Nonlinear Unit Research Articles

Investigation of Validity Purchasing Power Parity Hypothesis for Turkey: Non-Linear Unit Root Test

Tek fiyat kanunu, satın alma gücü paritesinin temel çerçevesini oluşturur. Satın alma gücü paritesi hipotezinin geçerliliği literatürde halen tartışılmaktadır. Bu çalışma, Türkiye için satın alma gücü paritesi hipotezinin yapısal kırılmalar ve doğrusal olmama koşullarında geçerliliğini incelemektedir. Bu hipotez zaman serisi birim kök sınamaları kullanılarak 2013-2023 dönemi için test edilmiştir. Çalışmada reel döviz kuru verileri kullanılmaktadır ve bu veriler TCMB'den elde edilmiştir. ADF, DF-GLS, Ziwot- Andrews, Lee-Strazicich ve ESTAR birim kök sınamalarına çalışmada yer verilmiştir. Çalışma sonucunda elde edilen bulgu, satın alma gücü paritesi hipotezinin Türkiye için geçerli olduğunu göstermektedir.

Flood prediction using nonlinear instantaneous unit hydrograph and deep learning: A MATLAB program

In this study, we developed a MATLAB program for flood prediction in a watershed. The program consists of three modules. The instantaneous unit hydrograph (IUH) generation module utilizes a power-law based interpolation method to generate IUHs. The generated IUH is a function of the rainfall excess intensity and therefore considers nonlinearity. The long short-term memory (LSTM) module employs “lstmLayer” from the MATLAB deep learning toolbox to predict total rainfall excess; this is then used to estimate the curve number (CN) value for each flood event. The LSTM module uses a land surface modeling dataset and rainfall-runoff data as inputs. The flood hydrograph generation module calculates effective rainfall hyetographs and then predicts flood hydrographs using a convolution integration. A detailed description of the program is provided along with an application example for real watersheds. The application results demonstrated that our program can be effectively used for flood prediction in practice, particularly for large flood events.

In-sensor nonlinear convolutional processing based on hybrid MTJ/CMOS arrays

In-sensor computing implemented by novel neuromorphic devices has been regarded as the potential technology to break the acquisition wall. Moreover, the nonlinear convolution inspired by the biological neural system outperforms the traditional linear convolution. Therefore, realizing the in-sensor nonlinear convolutional processing with the intrinsic nonlinearity of novel neuromorphic devices would be exciting and hardware friendly. Here, a new type of in-sensor nonlinear convolutional processing architecture is proposed based on STT-MTJ (spin transfer torque-magnetic tunnel junction) devices and simple peripheral circuits. The nonlinear dynamic characters of the STT-MTJ device are regulated by bias currents and magnetic fields. Meanwhile, the hybrid STT-MTJ/CMOS (complementary metal oxide semiconductor) circuit exhibits nonlinear dependence of the output voltage on bias currents and magnetic fields. In this way, a nonlinear convolutional unit is developed by the inherent property of hardware. Based on the in-sensor nonlinear convolutional unit, a convolutional network is simulated to perform the classification task, and a high accuracy is realized. This work indicates that the in-sensor nonlinear convolution offers a promising way to develop in-sensor computing at the edge intelligence devices.

Linear and nonlinear analysis for testing the hysteresis hypothesis in Türkiye

Unemployment is an important socioeconomic problem. Economic shocks especially affect the economies of developing countries negatively. The hysteresis hypothesis expresses the view that temporary shocks can have a permanent effect on unemployment rates. The hysteresis hypothesis can be considered as an objection to the natural rate hypothesis. From a unit root perspective, if the series contain a unit root, hysteresis hypothesis is valid. If not, hysteresis hypothesis is not valid. This study aims to test the hysteresis hypothesis by using data covering the period of 2014M01-2023M07 in the Turkish economy. In the study, general unemployment and youth unemployment rates have been discussed. Some of the most commonly used linear and nonlinear unit root tests in applied studies have been included in the study in order to make comparisons. By detecting that the series are nonstationary according to linear and nonlinear unit root tests, it can be inferred that hysteresis hypothesis is valid in Türkiye. This shows that the effects of shocks are permanent. Effective policies against unemployment need to be developed.

