Exponential Method Research Articles

Abundant and accurate computational wave structures of the nonlinear fractional biological population model

In this paper, the generalized exponential (GExp) method has been employed to construct novel solitary wave solutions of the nonlinear fractional biological population (FBP) model. This model is used to demonstrate the relation of the population with deaths and births. Many novel traveling wave solutions have been formulated in distinct forms such as exponential, hyperbolic and trigonometric forms. These solutions have been explained in three different axes. The first axis is plotting them in their three optional (real, imaginary and absolute value), the second axis is handling these solutions for constructing the requested conditions for applying trigonometric quintic B-spline (TQBS) scheme. The second one determines the accuracy of the obtained analytical solutions by showing the error’s value between the analytical and numerical solutions. At the same time, the third one is comparing our analytical and numerical solutions, which have recently been published that explain the paper’s contribution and novelty.

A novel exponential degradation approach for predicting the remaining useful life of roadheader bearings

Based on the optimized exponential-degradation model (OEDM), a novel approach for predicting the remaining useful life(RUL) of roadheader bearings under different working conditions is proposed in this study. Specifically, the exponential process is used to construct the degradation process from a single performance characteristic under variable operating conditions, the generalized expectation maximization is employed to estimate model parameters, and the proposed degradation model is updated after new data is available. In the traditional exponential degradation method, the hyperparameters are only optimized, which leads to low calculation accuracy under severe working conditions. In the proposed method, the Bayesian algorithm and the Drift Brownian motion algorithm were respectively employed to optimize hyperparameters and stochastic parameters to ensure the high accuracy of the prediction results. In addition, degradation characteristics combined with sensory data acquired through condition monitoring were used to continuously update the RUL in the proposed degradation model. Finally, the effectiveness of the proposed model is verified by a simulation case and a case study. The results show that compared with the linear degradation model and the general exponential degradation model, the proposed OEDM performs well in practical applications and has a higher prediction accuracy. This study provides a reference for predictive maintenance of critical parts of tunneling machinery and cost reduction of tunneling.

Exponential asymptotics of woodpile chain nanoptera using numerical analytic continuation

AbstractTraveling waves in woodpile chains are typically nanoptera, which are composed of a central solitary wave and exponentially small oscillations. These oscillations have been studied using exponential asymptotic methods, which typically require an explicit form for the leading‐order behavior. For many nonlinear systems, such as granular woodpile chains, it is not possible to calculate the leading‐order solution explicitly. We show that accurate asymptotic approximations can be obtained using numerical approximation in place of the exact leading‐order behavior. We calculate the oscillation behavior for Toda woodpile chains, and compare the results to exponential asymptotics based on previous methods from the literature: long‐wave approximation and tanh‐fitting. We then use numerical analytic continuation methods based on Padé approximants and the adaptive Antoulas–Anderson (AAA) method. These methods are shown to produce accurate predictions of the amplitude of the oscillations and the mass ratios for which the oscillations vanish. Exponential asymptotics using an AAA approximation for the leading‐order behavior is then applied to study granular woodpile chains, including chains with Hertzian interactions—this method is able to calculate behavior that could not be accurately approximated in previous studies.

Adaptive techniques for solving chaotic system of parabolic-type

Time-dependent partial differential equations of parabolic type are known to have a lot of applications in biology, mechanics, epidemiology and control processes. Despite the usefulness of this class of differential equations, the numerical approach to its solution, especially in high dimensions, is still poorly understood. Since the nature of reaction-diffusion problems permit the use of different methods in space and time, two important approximation schemes which are based on the spectral and barycentric interpolation collocation techniques are adopted in conjunction with the third-order exponential time-differencing Runge-Kutta method to advance in time. The accuracy of the method is tested by considering a number of time-dependent reaction-diffusion problems that are still of current and recurring interests in one and high dimensions.

Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrödinger equations

Finding optical soliton solutions to nonlinear partial differential equations has become a popular topic in recent decades. The primary goal of this study is to identify a diverse collection of wave solutions to a generalized version of the nonlinear Schrödinger equation. We investigate two modifications to the generalized exponential rational function method to derive the expected results for this model. The first method is primarily based on using elementary functions such as exponential, trigonometric, and hyperbolic forms, which are commonly used to calculate the results. As for the second method, it is based on applying Jacobi elliptic functions to formulate solutions, whereas the underlying idea is the same as with the first method. As a means of enhancing the reader’s understanding of the results, we plot the graphical properties of our solutions. Based on this article’s results, it can be concluded that both techniques are easy to follow, and yet very efficient. These integration methods can determine different categories of solutions all in a unified framework. Therefore, it can be concluded from the manuscript that the approaches adopted in the manuscript may be regarded as efficient tools for determining wave solutions of a variety of partial differential equations. Due to the high computational complexity, the main requirement for applying our proposed methods is to employ an efficient computing software. Here, symbolic packages in Wolfram Mathematica have been used to validate the entire results of the paper.

Identifikasi Lokasi Potensial dan Prioritas Pengembangan Agroindustri Aren di Kabupaten Tasikmalaya, Jawa Barat

Sugar palm is a plantation crop that has benefits economic, ecological, social and cultural, but the exploitation of palm sugar is generally still taking the results of plants that grow naturally. Identification of the distribution of sugar palm plants needs to be done to obtain priority locations for the development of sugar palm agro-industry. The potential location shows that the sugar palm has a comparative and competitive advantage compared to other plantation commodities. Comparative and competitive advantages can be determined using the Location Quotient (LQ) and Differential Shift (DS) methods, while the priority for developing sugar palm agro-industry products is determined by the exponential comparison method with criteria 1) market potential, 2) environmental sustainability and waste minimization, 3) availability of raw materials and supporting material, 4) local government support, 5) human resource capability, 6) availability of applicable technology, 7) competitiveness of similar products and substitute products, and 8) efficiency of production costs. The results showed that the potential location of sugar palm plants were found in five districts in Tasikmalaya Regency, among others Ciawi districts, Cigalontang districts, Jamanis districts, Jatiwaras districts, and Sukahening Districts. The priority of developing agroindustry products based on the analysis of the corresponding exponential comparison method is palm sugar (10.21), palm fruit (10.20), palm fiber (10.19), ant sugar (10.17) and palm starch flour (10.06).

A New Method Applied for the Determination of Relative Weight Ratios Under the TensorFlow Platform When Estimating Coseismic Slip Distribution

AbstractWhen estimating a coseismic slip distribution with multiple observation types, the relative weight ratios (the contribution ratios of all kinds of actual observations in the joint inversion, which should be positive by default) and regularization parameter critically impact the inversion accuracy. In this paper, we propose a new method for determining the relative weights of multiple observations of jointing inversion slip distributions. This method regards the observations and the relative weight ratios as the training data sets and training parameters, respectively; in addition, the constructed function was optimized by the gradient descent method and the exponential decay learning rate method under the TensorFlow platform (GDED). We compared the GDED method with the Helmert variance component estimation method (HVCE) and Akaike's Bayesian information criterion method (ABIC) by designing eight simulation experiments. These simulations included changing the errors and resolutions of the observations, the grid size, the strike angle and the dip angle of the fault, the moment magnitudes of earthquakes, the number of observation types, and the complexity of subduction‐zone earthquakes. We analyzed and discussed the characteristics of the above three methods in determining the relative weight ratios during the joint inversion process. The results of these simulation experiments showed that the GDED method and the ABIC method perform much better than the HVCE method when negative variance occurs in the HVCE method, while the accuracies of the slip distributions produced by the three methods were similar when no negative variance occurred; the GDED method can be used to prevent the occurrence of negative variance compared to the HVCE method and is more time efficient than the ABIC method. Furthermore, we applied these methods to invert the source parameters of the 2015 Mw 8.3 Illapel earthquake (in Chile), and the inversion results showed that the slip of the Illapel earthquake was mainly distributed at depths of approximately 10–50 km. The maximum slip of the Illapel earthquake was approximately 7.9 m, distributed 50–70 km northwest of the epicenter at depths of approximately 10–20 km.

