model that represents the influence of an external actor (influencer) on a network of actors (influenced). The model is an adaptation of control systems within the family of formulations inspired by the Kuramoto Model of synchronisation. Capturing influence as a capacity to affect the character or behaviour of another, we study an external node's ability to influence the synchronisation of the Kuramoto system while its global behaviour is pulled to the external node's frequency and away from its natural mean frequency. In our work, stochastically generated dynamical weights assigned to the links between the network and the external influencer whereby links from one system to the other are assigned via one-sided heavy tail noise, generated by the Gamma distribution. We perform numerical experiments to examine transition points in the ability of the external node to alter the behaviour of the influenced network; either to disrupt synchronisation or to drive it to collective frequencies determined by the external node. We examine the dependence of transition points on the external node's frequency, where too ambitious a driving frequency fails to influence the system while retaining a synchronised state, and reducing achieves a state of synchronisation at a frequency shifted from the mean natural frequency. We also look at the analytic approximation for the system close to synchronisation and fragmentation to understand its behaviour around this limit.

We propose an improved mean-field analysis of cellular automata models of single-lane vehicular traffic. By combining aspects of the Car-Oriented-Mean-Field (COMF) theory and the 2-site cluster method, which have been previously successfully applied to similar models, we aim to capture both short- and long-range correlations more accurately. In contrast to classical mean-field theories, the improved method is well suited for models with inhomogeneous stationary states and able to capture the essential properties of phase separation, e.g. in models with slow-to-start rules. The improved accuracy and new physical insights are illustrated through an application to the VDR model with $v_{\text{max}}=1$.

The distribution of node depths in a network is crucial for analyzing network structure. Two measures, rank and layer, quantify how deep inside a network a node is. The rank is the node's distance to the closest leaf, a node of degree 1. The layer is the number of times all leaves must be stripped off for the node to become a leaf. We derive exact recursive expressions for the rank and layer distributions in random recursive trees. We show that the rank and layer distributions decay factorially and geometrically, respectively, and prove the self-averaging of the numbers of nodes with fixed rank or layer. Unlike previous studies, our approach does not depend on labels or a root node, providing a more versatile framework for analyzing rank and layer distributions in complex networks.

Designing networks that minimize distances and satisfy structural constraints is a fundamental task across transportation, communication, and biological systems. Here, we consider the problem of finding, for a given degree sequence, the network structure displaying the smallest possible average shortest-path length. While exact solutions are available in linear time for trees, such an optimization problem becomes computationally infeasible as soon as loops are allowed in the networks. We propose a fast algorithm to construct approximate solutions to such a degree-constrained distance-minimization problem. Accordingly, edges are first created between high-degree nodes; then, additional connections are placed following the rules of the standard configuration model. In spite of its simplicity, the algorithm displays outstanding performance as demonstrated in our systematic experiments on both synthetic and real degree sequences. Our method is particularly effective on synthetic degree sequences displaying medium levels of heterogeneity. When applied to degree sequences of real networks, the proposed algorithm is able to reduce the all-pair shortest path of real structures by 20%, on average. We perform a validation on small-sized networks, where we compare the shortest-path distance of the networks generated with our algorithm against those obtained via simulated annealing optimization. Although simulated annealing yields slightly better structures, our proposed algorithm provides nearly identical solutions at a substantially lower computational cost, making it a solid method in applications concerning large-scale systems.