Distributed scheduling for multi-energy synergy system considering renewable energy generations and plug-in electric vehicles: A level-based coupled optimization method

Multi-energy synergy systems integrating high-penetration large-scale plug-in electric vehicles, distributed renewable energy generations, and battery energy storage systems have great potential to reduce the reliance of the grid on traditional fossil fuels. However, the random charging characteristics of plug-in electric vehicles and the uncertainty of photovoltaics may impose an additional burden on the grid and affect the supply–demand equilibrium. To address this issue, judicious scheduling optimization offers an effective solution. In this study, considering charge and discharge management of plug-in electric vehicles and intermittent photovoltaics, a novel Multi-energy synergy systems scheduling framework is developed for solving grid instability and unreliability issues. This formulates a large-scale mixed-integer problem, which calls for a powerful and effective optimizer. The new binary level-based learning optimization algorithm is proposed to address nonlinear large-scale high-coupling unit commitment problems. To investigate the feasibility of the proposed scheme, numerical experiments have been carried out considering multiple scales of unit numbers and various scenarios. Finally, the results confirm that the proposed scheduling framework is reasonable and effective in solving unit commitment problems, can achieve 3.3% cost reduction and demonstrates superior performance in handling large-scale energy optimization problems. The integration of plug-in electric vehicles, distributed renewable energy generations, and battery energy storage systems is verified to reduce the output power of 192.72 MW units during peak periods to improve grid stability. Therefore, optimizing energy utilization and distribution will become an indispensable part of future power systems.

A new fractional integration approach based on neural network nonlinearity with an application to testing unemployment hysteresis

This paper proposes a nonlinear fractional unit root approach which is known as the autoregressive neural network–fractional integration (ARNN–FI) test. This new fractional integration test is based on a new multilayer perceptron of a neural network process, proposed in Yaya et al. (Oxf Bull Econ Stat 83(4):960–981, 2021). The asymptotic theory and the properties of the proposed test are given. By setting up a Monte Carlo simulation experiment, the simulation results reveal that as the number of observations increases, size and power distortions would disappear in the test. The empirical application based on this new test reveals that the unemployment rates of three European countries are neither stationary nor mean-reverting in line with the hysteresis hypothesis.

Application of S-transform-based nonlinear processing for accurate LIBS quantitative analysis of iron ore slurry.

Real-time Fe content monitoring in iron ore slurry is crucial for evaluating concentrate quality and enhancing mineral processing efficiency. Laser-induced breakdown spectroscopy (LIBS) is a promising technique for the online monitoring of elemental content at industrial sites. However, LIBS measurements are hampered by the matrix effect and the self-absorption effect, limiting the precision of linear analytical processes. To overcome this, we propose to introduce a nonlinear processing unit based on the S-transform to incorporate nonlinearity into the data analysis process. This approach integrates a feature selection unit based on the spectral distance variable selection method (SDVS), a nonlinear processing unit based on the S-transform (ST), and a partial least squares regression model (PLS). To demonstrate the improvement in accuracy achieved through nonlinear processing, a comparative analysis involving five models, Raw-PLS, SDVS-PLS, ST-PLS, SDVS-ANN, and SDVS-ST-PLS, is conducted. The results reveal a significant improvement in the performance of the SDVS-ST-PLS model, effectively facilitating the successful application of the LIBSlurry analyzer to the mineral flotation process.

Experimental surface runoff hydrographs from linear impervious subcatchments for rainfalls of extremely high intensity

This study focuses on lab-scale experimental runoff hydrographs from a linear completely impervious plane subcatchment. An improved method of surface runoff physical modelling was developed, allowing for expanded laboratory hydrograph simulations up to a linear scale of 10. Model rains of different intensities and durations were applied, and digital online data processing techniques were employed to ensure high time resolution and accurate flow rate determination. The experimental hydrographs were analyzed in a dimensionless form to facilitate generalization and comparison with widely used nonlinear reservoir method and unit hydrograph method. Wave-like fluctuations of the flow rate were observed in most experimental hydrographs as they approached the maximum runoff. The dimensionless phase time of the experimental hydrographs showed an increasing trend with higher rainfall intensity, and a power-law equation was derived to approximate this relationship. An averaged dimensionless runoff hydrograph was obtained by processing individual hydrographs, and it was approximated by the DR-Hill-Zerobackground model for the initial stage during the rainfall and by the Weibull model for the later stage, after the rainfall stopped. The findings of this study have significant implications for modelling surface runoff from small urban subcatchments, particularly under critical rainfall events with extremely high intensity.

