Nonlinear Threshold Research Articles

A state-dependent impulsive system with ratio-dependent action threshold for investigating SIR model

<abstract><p>In general, there is an imperative to amalgamate timely interventions and comprehensive measures for the efficacious control of infectious diseases. The deployment of such measures is intricately tied to the system's state and its transmission rate, presenting formidable challenges for stability and bifurcation analyses. In our pursuit of devising qualitative techniques for infectious disease analysis, we introduced a model that incorporates state-dependent transmission interventions. Through the introduction of state-dependent control, characterized by a non-linear action threshold contingent upon the combination of susceptible population density and its rate of change, we employ analytical methods to scrutinize various facets of the model. This encompasses addressing the existence, stability, and bifurcation phenomena concerning disease-free periodic solutions (DFPS). The analysis of the established Poincaré map leads us to the conclusion that DFPS indeed exists and maintains stability under specific conditions. Significantly, we have formulated a distinctive single-parameter family of discrete mappings, leveraging the bifurcation theorems of discrete maps to dissect the transcritical bifurcations around DFPS with respect to parameters such as $ ET $ and $ \eta_{1} $. Under particular conditions, these phenomena may give rise to effects like backward bifurcation and bistability. Through the analytical methodologies developed in this study, our objective is to unveil a more comprehensive understanding of infectious disease models and their potential relevance across diverse domains.</p></abstract>

The Impact of Dockless Bike‐Sharing and Built Environment on Ride‐Sourcing Trips

Understanding the factors influencing ride‐sourcing trips is crucial for enhancing the quality of personalized mobility and optimizing the allocation of transportation system resources. However, the nonlinear effects of dockless bike‐sharing (DBS) and the built environment (BE) across different spatiotemporal contexts have not been adequately addressed in previous research. This study aims to bridge this gap by analyzing order data and BE characteristics in Tianjin, China. Utilizing the Gradient Boosting Decision Tree (GBDT) model and Accumulated Local Effects (ALE) plots, this study explores the relative importance and nonlinear thresholds of these factors on ride‐sourcing trips. The findings reveal that DBS trips during weekday AM peak hours exert significantly negative effects on ride‐sourcing, whereas the impact during weekend AM peaks and daily PM peaks is positive. Furthermore, variables such as active population density, metro accessibility, and residential, entertainment, and cultural BEs have positive nonlinear impacts on ride‐sourcing trips. These insights offer policy implications and resource allocation recommendations for both government bodies and operators.

Chicken swarm optimization modelling for cognitive radio networks using deep belief network-enabled spectrum sensing technique.

Cognitive radio networks (CRN) enable wireless devices to sense the radio spectrum, determine the frequency state channels, and reconfigure the communication variables to satisfy Quality of Service (QoS) needs by reducing energy utilization. In CRN, spectrum sensing is an essential process that is highly challenging and can be addressed by several traditional techniques, such as energy detection, match filtering, etc. For now, the current models' performance is impacted by the comparatively low Signal to Noise Ratio (SNR) of recognized signals and the insignificant quantity of traditional signal samples. This research proposals a new spectral sensing technique for cognitive radio networks (SST-CRN) that addresses the drawbacks of predictable energy detection models. With the use of a deep belief network (DBN), the suggested model contributes to accomplish a nonlinear threshold based on the chicken swarm algorithm (CSA). The proposed DBN enabled SST-CRN technique goes through two phases in a organized process: offline and online. Throughout the offline phase, the DBN model is methodically trained on pre-gathered data, developing the aptitude to identify problematic patterns and examples from the spectral features of the radio environment. This stage involves extensive feature extraction, validation, and model development to ensure that the DBN can professionally represent complicated spectral dynamics. Additionally, online spectrum sensing is conducted during the real communication phase to enable real-time adaptation to dynamic changes in the spectrum environment. Offline spectrum sensing is typically performed during a devoted sensing period before actual communication begins. When combined with DBN's deep learning capabilities and CSO's innate nature-inspired algorithms, a synergistic framework is created that enables CRNs to explore and allocate incidences on their own with astonishing accuracy. The proposed solution considerably improves the spectrum efficiency and resilience of CRNs by harnessing the power of DBN, which leads to more effective resource utilization and less interference. The Simulation results show that our proposed strategy produces more accurate spectrum occupancy assessments. The result parameters such as probability of detection, SNR of -24dB, the SST-CRN perfect has increased a developed Pd of 0.810, whereas the existing methods RMLSSCRN-100 and RMLSSCRN-300 have accomplished a lower Pd of 0.577 and 0.736, respectively. Our deep learning methodology uses convolutional neural networks to automatically learn and adapt to dynamic and complicated radio environments, improving accuracy and flexibility over classic spectrum sensing approaches. Future research might focus on improving CSO algorithms to better optimize the spectrum sensing process, enhancing the reliability of DBN-enabled sensing techniques.

