Allometric scaling laws, such as Kleiber's law for metabolic rate, highlight how efficiency emerges with size across living systems. The brain, with its characteristic sublinear scaling of activity, has long posed a puzzle: why do larger brains operate with disproportionately lower firing rates? Here we show that this economy of scale is a universal outcome of avalanche dynamics. We derive analytical scaling laws directly from avalanche statistics, establishing that any system governed by critical avalanches must exhibit sublinear activity-size relations. This theoretical prediction is then verified in integrate-and-fire (IF) neuronal networks at criticality and in classical self-organized criticality (SOC) models, demonstrating that the effect is not model-specific but generic. The predicted exponents align with experimental observations across mammal species, bridging dynamical criticality with the allometry of brain metabolism. Our results reveal avalanche criticality as a fundamental mechanism underlying Kleiber-like scaling in the brain.
Exploiting quantum features allows for estimating external parameters with precision well beyond the capacity of classical sensors, a phenomenon known as quantum-enhanced precision. Quantum criticality has been identified as a resource for achieving such enhancements with respect to the probe size. However, such protocols demand complex probe preparation and measurement, and the achievable enhancement is ultimately restricted to narrow parameter regimes. On the other hand, non-equilibrium probes harness dynamics, enabling quantum-enhanced precision with respect to time over a wide range of parameters through simple probe initialization. Here, we unify these approaches through a Stark-Wannier localization platform, where competition between a linear gradient field and particle tunneling enables quantum-enhanced sensitivity across an extended parameter regime. The probe is implemented on a 9-qubit superconducting quantum device, in both single- and double-excitation subspaces, where we explore its performance in the extended phase, the critical point and the localized phase. Despite employing only computational-basis measurements, we have been able to achieve near-Heisenberg-limited precision by combining outcomes at distinct evolution times. In addition, we demonstrate that the performance of the probe in the entire extended phase significantly outperforms the performance in the localized regime. Our results highlight Stark-Wannier systems as versatile platforms for quantum sensing, where the combination of criticality and non-equilibrium dynamics enhances precision over a wide range of parameters without stringent measurement requirements.
Self-organized criticality (SOC) provides a universal framework for understanding the emergence of scale-invariant behaviors in complex systems, yet its physical realization in programmable artificial systems remains challenging. We present an aquatic robot swarm, in which individuals interact via optical attraction and hydrodynamic repulsion, demonstrating key SOC features: avalanches with sizes and durations following power-law distributions, stability of scaling exponents under system upscaling, and self-organized evolution toward a steady state independent of system parameters. In the presence of external stimuli, the system not only maintains criticality but also spontaneously forms directed structures and exhibits adaptive behaviors such as collective pushing, showcasing emergent capabilities arising from local interactions. This work provides a controllable experimental platform for studying SOC in dynamic physical environments and provides insights for developing adaptive autonomous swarm systems that require minimal programming.
Phase transitions and thermodynamic properties of an Ising antiferromagnetic bilayer honeycomb lattice with competing interlayer interactions were investigated. By applying a cluster mean-field method, we study the role of exchange interactions on the interplay between thermal fluctuations and quantum effects introduced by a transverse magnetic field. The presence of competing interactions can lead to the onset of first-order phase transitions, but our findings reveal that the nature of these phase transitions can be changed by the transverse magnetic field, introducing continuous phase transitions at low temperatures. Our results also support that this change in the nature of phase transitions, called quantum annealed criticality, is associated with a large accumulation of entropy and an enhanced magnetocaloric effect at low temperatures. Therefore, magnetically anisotropic bilayer honeycomb systems provide a promising platform for the implementation of cooling and heating technologies based on enhanced magnetocaloric effect near quantum criticality.
We report a breakthrough discovery of Turing-driven spiral defect chaos (SDC) governed by stationary nucleation sites in time-discrete oscillatory systems-a phenomenon defying classical instability paradigms. Unlike conventional SDC requiring spiral tip migration, this novel state features frozen spiral cores that trigger global chaos through random birth-death processes at fixed spatial coordinates while maintaining absolute immobility. Three universal critical behaviors emerge: (1) Spiral lifetimes follow scale-free power-law distributions with a fixed exponent ([Formula: see text]), independent of control parameters; (2) Spiral tip densities exhibit parameter-invariant scaling laws, collapsing onto a single master curve approximating normal distributions; (3) Self-organized criticality enables multiscale pattern coexistence. Theoretical analyses trace this to a Turing bifurcation, where diffusion destabilizes homogeneous periodic states into "static-source/dynamic-propagation" dissipative structures. This mechanism establishes a new paradigm: localized fluctuations at immobilized tips drive global chaos-resolving the paradox of motionless yet destructive spiral cores. Our findings provide fundamental insights for designing cardiac defibrillators exploiting stationary spiral sources and forecasting ecological invasion fronts dominated by critical fluctuations.
