Stability Analysis Research Articles

Generalization Guarantees of Gradient Descent for Shallow Neural Networks

Abstract Significant progress has been made recently in understanding the generalization of neural networks (NNs) trained by gradient descent (GD) using the algorithmic stability approach. However, most of the existing research has focused on one-hidden-layer NNs and has not addressed the impact of different network scaling. Here, network scaling corresponds to the normalization of the layers. In this article, we greatly extend the previous work (Lei et al., 2022; Richards & Kuzborskij, 2021) by conducting a comprehensive stability and generalization analysis of GD for two-layer and three-layer NNs. For two-layer NNs, our results are established under general network scaling, relaxing previous conditions. In the case of three-layer NNs, our technical contribution lies in demonstrating its nearly co-coercive property by utilizing a novel induction strategy that thoroughly explores the effects of overparameterization. As a direct application of our general findings, we derive the excess risk rate of O(1/n) for GD in both two-layer and three-layer NNs. This sheds light on sufficient or necessary conditions for underparameterized and overparameterized NNs trained by GD to attain the desired risk rate of O(1/n). Moreover, we demonstrate that as the scaling factor increases or the network complexity decreases, less overparameterization is required for GD to achieve the desired error rates. Additionally, under a low-noise condition, we obtain a fast risk rate of O(1/n) for GD in both two-layer and three-layer NNs.

Real-time analysis of liquid jet sample delivery stability for an X-ray free-electron laser using machine vision

Automated evaluation of optical microscopy images of liquid jets, commonly used for sample delivery at X-ray free-electron lasers (XFELs), enables real-time tracking of the jet position and liquid jet hit rates, defined here as the proportion of XFEL pulses intersecting with the liquid jet. This method utilizes machine vision for preprocessing, feature extraction, segmentation and jet detection as well as tracking to extract key physical characteristics (such as the jet angle) from optical microscopy images captured during experiments. To determine the effectiveness of these tools in monitoring jet stability and enhancing sample delivery efficiency, we conducted XFEL experiments with various sample compositions (pure water, buffer and buffer with crystals), nozzle designs and jetting conditions. We integrated our real-time analysis algorithm into the Karabo control system at the European XFEL. The results indicate that the algorithm performs well in monitoring the jet angle and provides a quantitative characterization of liquid jet stability through optical image analysis conducted during experiments.

Seismic Design of Underground Structures’ Vulnerability – Review.

This article examines the vulnerability of underground structures to seismic activity, with a particular focus on design and mitigation strategies. Underground buildings are essential to the development of modern infrastructure and must include tunnels, subway stations, and storage facilities. Because of its deep location, seismic design and earthquake performance are both more challenging. In this study of seismic susceptibility, topics such as ground motion characterization, soil-structure interaction, structural reaction, and failure mechanisms specific to underground structures are discussed. According to the paper, their susceptibility can be affected by geotechnical conditions, the kind of structures they have, and the construction methods that are used. The seismic stability design and analysis process involves measuring the dynamic response of subsurface structures to seismic loads. The goal is to keep earthquake and seismic forces from toppling structures in any way that is possible. Advanced analytical and numerical approaches are used in seismic stability design. Some examples of these methods are finite element analysis (FEA), discrete element modeling (DEM), and the boundary element method (BEM). In addition to that, it investigates contemporary methodologies for assessing seismic vulnerability as well as international design standards. In addition, seismic retrofitting and design advances for underground structures are analyzed and discussed in this paper. This document compiles and evaluates previous research to gain an understanding of the seismic susceptibility of subsurface structures and to promote more seismic engineering research on this extremely important topic.