Improved exponential cuckoo search method for sentiment analysis

Improved exponential cuckoo search method for sentiment analysis

Evaluation of Bozem and Drainage Channels of Jade Hamlet Residential in Gresik

Drainage refers to a vital component for water disposal so that a region or area can hinder potential puddle due to excessive water on the land surface. Therefore, a good plan adjusting the land condition of residential area belongs to a fundamental matter. Jade Hamlet Residence is located on Hulaan highway, Hulaan Urban Village, Menganti District, Gresik Regency, covering an area ±20 hectares and consisting of housing area, park, public facility, and catchment area. The drainage channel at this residence serves as the drainage for rain water and household dirty water disposal. During the rainy season in 2018 and 2019, the channel and bozem or drainage basin of this residence encountered overflowing and eventually caused puddle. To overcome this problem, the capacities of bozem and channel are in need of analysis and evaluation so as to figure out the runoff volume that can be accommodated in the bozem and investigate the discharge planned in the drainage channel by employing Log Person III method, chi-square distribution fit test, Kolmogorov-Smirnov test, rational formula, and exponential method. The results of analysis and evaluation demonstrated that the bozem capacity could not afford the runoff discharge (298.35 m3 309.55 m3), thereby demanding additional length and depth against the existing bozem. Meanwhile, the calculation of flood discharge planned for the drainage channels of S4.Ry3, S6.Ry1, S6.D1, S6.I2, S6.Cs1, S6.Rc1, S6.Rc2 indicate that they need redesigning by altering the channel dimension as the discharge capacity exceeds the channel.

Accuracy of methods for simulating daily water surface evaporation evaluated by the eddy covariance measurement at boreal flux sites

Evaporation from the surface of water is a vital component of the hydrological cycle. Accurately simulating evaporation is crucial for modeling hydrological processes, ensuring ecosystem water efficiency, and managing water resources. Previous methods for evaluating evaporation have generally been limited to a single site and on a regional scale. Based on eddy covariance measurements of 14 boreal flux sites, the accuracy of 26 methods for simulating daily water surface evaporation was comprehensively evaluated in this study. Most methods accurately simulated daily evaporation at most sites with a KGE >0.60. The combination methods with simultaneous calibration of the energy and aerodynamic terms and the double-parameter aerodynamic methods based on the linear and exponential functions showed the best performance, with the median KGE of the evaluated sites ranging from 0.72 to 0.76. The Bowen ratio energy balance (BREB) method embedded with Tw, Rs-based two-variable empirical methods, double-parameter aerodynamic methods, and the combination method of the energy term based on net radiation (Rn) and the aerodynamic term based on the exponential function method performed better than the other methods of the same type. The relative error (RE) simulated by most methods was generally within ± 30 %, with the median RE of all sites within ± 10 % for each method. The combination methods tended to overestimate the level of evaporation, whereas the BREB-type and aerodynamic methods tended to underestimate the extent of evaporation. The simulation accuracy of the daily evaporation showed significant variance among the sites. It showed the best model performance at two FLUXNET and two sites taken from the literature, in which 75 % of the methods were able to accurately simulate daily evaporation with a Kling–Gupta efficiency (KGE) >0.80. All methods performed poorly at the three sites from the literature and were mainly due to the lack of measured variables with a strong correlation with the latent heat flux (LE). The FLUXNET sites generally showed better performance. The observed LE of the sites with the best model performance generally showed a unimodal distribution throughout the year. The simulation accuracy of non-unimodal distribution sites mainly depended on the correlation between the LE and related variables. The combination of the energy term based on Rn and the aerodynamic term based on the power function method showed the best model stability. This finding indicated that the calibrated method was robust and showed high stability in simulating daily evaporation, and it was recommended for application in other sites or regions. The optimization of parameters calibrated in this study may improve the accuracy of simulating the daily evaporation for the application of the Penman and Priestley–Taylor equations when the water heat storage measurement is missing.