Quantum phase transitions are an established setting for emergent phenomena driven by strong electronic correlations, including strange metals and unconventional superconductivity. These phenomena have been explored extensively in Kondo-lattice materials tuned to an antiferromagnetic quantum critical point (QCP), but superconductivity emerging near ferromagnetic quantum criticality has not yet been observed, and the conditions under which it occurs in proximity to ferromagnetism remain undetermined. Here, we report a new setting for superconductivity in the ferromagnetic Kondo-lattice material Ce[Formula: see text]CoGe[Formula: see text], which has a ferromagnetic ground state at ambient pressure and evolves to antiferromagnetism under applied pressure. The antiferromagnetic transition is suppressed to a zero-temperature QCP, accompanied by strange-metal behavior. Superconductivity does not occur at the QCP, but instead appears at pressures beyond the magnetic instability. These findings suggest that Ce[Formula: see text]CoGe[Formula: see text] represents a distinct class of correlated materials exhibiting a unique scenario for the emergence of superconductivity, likely associated with unconventional pairing mechanisms beyond spin fluctuations.
The origin of superconductivity in oxide interfaces and its relation to ferroelectricity remains an open question. At LaAlO3/SrTiO3 interfaces, quantum confinement and inversion symmetry breaking create a two-dimensional electron gas near a ferroelectric quantum critical point, yet direct evidence linking phonon dynamics to electron pairing has been lacking. Here we directly probe lattice vibrations and atomic structure at LaAlO3/SrTiO3 interfaces across the superconducting phase diagram using vibrational spectroscopy with momentum selectivity in a scanning transmission electron microscope. We find that superconductivity across the doping series correlates with inversion symmetry breaking and the appearance of high-frequency localized phonons. These tunable, polar vibrations-confined near the interface-exhibit strong electron-phonon coupling and evolve systematically with carrier density. Our findings establish a link between lattice instability, superconductivity and strong electron-phonon coupling mediated by tunable localized phonons, providing new insights into possible microscopic pairing pathways in quantum paraelectric systems.
Retraction of DOI: 10.1103/qyby-5yvg.
The thermodynamic properties of time-delayed dynamics remain largely unexplored, especially for systems that exhibit asymptotically nonstationary behavior. Here, we investigate heat dissipation in two classes of marginally stable linear time-delayed Langevin dynamics: (i) diffusive criticality, which asymptotically manifests as scaled Brownian diffusion, and (ii) oscillatory criticality, which shows oscillation with diffusive amplitude. By analytical derivations, we find fundamentally different thermodynamic signatures: the average heat dissipation rate asymptotically approaches a constant for diffusive criticality but diverges linearly with oscillations for oscillatory criticality, despite both showing linearly growing variance over time. We discuss in detail how the heat dissipation rate behaves differently as the dynamics asymptotically approaches these two criticality classes from the stable regime. We also numerically study the probability distributions of heat dissipation rates for both types of critical dynamics. Our results demonstrate that nonstationary time-delayed dynamics with similar time-dependence of variance can yield qualitatively distinct heat dissipation behaviors, depending on the underlying dynamical details. This work provides a concrete foundation for future investigations into thermodynamic properties of general nonlinear time-delayed systems.
Visibility graphs are spatial interpretations of time series. When derived from the time evolution of physical systems, the graphs associated with such series may exhibit properties that can reflect aspects such as ergodicity, criticality, or other dynamical behaviors. It is important to describe how the criticality of a system is manifested in the structure of the corresponding graphs or, in a particular way, in the spectra of certain matrices constructed from them. In this paper, we show how the critical behavior of an Ising spin system manifests in the spectra of the adjacency and Laplacian matrices constructed from an ensemble of time evolutions simulated via Monte Carlo (MC) Markov chains, even for small systems and short MC steps. In particular, we show that the number of spanning trees-or its logarithm-which represents a kind of structural entropy or topological complexity here obtained from Kirchhoff's theorem, can, in an alternative way, describe the criticality of the spin system. These findings parallel those obtained from the spectra of correlation matrices, which similarly encode signatures of critical and chaotic behavior.