Experimentation and simulation study of electromechanical response characteristics of a 2-2 type cement-based piezoelectric composite sensor

In the manuscript, the piezoelectric functional element was prepared by slicing and adding method using piezoelectric ceramic PZT-5H and ordinary silicate cement 42.5 was as base materials, and then a 2-2 type cement-based piezoelectric composite sensor was prepared by an encapsulated epoxy resin. The experimental and simulation analysis was carried out to obtain the quasi-static linear sensitivity of the electromechanical response of the sample under conditions of compressive loading. The development process of the sample from local failure to overall fragmentation was observed using a high-speed camera. Found that the electrical nonlinear threshold of 35 MPa appeared before the mechanical nonlinear threshold. Further, the results showed that when the loading frequency was increased from 5 to 15 Hz under equal amplitude, the response waveform remained unchanged, however, the electrical displacement was attenuated by 19.7%. Packaging schemes using various lengths and thicknesses of an epoxy layer were conducted by using simulation. It is indicated that, under the premise of ensuring the protection package and considering the manufacturing process, the length of the package side could increase appropriately, and the single-side package side length is set to 4 mm. When the thickness of the package layer becomes less, it would be better.

How Does the Historic Built Environment Influence Residents’ Satisfaction? Using Gradient Boosting Decision Trees to Identify Critical Factors and the Threshold Effects

Historic cities, rich in heritage values and evocative of collective memories and meanings, also constitute crucial living environments for urban residents. These cities increasingly face challenges from urbanization and globalization, leading to cultural discontinuities and the homogenization of cityscapes. Such developments can diminish residents’ sense of belonging and identification with their cities. Emphasizing local residents’ satisfaction is thus essential to urban conservation. This study, using data from Dandong, China, employs Gradient Boosting Decision Trees (GBDT) to identify factors affecting residents’ satisfaction in historic built environments. The analysis reveals that over half of the variability in satisfaction is linked to distinct features of the historic environment. Among the fourteen key influencers identified, contextual order emerges as the most impactful factor, notable for its significant effects and interactions with other variables. This study also uncovers pronounced non-linear effects and thresholds for physically measured characteristics. For instance, open space markedly boosts satisfaction when exceeding 34%, satisfaction diminishes with travel times to heritage sites longer than 6.7 min, and satisfaction decreases when the entropy index for diversity surpasses 0.758. These findings provide critical insights for guiding urban conservation strategies and promoting a data-driven approach to enhance residents’ satisfaction in historic urban settings.

Nonlinear Effects in the Asymmetric Copula-Based Stochastic Frontier Model

Several stochastic frontier production analysis problems are not linear regression problems; two error components (inefficiency and noise) may not have symmetric dependence. In nonlinear problems, the data are divided into two or more regimes according to turning points or change points; the relationships between the output and all the inputs are allowed to differ between regimes. In the problem of two-error dependence, the inefficiency component generally plays a more dominant role than the noise component, thereby the output of each firm is mainly influenced by the inefficiency; in such cases, the symmetric dependence is not suitable. It is, therefore, desirable to come up with a new nonlinear asymmetric copula-based stochastic frontier model (SFM). Two nonlinear structures, namely kink and threshold and skew-normal copula, are suggested to SFM to deal with these problems. The Monte Carlo simulations and analysis of a real data set are employed to evaluate the accuracy and performance of proposed models. The results show that the proposed models show a higher performance when compared with the conventional linear SFM with symmetric two-error dependence.

Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium

We analyse a theory for thermal convection in a Darcy porous material where the skeletal structure is one with macropores, but also cracks or fissures, giving rise to a series of micropores. This is thus thermal convection in a bidisperse, or double porosity, porous body. The theory allows for non-equilibrium thermal conditions in that the temperature of the solid skeleton is allowed to be different from that of the fluid in the macro- or micropores. The model does, however, allow for independent velocities and pressures of the fluid in the macro- and micropores. The threshold for linear instability is shown to be the same as that for global nonlinear stability. This is a key result because it shows that one may employ linearized theory to ensure that the key physics of the thermal convection problem has been captured. It is important to realize that this has not been shown for other theories of bidisperse media where the temperatures in the macro- and micropores may be different. An analytical expression is obtained for the critical Rayleigh number and numerical results are presented employing realistic parameters for the physical values which arise.Article HighlightsA two-temperature regime for a bidisperse Darcy porous medium is proposed to study the thermal convection problem.The optimal result of coincidence between the linear instability and nonlinear stability critical thresholds is proven.Numerical analysis enhances that the scaled heat transfer coefficient between the fluid and solid and the porosity-weighted conductivity ratio stabilize the problem significantly.

The threshold value of ground motion acceleration characterizing the nonlinear response of sites

Assessing the nonlinearity of a site plays a crucial role in earthquake engineering. For some building structures and lifeline projects that need safety assessment after earthquakes, the analysis of nonlinear degree of sites can help accurately revealing the amplification effect of sites and evaluating the damage degree of buildings which is convenient for subsequent reinforcement and demolition work. The quantitation of nonlinear threshold of sites is an important method to evaluate the degree of site nonlinearity. In this paper, a nonlinear characteristic index reflecting the degradation of shear modulus is proposed based on the instantaneous frequency of the site calculated by using the vector auto-regression moving average (VARMA) model. Then, seismic records of class Ⅰ, Ⅱ, Ⅲ and Ⅳ sites specified as per code for seismic design of buildings in China are selected from the KiK-net network in Japan, and the threshold value of ground motion acceleration characterizing the nonlinear response of sites are provided. Finally, the variation of the nonlinear characteristic index (shear modulus degradation) vs. different (peak ground acceleration) PGA for four types of sites are presented.

Multipole engineering by displacement resonance: a new degree of freedom of Mie resonance

The canonical studies on Mie scattering unravel strong electric/magnetic optical responses in nanostructures, laying foundation for emerging meta-photonic applications. Conventionally, the morphology-sensitive resonances hinge on the normalized frequency, i.e. particle size over wavelength, but non-paraxial incidence symmetry is overlooked. Here, through confocal reflection microscopy with a tight focus scanning over silicon nanostructures, the scattering point spread functions unveil distinctive spatial patterns featuring that linear scattering efficiency is maximal when the focus is misaligned. The underlying physical mechanism is the excitation of higher-order multipolar modes, not accessible by plane wave irradiation, via displacement resonance, which showcases a significant reduction of nonlinear response threshold, sign flip in all-optical switching, and spatial resolution enhancement. Our result fundamentally extends the century-old light scattering theory, and suggests new dimensions to tailor Mie resonances.

Threshold response of ecosystem water use efficiency to soil water in an alpine meadow

Ecosystem water use efficiency (WUE) is a coupled index of carbon (gross ecosystem productivity, GEP) and water fluxes (transpiration, Tr or evapotranspiration, ET), reflecting how ecosystem uses water efficiently to increase its carbon uptake. Though ecosystem WUE is generally considered to decrease with increasing precipitation levels, it remains elusive whether and how it nonlinearly responds to extreme water changes. Here, we performed a 5-year precipitation halving experiment in an alpine meadow, combined with extremely interannual precipitation fluctuations, to create a large range of soil water variations. Our results showed that WUETr and WUEET consistently showed a quadratic pattern in response to soil water. Such quadratic patterns were steadily held at different stages of growing seasons, with minor changes in the optimal water thresholds (25.0–28.4 %). Below the water threshold, more soil water stimulated GEP but reduced Tr and ET by lowering soil temperature, resulting in a positive response of ecosystem WUE to soil water. Above the threshold, soil water stimulated GEP less than Tr (ET), leading to a negative response of ecosystem WUE to soil water. However, biological processes, including plant cover and belowground biomass as well as vertical root biomass distribution, had less effect on ecosystem WUE. Overall, this work is among the first to reveal the nonlinearity and optimal water thresholds of ecosystem WUE across a broad range of soil water, suggesting that future extreme precipitation events will more frequently surpass the water threshold and differently change the coupling relationships of carbon and water fluxes in alpine grasslands.

