Reconstructing causal dynamic networks from multivariate time series is a foundational problem in complex systems science. Yet, the key scientific issue is not simply causality detection, but causal interpretability. Interpretable causality is the foundation for testable mechanistic hypotheses, transferable forecasting, and principled decision-making for intervention and control. In real-world complex systems, causal inference is often compromised by noise, missing data, high dimensionality, nonlinearity, time delays, heterogeneity, and partial observability. Classic approaches to interpretable causality yield explicit, inspectable quantities such as causal graphs, coefficients, and governing equations. However, this methodological shift has heightened expectations: AI-extended approaches are increasingly required to recover explicit causal mechanisms rather than opaque predictive dependencies, thereby preserving interpretability. This review summarizes four classic methods and their AI-extended counterparts based on time series data, including Granger frameworks, information-theoretic measures, nonlinear state–space/manifold reconstruction, and mechanistic differential-equation learning. Next, we elucidate their motivations, core principles, the origins of interpretability, and the assumptions required for meaningful conclusions. Finally, we highlight representative applications across climate studies, neuroscience, epidemiology, finance, social science, ecology and molecular biology, followed by a discussion of comparative analysis, open challenges, and future research directions.
Electroweak radiative corrections form a crucial ingredient in modern precision calculations for particle processes at high-energy colliders such as the Large Hadron Collider. The salient features of electroweak corrections as well as currently used techniques and concepts for their calculation are reviewed. Recent progress in this enterprise is illustrated in a discussion of electroweak multi-gauge-boson production processes: massive di-boson production, vector-boson scattering, and massive tri-boson production.
The year 2024 marked the 50th anniversary of the discovery of the J/ψ particle, which unveiled the charm quark and the charmonium spectrum, instigating the “November Revolution” in particle physics. This discovery catalyzed the development of quenched potential models, most notably the Cornell model, which provided a foundational quantitative description of the hadronic spectrum. However, the landscape of hadron spectroscopy has been profoundly transformed since the turn of the 21st century with the observation of numerous charmonium-like states, such as X(3872), which exhibit properties starkly at odds with quenched model predictions. These discrepancies, exemplified by the “X(3872) low-mass puzzle” and the “Y problem” associated with vector states like Y(4260), underscore the critical limitations of the quenched approximation and signal the necessity for a new theoretical paradigm. This review synthesizes recent advances in hadronic spectroscopy, arguing that the unquenched picture, which incorporates coupled-channel effects such as hadronic loops, is essential for a unified description of these new states and associated anomalies. We demonstrate how unquenched effects provide compelling solutions to long-standing puzzles in charmonium decays (e.g., the “ρπ puzzle” and anomalous dipion transitions), predict and explain the existence of exotic charged states like Zc(3900) and Zb(10610) via mechanisms such as Initial Single Pion Emission, and offer a framework for understanding interactions between charmonia and with nucleons. Furthermore, we emphasize the universality of unquenched effects, extending their application to bottomonium and light-flavor sectors. As experimental precision continues to improve, we advocate for the systematic development of unquenched hadronic spectroscopy, which heralds a new era of high-precision theoretical and experimental studies, moving decisively beyond the quenched approximation to achieve a more complete understanding of non-perturbative behavior of the strong interaction.
Bound states of solitons, alias “soliton molecules”, in fiber-laser cavities is one of central topics in the ongoing experimental and theoretical work in nonlinear optics. This topic has drawn much interest as a unique platform for the studies of dynamics of dissipative solitons, and also due to its vast potential for various applications in optics and photonics. This article presents a systematic review of theoretical and experimental findings for bound states of two and several dissipative solitons in fiber lasers. The theoretical basis underlying the formation and stabilization of soliton molecules in the fibers, which is provided by the complex Ginzburg–Landau equations and bound states of such equations, is presented in necessary detail, which is followed by a detailed presentation of experimental findings, including very recent ones. In particular, included are the results for the multi-soliton bound states in the fibers, as well as for the bound states in the temporal and frequency domains, single-component (scalar) and two-component (vector), two- and multi-soliton modes, as well as for bound states of spatiotemporal dissipative solitons in the lasers based on multimode fibers.
Precision timing has played a critical role in high-energy physics experiments, particularly for particle identification and the suppression of pileup under the challenging conditions expected at future colliders like the High-Luminosity Large Hadron Collider (HL-LHC). Over the past decades, significant advancements in timing measurement technologies have been made to meet the demands of increasingly complex collider environments. After introducing the motivation for precision timing in collider experiments, the underlying physical principles of timing measurements and the most important factors influencing the time resolution of a detector, this review presents a survey of key detector technologies developed in recent years, including scintillators read out by silicon photo-multipliers (SiPMs), low-gain avalanche diodes (LGADs), multi-gap resistive plate chambers (MRPCs). The integration of precision timing into large-scale systems is discussed with examples from detectors at current collider experiments. Finally, we explore emerging technologies and future directions in the field, highlighting their potential impact on the next generation of high-energy physics experiments.