In Jewish tradition, the boundary between days is not midnight, but nightfall. Nightfall is when one must pray ma'ariv, count the omer, and may engage in activity after Shabbat. While there are slightly different definitions of nightfall for Shabbat restrictions (Motsa'ei Shabbat) versus other purposes (Ts'eit HaKokhavim), most minhagim define nightfall to be when three stars of some specified size and proximity are visible in the sky. This definition presents some difficulty. Not only are these conditions difficult to define, they are further complicated by weather, cloud cover, and light pollution. Observant Jews therefore usually approximate these times by defining nightfall to be when the sun has reached a certain distance below the horizon. Although these approximations have been effective, modern astronomy enables us to calculate precisely when these conditions are met. This work applies these techniques to calculate the time of Ts'eit HaKokhavim and Motsa'ei Shabbat evaluates the accuracy of the approximations, and explores the effects of light pollution on these times. While Ts'eit HaKokhavim is reasonably well-approximated by standard methods, the conditions for Motsa'ei Shabbat generally occur after the time predicted by the approximations. Light pollution does not shift Ts'eit HaKokhavim by more than a minute but significantly changes Motsa'ei Shabbat. In fact, light pollution causes the conditions of Motsa'ei Shabbat to never be met on at least some nights in every population center. Finally, I provide a tool (halakhic-nightfall.streamlit.app) for calculating Ts'eit HaKokhavim and Motsa'ei Shabbat at an arbitrary time and location on Earth.

We study seven major crypto-perpetual liquidation cascades (2022-2025), and in the largest of them we can watch the mechanism directly. From the on-chain fill log of a fully transparent venue we measure the branching ratio of that event – the October 2025 crash, the largest on record – in flight, with both of its factors observed and no free constants. It ran deeply subcritical: the structural ratio and the amplification bookkeeping both place it at $\hat\lambda \approx 0.1-0.2$ throughout, while a third, flow-based estimator falls through the climax rather than rising. All three agree on subcriticality within the venue, not on a common numerical level. Alongside them, 88% of all post-onset forced selling landed within thirty minutes and 63% of it was absorbed off-book by the venue's backstop, which drives the branching ratio down precisely at the climax. Across the full set of seven, at onset – the minute ending the steepest hour of each crash – the order parameter (mean inter-asset coupling) jumps by between 1.6 and 4.4 baseline standard deviations into a near-fully-ordered phase, while the susceptibility proxy $\chi$ collapses in five of the seven events and diverges in none; the jump is invariant under subsampling. The transition is abrupt and scale-robust rather than critical, and its in-cascade signature lives in the liquidity sector: price impact spikes on two venues and two instruments while open interest clears by 25-70%. The natural mechanistic account, a Galton-Watson cascade with $\lambda = k \tilde\rho$, is then eliminated as a description of the pre-cascade state: both of its falsifiable predictions fail at simulated power >= 0.96, on proxied and on directly measured regressors alike. Severity is set by shock times map-in-path times liquidity withdrawal rather than by a diverging multiplier, which is why none of the scalar pre-state measures we can construct grades it.

Higher-order network datasets are dispersed across publications, institutional archives, and software-specific collections, making them difficult to discover, compare, and reuse. We introduce the Aachen Higher-Order Repository of Networks (AHORN), a curated repository of standardized higher-order network datasets derived from publicly released sources. Each dataset entry links a converted dataset to its source, metadata, citation guidance, conversion code, and version history. The repository supports browsable and machine-readable discovery, revision-specific downloads, format validation, and exports for interoperable reuse. We describe the repository architecture, curation workflow, access tools, and the coverage and limitations of the catalog snapshot analyzed in this article.

In real organizations, performance appraisal serves as an important means of evaluating employees' work outcomes and behaviors, while performance pay directly links compensation to the evaluation results. However, in traditional spatial public goods games, the total payoff of a group is equally distributed among all participants without considering individual differences in contributions, an approach that ignores the heterogeneity of individual efforts. To overcome this limitation, we propose a spatial public goods game model based on performance appraisal, in which individual payoffs are divided into two parts: an equally distributed component and a performance-weighted component. Specifically, each individual receives scores from its neighboring groups, and the individual's reputation is dynamically updated by accumulating these scores, which further modulates the fitness function during strategy imitation. Extensive numerical simulation results demonstrate that the performance appraisal mechanism significantly promotes the emergence of cooperative behavior. The reputation reinforcement mechanism amplifies this positive effect by creating fitness advantages for high-reputation individuals. These findings suggest that incorporating performance appraisal into payoff allocation helps mitigate social dilemmas and promote collective cooperation.