Proximal policy optimization guidance algorithm for intercepting near-space maneuvering targets

This paper studies a novel guidance framework of the vehicle against a high-speed and maneuvering target based on deep reinforcement learning (DRL) considering the energy consumption, autopilot lag dynamics, and input saturation, which can effectively cope with the high flight-path angle error flight phase and various uncertainties. The guidance framework proposes an end-to-end mapping transformation between the guidance command and observation states consisting of line-of-sight (LOS) angle, relative distance, and their rate measured by the seeker. At the same time, the observability of the LOS angle and relative distance is included in constructing the reward function. Besides, the relative engagement kinematic model of the interceptor-target is established and combined with the PPO guidance algorithm, jointly described as a Markov decision process (MDP). Notably, the guidance framework is optimized using the improved proximal policy optimization (PPO) algorithm and demonstrated in a simulated terminal phase in the near-space. Specifically, the PPO guidance algorithm is structured by the policy (actor) neural network and the critic neural network, and both are standard fully-connected neural networks. Subsequently, observation states and rewards are fully collected and applied by introducing the experience replay method. Also, the exponential decay learning rate method, mini-batch stochastic gradient ascent (SGA) method, zero-score standardization, and Adam optimizer are proposed to train the reinforcement learning algorithm more efficiently. Moreover, the proposed guidance framework has an excellent generalization capability and guarantees the implementation of fixed and stochastic engagement scenarios, which means that the interceptor can realize the unlearned practical combat scenarios. The robust capacity is indicated and validated using Monte Carlo simulation under various uncertainties. Moreover, the DRL guidance framework can satisfy the onboard application requirement.

A Scaling Transition Method from SGDM to SGD with 2ExpLR Strategy

In deep learning, the vanilla stochastic gradient descent (SGD) and SGD with heavy-ball momentum (SGDM) methods have a wide range of applications due to their simplicity and great generalization. This paper uses an exponential scaling method to realize a smooth and stable transition from SGDM to SGD, which combines the advantages of the fast training speed of SGDM and the accurate convergence of SGD (named TSGD). We also provide some theoretical results on the convergence of this algorithm. At the same time, we take advantage of the learning rate warmup strategy’s stability and the learning rate decay strategy’s high accuracy. A warmup–decay learning rate strategy with double exponential functions is proposed (named 2ExpLR). The experimental results on different datasets for the proposed algorithms indicate that the accuracy is improved significantly and that the training is faster and more stable.

Modelling the Transmission Dynamics of Meningitis among High and Low-Risk People in Ghana with Cost-Effectiveness Analysis

Meningitis is an inflammation of the meninges, which covers the brain and spinal cord. Every year, most individuals within sub-Saharan Africa suffer from meningococcal meningitis. Moreover, tens of thousands of these cases result in death, especially during major epidemics. The transmission dynamics of the disease keep changing, according to health practitioners. The goal of this study is to exploit robust mechanisms to manage and prevent the disease at a minimal cost due to its public health implications. A significant concern found to aid in the transmission of meningitis disease is the movement and interaction of individuals from low-risk to high-risk zones during the outbreak season. Thus, this article develops a mathematical model that ascertains the dynamics involved in meningitis transmissions by partitioning individuals into low- and high-risk susceptible groups. After computing the basic reproduction number, the model is shown to exhibit a unique local asymptotically stability at the meningitis-free equilibrium E † , when the effective reproduction number R 0 < 1 , and the existence of two endemic equilibria for which R 0 † < R 0 < 1 and exhibits the phenomenon of backward bifurcation, which shows the difficulty of relying only on the reproduction number to control the disease. The effective reproductive number estimated in real time using the exponential growth method affirmed that the number of secondary meningitis infections will continue to increase without any intervention or policies. To find the best strategy for minimizing the number of carriers and infected individuals, we reformulated the model into an optimal control model using Pontryagin’s maximum principles with intervention measures such as vaccination, treatment, and personal protection. Although Ghana’s most preferred meningitis intervention method is via treatment, the model’s simulations demonstrated that the best strategy to control meningitis is to combine vaccination with treatment. But the cost-effectiveness analysis results show that vaccination and treatment are among the most expensive measures to implement. For that reason, personal protection which is the most cost-effective measure needs to be encouraged, especially among individuals migrating from low- to high-risk meningitis belts.