Microdisk modulator-assisted optical nonlinear activation functions for photonic neural networks

On-chip implementation of optical nonlinear activation functions (NAFs) is essential for realizing large-scale photonic neural chips. To improve the reconfigurability and enrich the functions of photonic neural network (PNN), an NAF unit with a unique capability of performing multiple types of NAFs is highly preferred. In this work, we propose and experimentally demonstrate a microdisk modulator (MDM)-assisted NAF unit, in which multiple types of electro-optic NAFs with a high response speed and multiple types of all-optical NAFs with a low latency and reduced power consumption are performed in a single device. The fabricated MDM has an add-drop configuration, in which a lateral PN junction is incorporated to achieve high-speed resonance wavelength tuning. With the use of the high-speed nonlinear electro-optic effect, three different kinds of electro-optic NAFs including sigmoid function, radial basis function (RBF), and negative rectified linear unit (ReLU) function are realized by exploiting the free-carrier dispersion effect on silicon. Moreover, thanks to the strong optical confinement in the disk cavity, all-optical NAFs can be performed by exploiting the thermo-optic effect on silicon. In the experiment, four different kinds of all-optical NAFs including softplus function, RBF, clamped ReLU function, and leaky ReLU function are demonstrated. With the use of the realized clamped ReLU function, a convolutional neural network is simulated to perform a handwritten digit classification benchmark task, and an accuracy as high as 98 % is demonstrated. Thanks to its strong electro-optic and thermo-optic effects, the proposed MDM provides a unique capability of performing multiple types of electro-optic and all-optical NAFs, which is potential to be served as a flexible nonlinear unit in large-scale PNN chips.

Linear Quadratic Optimal Robust Multivariable Proportional-Integral Control Design for a Boiler-Turbine Unit

Abstract Boiler-turbine unit is a highly nonlinear, coupled, and ill-conditioned system. Moreover, the presence of physical constraints, such as actuator magnitude and rate limits, makes the system difficult to control. This paper employs a fixed multivariable proportional-integral (PI) controller of the I–P structure for robust linear quadratic (LQ) compensation of a nonlinear boiler-turbine benchmark. In order to ensure that a single PI controller works for the whole operating region of this nonlinear system, the linearized model of the system is represented as a norm-bounded, time-varying uncertain system. The ranges of the uncertain parameters of this linearized model are determined from different operating points of the nonlinear system. To design the PI controller for the uncertain system, first, it is transformed into a state feedback design for an augmented uncertain system and then the state feedback gains satisfying some LQ performance limit are computed by solving a linear matrix inequality (LMI) problem. As the uncertainty in the feedforward matrix of the linearized model cannot be considered in the above design process, an LMI-based method is developed to check if the designed PI controller performance in H∞ sense is close to the one if the neglected uncertainty is included. The performance of the controller is tested on the nonlinear boiler-turbine unit under several operating conditions and physical constraints. Comparisons are also made with some existing PI controllers, to show the superiority of the proposed robust PI controller.

Analyzing the efficient market hypothesis with asymmetric persistence in cryptocurrencies: Insights from the Fourier non-linear quantile unit root approach

We test the efficient market hypothesis (EMH) in Bitcoin (BTC) and Ethereum (ETH) using the further Fourier nonlinear quantile (FNQKS) unit root test by Bahmani-Oskooee et al. (2020). While conventional tests support EMH in the cryptocurrency market, the FNQKS unit root test does not support EMH. Considering non-linearity, Fourier breaks, and non-normal distribution in BTC and ETH exhibit asymmetric persistence. This allows investors to make adjustments to their portfolios in response to both negative and positive shocks.

Wave propagation in mass-in-mass Duffing type non-linear metamaterial implementing Jacobi’s elliptic balance method

A comprehensive strategy for computing the dispersion relationship of a nonlinear metamaterial having Duffing-type cubic nonlinearity at the attached oscillator is presented in this paper. Jacobi’s elliptic balance method is implemented to obtain the steady-state response of the non-linear metamaterial unit cell. An ingenious approach of defining the force term in equation motion not only reduces the system to a simplified uncoupled form but also facilitates the incorporation of the effect of amplitude dependency. Furthermore, the dispersion relationship can conveniently be obtained by applying Bloch’s theorem. Under undamped conditions, the precise response of both the inner and outer mass of the nonlinear metamaterial is determined; whereas, a set of algebraic nonlinear equations is established and numerically solved for the damped system. The attenuation band shifts to the higher frequency range with increasing nonlinearity and excitation amplitude. The effect of excitation amplitude is predominant as compared to the nonlinearity of the spring in altering the dispersion plots. As damping increases, the sharp attenuation drop becomes blunt, and further increment of damping leads to the resonator and outer mass oscillating in nearly perfect harmony and thereby causing the dispersion plots to resemble those of a monoatomic chain.