Detecting structure in complex networks, especially those arising from physical systems, is a central problem across the sciences. One approach is via rich club analysis, which identifies important vertices using a centrality metric and measures whether those vertices are more tightly interconnected than expected by chance. While informative, this approach captures only pairwise interactions, missing out on higher-order ones known to shape the structure and function of many complex systems. We propose a hyper-rich club pipeline that asks whether central vertices are more tightly interconnected than expected by chance through hyperedges encoding higher-order interactions, which also enables the inclusion of important, often omitted, directional information. We work in a broad class of hypergraphs, which we call general directed hypergraphs, that includes as special cases undirected hypergraphs, head-and-tail directed hypergraphs, and totally ordered hypergraphs (a hypergraph related to directed simplicial complexes from topological data analysis). This unifies several non-equivalent notions of directed hypergraph under one definition. On these hypergraphs we define a hyper-rich club framework whose concrete construction depends on explicit choices the domain scientist fixes according to their research goals. Particular choices recover the existing rich club notions for graphs and undirected hypergraphs, and yield the first such notion for each version of directed hypergraphs. We demonstrate that the pipeline recovers meaningful structure in data by studying networks of very different origins: connectomes, temporal networks of infectious spread, networks of poems, and the XGI hypergraph database, in each case detecting structure the standard graph rich club misses.

Sonification operates across scientific, artistic, and design contexts, yet its identity remains conceptually ambiguous: is it music, a scientific method, or a hybrid practice? This paper presents a philosophical framework that treats sonification as a coherent, transcategorical practice. Drawing on Gustavo Bueno's materialist gnoseology, we identify its operative core through systematic data-to-sound relationships that define its technical identity. Complementing this with Gilbert Simondon's philosophy of individuation, we show conceptually how sonification adapts across contexts while preserving its operative structure. By distinguishing between technical identity and pragmatic use, this framework clarifies the relationship between sonification, music, and aesthetics, providing researchers and practitioners with a philosophical framework to navigate the field's diversity while maintaining its epistemic and operational integrity.

Content-based detection of unreliable news is increasingly difficult, as low-reliability sources mimic credible journalism and generative AI makes fabricated content harder to flag. We ask whether network structure can improve news reliability classification, taking a domain-level approach that shifts the focus from individual articles to source reliability. From URL-sharing patterns in Telegram chats, we build a statistically validated domain co-sharing network and find assortative mixing by reliability: low-reliability domains group together, as do reliable ones. Exploiting this structure, we compare Graph Neural Networks against network-unaware baselines using both content-aware features (multilingual text embeddings) and content-agnostic features (spreading dynamics). GNNs consistently outperform Multi-Layer Perceptrons on identical features, with GraphSAGE best in both settings (accuracy 0.63 with content, 0.53 without), a 13-14% relative gain over the network-unaware baseline. Network topology thus systematically improves domain reliability assessment, and remains effective even when content analysis is infeasible.

Decentralized populations of Large Language Model (LLM) agents can spontaneously reach consensus on shared conventions, yet the microscopic mechanisms by which their internal stochasticity shapes macroscopic ordering remain unexplored. We study a minimal LLM Naming Game in which the listener's decision is a single-token LLM call at decoding temperature $T$, replacing the inventory check of the deterministic Naming Game. Each interaction decomposes into an in-inventory and an out-inventory channel with conditional rates $\pi(T)\!\equiv\!P(\text{YES}\mid w\in P_j)$ and $\phi(T)\!\equiv\!P(\text{YES}\mid w\notin P_j)$, whose balance controls an ordering-disordering drift. A mean-field theory of the two-rate dynamics yields an analytical ordering condition that generalizes the consensus threshold of the stochastic Naming Game to a critical line in the $(\pi,\phi)$ plane. Across three open-weight architectures, consensus is always reached, but through three distinct listener regimes: permissive (repaint-noise dominated), near-deterministic, and conservative (missed-collapse dominated). The effective finite-size exponent $\beta(T)$ in $t_{\rm conv}\!\sim\!N^{\beta}$ shifts with temperature, and the temperature-sensitivity $\alpha$ in $t_c\!\sim\!e^{\alpha T}$ ranges from ${\approx}\,0.67$ to ${\approx}\,0$ across architectures. Decoding temperature thus emerges as an architecture-dependent control parameter for decentralized LLM populations, quantitatively characterized by the statistical-physics toolkit.