Fe3O4 microplate filled PEI matrix composite with remarkable nonlinear conductive characteristics, dielectric property, and low percolation threshold

As the presence of a percolating network formed by filler is indispensable for field grading composite, particulate fillers often result in high filler content that can be unfavorable in some aspects. The utilization of fillers with high aspect ratio is an effective way of reducing percolation threshold. In this work, Fe3O4 microplate (FMP) was prepared by a PVP-assisted hydrothermal method and it was adopted to fabricate composite films with different filler content by using polyetherimide (PEI) as the matrix. The composite film exhibited a percolation threshold of approximately 8 phr. The nonlinear coefficient measured 6.28 at a filler content of 10 phr. The nonlinearity in the conductive behavior of the composites was attributed to tunneling effect and Schottky emission. The filling of the FMP into PEI resulted in increase in dielectric constant and the dielectric loss maintained low. This study suggests that the FMP is a promising filler of low-filler-content field grading composite.

Effects of ablation velocity on ablative Rayleigh–Taylor instability

The influence of the ablation velocity Va on the evolution of single-mode ablative Rayleigh–Taylor instability from the linear to the deeply nonlinear phases is investigated via two-dimensional numerical simulations. Linear growth rates from simulations agree well with the asymptotic theory except for larger discrepancies in the intermediate Froude number regime. The weakly nonlinear growth behavior of the bubble amplitude is found dependent on a critical perturbation wavenumber in a broad Froude number regime. For a linearly stable mode, its nonlinear excitation threshold is higher for larger Va and thus harder to be exceeded. For short-wavelength modes taking significant ablation effects, the bubble penetration velocity is found to reaccelerate after the first saturation and eventually saturate at a larger value with larger Va, due to stronger vortex-acceleration effects and more significant increase in g.

Book-ahead ride-hailing trip and its determinants: Findings from large-scale trip records in China

The cruising of ride-hailing vehicles generates negative externalities such as traffic congestion and vehicular emissions. These externalities can be mitigated by reducing cruising driving via operating book-ahead ride-hailing services, where the platform dispatches and routes drivers based on precise information on travelers’ departure time and origin–destination (OD). However, the effects of factors influencing book-ahead ride-hailing trips have rarely been empirically examined with real data. Using six-month trip data from China, this study employs a gradient boosting decision tree (GBDT) method with hyperparameters optimized by the Bayesian optimization algorithm to examine the factors associated with book-ahead ride-hailing trips across OD pairs (hexagon cells-to-hexagon cells) at various spatial scales. The relative importance rankings generated from this study indicate that trip features, weather conditions, and accessibility to transportation hubs are significant determinants correlated with the usages of book-ahead ride-hailing. The partial dependence plots demonstrate the nonlinear threshold effects of these determinants on the hourly number of book-ahead ride-hailing per OD pair. Moreover, this study compares the differences in associations between peak and non-peak hours as well as weekdays and weekends. The disparity in the nonlinear threshold effects between weekdays and weekends is only observable during the evening peak period and not at other times. These findings provide valuable insights into developing practical strategies for promoting book-ahead ride-hailing services.

Prediction of survival in patients with infected pancreatic necrosis: a prospective cohort study.

