Most complex social, biological, and technological systems can be described by dynamic networks. Reconstructing the structure of complex networks from measurable data of some or all nodes is a challenge in many branches of science. External influences are always present and act as noises to the networks of interest, and various difficulties extensively appear in the reconstruction of real-world networks: such as complexity of network structures; strong nonlinearity of network dynamics; diverse and unknown impacts from the interiors of nodes and externals of networks, i.e., noises; many hidden nodes of which data are not measurable in networks; and different time delays of interactions. Partial or all the above mentioned difficulties are present in reconstruction of noise-driving dynamic network. Different methods are proposed to solve these difficulties, including variable-variable correlations, velocity-variable correlations, high-order correlation, time-lagged covariance of data measurements taken at different times, and so on. This review shows partial developments of a special topic in this wide field. Moreover, we expect that all the methods in this review can be applied to the reconstruction of many realistic dynamic networks.

The recent success of foundation models and deep learning has far outpaced our theoretical understanding of how large-scale neural networks learn and generalize. Statistical physics provides a natural language for describing such high-dimensional, nonlinear, and strongly coupled systems, offering concepts such as mean-field theory, phase transitions, energy landscapes, and stochastic dynamics. In this topical review, we adopt a statistical-physics way of thinking — from concepts including phases and criticality, and free-energy viewpoints, to methods such as kernel and Gaussian-process limits, mean-field and dynamical mean-field theories, random-matrix tools, and Fokker–Planck formalisms, and to a mindset emphasizing universality, scaling, and tractable limits with explicit validity regimes. We survey recent progress on understanding modern deep learning through this lens, including mean-field analyses of wide networks, spectral and geometric perspectives on loss landscapes, stochastic-gradient-based training viewed as a dynamical process, and phase-transition analogies that organize phenomena such as overparameterization, generalization, and representation change. Our goal is to synthesize these threads into a coherent framework that clarifies what each approximation explains, when it is expected to hold, and how apparently competing narratives relate or diverge. Together, these perspectives form a unified physical framework that views representation learning as a collective phenomenon in high-dimensional systems, bridging deterministic and stochastic regimes of gradient-based optimization.

In view of high cost of experiment equipment, complex independent detection for three components of near field and extreme difficulty of phase extraction for optical near-field measurement, one concise method is proposed to acquire optical near-field distribution. Under the condition that the optical field existing both in near and far field, the near field is obtained through the differential and integral calculation of the far-field information in terms of the vector Helmholtz equation. As an exemplification, the near field excited by the Archimedes’ spiral slit is derived from the diffraction far field, which can be easily obtained using the common devices, and the presented spiral phase distributions of optical vortices consistent with the theoretical prediction confirm the effectiveness of the proposed method. This method realizes independent detection for three components of near field and fulfills the acquirement of near-field phase information without any complex and costly device, and it has the advantages of low cost, high efficiency and environmental independence. This method may pave one promising way for optical near-field detection.

Acoustic vortices carrying orbital angular momentum, often generated using metagratings, provide an effective approach for wavefront engineering, particle manipulation, and underwater information transfer. However, most existing acoustic metagratings rely on fixed structural configurations, which inherently restrict their tunability and multifunctionality. Here, we propose a three-dimensional reconfigurable reflective acoustic metagrating for dynamic manipulation of vortex fields. The device consists of two gradient-depth air-groove supercells, in which the reflection response can be actively reconfigured by tuning the depth of paired grooves. Based on a generalized conservation principle of topological charge in metagrating diffraction, we demonstrate controllable conversion of incident acoustic vortex beams into reflected vortex states with different diffraction channels. In particular, near-perfect switching between anomalous reflection and specular reflection is achieved with high conversion efficiency. In addition to structural reconfiguration, frequency-dependent modulation provides an additional degree of freedom for dynamically tailoring the reflected vortex field. Our results reveal a simple yet robust mechanism for tunable vortex-beam reflection and offer a compact platform for multifunctional acoustic devices, with potential extensions to other wave systems such as electromagnetic and elastic waves.

Traditional microwave absorbers with limitations of narrow band absorption, single functionality, and difficulty in conforming to complex surfaces are no longer sufficient to meet the demands of modern equipment for multispectral stealth. This paper proposes a flexible optically transparent metasurface (FOTMS) with simultaneously ultra-broadband millimeter-wave absorption and infrared (IR) stealth. Tri-layer indium tin oxide (ITO) patterned layers were designed and etched onto flexible transparent polyethylene terephthalate (PET) substrate, achieving radar-IR bi-stealth, optical transparency and a flexible configuration. Both simulated and experimental results indicate that the metasurface features absorptivity more than 90% within 15–38.7 GHz, while exhibits 10 dB radar cross section (RCS) reduction for curved configurations. Additionally, the metasurface displays polarization insensitivity and stability at different incidences and polarization angles. Meanwhile, the entire structure maintains a high optical transmittance of 85.09%, and the average infrared emissivity of metasurface is 0.47 for 3–14 μm. This work provides an effective strategy for optical windows and multispectral stealth.

