Hierarchical clustering and community detection are important problems in machine learning and complex network analysis. A common approach to identify clusters is to simply cut dendrograms at some threshold. However, single-level cuts are often suboptimal in terms of capturing underlying structure in the data, especially when the dendrogram is unbalanced. In this paper, we present the adaptive cut, a novel method that leverages the hierarchical structure of dendrograms by employing multi-level cuts to overcome the limitations of single-level approaches. The adaptive cut optimizes an objective function using a Markov chain Monte Carlo with simulated annealing, resulting in better partitions. We demonstrate the effectiveness of the adaptive cut through applications to link clustering and modularity optimization, but note that the method is applicable to any clustering task that relies on a dendrogram and an objective function. Beyond the adaptive cut, we introduce the balancedness score, an information-theoretic metric that quantifies how balanced a dendrogram is. Balancedness predicts the potential benefits of using multi-level cuts. For the community detection examples, we evaluate our method on more than 200 real-world networks and multiple synthetic datasets, demonstrating significant improvements in partition density and modularity over traditional single-cut approaches. In addition, we show the generality of the adaptive cut by applying it across various hierarchical clustering techniques and objective functions. Our results indicate that the adaptive cut provides a robust and versatile tool for improving clustering outcomes.

In an emerging pandemic, policymakers need to make important decisions with limited information, for example choosing between a mitigation, suppression or elimination strategy. These strategies may require trade-offs to be made between the health impact of the pandemic and the economic costs of the interventions introduced in response. Mathematical models are a useful tool that can help understand the consequences of alternative policy options on the future dynamics and impact of the epidemic. Most models have focused on direct health impacts, neglecting the economic costs of control measures. Here, we introduce a model framework that captures both health and economic costs. We use this framework to compare the expected aggregate costs of mitigation, suppression and elimination strategies, across a range of different epidemiological and economic parameters. We find that for diseases with low severity, mitigation tends to be the most cost-effective option. For more severe diseases, suppression tends to be most cost effective if the basic reproduction number $R_0$ is relatively low, while elimination tends to be more cost-effective if $R_0$ is high. We use the example of New Zealand's elimination response to the Covid-19 pandemic in 2020 to anchor our framework to a real-world case study. We find that parameter estimates for Covid-19 in New Zealand put it close to or above the threshold at which elimination becomes more cost-effective than mitigation. We conclude that our proposed framework holds promise as a decision-support tool for future pandemic threats, although further work is needed to account for population heterogeneity and other factors relevant to decision-making.

The dynamical evolution of complex networks underpins the structure-function relationships in natural and artificial systems. Yet, restoring a network's formation from a single static snapshot remains challenging. Here, we present a transferable machine learning framework that infers network evolutionary trajectories solely from present topology. By integrating graph neural networks with transformers, our approach unlocks a latent temporal dimension directly from the static topology. Evaluated across diverse domains, the framework achieves high transfer accuracy of up to 95.3%, demonstrating its robustness and transferability. Applied to the Drosophila brain connectome, it restores the formation times of over 2.6 million neural connections, revealing that early-forming links support essential behaviors such as mating and foraging, whereas later-forming connections underpin complex sensory and social functions. These results demonstrate that a substantial fraction of evolutionary information is encoded within static network architecture, offering a powerful, general tool for elucidating the hidden temporal dynamics of complex systems.

Quantum computing offers powerful new approaches for modeling complex social phenomena. Here, we propose and demonstrate quantum simulations of opinion dynamics, leveraging quantum superposition, measurement-induced state collapse, and entanglement to model realistic psychological and social processes. Specifically, we develop quantum models of opinion dynamics, solving exactly and simulating on IBM Quantum hardware. Our results, based on quantum devices and validated with practical quantum circuits, illustrate how quantum effects can enhance understanding of consensus formation, polarization, and collective decision-making. These findings pave the way for further exploration into quantum-enhanced social modeling, highlighting the potential of near-term quantum computers for simulating collective behavior in complex systems.

Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs. This has led to a proliferation of specialized hypergraph centrality measures, but the field remains fragmented and lacks a unifying framework. This paper addresses this gap by providing the first systematic survey of 39 distinct measures. We introduce a novel taxonomy classifying them as: (1) structural (topology-based), (2) functional (impact on system dynamics), or (3) contextual (incorporating external features). We also present an experimental assessment comparing their empirical similarity and computation time. Finally, we discuss applications, establishing a coherent roadmap for future research in this area.

Multilayer network science has emerged as a central framework for analysing interconnected and interdependent complex systems. Its relevance has grown substantially with the increasing availability of rich, heterogeneous data, which makes it possible to uncover and exploit the inherently multilayered organisation of many real-world networks. In this review, we summarise recent developments in the field. On the theoretical and methodological front, we outline core concepts and survey advances in community detection, dynamical processes, temporal networks, higher-order interactions, and machine-learning-based approaches. On the application side, we discuss progress across diverse domains, including interdependent infrastructures, spreading dynamics, computational social science, economic and financial systems, ecological and climate networks, science-of-science studies, network medicine, and network neuroscience. We conclude with a forward-looking perspective, emphasizing the need for standardized datasets and software, deeper integration of temporal and higher-order structures, and a transition toward genuinely predictive models of complex systems.

