RESUMEN
In many real-world networks, interactions between nodes are weighted to reflect their strength, such as predator-prey interactions in the ecological network and passenger numbers in airline networks. These weighted networks are prone to cascading effects caused by minor perturbations, which can lead to catastrophic outcomes. This vulnerability highlights the importance of studying weighted network resilience to prevent system collapses. However, due to many variables and weight parameters coupled together, predicting the behavior of such a system governed by a multi-dimensional rate equation is challenging. To address this, we propose a dimension reduction technique that simplifies a multi-dimensional system into a one-dimensional state space. We applied this methodology to explore the impact of weights on the resilience of four dynamics whose weights are assigned by three weight assignment methods. The four dynamical systems are the biochemical dynamical system (B), the epidemic dynamical system (E), the regulatory dynamical system (R), and the birth-death dynamical system (BD). The results show that regardless of the weight distribution, for B, the weights are negatively correlated with the activities of the network, while for E, R, and BD, there is a positive correlation between the weights and the activities of the network. Interestingly, for B, R, and BD, the change in the weights of the system has little impact on the resilience of the system. However, for the E system, the greater the weights the more resilient the system. This study not only simplifies the complexity inherent in weighted networks but also enhances our understanding of their resilience and response to perturbations.
RESUMEN
Based on the polynomial theory, the error propagation characteristics of the widely used N-step discrete Fourier transform (N-DFT) phase-shift algorithm were analyzed via theoretical analysis, under the effect of Gamma distortion and phase detuning. The results showed that the N-DFT algorithm could not simultaneously suppress both types of error. A robust linear phase-shift (RLPS) algorithm was designed, the performance of the RLPS and 8-DFT algorithms in terms of spectral response, detuning robustness, and G S / N was briefly analysis by Manuel Servin method. The Simulation analysis and comparison of the results show that the RLPS algorithm could suppress both types of error simultaneously, which exhibited better stability and accuracy than N-DFT and exponential algorithms, particularly in gradient measurement stability, peak-to-valley (PV) and root-mean-square (RMS) error suppression. Moreover, a physical experiment apparatus was built to test unidirectionally inclined plane mirror and concave mirror using the RLPS, N-DFT, and exponential algorithms. The results showed that the RLPS algorithm could significantly improve the measurement stability and accuracy in the presence of detuning and without screen Gamma calibration.
RESUMEN
The performance of Ag-8.5Au-3.5Pd alloy wire after cold deformation and annealing were analyzed by SEM (scanning electron microscope), strength tester and resistivity tester. The processing process and performance change characteristics of Ag-8.5Au-3.5Pd alloy wire were studied. The results show that alloy wire grains gradually form a fibrous structure along with the increase in deformation. The strength of the wire increases with the increase in deformation rate, but the increase trend becomes flat once the deformation rate is higher than 92.78%; the resistivity of Ag-8.5Au-3.5Pd alloy wire decreases with the increase in annealing temperature, reaching minimum (2.395 × 10-8 Ω·m) when the annealing temperature is 500 °C; the strength of Ag-8.5Au-3.5Pd alloy wire decreases with the increase in annealing temperature. When the annealing temperature is 500 °C, the strength and elongation of the φ0.2070 mm Ag-8.5Au-3.5Pd alloy wire are 287 MPa and 25.7%, respectively; the fracture force and elongation of φ0.020 mm Ag-8.5Au-3.5Pd alloy wire are 0.0876 N and 14.8%, respectively. When the annealing temperature is 550 °C, the metal grains begin to grow and the mechanical performance decrease; the φ0.020 mm Ag-8.5Au-3.5Pd alloy wire have good surface quality when the tension range is 2.5-3.0 g.
RESUMEN
Catastrophic and major disasters in real-world systems, such as blackouts in power grids or global failures in critical infrastructures, are often triggered by minor events which originate a cascading failure in interdependent graphs. We present here a self-consistent theory enabling the systematic analysis of cascading failures in such networks and encompassing a broad range of dynamical systems, from epidemic spreading, to birth-death processes, to biochemical and regulatory dynamics. We offer testable predictions on breakdown scenarios, and, in particular, we unveil the conditions under which the percolation transition is of the first-order or the second-order type, as well as prove that accounting for dynamics in the nodes always accelerates the cascading process. Besides applying directly to relevant real-world situations, our results give practical hints on how to engineer more robust networked systems.