Mixed Grass Species Enhances Root Production and Plant–Soil Reinforcement

ABSTRACTVegetation is a widely used eco‐friendly approach for slope reinforcement and ecological restoration. As a potential planting strategy, mixed planting of plants is often recommended to improve biodiversity, but the effects of mixed planting on soil reinforcement and slope stability are not yet clear. To address this issue, a study on two typical herbaceous slope protection plants, Chrysopogon zizanioides and Cynodon dactylon, were conducted. The biomechanical characteristics of different herbaceous plants were analyzed, and their root distribution and soil reinforcement performance under single and mixed planting were explored. Results show that mixed planting could significantly increase the number and root area ratio of root systems. At 0.1 cm depth after 42 days, the root number under mixed planting increased by 111.42% compared to vetiver grass monoculture and by 19.57% compared to bermuda grass monoculture. Mixed planting can provide stronger soil reinforcement by increasing apparent cohesion, with a maximum increase in apparent cohesion of 47.9%. The results of slope stability analysis showed that vegetation mainly relied on mechanical reinforcement in the root zone and hydrological reinforcement outside the root zone. After 42 days of growth, mixed planting at 0.1 m depth increased slope stability by 11.94% compared to vetiver grass monoculture and by 27.12% compared to bermuda grass monoculture, with both mechanical and hydrological effects of vegetation significantly enhanced. These findings suggest that mixed planting can promote plant development and growth, improve root production, and enhance plant–soil reinforcement and slope stability during the early establishment of vegetation. Therefore, in formulating slope reinforcement and ecological restoration strategies, more consideration can be given to mixed planting of plants, maximizing the utilization of competition characteristics between plants, and reducing the risk of shallow landslides while improving biodiversity.

Stability analysis of nanofluid with aluminum oxide and polyacrylamide for enhanced oil recovery: insight into experimental investigation

Stability analysis of nanofluid with aluminum oxide and polyacrylamide for enhanced oil recovery: insight into experimental investigation

Can isothermal plane Couette flow in fluid overlying porous layer be linearly unstable?

The present study aims to examine the temporal linear stability analysis of isothermal plane Couette flow over a porous layer using the two-domain approach. The flow in the porous layer is described by the unsteady Darcy–Brinkman equations, whereas it is characterised by the Navier–Stokes equations in the fluid layer. In contrast to the Darcy model, it is observed that the isothermal plane Couette flow becomes unstable for such a superposed system on the inclusion of the Brinkman term. From the stability analysis, the two-dimensional mode is found to be least stable, and two modes of instability, namely porous mode and mixed mode are obtained under the consideration of the Darcy–Brinkman model along with advection term (DBA model). For Darcy number $(\delta )=0.01$ , depending on the value of the stress-jump coefficient, mixed mode controls the instability of the system at small values of depth ratio $(\hat {d})$ , and it disappears for relatively high values of $\hat {d}$ , where the porous mode dominates. In addition, it has been observed that when $\hat {d}=0.1$ , the critical mode of instability is found to be mixed for $\delta >0.02$ and porous for $\delta \le 0.02$ . The stress-jump coefficient destabilises the flow in terms of energy production through perturbed stresses at the interface. As observed in the case of isothermal plane Poiseuille flow studied by Chang, Chen & Straughan (J. Fluid Mech., vol. 564, 2006, pp. 287–303), here also depth ratio (Darcy number) stabilises (destabilises) the flow. However, this characteristic does not remain valid when the advection term is eliminated from the considered momentum equation. For a certain range of $\hat {d} (\delta )$ , the destabilising (stabilising) characteristic of the respective parameters are encountered when the fluid mode of instability prevails.

Analysis of PH, foam stability, and antioxidant activity in soap formulation from extract of pedada leaves (Sonneratia caseolaris) and pandan leaves (Pandanus amaryllifolius)

Plant-based antioxidant soap formulations need to continue to be developed. Soap formulated from extracts of pedada leaves (Sonneratia caseolaris) and pandan leaves (Pandanus amaryllifolius) has been observed using 5-15 mL acetone or ethanol solvents for pedada leaf extraction, and extract concentrations of 0-40% and cocamide-DEA 2-8% for pandan leaves. The formulation results obtained from observing soap products from pedada leaf and pandan leaf extracts have pH, foam stability, antioxidant activity, and detergency power that comply with standards. Contour plot analysis for both formulations shows that the pH of the soap will decrease as the amount of solvent used decreases. Meanwhile, the addition of cocamide DEA increases the pH of liquid soap. Foam stability increases with increasing solvent amount but slightly decreases with the addition of cocamide-DEA.