Infected pancreatic necrosis (IPN) is a severe complication of acute pancreatitis, with mortality rates ranging from 15 to 35%. However, limited studies exist to predict the survival of IPN patients and nomogram has never been built. This study aimed to identify predictors of mortality, estimate conditional survival (CS), and develop a CS nomogram and logistic regression nomogram for real-time prediction of survival in IPN patients. A prospective cohort study was performed in 335 IPN patients consecutively enrolled at a large Chinese tertiary hospital from January 2011 to December 2022. The random survival forest method was first employed to identify the most significant predictors and capture clinically relevant nonlinear threshold effects. Instantaneous death risk and CS was first utilized to reveal the dynamic changes in the survival of IPN patients. A Cox model-based nomogram incorporating CS and a logistic regression-based nomogram were first developed and internally validated with a bootstrap method. The random survival forest model identified seven foremost predictors of mortality, including the number of organ failures, duration of organ failure, age, time from onset to first intervention, hemorrhage, bloodstream infection, and severity classification. Duration of organ failure and time from onset to first intervention showed distinct thresholds and nonlinear relationships with mortality. Instantaneous death risk reduced progressively within the first 30 days, and CS analysis indicated gradual improvement in real-time survival since diagnosis, with 90-day survival rates gradually increasing from 0.778 to 0.838, 0.881, 0.974, and 0.992 after surviving 15, 30, 45, 60, and 75 days, respectively. After further variables selection using step regression, five predictors (age, number of organ failures, hemorrhage, time from onset to first intervention, and bloodstream infection) were utilized to construct both the CS nomogram and logistic regression nomogram, both of which demonstrated excellent performance with 1000 bootstrap. Number of organ failures, duration of organ failure, age, time from onset to first intervention, hemorrhage, bloodstream infection, and severity classification were the most crucial predictors of mortality of IPN patients. The CS nomogram and logistic regression nomogram constructed by these predictors could help clinicians to predict real-time survival and optimize clinical decisions.

Multi-order analytical solving computation of rainstorm causal decomposition during typhoons using a designed key–lock quasi-Newton optimizing derivation

To precisely identify multi-dimensional spatiotemporal rain-making parameters, generate an approximate Hessian matrix, and solve the nonlinear ill-posed problem, this study uses composite logical tangent hyperbolic functions to construct the rain-generating simulation model as nonlinear algebraic equations with designed key–lock quasi-Newton optimization for deriving multi-order objective functional derivatives for rainstorm causal decomposition into advanced functional, analytical solution (lock) and Newton's conditional constraints. Specifically, the rank-two approximate structure of the Levenberg–Marquardt and Broyden–Fletcher–Goldfarb–Shanno quasi-Newton algorithms are modified as the symmetric rank-four structure to efficiently calculate a positive definite stable Hessian and solve the constrained nonlinear rain-making threshold. The model projects various rain-making factors into multi-rank loading scores, characterizing rain-generating mechanisms and causal components as associated DNAs. To accelerate/modify directional convergence, avoid local minimum, and detect global optimum, the devised vectorized limited switchable step sizes are optimized using advanced double-bracketing approaches combined with candidate parameters' correction vectors (key) and referenced step-size distributions solved by Newton's constrained analytical solution to reduce heterogeneous differences and eliminate the conventional overestimated Hessian. The identified rain-making DNAs reveal that typhoons with similar DNAs move in similar directions. Specifically, rain-making DNAs in Taipei Category 1 were correlated with wind force/direction and cloud height along PCs 1, 3, 4, and 7, and those in Category 2 were correlated with cloud-cover distribution along PCs 1, 2, and 5. The identified rain-making thresholds of typhoons with constant direction/structure showed a weaker steady state, whereas the unsteady rest produced multi-peak rainfall hydrographs. Rain evolution analysis reveals that cloudy rainbands, carried by the wind field, move along the Tamsui River valley when traveling between northeast and south-southeast of Taipei; converge with gradient and geostrophic winds when traveling between east-northeast and southwest; merge with southwest monsoon when traveling between west-southwest and northeast of Kaohsiung.

Exploring the nonlinear effect of shadow economies on sustainable development in Africa: does the level of financial market development matter?

PurposeThis study aims to examine the nonlinear threshold effect of shadow economy on sustainable development in Africa while providing additional evidence on how this nonlinear threshold effect play out in economies with high and low developed financial/credit markets.Design/methodology/approachThis study uses 37 African economies between 2009 and 2017 in a dynamic GMM panel model that controls for country, year and technological effects to ensure consistency and reliability of results and findings.FindingsThe results reveal that there is an inverted nonlinear U-shape nexus between the size of shadow economy and sustainable development in both short run and long run in Africa and across economies with high and low developed credit/financial market. Also, the threshold points beyond which the size of shadow economies dampens sustainable development is lower for economies with high financial/credit market development and higher in the long run.Practical implicationsThese results have policy implications and recommendations and suggest that shadow economies can be beneficial to sustainable development particularly when the size of shadow economies are restrained from increasing beyond certain thresholds/levels. Moreso, to restrict the adverse effect of shadow economies on sustainable development, policymakers can rely on developing their financial/credit markets to tame the destructive nature of shadow economies on sustainable development. These results are robust to technological, year/time and country effects.Originality/valueTo the best of the author’s knowledge, this study examines for the first in the context of Africa, the nonlinear effect of shadow economies on sustainable development under low and high developed financial markets.

