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.

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.

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.

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.