Poverty and financial development: an asymmetric and nonlinear ARDL analysis for India

PurposeThe primary objective of the paper is to examine the asymmetric Cointegration and asymmetric causality between financial development and poverty alleviation on annual data in Indian context over the period from 1980 to 2019.Design/methodology/approachFirst nonlinearity test by Brooks et al. (1999) is applied to ascertain the nonlinear behavior of the variables used. Once the nonlinear behavior of variables is confirmed, asymmetric and nonlinear unit root tests by Kapetanios and Shin (2008) are applied to check for the order of integration of selected variables. Next, nonlinear autoregressive distributed lag model (NARDL) is employed to analyze the asymmetric Cointegration. Finally, Hatemi-j- asymmetric causality tests is applied to work out the direction of asymmetric causality.FindingsThe empirical findings document the existence of asymmetries in the short-run as well as long-run between poverty and financial development. The asymmetry reveals that negative financial development shocks leave a more profound impact on poverty alleviation than their positive equivalents. The findings of Wald's test also confirm the presence of asymmetric Cointegration. The asymmetric cumulative dynamic multipliers used to examine the behavior of asymmetries and adjustments with respect to time lend credence to the results calculated using NARDL estimator. This result exhibits the robustness of the model. Furthermore, the result emanating from recently introduced asymmetric causality test reveals a unidirectional asymmetric causality between negative shocks in financial development and poverty. The findings of the present study necessitate the need for investigating asymmetric and nonlinear effects in finance–poverty nexus, which existent literature has completely neglected, in order to have relevant policy conclusions.Research limitations/implicationsThe study used “Per capita consumption expenditure” as a measure for poverty due to lack of continuous time series data on headcount ratio. In future, researchers can extend this study by incorporating headcount ratio as a measure of poverty in their respective works. There is further scope of research on this issue by finding out the impact of formal and informal sources of credit on poverty separately. A panel data study for developing countries over a period of time could further confirm/negate the findings of the present study.Originality/valueTo the best of the authors’ knowledge none of the studies in Indian context has scrutinized asymmetric and nonlinear impact of financial development on poverty. To dredge up asymmetric structures at work, the authors have used the highly celebrated NARDL estimator. To enrich the existent body of knowledge along the lines of asymmetric (nonlinear) linkages, the authors have also used recently introduced asymmetric causality test by Hatemi-j-(2012) to find out the direction asymmetric causality.

Generalization of Auto-Regressive Hidden Markov Models to Non-Linear Dynamics and Unit Quaternion Observation Space

Generalization of Auto-Regressive Hidden Markov Models to Non-Linear Dynamics and Unit Quaternion Observation Space

A Split-Frequency Filter Network for Hyperspectral Image Classification

The intricate structure of hyperspectral images comprising hundreds of successive spectral bands makes it challenging for conventional approaches to quickly and precisely classify this information. The classification performance of hyperspectral images has substantially improved in the past decade with the emergence of deep-learning-based techniques. Due to convolutional neural networks’(CNNs) excellent feature extraction and modeling, they have become a robust backbone network for hyperspectral image classification. However, CNNs fail to adequately capture the dependency and contextual information of the sequence of spectral properties due to the restrictions inherent in their fundamental network characteristics. We analyzed hyperspectral image classification from a frequency-domain angle to tackle this issue and proposed a split-frequency filter network. It is a simple and effective network architecture that improves the performance of hyperspectral image classification through three critical operations: a split-frequency filter network, a detail-enhancement layer, and a nonlinear unit. Firstly, a split-frequency filtering network captures the interactions between neighboring spectral bands in the frequency domain. The classification performance is then enhanced using a detail-improvement layer with a frequency-domain attention technique. Finally, a nonlinear unit is incorporated into the frequency-domain output layer to expedite training and boost performance. Experiments on various hyperspectral datasets demonstrate that the method outperforms other state-of-art approaches (an overall accuracy(OA) improvement of at least 2%), particularly when the training sample is insufficient.

Hierarchical unit cell employing a nonlinear energy sink for passive, low-pass amplitude filtering of acoustic waves

In this letter we present a hierarchical unit cell incorporating a nonlinear energy sink (NES) that functions as a low-pass amplitude filter. The hierarchical unit cell is composed of an outer and inner mass coupled by essentially nonlinear springs. Other than its nonlinear coupling to the outer mass, the inner mass is otherwise unconstrained and thus acts as an NES. Using numerical simulations, we show that the nonlinear unit cell passively filters incident waves as a function of their amplitude. The resonator is inactive at low amplitudes, permitting waves to pass. At high amplitudes, the NES activates and its resonant behavior reflects incident waves. Consequently, the unit cell effectively operates as an amplitude limiter for specific signal frequency and amplitude ranges. Notably, the passing of low-amplitude incident energy while bypassing the nonlinearity results in very little distortion in transmitted signals. We analytically investigate this behavior further using a harmonic balance method. The analysis supports the transmission filtering behavior as well as the activation of the nonlinear energy sink. Lastly, we design and construct the nonlinear unit cell and perform tests using incident and transmitted waveguides composed of monatomic chains. Both the nonlinear unit cell and monatomic chains are assembled using steel masses and additively-manufactured springs. We test the fabricated filter using low and high amplitude signals and observe amplitude filtering at various excitation frequencies that document strong agreement with numerical simulations and the analytical model. The ability to passively reflect high amplitude waves, and transmit low amplitude waves with minimal distortion, may inspire new devices for hearing protection, or for isolating and protecting sensitive equipment and instruments.