An active queue management method for multiple bottleneck networks based on distributed average tracking

The active queue management (AQM) is a key technology for the information infrastructure and the Internet. The AQM for multiple bottleneck networks is especially challenging than that for single-bottleneck networks because the stability analysis of multiple bottleneck networks is more complex. In this paper, the active queue management problem for multiple bottleneck networks is considered. A novel random early detection algorithm is designed based on distributed average tracking technology, which is used to estimate the global queue length and improve the network's performance. Sufficient conditions for global asymptotic stability of the closed-loop active queue management system are presented, and some simulation results with NS-2 are given. Compared with the RED algorithm, simulation results show that the presented algorithm has smaller oscillations at routers, which highlights its effectiveness.

Static voltage stability analysis of integrated smart energy systems

The analysis of multi-energy flows forms the cornerstone for the study of state estimation, safety assessment, and optimization in integrated smart energy systems (ISES). The interactions between various energy flows and the inherent variability of renewable energy sources often lead to significant challenges to the static stability of ISES. This paper investigates the static voltage stability of ISES under multi-energy coupling conditions through multi-energy flow analysis in electric-gas-thermal energy systems. First, a steady-state model of the ISES is constructed by representing the interconnected energy subsystems as equivalent sources and loads in the power grid. Subsequently, through the coupling elements of ISES, the power flows of the natural gas system (NGS) and the district heating system (DHS) are converted into active power in the electrical power system (EPS), resulting in an equivalent power flow equation for the ISES. Then, using Brouwer’s fixed-point theorem, the analytical sufficient conditions for solving the equivalent power flow equation are derived. Finally, a simulation model based on MATLAB/Simulink is established. The steady-state criterion for ISES is obtained in this paper, and the correctness and effectiveness of the proposed conclusions are verified by the simulation results.

Quadratic Programming Problems and Its Solution Techniques With Neural Network Modeling

ABSTRACTThis paper presents a study on quadratic programming problems (QPP) and introduces a new neural network model with feasibility analysis. The stability analysis of QPP using neural network modeling is also discussed. The proposed neural network model has a simple form, and its optimal feasibility for both primal and dual QP problems is established. The model demonstrates a good convergence rate with a minimal number of iterations, achieving a very fast convergence to the exact solutions of both the primal and dual QP problems. The optimal solutions for the original QP problem and its dual QPP are obtained. Finally, two simple numerical examples are simulated to illustrate the findings.

Discontinuity Stability Analysis for Carbon Dioxide Enhanced Oil Recovery

Discontinuity Stability Analysis for Carbon Dioxide Enhanced Oil Recovery

Effect of rotation on wake vortices in stratified flow

Stratified wakes past an isolated conical seamount are simulated at a Froude number of $Fr = 0.15$ and Rossby numbers of $Ro = 0.15$ , 0.75 and $\infty$ . The wakes exhibit a Kármán vortex street, unlike their unstratified, non-rotating counterpart. Vortex structures are studied in terms of large-scale global modes, as well as spatially localised vortex evolution, with a focus on rotation effects. The global modes are extracted by spectral proper orthogonal decomposition (SPOD). For all three studied $Ro$ ranging from mesoscale, submesoscale and non-rotating cases, the frequency of the SPOD modes at different heights remains coupled as a global constant. However, the shape of the SPOD modes changes from slanted ‘tongues’ at zero rotation ( $Ro=\infty$ ) to tall hill-height columns at strong rotation ( $Ro=0.15$ ). A novel method for vortex centre tracking shows that, in all three cases, the vortices at different heights advect uniformly at approximately $0.9U_{\infty }$ beyond the near wake, consistent with the lack of variability of the global modes. Under system rotation, cyclonic vortices and anticyclonic vortices (AVs) present considerable asymmetry, especially at $Ro = 0.75$ . The vorticity distribution as well as the stability of AVs are tracked downstream using statistics conditioned to the identified vortex centres. At $Ro=0.75$ , intense AVs with relative vorticity up to $\omega _z/f_{c}=-2.4$ (where $\omega_z$ is the vertical vorticity and $f_c$ is the Coriolis frequency) are seen with small regions of instability and they maintain large $\omega _z/f_{c}$ magnitude in the far wake. Recent stability analysis that accounts for stratification and viscosity is found to improve on earlier criteria and show that these intense AVs are stable.