Sleep deprivation (SD) changes brain-wide dynamics, but the circuit-level perturbation that can generate this systems-level shift remains unclear. We scanned 26 participants at seven time points across 36 h of continuous wakefulness and assessed criticality from resting-state functional Magnetic Resonance Imaging (rs-fMRI) blood-oxygen-level-dependent (BOLD) signals using neuronal avalanche metrics (branching ratio and mean avalanche size). The branching ratio increased from 0.98 at baseline to 1.08 after 36 h, indicating a progressive shift from near-critical to supercritical propagation. Interestingly, the shift was heterogeneous. Visual and sensorimotor networks showed the largest deviations, whereas the limbic network remained close to criticality. Criticality changes tracked accumulated subjective sleep pressure but were largely dissociated from psychomotor vigilance lapses. SD also reshaped functional network organization, with the functional connectivity (FC) degree distribution shifting toward more high-degree nodes. In a recurrent excitatory-inhibitory network model, gamma-band power provided an interpretable proxy for effective gain and inhibitory control. Using this proxy, selectively reducing inhibitory efficacy was sufficient to capture the direction of the near-critical-to-supercritical drift and a limbic-like resilience pattern, supporting inhibitory decay as a plausible candidate circuit-level mechanism linking SD to large-scale propagation instability.
We investigate the critical phenomena of the asymmetric quantum Rabi model (AQRM), where parity symmetry is broken by an external bias. Through both analytical and numerical calculations, we identify second-order and first-order phase transitions, with the latter absent in the standard quantum Rabi model. We derive an analytical two-variable scaling function that describes the finite-frequency scaling behavior of the AQRM, and numerical results confirm this framework. The introduction of bias leads to additional critical exponents, including a bias-related critical exponent ν_{h} and susceptibility exponent γ. Moreover, we demonstrate that critical scaling persists even below the conventional critical coupling, indicating the emergence of field-induced quantum criticality. These findings establish a robust theoretical framework for understanding universal quantum criticality in light-matter systems.
Conventional machine learning treats learning as parameter optimization, lacking a first-principles framework for phenomena like criticality, generalization, and causal structure. We introduce Data Field Theory (DFT), a mathematical framework modelling learning as the evolution of a data field governed by stochastic partial differential equations on Riemannian manifolds. This work aims to validate DFT's core predictions in settings where its geometric assumptions hold, while honestly assessing its empirical limitations. We formulate learning as a field φ : M × ℝ ≥ 0 → ℝ k evolving on a spherical manifold. To test DFT, we implement a hierarchical classification task using synthetic data drawn from von Mises-Fisher distributions, ensuring match with the manifold geometry. We derive four key predictions: (1) critical exponents near concept formation, (2) a spectral robustness law linking Eigen gaps to out-of-distribution (OOD) error, (3) finite-speed causal propagation from hyperbolic regularization, and (4) approximate rotational equivariance via a Ward identity. We also conduct a preliminary real-data experiment projecting MNIST digits onto the sphere. Synthetic experiments validate all four predictions: (1) Correlation length diverges as ξ ( t ) ~ | t - t c | - ν with ν = 0.63 ± 0.04, accompanied by 1/f fluctuations; (2) OOD generalization error scales as ϵ OOD ∝ m gap - 2 (ρ = -0.78, p < 10-6); (3) Causal propagation speed c eff = 0.98 ± 0.03 (theory maximum c max = 1.0) under hyperbolic regularization; and (4) Ward identity residual R = 0.0032 ± 0.0008 converging as R∝h 1.02. However, on real-world MNIST-sphere data, DFT achieves only 15.7% accuracy versus 51.7% for k-NN, revealing critical limitations. DFT successfully predicts emergent phenomena criticality, spectral robustness, bounded causality, and approximate equivariance under ideal geometric conditions, supporting its theoretical validity. The poor real-data performance highlights key gaps: the current framework lacks adaptive metric learning, noise robustness, and hierarchical feature extraction present in real images. These results establish DFT as a principled mathematical foundation for learning as field dynamics while clearly delineating necessary extensions for practical applicability.