What Affects Bus Passengers’ Travel Time? A View from the Built Environment and Weather Condition

The study aims to examine the impact of the built environment and weather conditions on travel time for bus passengers in Weinan, China. Various sources of data, including smart card data, bus GPS data, bus station data, road information data, and smart card swiping time, were integrated and analyzed. The study employed the light gradient boosting machine (LightGBM) model and SHapley Additive exPlanations (SHAP) value to assess the feature importance and nonlinear effects of different types of POI density, weather conditions, and time series on bus passengers’ travel time. The study findings indicate that several factors are associated with bus passengers’ travel time, including destination residential density, destination diversity, destination life service density, origin science and education density, origin residential density, origin diversity, humidity, visibility, boarding time between 7 and 8 a.m., and precipitation. This study also reveals nonlinear threshold effects. The study findings provide valuable insights that can be utilized to optimize the bus network and develop low-carbon-oriented land-use planning.

Temperature dependence of the properties of the Li0.81Ag0.19InSe2 nonlinear crystal

The factors that determine the prospects of a crystal for frequency conversion of laser radiation in a wide range to the mid and far infrared (IR) ranges are nonlinear parameters and laser damage threshold (LDT). The latter is determined by the band gap and thermophysical characteristics. This work was devoted to studying the features of the structure change of the Li0.81Ag0.19InSe2 crystal in the temperature range 90–490 K. The temperature dependences of the thermal expansion coefficients, dispersion and optical characteristics in this range were studied. A relationship between the temperature change in the structure and other parameters has been established. In Li0.81Ag0.19InSe2 crystals, pyroluminescence was observed during heating or cooling in the range of 100–300 K, which indicates the crystal is attributed to pyroelectrics. The dispersion characteristics (nx, ny and nz) for wavelengths of 2 and 7 μm were studied, the values of birefringence Δn (nz - nx) were calculated in the temperature range 300–500 K. The detected fluctuations of Δn in the temperature range from 300 to 478 K may be associated with structural changes.

Thermorefractive noise reduction of photonic molecule frequency combs using an all-optical servo loop.

Phase and frequency noise originating from thermal fluctuations is commonly a limiting factor in integrated photonic cavities. To reduce this noise, one may drive a secondary "servo/cooling" laser into the blue side of a cavity resonance. Temperature fluctuations which shift the resonance will then change the amount of servo/cooling laser power absorbed by the device as the laser moves relatively out of or into the resonance, and thereby effectively compensate for the fluctuation. In this paper, we use a low noise laser to demonstrate this principle for the first time in a frequency comb generated from a normal dispersion photonic molecule micro-resonator. Significantly, this configuration can be used with the servo/cooling laser power above the usual nonlinearity threshold since resonances with normal dispersion are available. We report a 50 % reduction in frequency noise of the comb lines in the frequency range of 10 kHz to 1 MHz and investigate the effect of the secondary servo/cooling noise on the comb.

The Impact of Banking Competition on Bank Financial Stability: Evidence from ASEAN 5 Countries

In the era of the global economy, increasing banking competition will encourage an increase in banking transactions and activities. Banking transactions and activities will affect a country's financial stability. The purpose is to obtain the nonlinear effect of banking competition on financial stability at a specific regime. Previous research assumed that this impact applies to every economic regime. The impact of banking competition on financial stability can change at certain regime levels. Nonlinear impact occurs according to the regime. The method is based on a nonlinear threshold regression model. The researchers obtained the data from five ASEAN countries. The findings of this research are in-depth information about the financial system stability model. Analysis of the effect of variance supports the inconsistency of the effects found by several previous researchers. Practical implications are aimed at policymakers to make different decisions at the GDP level, CAR and Liquidity. The economic regime in each country is different, so this analysis is constructive for policymakers to see the conditions of banking competition and financial system stability at a certain regime level. The originality article systematically offers an analysis that assumes the effect can change at a certain regime level.JEL Classification: E5, G15, G01, G32, C24