Low-carbon liquid fuels play a key role in energy system decarbonization scenarios. This study uses a multi-sector capacity expansion model of the contiguous United States to examine fuels production in deeply decarbonized energy systems. Our analysis evaluates how the shares of biofuels, synthetic fuels, and fossil liquid fuels change under varying assumptions about resource constraints (biomass and CO2 sequestration availability), fuel demand distributions, and supply flexibility to produce different fuel products. Across all scenarios examined, biofuels provide a substantial share of liquid fuel supply, while synthetic fuels deploy only when biomass or CO2 sequestration is assumed to be more limited. Fossil liquid fuels remain in all scenarios examined, primarily driven by the extent to which their emissions can be offset with removals. Limiting biomass increases biogenic CO2 capture within biofuel pathways, while limiting sequestration availability increases the share of captured atmospheric (including biogenic) carbon directed toward utilization for synthetic fuel production. While varying assumptions about liquid fuel demand distributions and fuel product supply flexibility alter competition among individual fuel production technologies, broader energy system outcomes are robust to these assumptions. Biomass and CO2 sequestration availability are key drivers of energy system outcomes in deeply decarbonized energy systems.

Training large language models with Reinforcement Learning with Verifiable Rewards (RLVR) exhibits a set of distinctive and puzzling behaviors that remain poorly understood, including a two-stage learning curve, a V-shaped response-length trajectory, and a pronounced vulnerability to catastrophic forgetting. In this work, we propose that these behaviors are emergent collective phenomena governed not by neural implementation details, but by the topological evolution of the latent reasoning graph in semantic space. By demonstrating a dynamical isomorphism between a 1.5B-parameter LLM and a minimal Concept Network Model (CoNet), we trace the causal source to the self-organization of a sparse concept web pinned to an average degree of two. This geometric perspective provides a unified physical explanation for the observed anomalies: the V-shaped trajectory tracks the evolution from parallel local skill optimization to global network integration; catastrophic forgetting stems from the topological disconnection of critical ``trunk'' edges; and policy collapse arises from the accumulation of sequential transitions at the web's leaf nodes, where broad exploration abruptly freezes into rigid, high-reward trajectories. Identifying a ``maximally frustrated state'' at the transition between learning stages, we propose Annealed-RLVR, a principled algorithm that injects a targeted SFT ``heating'' step to resolve this topological bottleneck. Experiments confirm that this theory-driven intervention outperforms standard RLVR on both in-distribution and out-of-distribution benchmarks (including Minerva and AIME). By recasting RLVR from black-box optimization into a predictable process of structural self-organization, our work provides a new physical intuition for engineering the emergent reasoning capabilities of future AI systems.

We study the opinion dynamics in a population by considering a variant of Kuramoto model where the phase of an oscillator represents the opinion of an individual on a single topic. Two extreme phases separated by $\pi$ represent opposing views. Any other phase is considered as an intermediate opinion between the two extremes. The interaction (or attitude) between two individuals depends on the difference between their opinions and can be positive (attractive) or negative (repulsive) based on the defined thresholds. We investigate the opinion dynamics when these thresholds are varied. We observe explosive transition from a bipolarized state to a consensus state with the existence of scattered and tri-polarized states at low values of threshold parameter. The system exhibits multistability between various states in a sizeable parameter region. These transitions and multistability are studied in populations with different degrees of diversity represented by the width of conviction distribution. We found that a more homogeneous population has greater tendency to exhibit bipolarized, tri-polarized and clustered states while a diverse population helps mitigate polarization among individuals by reaching to a consensus sooner. Ott-Antonsen analysis is used to analyse the system's long term macroscopic behaviour and verify the numerical results. We also study the effects of neutral individuals that do not interact with others or do not change their attitude on opinion formation, nature of transitions and multistability. Furthermore, we apply our model to language data to study the assimilation of diverse languages in India and compare the results with those obtained from model equations.

Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law, the size-rank law and the size-probability law form a group-like structure. We identify human languages that are members of the class. All languages showing sufficient agreement with Zipf's law are potential members of the class. In contrast, there are communication systems in other species that cannot be members of that class for exhibiting an exponential distribution instead but dolphins and humpback whales might. We provide a new insight into plots of frequency versus rank in double logarithmic scale. For any system, a straight line in that scale indicates that the lengths of optimal codes under non-singular coding and under uniquely decodable encoding are displaced by a linear function whose slope is the exponent of Zipf's law. For systems under compression and constrained to be uniquely decodable, such a straight line may indicate that the system is coding close to optimality. We provide support for the hypothesis that Zipf's law originates from compression and define testable conditions for the emergence of Zipf's law in compressing systems.

This review examines the roles of adaptation and synchronization in music performance, drawing on concepts from complex systems theory to understand the dynamic interactions between musicians, music, and listeners. Adaptation is explored through how musicians adjust their cognitive, emotional, and motor systems across the stages of preparation, execution, and reception, while synchronization is emphasized as essential for aligning internal states, coordinating actions with other performers, and engaging with the audience. The review highlights the interdisciplinary nature of music performance research, integrating cognitive, motor, and emotional processes to enhance both individual and collective musical expression. It also addresses the psychological state of flow, which arises from synchronized neurocognitive mechanisms that optimize performance. Additionally, the emotional synchronization facilitated by music is explored, emphasizing its role in both individual emotional coherence and social coordination within musical ensembles. Finally, the review highlights recent findings on interpersonal and inter-brain synchronization, particularly in live music performances and improvisation, showing how synchronization fosters creativity, social cohesion, and a shared collective experience.