Antimicrobial resistance (AMR) is a major global public health concern, and antimicrobial use in animal agriculture represents an important component of broader One Health stewardship efforts. While veterinary antimicrobial policies have traditionally emphasized prescribing rules and professional behavior, less is known about how economic regulations governing pharmaceutical markets shape incentives linked to antimicrobial use. This study examines the effects of France's 2015 ban on commercial rebates and discounts on veterinary antimicrobial prices. Using listed product prices from purchase catalogues obtained from veterinary practices sourcing products through a leading French wholesaler from 2013 to 2021, we apply an interrupted time series design combined with a hedonic pricing framework to assess policy-related price dynamics. The hedonic results indicate substantial price segmentation by antimicrobial criticality, target species, administration route, marketing authorization status, and manufacturer size. The interrupted time series results show that the ban was associated with an immediate price decline of approximately 15% at implementation and a subsequent weakening of the pre-existing upward price trend. Price responses were largely uniform across critically important antimicrobials (CIAs) and non-CIAs, with only minor divergence in longer-run trends by antimicrobial criticality. Evidence of anticipatory price adjustments following the policy's announcement further suggests that market actors responded to regulatory signals before formal implementation. These findings indicate that regulatory interventions targeting financial arrangements in veterinary pharmaceutical markets can alter pricing incentives and complement traditional stewardship strategies by reshaping the economic context in which antimicrobial use decisions are made.
Interface authorization in flexible automated mine ventilation duct production lines is difficult because heterogeneous users and services access safety-critical resources under time-varying cyber-physical risk that static RBAC/ACL rules cannot capture. This study presents HGRAD, a heterogeneous-graph risk-adaptive access control framework for industrial cyber-physical systems. HGRAD models each access event as a dynamic graph with four node types: user nodes encode operator identity, role, and history; interface nodes represent exposed PLC/MES/service access points and protocol/load states; resource nodes denote commands, records, or work-order objects with different sensitivities; and physics-informed risk nodes provide conservative structural-risk proxies for critical resources. A Temporal-HGT encoder and relation-specific hierarchical attention capture temporal context, structural semantics, and abnormal-path salience, while an intervention-inspired log-based filter, adversarial perturbation, Shapley audit weighting, and MC-Dropout uncertainty estimation support adaptive authorization rather than fixed-threshold decisions. In the TON_IoT benchmark mapping, the physics-informed node is derived only from benchmark-log proxy signals, including access intensity, operation criticality, freshness, and resource criticality; it is not generated by real mine ventilation sensors, plant-side finite-element outputs, or field digital-twin measurements. HGRAD achieves the strongest validation and held-out benchmark performance among compared baselines. The results are therefore benchmark-level proof of concept for access-control design, not evidence of completed industrial deployment or field-validated mine-safety performance.
A quantum critical point develops when matter undergoes a continuous transformation between distinct ground states at absolute zero. It hosts pronounced quantum fluctuations, which render the system highly susceptible to external perturbations. While light-matter coupling has rapidly moved forward as a means to probe and control quantum materials, the capacity of quantum critical fluctuations in the photon-mediated responses has been largely unexplored. Here we advance the notion that directly coupling a quantum critical mode to a quantized cavity field dramatically facilitates the realization of the elusive superradiant phase transition in equilibrium, circumventing at once the key obstacles that have prevented its attainment in spite of decades of pursuit. The superradiant phase transition develops far below the ultrastrong regime of light-matter couplings, and the transition is accompanied by the light-matter hybrid system showing strongly enhanced intrinsic squeezing and amplified quantum Fisher information. We also identify candidate cavity quantum materials platforms for validating the proposed effect. Our findings suggest a general principle by which quantum criticality amplifies the response to cavity photons. They also demonstrate that cavity coupling accesses the elevated quantum entanglement of the underlying matter at quantum criticality, thereby pointing to a pathway towards realizing the potential of highly collective quantum materials to expand the capacities of quantum information science.
Safety-critical Industrial Internet of Things (IIoT) sensor networks deployed in disaster scenarios require intelligent routing mechanisms that prioritize mission-critical packets without relying on centralized coordination. Federated learning on resource-constrained edge nodes presents three primary challenges: the absence of an interpretable supervisory signal, the inability to act conservatively based on per-inference confidence, and vulnerability to partial node availability. The proposed FedCARE framework addresses these issues by employing a Mamdani Fuzzy Inference System to generate traceable criticality labels from multi-modal sensor telemetry, a dropout-aware aggregation protocol that normalizes over only reachable nodes, and a confidence-gated resolver that defers to symbolic fuzzy classification when model confidence is insufficient, otherwise applying an auditable maximization rule to prevent under-prioritization of safety-critical data. Evaluation on 50-, 100-, and 200-node Watts-Strogatz topologies under fault rates up to 50%, using the Edge-IIoTset and WUSTL-IIoT-2021 benchmarks, demonstrates 99.00% critical recall and up to 1.8× higher overall-packet delivery compared to RPL-RP under severe fault conditions. Routing improvements are primarily attributed to fuzzy criticality labeling and multi-path replication. These findings indicate that fuzzy-supervised federated inference offers a practical and interpretable solution for safety-critical IIoT routing, with an observed energy overhead of 7.8% per delivered packet.