Nonperturbative phase boundaries in the Gross-Neveu model from a stability analysis

Two out of three phase boundaries of the 1+1-dimensional Gross-Neveu model in the chiral limit can be obtained from a standard, perturbative stability analysis of the homogeneous phases. The third one separating the massive homogeneous phase from the kink crystal is nonperturbative and could so far only be inferred from the full solution of the model. We show that this phase boundary can also be obtained via a modified stability analysis, based on the thermodynamic potential of a single kink or baryon. The same method works for the massive Gross-Neveu model, so that all phase boundaries of the Gross-Neveu model could have been predicted quantitatively without prior knowledge of the full crystal solution. Published by the American Physical Society 2024

Normalized acceleration based online tuning of variable-order fractional derivatives: a case study on quadcopter position control

In recent years, the use of Variable-Order (VO) fractional operators in control system design has been gaining popularity due to their adaptive nature, enabled by their dynamically adjustable fractional derivative and integral orders. This paper presents an online tuning method for adjusting the VO fractional derivatives in fractional controllers. The method is formulated to strategically accelerate or decelerate the system response's rate of change to enhance reference tracking and disturbance rejection performance while preserving closed-loop stability. It uses the normalised acceleration of the system response, a metric that provides insights into the ‘fastness’ or ‘slowness’ of the system response. The effectiveness of the proposed online tuning method is validated through a case study on quadcopter position control. Our research includes both simulation and real-time testing of Variable-Order Fractional PD (VOFPD) controllers, which utilise our online tuning method to adjust their fractional derivatives in real-time. Stability analysis via the D-decomposition method confirms that the quadcopter's closed-loop stability is preserved. Comparative results show significant improvements in reference tracking and disturbance rejection in terms of time-domain criteria.

Improving the stability of high-speed trains using an innovative passive yaw damper

Ensuring lateral stability is essential for achieving excellent operation safety and ride comfort of high-speed trains. However, complicated operational environments, particularly various wheel-rail contact geometries, would result in the occurrence of hunting instability. This study presents an innovative passive yaw damper to improve the stability of a high-speed train undergoing extreme wheel-rail contact conicities. A sensitivity analysis of the vehicle stability is first performed to demonstrate the importance of the dynamic stiffness of yaw dampers, promoting the application of the innovative damper. Experimental characterisation procedures enable the detailed investigation into the static and dynamic characteristics of the innovative damper, which are compared with those of conventional passive dampers to highlight the difference. To simulate the dynamic behaviour of the yaw damper, a numerical modelling method based on the Maxwell model is proposed. Using this method, the effectiveness of the innovative damper is assessed in terms of improving the vehicle stability at various wheel-rail conicities. The results show that the innovative yaw damper can ensure carbody stability at low conicity and bogie stability at high conicity, superior to conventional dampers, which fail to balance the vehicle stability at distinct conicities and usually result in hunting instability in specific wheel-rail contact states.

Robust reference gene selection in Norway spruce: essential for real-time quantitative PCR across different tissue, stress and developmental conditions

Accurate gene expression analysis in Norway spruce (Picea abies) under diverse stress conditions requires the identification of stable reference genes for normalization. Notably, the literature lacks reports on suitable reference genes in Norway spruce. Here, we aimed to address this gap by identifying suitable reference genes for quantitative real-time PCR in Norway spruce across various stress conditions (drought, heat, pathogen infection) in seedlings, tissues (needle, phloem, root), and developmental stages (seedlings, mature trees). We evaluated the stability of 15 candidate reference genes and assessed their expression stability using five statistical algorithms (ΔCt, geNorm, NormFinder, BestKeeper, and RefFinder). Our results highlight ubiquitin-protein ligase (SP1), conserved oligomeric Golgi complex (COG7), and tubby-like F-box protein (TULP6) as the most stable reference genes, while succinate dehydrogenase (SDH5) and heat shock protein 90 (HSP90) were the least stable under various experimental conditions. COG7 and TULP6 are novel candidate reference genes reported for the first time. The expression stability of the identified reference genes was further validated using dehydrin-like protein 5 (PaDhn5) under drought conditions in Norway spruce. Pairwise variation analysis suggests that two reference genes were sufficient to normalize gene expression across all sample sets. This study provides a comprehensive analysis of reference gene stability under different experimental conditions and a catalog of genes for each condition, facilitating future functional genomic research in Norway spruce and related conifers.

