Urban Transportation Network Design (TND) is a highly complex system engineering. It has always been regarded as a very difficult problem in urban planning and transportation. This study tries to sort out and summarize the existing research system and development process in this field. From the perspective of mathematical modeling, the multi-objective property, nonlinear characteristics, uncertainty and NP-hard computational complexity of the TND problem are explained one by one, and a series of solution difficulties derived from them also appear. Classical optimization methods, such as linear programming, integer programming, bi-level programming models and so on, have advantages in solving structured problems. But their limitations in large-scale dynamic situations are also pointed out. In comparison, new intelligent and simulation optimization methods, such as heuristic algorithms, data-driven modeling strategies and simulation-optimization coupling frameworks, provide more potential ways to solve complex traffic network design problems. The current mainstream research paradigm can be summarized as the progressive process of "theoretical analysis—optimization solution—simulation verification". Different tools work together in this process to deepen the understanding of the problem and improve the solution efficiency. Network planning with dynamic and multiple uncertainties still faces many unsolved difficulties. Big data technology, artificial intelligence methods and the interdisciplinary integration may become the key driving forces for the future breakthrough in the TND field. This review aims to provide basic theoretical reference and framework support for the follow-up related research.

Blood oxygen saturation is a critical physiological parameter for evaluating human cardiopulmonary function and blood oxygen-carrying capacity. Non-invasive pulse oximeters based on the principle of photoplethysmography (PPG) have been widely used in clinical monitoring and home health care due to their simple operation and rapid response. This paper reviews the core technologies of pulse oximeters, focusing on the operating principles of their photoelectric sensor modules, hardware circuit design, key performance indicators, and the challenges they face. The article discusses in detail the differences between transmissive and reflective sensors, as well as the design of key circuits in signal processing such as amplification, filtering, and analog-to-digital conversion. Furthermore, it points out the impact of factors such as motion artifacts, low perfusion, and skin color differences on measurement accuracy. Finally, the future development of oximeters towards intelligence, multi-functionality, and high robustness is prospected. This paper aims to provide a theoretical reference for the design optimization and performance improvement of oximeters.

This study used information entropy as the core mathematical tool and focused on six typical global cultural scales: the Chinese pentatonic scale, the Indian 22-shruti scale, the Arabic 17 tone and other rhythmic scales, the European natural major scale, the Japanese mode scale, and the Indian pentatonic scale. By quantifying the uncertainty of interval distribution, the mathematical laws behind different cultural music aesthetics have been revealed. This study first constructed a frequency system for each scale and conducted interval statistics. Then, the Shannon entropy formula was used to calculate the entropy value, and the entire process was automatically calculated through Python programming. Finally, the deep logic of entropy value differences was explained in combination with cultural background. The results indicate that entropy is highly correlated with the number of core notes and the diversity of intervals in the scale: low entropy scales (2.0-2.8 bits) correspond to the cultural aesthetics of regular harmony, while high entropy scales (3.1-3.7 bits) relate to improvisation and diverse music styles, providing a quantitative analysis framework for cross-cultural music research.

In classical Newtonian theory, space and time are treated as separate entities, where time flows independently and space is Euclidean. However, this framework becomes inadequate in describing phenomena involving light and strong gravitational fields. This limitation motivates the development of general relativity, in which space and time are unified into a single geometric structure—spacetime, and gravity is interpreted as its curvature. Within this framework, the principles of geometry and symmetry determine the form of physical laws and their observable consequences. In this work, literature analysis and theoretical derivation methods are employed to study two classical observational tests of general relativity—gravitational redshift and light deflection—from a geometric and symmetry-based perspective, along with comparison to Newtonian theory. The results show that both phenomena arise naturally from the geometric structure of spacetime and can be described within a unified framework. Spacetime symmetries lead to conserved quantities, which provide an effective method for analyzing photon trajectories. The comparison with Newtonian theory highlights that the differences in predictions originate from the underlying geometric structure of spacetime.

The adjoint relation of linear operators is a core structure in inner product spaces. Normal operators, due to their commutativity with their adjoints, possess elegant spectral properties. Classical theory shows that a normal operator and its adjoint share the same eigenvectors with conjugate eigenvalues. However, this conclusion is confined to the normal case and typically relies on the spectral theorem or triangularization techniques. This paper generalizes the idea of spectral symmetry to arbitrary diagonalizable operators and reveals its essence from a purely geometric perspective. For a diagonalizable operator on a finite-dimensional complex inner product space, we construct a new operator based on its eigenspace decomposition, which acts as the conjugate of the eigenvalues on each eigenspace. Furthermore, by constructing a new inner product that depends on the eigenspace decomposition, the original operator and this new operator become mutual adjoints under this new inner product, and their relationship with the standard adjoint is established via a similarity transformation. The positive self-adjoint operator introduced herein captures the geometric inclination of the eigenspaces with respect to the original inner product. When the operator is normal, this construction reduces to the classical case. This paper provides a unified geometric explanation of the connection between the spectral structure of diagonalizable operators and the adjoint relation, offering a new perspective for operator theory and matrix analysis.