In this study we present a comprehensive sensitivity atlas for Big Bang Nucleosynthesis (BBN) in which we quantify the dependence of the primordial abundances of helium-4, deuterium, and lithium-7 as well as $N_{\rm{eff}}$ on variations in 14 fundamental particle physics and cosmological parameters and 63 thermonuclear reaction rates. We use the publicly available BBN code \faGithub \href{https://github.com/vallima/PRyMordial}{\,\texttt{PRyMordial}} to compute each sensitivity using two nuclear reaction rate compilations and two weak-rate normalization schemes, and provide a model independent reference applicable to Beyond the Standard Model (BSM) models in which MeV scale physics is modified. In addition, we rank each parameter's contribution to the theoretical uncertainty budget. We compare our predictions against the latest observational determinations of the primordial abundances, including a recent LBT measurement of the helium-4 abundance \cite{Aver:2026dxv} which roughly halves the observational uncertainty relative to previous determinations. We present these results both fixing $ΔN_{\rm eff}$ at its Standard Model (SM) value, and allowing it to be a free parameter using the latest uncertainty from the combined CMB+BAO+BBN 2026 value \cite{Goldstein:2026iuu}. When $ΔN_{\rm eff}$ is allowed to be a free parameter, it dominates the theoretical uncertainty of the helium-4 abundance, highlighting the importance of upcoming observations from the Simons Observatory \cite{SimonsObservatory:2025wwn}. As illustrative applications, we examine the deuterium tension and the Lithium Problem in light of our sensitivity analysis. The full set of numerical results and figures is publicly available on GitHub \faGithub \href{https://github.com/Anne-KatherineBurns/bbn-sensitivity-atlas}{\,\texttt{bbn-sensitivity-atlas}}.
Patterns in time and space spanning a wide range of scales abound in nature, from the circadian oscillations in cyanobacteria to epidemic cycles, from the exquisite skins in zebras to the spatial structure of ecological habitats. For many of these systems, deterministic descriptions may necessitate fine tuning of parameters in order for patterns to form, in a way that is incompatible with their observed natural robustness. Furthermore, endogenous stochasticity such as that coming from fluctuations in small copy numbers of the interacting basic variables may be significant for these systems, in addition to external sources of noise that act as a macroscopic bias to deterministic, reproducible dynamics. Here we survey natural systems for which demographic noise has been shown to be important, and for which an individual-based description that is intrinsically stochastic is needed. This amounts to characterizing their microscopic dynamics via master equations, which return the probability for observing a system in a given state, at a given time. The application of perturbative expansions to obtain approximate analytical and numerical solutions of the master equations describing these specific systems, shows how the effects of demographic noise emerge in a perturbative fashion, and how endogenous stochasticity can be self-consistently amplified, yielding almost regular oscillations, termed quasi-cycles. These quasi-cycles appear for parameter values that lie outside the regions in parameter space where deterministic oscillations are predicted, thereby enhancing robustness. Thus, counter intuitively, noise can organize in regular quasi-periodic orbits, thereby building macroscopic order from microscopic disorder. This intriguing concept, introduced for the temporal domain, can be extended to the realm of spatial systems: demographic noise can seed the emergence of stochastic Turing patterns, which have been observed in systems ranging from developmental patterns, hallucinations to microbial biofilms. We illustrate the analytical approach by making reference to simple toy models and highlight the constructive role that demographic noise can play in seeding stochastic self-organized patterns in specific systems, both in time and space.
The analysis of functional magnetic resonance imaging (fMRI) data has been fundamentally shaped by network science, which models the brain as a graph of nodes (regions) and edges (pairwise interactions). This pairwise functional connectivity approach has revealed key principles of brain organization but rests on a reductionist assumption: that all interactions are dyadic. This paradigm is inherently limited, as it cannot capture polyadic dependencies or emergent collective phenomena where the interaction between two nodes is modulated by the state of others. Such higher-order interactions (HOIs) are hypothesized to be crucial for complex cognitive functions like multi-sensory integration and decision-making. This review synthesizes the rapid evolution of methods for assessing HOIs in fMRI-based functional networks. We begin by defining HOIs and introducing the mathematical frameworks of hypergraphs and simplicial complexes, which formally represent interactions among groups of brain regions. We then provide a comprehensive overview of the methodologies for detecting and quantifying HOIs, categorizing them into three major families: (1) multivariate statistical models that disentangle direct from indirect effects; (2) information-theoretic measures, such as Partial Information Decomposition and O-information, which quantify the synergistic and redundant information shared among multiple regions; and (3) machine learning techniques, including sparse regression and graph neural networks, that learn complex HOIs directly from data. We critically examine the application of these methods in neuroscience, highlighting growing evidence that HOIs provide a more sensitive and mechanistically informative view of brain function in health and disease. They have proven superior to pairwise connectivity in classifying neurological and psychiatric disorders – including Alzheimer’s disease, autism spectrum disorder, and schizophrenia – and in revealing the brain’s dynamic, integrative processes underlying cognition. Finally, we address the significant methodological challenges facing the field, such as distinguishing genuine HOIs from lower-order effects and the computational complexity of analysis, and outline future directions, including the integration of multimodal data and the translation of HOIs into clinical biomarkers.