Climate change is modifying the frequency and intensity of extreme hazards in a non-uniform spatial manner, increasing the risk of damage for existing physical systems. Vulnerability modeling based on vulnerability curves provides a quantitative link between hazard intensity and physical damage, supporting adaptation strategies. This paper proposes conceptual frameworks for vulnerability models of physical systems in the context of climate change, aimed at supporting vulnerability based adaptation. A theoretical use case illustrates the methodology: potential damage on power transmission towers facing wind gust hazards across France, modeled through vulnerability curves. Despite strong assumptions, this theoretical case study demonstrates how vulnerability models can guide adaptation by reducing intrinsic vulnerability, adapting the physical system to maintain acceptable damage levels under evolving climate extremes.

Discrete Forman-Ricci curvature is a quantity associated to each edge of a graph that describes its local geometry. It has proven to be a useful tool in network analysis in a variety of applications. Recent work by Roost et al.\ (2024) proposed the use of Markov bases to sample from the space of graphs with prescribed vertex degrees and curvatures. In the present work, we further develop the algebraic and combinatorial theory of these Markov bases. We show that the degree of an indispensable Markov move grows at least quadratically in the maximum degree of the graph. In light of this result, a compact description of all Markov basis elements seems unattainable at present. Instead, we find a lattice basis for this problem using only degree three Markov moves, which allows us to employ recently-developed reinforcement learning methods for finding Markov moves that can be applied to a specific graph.

Successive personal best performances provide a natural measure of progression in an athlete's career. Classical record theory predicts a universal gap distribution, $P(g)\sim 1/g$, for independent and identically distributed (i.i.d.) sequences. However, sporting careers are shaped by learning, aging, changes in ability, and external influences that violate these assumptions. We investigate the statistics of inter-record gaps, defined as the number of innings between successive personal best scores, in cricket. Using career records of leading Test, ODI, and T20 players obtained from ESPN Cricinfo. We find that the empirical distributions are well described by truncated power law $P(g) \propto g^{-\alpha} e^{-\lambda g}$ with exponents in the range (0.799 $\leq \alpha \leq$ 0.843). Much of this deviation disappears when the temporal ordering of innings is destroyed, indicating that career evolution plays a key role in shaping record occurrence. Bootstrap-shuffled careers, which preserve individual score distributions and career lengths while removing temporal ordering, yield significantly larger exponents ($\alpha \approx 0.939\text{--}0.979$). These findings show that the progression of personal best performances retains information about the temporal organization of a player's career and cannot be fully explained by simple stochastic record processes. More generally, they illustrate how record statistics are altered in nonstationary and path-dependent systems.

The Internet, a living cell, a circle of friends, a billion-dollar construction project: these systems share almost nothing – yet, drawn as networks, they look astonishingly alike. Each has a few giant hubs among a multitude of sparsely connected nodes, short paths between any two parts, dense local clustering, communities, and many redundant routes. For two decades such patterns have been credited to "preferential attachment," the rich getting richer – a rule that, taken literally, asks every newcomer to survey the whole network before it links. This book makes a simpler case, and defends it one mechanism at a time: the global regularities of real networks are not imposed from above but emerge from purely local rules, in which each new node acts only on a node it has reached and that node's immediate neighbours. A surfer following links, a friend introducing a friend, a gene copied with its connections – none consults the network as a whole, yet each builds, in the aggregate, the full and unmistakable signature of a real complex system. Written for the curious reader as much as the specialist, with the ideas told in plain language and the mathematics set aside in boxes that can be skipped, it shows how citation graphs, the web, social ties, protein interactions, and project schedules all grow themselves from the same handful of local rules – one local decision at a time.