Gallium nitride (GaN) nanowires have emerged as transformative materials for optoelectronic applications, particularly photodetection, owing to their unique combination of wide bandgap, high thermal stability, and intrinsic ultraviolet sensitivity. This review surveys recent progress in GaN nanowire-based photodetectors, focusing on structural design, performance optimization, and application development. GaN nanowires provide low dislocation density, high surface-to-volume ratio, and efficient strain relaxation, thereby overcoming the limitations of traditional planar GaN devices. Various device architectures, including photoconductive, positive−negative (p–n) and positive−intrinsic−negative (p–i–n) junction, metal–semiconductor–metal, and piezo–phototronic detectors, are examined with respect to their performance metrics and operational principles. Integration with two-dimensional materials, perovskites, and organic materials further enhances responsivity and enables self-powered operation. Applications extend to imaging, sensing, logic operations, and flexible electronics. Remaining challenges include achieving large-scale uniformity, high response speed, and good device stability. Future research should prioritize improved fabrication processes and novel heterostructure exploration to advance both performance and practical deployment.

Regarded as the closest realization of the quantum Ising model in a magnetic field, which features stable quasiparticles with an emergent E_8 symmetry, CoNb₂O₆ keeps being a source of inspiration by manifesting intricacies beyond this model. A notable example is the recent finding of an unexpected band of localized gapless fermionic excitations around the field-induced quantum critical point (QCP), whose origin remains unclear. Despite differences in many aspects compared to CoNb₂O₆, BaCo₂V₂O₈ in a magnetic field also exhibits the E_8 physics, while allowing for better scrutiny of the critical excitations associated with its well-separated one- and three-dimensional QCPs. Here we study the low-lying magnetic excitations within the antiferromagnetic order of BaCo₂V₂O₈ by performing ultralow-temperature heat transport measurements. The field-independent thermal conductivity at the lowest temperatures and the suppressed thermal conductivity with an increasing field at higher temperatures point to heat-carrying phonons scattered by magnetic excitations. For the magnetic excitations, importantly, we find no evidence for the emergence, around the one-dimensional QCP, of gapless fermionic excitations similar to those observed in CoNb₂O₆. Based on the contrasting cases of BaCo₂V₂O₈ and CoNb₂O₆, we propose that the frustrated alignment of chains and the proximity of two QCPs in CoNb₂O₆ may put this system in a unique place to host the gapless fermionic excitations.

The coexistence of ferroelectricity and magnetism in a single-phase oxide is rare because the electronic requirements for these two orders are often incompatible. Here, using first-principles calculations and parallel-tempering Monte Carlo simulations, we propose stoichiometric VHfO₄ as a hafnia-derived multiferroic that overcomes this constraint through ordered cation design rather than dilute magnetic doping. We found that VHfO₄ adopts a symmetry-lowered polar Pc structure derived from the ferroelectric \mathit{P}\mathit{c}\mathit{a}{2}_1 phase, with layered V/Hf ordering, local dynamical stability, and switchable ferroelectricity with a large spontaneous polarization. The ordered V sublattice introduces competing exchange interactions that favor an antiferromagnetic ground state at zero strain. Epitaxial strain further drives transitions into additional phases, including a noncollinear spiral-like state and a predominantly in-plane antiferromagnetic state. We also find that out-of-plane lattice distortions along the polar axis strongly modify the exchange interactions and magnetic phase stability, indicating a strain-mediated pathway for electric-field control of magnetism. These results establish VHfO₄ as a promising artificial-superlattice candidate for exploring multiferroicity and magnetoelectric coupling in hafnia-based oxides.

In this work, we adopt the diquark model, construct the diquark−diquark−antiquark type currents with the light quarks uus in two octets, and study the uusc\overline{c} pentaquark states in the framework of the QCD sum rules systematically. We obtain the mass spectrum of the hidden-charm-singly-strange pentaquark states with the quantum numbers I{J}^P=1{\frac{1}{2}}^{-}, 1{\frac{3}{2}}^{-} and 1{\frac{5}{2}}^{-}. And we can search for those P_{cs} states in the processes {\mathrm{\Sigma }}_b^{+}\to P_{cs}^{+}\varphi \to J/\psi {\mathrm{\Sigma }}^{+}\varphi and {\mathrm{\Xi }}_b^0\to P_{cs}^{+}{K}^{-}\to J/\psi {\mathrm{\Sigma }}^{+}{K}^{-}.

²³⁵U and ²³⁸U are fundamental materials in thermal and fast neutron breeding studies. Accurate evaluation of their fission product yields is of critical importance for advanced reactor design and nuclear waste management. In this work, a baseline Bayesian neural network model (BNN₀) with two hidden layers of 20 neurons each was constructed. An improved model, BNN₃, was developed by incorporating additional physics-informed features, namely the odd−even effect, \beta-decay energy, and isospin, into the network inputs. Comparative analyses of the general distributions of the fission yields and isotopic chain structures demonstrate that BNN₃ exhibits significantly improved reconstruction accuracy and consistency with the target cumulative fission-yield distributions. For 16 representative fission products, the energy-dependent yield predictions of BNN₃ show better agreement with both experimental data and evaluated libraries, accompanied by noticeably narrower confidence intervals. These results indicate that the incorporation of relevant physical information improves the model’s sensitivity to underlying fission mechanisms and enhances its capability to reproduce the systematic characteristics of cumulative fission-yield distributions. Together, these strategies contribute to more accurate and robust nuclear data modeling, providing a methodological foundation for the evaluation and development of next-generation nuclear data libraries.