Time-varying Intensity Research Articles

Stochastic Analysis of a Large-Span Continuous Girder High-Speed Railway Bridge under Fully Non-Stationary Earthquake

The main objective of the present work is to evaluate the stochastic seismic response of a large-span continuous girder high-speed railway (CGHSR) bridge subjected to fully non-stationary seismic excitation. The stochastic ground motion is determined by a fully non-stationary ground acceleration model with both the time-varying intensity and frequency content. The stochastic seismic analysis of the large-span CGHSR bridge under a tri-directional earthquake, taking into consideration the wave passage effect, is performed using the pseudo excitation method (PEM) in frequency domain and the Monte Carlo sampling (MCS) method in time domain. A framework is proposed to determine the pseudo static displacement for the PEM under fully non-stationary seismic excitation, using the proper orthogonal decomposition (POD). A comparative study on the stochastic seismic response of the bridge is conducted using both the fully and modulated non-stationary ground acceleration. The results show that the structural nodal displacements estimated by the PEM agree well with those obtained by the MCS method. The proposed POD-based method works well in estimating the structural quasi-static displacement. Ignoring the frequency non-stationarity of the earthquake may underestimate the quasi-static displacement caused by the surface waves.

Autapse-induced logical resonance in the FitzHugh–Nagumo neuron

It was demonstrated that the chaos-driven FitzHugh–Nagumo (FHN) neuron can be considered as a logic system to implement the reliable logical operations through the mechanism of logical resonance. Autapse (meaning the self-synapse) widely exists in various kinds of neurons, and it significantly affects the neuronal dynamics and functionalities. However, the effects of autapse on logical resonance have not been reported yet. Here, we explore the effects of autapse on the reliability of AND & NAND logical operations based on the autaptic FHN neuron model with time-varying coupling intensity. The numerical results demonstrate that there are the optimal ranges of parameters (including autaptic time delay, amplitude, frequency and phase fluctuation of autaptic coupling intensity) at which the reliability of logical operations can be maximized. Namely, autapse-induced logical resonance can be realized in the autaptic FHN neuron model. More interestingly, multiple logical resonances can be obtained by regulating autaptic time delay, phase fluctuation of autaptic coupling intensity, as well as frequency ratio between and autaptic coupling intensity and external periodic driving force. Finally, an intuitive interpretation for autapse-induced logical resonance is given based on the motion of the particle in the potential landscape.

The Longitudinal Association Between Cigarette Coupon Receipt and Short-term Smoking Cessation Among US Adults.

To help offset the increased price of cigarettes and promote brand loyalty, tobacco companies distribute coupons, particularly to price-sensitive consumers. Few studies, however, have examined the longitudinal association between coupon receipt and smoking cessation. Using adult data from waves 1-5 (2013-2019) of the Population Assessment of Tobacco and Health Study, we examined the longitudinal association between coupon receipt and short-term smoking cessation. Multivariable discrete-time survival models were fit to an unbalanced person-period dataset for adult respondents (≥18 years) with current established smoking status at baseline (person n = 9472, risk period n = 29 784). Short-term smoking cessation was measured as discontinued cigarette use (no past 30-day cigarette use at follow-up) and self-reported complete quitting. Coupon receipt was measured as a time-varying exposure, measured in the wave preceding the outcome. Tobacco dependence and time-varying cigarette use intensity were controlled as potential confounders. Effect modification by age, sex, race-ethnicity, and education was assessed by examining interaction terms. We found that adults who received a coupon were 19% less likely to quit smoking compared to adults who did not receive a coupon, adjusting for covariates (adjusted hazard rate [aHR]: 0.81, 95% CI: 0.74-0.89). None of the interaction terms were statistically significant, suggesting that the association between coupon receipt and short-term smoking cessation may not differ across the sociodemographic groups that we examined. Taken together, our results reveal that coupon receipt reduces the likelihood of short-term smoking cessation, and that this association does not differ by age, sex, race-ethnicity, or education. Tobacco companies distribute coupons for tobacco products to price-sensitive customers in the United States, and these coupons can be particularly effective in partly offsetting the impact of a tax increases and promoting brand loyalty. This study provides longitudinal evidence that coupon receipt is associated with a decrease in short-term smoking cessation among US adults who smoke cigarettes after adjusting for covariates and tobacco-related confounders. The findings from this study suggest that coupons are an effective tool for tobacco companies to prevent adults who smoke from quitting, and a national ban on coupons may help to facilitate smoking cessation.