Low-threshold all-optical nonlinear activation function based on injection locking in distributed feedback laser diodes.

We experimentally demonstrate an all-optical nonlinear activation unit based on the injection-locking effect of distributed feedback laser diodes (DFB-LDs). The nonlinear carrier dynamics in the unit generates a low-threshold nonlinear activation function with optimized operating conditions. The unit can operate at a low threshold of -15.86 dBm and a high speed of 1 GHz, making it competitive among existing optical nonlinear activation approaches. We apply the unit to a neural network task of solving the second-order ordinary differential equation. The fitting error is as low as 0.0034, verifying the feasibility of our optical nonlinear activation approach. Given that the large-scale fan-out of optical neural networks (ONNs) will significantly reduce the optical power in one channel, our low-threshold scheme is suitable for the development of high-throughput ONNs.

Modelling and control of nonlinear compressor unit in biohydrogen plant using multivariable model predictive control (MMPC)

Biohydrogen plants consist of several units, one of them is the compressor unit. The compressor unit serves to increase the pressure needed for the next processing unit. In real conditions, several disturbances may occur in the process, affecting the stability of the system. Therefore, process control is needed for this system. Co-simulation is done by integrating Aspen plus dynamics for the nonlinear model of the compressor unit and MATLAB/Simulink for the control system model and mathematical calculation. Multivariable model predictive control (MMPC) is considered to control the system of the compressor unit. Three MPC parameters such as sampling time (Ts), prediction horizon (P), and control horizon (M) are set to 0.5, 50, and 30 seconds. The co-simulation gives various results. The highest overshoot is 19.6278 kPa in CV3 when SP on CV1 changed. The longest settling time occurred in CV4 when SP in CV4 was changed, 47.2729 seconds. The highest IAE is 14.8831, which occurred in CV4 when the SP of CV4 changed, and ISE is 200.7517 in CV3 when the SP of CV1 is altered.

Asymmetric persistence and the unemployment hysteresis question in emerging markets: evidence from advanced quantile unit-root tests

Solving the unemployment hysteresis puzzle is vital to government policies, since the structural or cyclical nature of the problem constitutes the direction of the policies to be implemented. This study aims to provide new findings by examining the unemployment hysteresis puzzle for emerging markets from an asymmetric perspective. This study conducts a comprehensive analysis using both conventional and quantile unit root tests. We focus on the Fourier non-linear quantile unit root test, which considers heavy-tailed (non-normal) distributions, structural shifts, non-linearity, and asymmetric adjustment simultaneously. The results indicate that in the Dickey and Fuller test and its extensions, while the null hypothesis of the unit root is rejected in 33% of emerging markets, this rate increases to 55% in quantile Kolmogorov-Smirnov tests and dramatically to 72% in Fourier non-linear quantile unit root test. These findings provide fresh evidence for solving the unemployment hysteresis puzzle in emerging markets.

Convergence of economic growth and health expenditures in OECD countries: Evidence from non-linear unit root tests.

The relationship between human capital, health spending, and economic growth is frequently neglected in the literature. However, one of the main determinants of human capital is health expenditures, where human capital is one of the driving forces of growth. Consequently, health expenditures affect growth through this link. In the study, these findings have been attempted to be empirically tested. Along this axis, health expenditure per qualified worker was chosen as an indicator of health expenditure, and output per qualified worker was chosen as an indicator of economic growth. The variables were treated with the convergence hypothesis. Due to the non-linear nature of the variables, the convergence hypothesis was carried out with non-linear unit root tests. The analysis of 22 OECD countries from 1976 to 2020 showed that health expenditure converged for all countries, and there was a significant degree of growth convergence (except for two countries). These findings show that health expenditure convergence has significantly contributed to growth convergence. Policymakers should consider the inclusiveness and effectiveness of health policies while making their economic policies, as health expenditure convergence can significantly impact growth convergence. Further research is needed to understand the mechanisms behind this relationship and identify specific health policies most effective in promoting economic growth.