Antimicrobial resistance (AMR) presents a global challenge requiring a One Health approach that integrates data from both human and veterinary sectors. However, cross-sector analyses are limited due to the lack of interoperability between antibiotic consumption and resistance datasets. The aim of the study was to map the Anatomical Therapeutic Chemical (ATC) classification used in human health and its veterinary equivalent, ATCvet. Systemic antibacterials from therapeutic groups J01 (ATC) and QJ01 and QJ51 (ATCvet) were selected for analysis. Automatic mapping was performed by pairing ATC and ATCvet codes based on corresponding codes. To illustrate the reuse of this reference framework, the criticality assessments from the World Health Organization (WHO) and the World Organisation for Animal Health (WOAH) were mapped onto this table, enabling automated combined analysis. The mapping identified 430 ATC + ATCvet codes, of which 59.3% showed strict equivalence between the two classifications. Additionally, there were 371 unique substances, with 73.0% found in both classifications. The majority of antibiotic classes were shared between the two classifications, while some such as pleuromutilins and quinoxalines were exclusive to veterinary medicine. The discrepancies in classification were primarily linked to specific characteristics of the ATCvet classification system and veterinary-specific indications. Integration with criticality assessments revealed broad correspondence between WHO and WOAH prioritization, with most critically important classes shared across sectors. The distribution of antibiotic classes across animal species showed extensive overlap, particularly within livestock species, underscoring the need for harmonized analyses. The ATC-ATCvet mapping provides a structured and interoperable framework suitable for cross-sector analyses of AMR. This harmonization enables consistent identification of antibiotic molecules, facilitates the integration of heterogeneous datasets, and supports One Health studies by bridging human and veterinary data sources.
This article discusses inferential processing during reading for autistic and non-autistic readers. We demonstrate the criticality of inferential processing for successful text comprehension, alongside evidence that inferential processing is often less efficient for autistic people relative to non-autistic people. We consider the cognitive mechanisms that may underpin inference generation and highlight the RI-Val (Resonance, Integration and Validation) theory as a potential framework that will allow for considerable theoretical development in this area. The RI-Val theory specifies how validation processes during comprehension are tied to attention shifts, which is a significant development in the conceptualisation of discourse processing. This creates a testable account which, if examined using online methods, provides considerable scope for the development of scientific understanding in relation to the inferential and social-communication differences associated with autism.
Halofantrine (halo) is an antimalarial drug that has recently been proven to have the potential to treat Glioblastoma (GBM). The aim of the study is to explore the inhibitory effect of halos on GBM and its mechanism. The expression of ATP6V0D2 in GBM was analyzed using the Cancer Genome Atlas (TCGA), the comprehensive database of gene expression, and clinical patient samples. In vitro, we evaluated the inhibitory effect of halo on U251 cells; qPCR, Western blot, and immunofluorescence were used to detect the changes in ATP6V0D2 and autophagy-related genes and proteins. Transmission electron microscopy was used to detect the formation of autophagosomes. A stable ATP6V0D2 knockdown and overexpression model was constructed in U251 cells to verify the criticality of ATP6V0D2. The in vivo anti-tumor effect and mechanism of halo were evaluated using a U251 cell axillary tumor-bearing mouse model (independent experiment repeat number (n = 5) and tail vein administration injection. The expression level of ATP6V0D2 is relatively low in GBM patients. Halo upregulates ATP6V0D2 and induces cytotoxic autophagy (TA) in U251. Knockdown of ATP6V0D2 can inhibit halo-mediated TA and cytotoxicity, while overexpression can enhance these effects. Halo also demonstrated significant anti-GBM activity in vivo, and its mechanism was consistent with the results of in vitro studies. This study has preliminarily demonstrated that the anti-malarial drug halo can promote autophagy in GBM cells by upregulating the ATP6V0D2 gene, thereby exerting an anti-GBM effect. So far, no experimental studies have been conducted on the permeability of the blood-brain barrier within the halo body. Furthermore, the potential cardiac toxicity of halo is a point that deserves particular attention. Halo triggers cytotoxic autophagy in U251 cells by upregulating ATP6V0D2, establishing the key tumor suppressor factor status of ATP6V0D2 in GBM.