Traditional optical microscope systems are limited by their fundamental drawbacks such as large physical size, limited functions and poor contrast resolution for examining microscopic specimens, but polarization - multiplexed metalenses which represent a significant development in metasurface technology escape from these limits by combining multiple imaging methods into one flat structure through precisely controlling light polarization states with subwavelength nanostructures, and recent research stresses the cooperative work of geometric phase (for example, Pancharatnam - Berry phase) and propagation phase mechanisms making it possible to modulate phase depending on polarization by using hydrogenated amorphous silicon nanoantennas so that controlling the polarization of incoming light allows a single metalens to perform bright - field, edge - enhanced and wide - field imaging simultaneously without any mechanical adjustment, and this research uses a systematic literature review and case study approach to assess the design rules of polarization - multiplexed metalenses and their application in biological imaging and diagnosis, and the results show that polarization multiplexing breaks through the space - bandwidth product restrictions of conventional optical systems creating a compact microscope system with a resolution of 3.91 µm and a field of view of ±40° thus greatly improving the miniaturization and functional flexibility of the system.

Spintronics offers a transformative paradigm for next-generation, energy-efficient information technology by utilizing the intrinsic spin of electrons alongside their charge. While conventional spintronic devices have demonstrated ultrafast switching and non-volatility, their reliance on thick metallic layers limits ultra-dense integration. This paper reviews the emerging frontiers of spin current generation, focusing on the integration of topological insulators, two-dimensional (2D) materials, and quantum magnets. We examine the mechanisms of spin-orbit torque (SOT) and tunneling magnetoresistance (TMR), highlighting how reduced dimensionality and strong spin-orbit coupling in van der Waals heterostructures enable highly efficient spin manipulation. Furthermore, we address the persistent challenges of interfacial scattering and the ambiguity in defining spin currents in spin-orbit coupled systems. To resolve this, we emphasize the theoretical framework of the Spin Accumulation Coefficient (SAC), which provides a unified, first-principles approach to quantifying spin responses. By bridging theoretical modeling with recent experimental demonstrations of robust spin accumulation in materials like Bi2Te3 and MoS2, this study outlines a comprehensive pathway toward scalable, low-dissipation spintronic architectures.

This paper investigates whether and how government spending crowds out private investmen. It further analyzes the underlying reasons for the heterogeneous intensity of this crowding - out effect across different regions, business cycle states, and monetary policy regimes. Using a panel dataset of 25 OECD countries from 1995 to 2023, we find that a one-percentage-point increase in government spending reduces private investment by 0.10–0.15 percentage points, with the interest rate channel accounting for approximately 60% of this effect. The crowding-out intensity varies substantially across economic conditions: it is three times stronger under tight monetary policy than under accommodative regimes, nearly zero during recessions, and 40% weaker in economies with deeper financial markets. To interpret these patterns, we develop a structurally interpretable mean-field game (MFG) model based on the HJB-FPK framework, which endogenizes the interest rate path through strategic interactions among heterogeneous firms and market clearing. The model is disciplined by empirically estimated elasticities and impulse responses, with distributional fit evaluated via Wasserstein distances. Counterfactual simulations confirm that fiscal-monetary coordination and financial development levels are critical determinants of crowding-out severity. This study provides a unified framework bridging empirical evidence and theoretical micro-foundations, offering new insights into the design of fiscal policy under heterogeneous economic environments.

For epitaxial InAs/GaAs quantum dot infrared photodetectors (QDIPs), the central impediment to high-temperature operation above 150 K lies in the n-type doping step. Necessary though this doping is for generating an adequate photocarrier population, it simultaneously introduces deep-level defects, including DX centers, which in turn drive a sharp increase in dark current. Traditional optimization routes built around band-structure engineering are, at this stage, nearing their practical limits. Against that backdrop, the present review argues that a more foundational route may lie in borrowing the already mature surface chemical passivation strategies developed for colloidal quantum dots and translating their governing principles to epitaxial platforms. At atomic-scale resolution, surface and interface engineering of quantum dots can suppress defect-assisted tunneling and, just as critically, recover a large carrier escape activation energy. A stepwise examination is therefore undertaken: first, the physical origin of the doping-induced performance bottleneck is dissected; next, the contributions and constraints of established approaches, including dot-in-a-well (DWELL) architectures, are reviewed; and finally, the scientific rationale underlying this emerging surface/interface engineering paradigm is set out in detail. From that basis, future research directions are sketched prospectively, including the co-optimization of material growth, doping, and surface treatment, together with the exploration of hybrid-dimensional heterostructures, so as to furnish a systematic research framework for breaking through the QDIP performance bottleneck.