A mathematical model to study the role of dystrophin protein in tumor micro-environment.

In this research work, the authors have developed a mathematical model to examine the interaction between dystrophin protein and tumor. The authors formulated a system of ordinary differential equations to describe the dynamics of the dystrophin-tumor interaction system. Jacobian matrix and Routh-Hurwitz stability techniques were used to determine equilibrium points, perform stability and bifurcation analysis, and establish the conditions required for the stability of the proposed model. Numerical simulations are performed using Euler's method to investigate the temporal evolution of the proposed model under different parameter values, such as tumor growth rate and feedback strength of dystrophin protein. The numerical results are presented in tables, and corresponding to each table, a graphical analysis is done. The graphical analysis includes creating phase portraits to visually represent stability regions around the equilibrium points, bifurcation diagrams to identify critical points, and time series analysis to highlight the behavior of the proposed model. The authors explore how variations in dystrophin expression impact tumor progression, identifying potential therapeutic implications of maintaining higher dystrophin levels. This comprehensive analysis enhances our understanding of the dystrophin-tumor interaction, providing a basis for further experimental validation and potential therapeutic strategies.

AI-Powered Geotechnics: Enhancing Rock Mass Classification for Safer Engineering Practices

AbstractRock mass classification is fundamental for evaluating rock mass quality, essential for stability analysis and geotechnical design. Traditional classification methods are limited by joint observation technology, which typically gathers joint information from one-dimensional or two-dimensional perspectives, failing to comprehensively capture three-dimensional joint occurrences. This often necessitates empirical formulas for joint distribution, resulting in less precise joint parameter calculations. This paper reviews 44 seminal articles on rock engineering classification in construction and subterranean projects, tracing the evolution from foundational methods like Rock Quality Designation, Rock Mass Rating, Q-system, Basic Quality, and Hydropower Classification to contemporary techniques. It highlights the transformative impact of data science, particularly artificial intelligence, on rock engineering. The analysis reveals 73 distinct algorithms used 162 times in literature, with Support Vector Machines Support, Vector Regression, K-means clustering, K-Nearest Neighbors, Artificial Neural Networks and Random Forest being the most successful. This paper examines each method's advantage and limitations, discussing the challenges of algorithm deployment in the scientific community. The findings underscore the integration of machine learning and meta-heuristic optimization methods in rock engineering classification, offering valuable insights for future research and applications.

Transition to turbulence in hypersonic flow over a compression ramp due to upstream forcing

Several transition scenarios are present in a hypersonic compression-ramp flow. In our previous work (Cao et al., J. Fluid Mech., vol. 941, 2022, p. A8), a complete transition process induced by the global instability of a compression-ramp flow was revealed. In a globally stable flow, however, the transition to turbulence can be promoted by convective instabilities, which is the focus of this work. The same flow conditions as in our previous work (Mach number 7.7, Reynolds number $8.6\times 10^5$ based on the flat-plate length) are considered here. Owing to a smaller ramp angle, a weakly separated flow forms on the compression ramp, which supports no global instability. Resolvent analysis identifies low-frequency streamwise streaks as the optimal response of base flow to upstream forcing. Local stability analysis reveals Mack's second mode in the boundary layer downstream of reattachment. By introducing random disturbances upstream of separation in direct numerical simulations, we observe breakdown to turbulence downstream of reattachment. Two transition scenarios are revealed, and they are highly dependent on the amplitude of upstream disturbances. For a large amplitude, strong streamwise streaks develop near the reattachment region, which break down to turbulence quickly. However, when the disturbance amplitude is reduced, the second-mode instability dominates the transition to turbulence.

Finite-Time Partial Component Consensus for Nonlinear Leader-Following Multi-Agent Systems

The problem of finite-time partial component consensus (FTPCC) for first-order nonlinear multi-agent systems (MASs) is investigated in this paper for the first time. By incorporating the permutation matrix approach, we derive a novel error system for identical components, which facilitates stability analysis. Leveraging partial variable stability theory and related foundational knowledge, we devise two adaptable protocols. These protocols are tailored to achieve FTPCC in nonlinear MASs, one for systems without disturbances and another for those with bounded disturbances. To validate our findings, numerical examples are provided, demonstrating the effectiveness of the proposed results.