On the learnability of quantum state fidelity

Current quantum processing technology is generally noisy with a limited number of qubits, stressing the importance of quantum state fidelity estimation. The complexity of this problem is mainly due to not only accounting for single gates and readout errors but also for interactions among which. Existing methods generally rely on either reconstructing the given circuit state, ideal state, and computing the distance of which; or forcing the system to be on a specific state. Both rely on conducting circuit measurements, in which computational efficiency is traded off with obtained fidelity details, requiring an exponential number of experiments for full information. This paper poses the question: Is the mapping between a given quantum circuit and its state fidelity learnable? If learnable, this would be a step towards an alternative approach that relies on machine learning, providing much more efficient computation. To answer this question, we propose three deep learning models for 1-, 3-, and 5-qubit circuits and experiment on the following real-quantum processors: ibmq_armonk (1-qubit), ibmq_lima (5-qubit) and ibmq_quito (5-qubit) backends, respectively. Our models achieved a mean correlation factor of 0.74, 0.67 and 0.66 for 1-, 3-, and 5-qubit random circuits, respectively, with the exponential state tomography method. Additionally, our 5-qubit model outperforms simple baseline state fidelity estimation method on three quantum benchmarks. Our method, trained on random circuits only, achieved a mean correlation factor of 0.968 while the baseline method achieved 0.738. Furthermore, we investigate the effect of dynamic noise on state fidelity estimation. The correlation factor substantially improved to 0.82 and 0.74 for the 3- and 5-qubit models, respectively. The results show that machine learning is promising for predicting state fidelity from circuit representation and this work may be considered a step towards efficient end-to-end learning.

Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method

In this paper, the singular boundary method (SBM) in conjunction with the exponential window method (EWM) is firstly extended to simulate the transient dynamic response of two-dimensional saturated soil. The frequency-domain (Fourier space) governing equations of Biot theory is solved by the SBM with a linear combination of the fundamental solutions. In order to avoid the perplexing fictitious boundary in the method of fundamental solution (MFS), the SBM places the source point on the physical boundary and eliminates the source singularity of the fundamental solution via the origin intensity factors (OIFs). The EWM is carried out for the inverse Fourier transform, which transforms the frequency-domain solutions into the time-domain solutions. The accuracy and feasibility of the SBM-EWM are verified by three numerical examples. The numerical comparison between the MFS and SBM indicates that the SBM takes a quarter of the time taken by the MFS.

Adaptive PI Control Strategy for Optimal Microgrid Autonomous Operation

The present research produces a new technique for the optimum operation of an isolated microgrid (MGD) based on an enhanced block-sparse adaptive Bayesian algorithm (EBSABA). To update the proportional-integral (PI) controller gains online, the suggested approach considers the impact of the actuating error signal as well as its magnitude. To reach a compromise result between the various purposes, the Response Surface Methodology (RSMT) is combined with the sunflower optimization (SFO) and particle swarm optimization (PSO) algorithms. To demonstrate the success of the novel approach, a benchmark MGD is evaluated in three different Incidents: (1) removing the MGD from the utility (islanding mode); (2) load variations under islanding mode; and (3) a three-phase fault under islanding mode. Extensive simulations are run to test the new technique using the PSCAD/EMTDC program. The validity of the proposed optimizer is demonstrated by comparing its results with those obtained using the least mean and square root of exponential method (LMSRE) based adaptive control, SFO, and PSO methodologies. The study demonstrates the superiority of the proposed EBSABA over the LMSRE, SFO, and PSO approaches in the system’s transient reactions.

Epidemiological characteristics of two local COVID-19 outbreaks caused by 2019-nCoV Omicron variant in Guangzhou, China