Thermonuclear X-ray bursts from the surface of accreting neutron stars are the most common astrophysical explosions in our galaxy. They provide a unique window into the physics of neutron stars, the physics of matter under extreme conditions, and the physics of astrophysical thermonuclear explosions. X-ray bursts are powered by a broad range of nuclear reactions that need to be understood to interpret observations. The relevant nuclei are mostly neutron deficient and unstable, and thus experimental information and theoretical understanding is limited and an active area of research in nuclear science. We review the current status of the nuclear physics of X-ray bursts, with special emphasis on new experimental and theoretical information on a large number of reaction rates. As such we provide an overview of the broad experimental and theoretical methods currently used to advance the nuclear physics of X-ray bursts. The new information is used to update the public JINA REACLIB database with 32 new reaction rates based on experimental information, and a new dataset of theoretical statistical model reaction rates where no experimental information is available. Using several models for X-ray bursts that are powered by mixed hydrogen and helium burning, we take advantage of the updated nuclear data to review the current understanding of the nuclear reaction sequences in such X-ray bursts, the modeling of light curves, and predictions of the composition of nuclear ashes.
Electromagnetic wave scattering by subwavelength hole structures has received significant research interest in the past two decades, due to the unusual physical phenomena that arise in these media when external radiation is present, such as the extraordinary optical transmission (EOT) and strongly localized optical field at the hole apertures. It turns out that resonances, which are broadly defined as complex eigenvalues of the underlying Maxwell’s operator, play a major role in EOT and anomalous field enhancement for such media. These resonances can be induced by the geometry (such as tiny holes) or the medium parameter (such as permittivity values) of the problem, or their collaborative interactions. In this paper, we survey the mathematical theory that has been developed to understand the various resonances in subwavelength hole structures, along with quantitative analyses of their resonant scattering and the induced EOT phenomena. We also review computational methods proposed for modeling resonant wave scattering in these multiscale media and the mathematical frameworks established for applications in sensing and imaging. Finally, we discuss open problems and outstanding mathematical challenges in the field. The mathematical investigation of the resonances for this class of problems provides the fundamental theory as well as computational algorithms for the design of more efficient subwavelength optical devices and their applications. It also sheds light on the studies of other related spectral problems with the differential operators defined over multiscale media.
Although geometrical methods have been applied across many fields of physics, their systematic use in connection with bifurcations and nonlinear phenomena only emerged between 2019 and 2024, when Fisher information geometry was employed to study bifurcations, limit cycles, and other nonlinear dynamical phenomena, leading to the covariant formulation of geometric bifurcation theory (GBT). In this approach, incorporating Fisher information theory into the axioms of nonlinear dynamics yields a corresponding Riemannian metric, allowing for the representation of dynamical systems as Riemannian manifolds. The metric and its scalar curvature are particularly valuable tools for exploring nonlinear phenomena, especially in cases where standard methods provide limited or no solutions. This report aims to review the main contributions of this geometrical formalism within the framework of dynamical systems governed by differential equations. In particular, we present a detailed overview of the mathematical framework of GBT, including the construction of Riemannian manifolds from dynamical systems, the Fisher information metric, and the role of scalar curvature in detecting local and global bifurcations, limit cycles, and other nonlinear phenomena. We also discuss how GBT provides a solution to the second part of Hilbert’s sixteenth problem, and how this result aligns with earlier findings obtained some time ago through other methods under somewhat different circumstances. Finally, we highlight the current state of GBT and promising directions for future research.
In medicine, invasive procedures involve cutting or penetrating the skin to access the inside of the body, whereas non-invasive procedures do not. Non-invasive diagnostic and treatment methods offer several advantages, including reduced discomfort and fewer potential complications compared to invasive approaches. Computational hemodynamics has emerged as a valuable approach for diagnosing and treating diseases of the human circulatory system, particularly in guiding optimal treatment options. This interdisciplinary field combines computational modeling, fluid dynamics, and medical imaging to explore blood flow behavior under various physiological conditions and in the context of diseases. Blood viscosity is recognized to exhibit non-Newtonian rheological properties, meaning it can change with shear rate. Empirical research has revealed that blood displays intricate non-Newtonian fluid characteristics (i.e., shear-thinning, viscoelasticity, yield stress, and thixotropy). Consequently, various computational and clinical analyses use various non-Newtonian fluid models to model blood. However, researchers have not reached a consensus on a single non-Newtonian fluid model that adequately describes the non-Newtonian characteristics of blood. This study aims to provide a comprehensive review of all non-Newtonian fluid models along with the Newtonian model utilized in computational hemodynamics, highlighting the importance of understanding the complex rheological nature of blood and its impact on the dynamics of the circulatory system. In addition, this review examines various mathematical modeling approaches for the flow of blood in the circulatory system under different constraints, along with their solution methods, to suggest and optimize computational hemodynamics.
