Quantum transition simulations on complex networks capture superposition, interference, and decoherence beyond classical stochastic models. This review provides a unified, mathematically rigorous account of the theory, algorithms, and cross-domain applications of quantum-transition-based network simulation. Starting from the Schrödinger equation and density matrix formalism, we develop the Lindblad master equation for open system dynamics and extend it to hybrid quantum–classical stochastic differential equations and hierarchical equations of motion for non-Markovian environments. Three quantum walk classes are formalized—continuous-time, discrete-time, and quantum stochastic walks—showing how decoherence and network topology govern the transition from ballistic quantum spreading to classical diffusion. Four simulation algorithms are compared: exact diagonalization [O(D4) memory, O(D6) diagonalization cost, D ≤ 20 states]; Krylov subspace [O(D2m), D∼100 states]; quantum trajectory Monte Carlo [O(DM), D∼103 states]; and tensor networks [L∼104 sites, where L is the number of sites and D = dL is the Hilbert space dimension with local dimension d]. Seven metrics—fidelity, coherence, purity, participation ratio, mean first-passage time, von Neumann entropy, and spectral gap—are linked to experimental observables. Applications span physical systems (excitation transport), biological systems (environment-assisted quantum transport in the FMO complex), and socio-technical systems (opinion polarization). Key limitations and four emerging directions of machine learning-assisted optimization, non-Markovian hierarchical equations of motion, simulation-guided network design, and hybrid classical–quantum computation are identified.
For the three-dimensional hyperbolic crosses {k∈Z3,α,β,γ>0:1≤|k1|α|k2|β|k3|γ≤Rα+β+γ}, three types of estimates (from above) of the Lebesgue constants generated by them are possible depending on α, β, and γ. We improve the most problematic of them by showing that for R→∞, it may be RlnR rather than the previously known RlnR.
In this paper, we study bandwidth allocation problems arising in communication networks, where multiple traffic flows compete for limited network resources under route-capacity and link-capacity constraints. The considered bandwidth allocation model incorporates flow-population structures together with route-capacity restrictions and network-link capacity constraints. The model is reformulated as a split feasibility problem in real Hilbert spaces. This reformulation enables the use of projection-type iterative techniques for generating feasible network allocations satisfying both local route constraints and global network-capacity constraints simultaneously. Motivated by this framework, we introduce a new inertial iterative algorithm for solving split feasibility problems associated with bandwidth allocation models. The proposed method incorporates inertial extrapolation into a projection-based iterative structure, and its strong convergence is established under suitable assumptions. Several direct consequences of the main theorem are also derived, including non-inertial and reduced feasibility frameworks. Finally, numerical examples and a communication-network application are presented to illustrate the numerical behavior and feasibility properties of the proposed iterative framework for bandwidth allocation problems involving multiple routes, shared communication links, and flow-population constraints.
Each component of reinforced concrete (RC) frames absorbs and dissipates blast energy, mitigating damage to adjacent rooms. Finite element modeling and machine learning are combined to analyze the propagation of blast waves and wall fragments in RC frames. A validated model simulates explosion scenarios with five TNT equivalents and examines blast loading and dynamic responses of adjacent rooms. Orthogonal experimental design is adopted to analyze the attenuation effects of structural parameters (room dimensions, venting coefficient, wall strength and thickness), TNT equivalent, and the number of propagation rooms on power parameters propagated to adjacent rooms. The results reveal that the peak overpressure and impulse of the adjacent rooms decrease by approximately two and one orders of magnitude, respectively, compared with the preceding room. The ejection velocity of wall fragments decays exponentially with the number of propagation rooms, which is the primary factor attenuating the power parameters, followed by the masonry wall strength and thickness. A backpropagation neural network-based surrogate model is developed to predict the attenuation coefficients of the power parameters (peak overpressure, duration, and wall fragment ejection velocity), achieving prediction errors below 20%. The proposed prediction framework provides a computationally efficient alternative to full-scale numerical simulation for rapid damage assessment.
Component degradation in aero-engines can cause local model mismatch. Insufficient coordination between component-response updates and engine-level prediction correction may limit improvements in gas-path prediction accuracy. Therefore, a data-enhanced component degradation digital-twin framework is proposed for aero-engine gas-path parameter prediction. It connects degraded component-response updates with engine-level prediction correction through selective component replacement, gas-path and shaft interface coupling, and engine-level prediction coordination. Under prescribed low-pressure compressor (LPC) efficiency degradation, a multi-self-attention long short-term memory (MA-LSTM) network replaces the LPC input–output mapping. The physics-based representations of the remaining components are retained, forming a data-driven model integrated-mechanism model (DMIM). The learned component response is connected to downstream gas-path modules and shaft calculations through mass flow rate, total temperature, total pressure, total specific enthalpy and output torque. DMIM predictions are then coordinated with predictions from a parallel engine-level data-driven model using an altered Kalman filter strategy. The framework is evaluated using six simulated LPC-efficiency degradation scenarios comprising two degradation magnitudes and three degradation durations. The proposed framework achieves a mean coefficient of determination (R2) of 0.94, a mean absolute percentage error (MAPE) of 2.3%, and a maximum MAPE across predicted parameters of 3.9%. Compared with the original physics-based model and the standalone MA-LSTM model, the mean MAPE decreases by approximately 61.0% and 36.1%, respectively. These results indicate that coordinated component-level updates and engine-level prediction can improve overall gas-path parameter prediction under the specified degradation scenarios.