Objective: To understand the epidemiological characteristics of two local COVID-19 outbreaks caused by 2019-nCoV Omicron variant in Guangzhou, such as incubation period, serial interval, basic reproductive number (R0) and the influence of gathering places on R0, and provide evidence for the prevention and control of Omicron variant infection. Methods: The data of daily confirmed cases of Omicron variant infection from April 8 to May 8, 2022 in two COVID-19 outbreaks in Guangzhou were collected for model fitting. Weibull, Gamma and lognormal distribution were used to estimate incubation period and serial interval. Exponential growth method and the maximum likelihood estimation were used to estimate R0. Results: The median of incubation period was 2.94 (95%CI: 2.52-3.38) days and median of serial interval was 3.32 (95%CI: 2.89-3.81) days. The estimated R0 in small-size place was 4.40 (95%CI: 3.95-4.85), while the estimated R0 at airport was 11.35 (95%CI: 11.02-11.67). Conclusion: The incubation period of Omicron variant in two local COVID-19 outbreaks in Guangzhou is significantly shorter than that of delta variant. The higher the gathering degree in a place, the larger the R0. Due to its rapid transmission, COVID-19 epidemic is prone to occur. Therefore, the COVID-19 prevention and control strategy should be dynamically adjusted in time.

Inhibition of α-Synuclein Seeding-Dependent Aggregation by ssDNA Aptamers Specific to C-Terminally Truncated α-Synuclein Fibrils.

Neuropathologically, Parkinson's disease (PD) and dementia with Lewy bodies (DLB) are characterized by the accumulation of insoluble aggregates of α-synuclein (α-syn) in the Lewy bodies (LBs). In addition to full-length α-syn fibrils, C-terminally truncated α-syn is also abundant in the LBs that acts as seeds and facilitates the aggregation of the full-length α-syn in vitro and in vivo and induces toxicity. Hence, identifying molecules that can inhibit the seeding activity of these truncated forms is of great importance. Here, we report the first in vitro selection of aptamers targeting the fibrillar forms of different C-terminally truncated α-syn using systematic evolution by an exponential enrichment method followed by quantitative high-throughput DNA sequencing. We identify a panel of aptamers that bound with high specificity to different truncated forms of α-syn fibrils with no cross-reactivity toward other amyloid fibrils. Interestingly, two of the aptamers (named Apt11 and Apt15) show higher affinity to most C-terminally truncated forms of α-syn fibrils with an evident inhibition of α-syn-seeded aggregation in vitro by Apt11. This inhibition is further confirmed by circular dichroism, Congo red binding assay, and electronic microscopy. Moreover, Apt11 is also found to reduce the insoluble phosphorylated form of α-syn at Ser-129 (pS129-α-syn) in the cell model and also can inhibit α-syn aggregation using RT-QuIC reactions seeded with brain homogenates extracted from patients affected by PD. The aptamers discovered in this study represent potential useful tools for research and diagnostics or therapy toward PD and DLB.

Supply forecasting and profiling of urban supermarket chains based on tensor quantization exponential regression for social governance.

During the COVID-19 pandemic, the accurate forecasting and profiling of the supply of fresh commodities in urban supermarket chains may help the city government make better economic decisions, support activities of daily living, and optimize transportation to support social governance. In urban supermarket chains, the large variety of fresh commodities and the short shelf life of fresh commodities lead to the poor performance of the traditional fresh commodity supply forecasting algorithm. Unlike the classic method of forecasting a single type of fresh commodity, we proposed a third-order exponential regression algorithm incorporating the block Hankle tensor. First, a multi-way delay embedding transform was used to fuse multiple fresh commodities sales to a Hankle tensor, for aggregating the correlation and mutual information of the whole category of fresh commodities. Second, high-order orthogonal iterations were performed for tensor decomposition, which effectively extracted the high-dimensional features of multiple related fresh commodities sales time series. Finally, a tensor quantization third-order exponential regression algorithm was employed to simultaneously predict the sales of multiple correlated fresh produce items. The experiment result showed that the provided tensor quantization exponential regression method reduced the normalized root mean square error by 24% and the symmetric mean absolute percentage error by 22%, compared with the state-of-the-art approaches.

New solitary wave solutions and stability analysis for the generalized [formula omitted]-dimensional nonlinear wave equation in liquid with gas bubbles

In this study, solitary wave solutions for the generalized (3+1)-dimensional nonlinear wave equation (NLWE) are extracted using a new generalized exponential rational function method (GERFM). Numerous nonlinear behaviors in liquids with gas bubbles are described by this equation. The suggested method is used to derive the various kinds of new accurate soliton solutions for the equation. Also, the physical interpretations of some obtained solutions are represented. In addition, a modulational instability analysis framework is used to look at the system’s stability.