Magnon confinement and trapping refer to the localization of magnons — quasiparticles that represent collective spin-wave excitations in magnetic materials — within specific regions or structures. This concept is essential in magnonics, a subfield of spintronics that leverages spin waves for processing and transmitting information. Compared to conventional electronics, magnonics offers lower power consumption and faster operation, making it a promising technology for future devices. Magnons can be confined using both static and dynamic methods, often relying on potential wells and barriers to restrict their free propagation and trap them in designated locations. In this review, we will explore the main strategies for magnon confinement and trapping, including: magnetic field inhomogeneities, spin textures (i.e. domain walls, vortices, skyrmions) nanostructured materials (i.e. nanowires, disks, and magnonic crystals), topological states, chiral magnons and flat band formation, induced by dipole–dipole interactions and Dzyaloshinskii–Moriya interaction. Microwave cavities and resonant magnetic fields, as well as spin-torque effects and Bose–Einstein condensation contribute to magnon localization. Furthermore, spin-wave edge and cavity modes have been observed in two-dimensional magnetic materials and twisted moiré superlattices at a specific twist angle. Magnon trapping has broad applications in computing and data processing, particularly in the development of magnonic crystals, waveguides, and memory elements. Additionally, magnon systems are being explored for quantum computing, where confinement can enhance the coupling between magnons and other quasiparticles in hybrid quantum systems. Precision control of magnons could lead to next-generation spintronic devices, offering improved efficiency and scalability.
Spreading dynamics is a central topic in the physics of complex systems and network science, providing a unified framework for understanding how information, behaviors, and diseases propagate through interactions among system units. In many propagation contexts, spreading processes are influenced by multiple interacting factors, such as information expression patterns, cultural contexts, living environments, cognitive preferences, and public policies, which are difficult to incorporate directly into classical modeling frameworks. Recently, large language models (LLMs) have exhibited strong capabilities in natural language understanding, reasoning, and generation, enabling explicit perception of semantic content and contextual cues in spreading processes, thereby supporting the analysis of the different influencing factors. Beyond serving as external analytical tools, LLMs can also act as interactive agents embedded in propagation systems, potentially influencing spreading pathways and feedback structures. Consequently, the roles and impacts of LLMs on spreading dynamics have become an active and rapidly growing research area across multiple research disciplines. This review provides a comprehensive overview of recent advances in applying LLMs to the study of spreading dynamics across two representative domains: digital epidemics, such as misinformation and rumors, and biological epidemics, including infectious disease outbreaks. We first examine the foundations of epidemic modeling from a complex-systems perspective and discuss how LLM-based approaches relate to traditional frameworks. We then systematically review recent studies from three key perspectives, which are epidemic modeling, epidemic detection and surveillance, and epidemic prediction and management, to clarify how LLMs enhance these areas. Finally, open challenges and potential research directions are discussed.
This report reviews key developments in Carrollian physics with an emphasis on their role in the emerging framework of holography in asymptotically flat spacetimes. We begin by introducing the Carrollian limit, understood as a contraction of the Poincaré group obtained by formally taking the speed of light to zero. The geometric structures associated with this limit are described and argued to arise naturally on null hypersurfaces, most notably on null infinity, as well as black hole and cosmological horizons. Building on this, we examine the relation between the Bondi–Metzner–Sachs symmetries governing asymptotically flat gravity and the conformal Carrollian symmetries. Explicit examples of Carrollian field theories are constructed by implementing the limit on well-known relativistic field theories, with particular attention to Carrollian CFTs. We then present the Carrollian holography proposal, according to which gravity in asymptotically flat spacetimes is dual to a Carrollian CFT living at null infinity in one lower dimension. In this framework, the massless S-matrix written in position space at null infinity is naturally reinterpreted in terms of boundary Carrollian CFT correlators, called Carrollian amplitudes. We highlight their relation to celestial amplitudes and show how they naturally emerge from holographic CFT correlators through a correspondence between the flat space limit in the bulk and the Carrollian limit at the boundary. Using this correspondence, we provide strong evidence that flat space holography arises from a controlled and consistent limiting procedure applied to both sides of the AdS/CFT duality. We conclude by outlining future directions and open questions in the program.