Low-carbon assessment of building facades using dynamic CO2 intensity of electricity generation in Japan

To promote low-carbon power supply in a region, the demand due to building use should be synchronized with the optimal supply patterns. To this end, the usefulness of using the time-varying CO2 intensity of electricity in building design is discussed. Hourly intensities were first estimated and visualized for Tokyo, Japan, and the low-carbon impacts of improved façade performance were compared using case studies with a generic office model. Two cases were compared: one with increased solar shading performance of window glass and the other with combined measures of insulation, natural ventilation, and eaves. CO2 emission savings rate were more significant in the first case (19.4 %) than the second case (18.9 %) when a fixed annual emission intensity was used. In contrast, when hourly intensities were used, the savings rate was 18.1 % and 18.6 %, respectively, reversing the superiority. Consideration of the time-varying CO2 intensity could help evaluate building designs that limit electricity use during high CO2 intensity and shift it to periods of low CO2 intensity. The integration of time-varying factors not only in the mechanical system evaluation but also in building design itself should be integrated to promote the regional transition to a decarbonized society.

Recovered frog populations coexist with endemic Batrachochytrium dendrobatidis despite load-dependent mortality.

Novel infectious diseases, particularly those caused by fungal pathogens, pose considerable risks to global biodiversity. The amphibian chytrid fungus (Batrachochytrium dendrobatidis, Bd) has demonstrated the scale of the threat, having caused the greatest recorded loss of vertebrate biodiversity attributable to a pathogen. Despite catastrophic declines on several continents, many affected species have experienced population recoveries after epidemics. However, the potential ongoing threat of endemic Bd in these recovered or recovering populations is still poorly understood. We investigated the threat of endemic Bd to frog populations that recovered after initial precipitous declines, focusing on the endangered rainforest frog Mixophyes fleayi. We conducted extensive field surveys over 4 years at three independent sites in eastern Australia. First, we compared Bd infection prevalence and infection intensities within frog communities to reveal species-specific infection patterns. Then, we analyzed mark-recapture data of M. fleayi to estimate the impact of Bd infection intensity on apparent mortality rates and Bd infection dynamics. We found that M. fleayi had lower infection intensities than sympatric frogs across the three sites, and cleared infections at higher rates than they gained infections throughout the study period. By incorporating time-varying individual infection intensities, we show that healthy M. fleayi populations persist despite increased apparent mortality associated with infrequent high Bd loads. Infection dynamics were influenced by environmental conditions, with Bd prevalence, infection intensity, and rates of gaining infection associated with lower temperatures and increased rainfall. However, mortality remained constant year-round despite these fluctuations in Bd infections, suggesting major mortality events did not occur over the study period. Together, our results demonstrate that while Bd is still a potential threat to recovered populations of M. fleayi, high rates of clearing infections and generally low average infection loads likely minimize mortality caused by Bd. Our results are consistent with pathogen resistance contributing to the coexistence of M. fleayi with endemic Bd. We emphasize the importance of incorporating infection intensity into disease models rather than infection status alone. Similar population and infection dynamics likely exist within other recovered amphibian-Bd systems around the globe, promising longer-term persistence in the face of endemic chytridiomycosis.

Decarbonizing regional multi-model transportation system with shared electric charging hubs

In light of the growing concerns of global climate change, the pace of transportation electrification has greatly accelerated in recent years as an effort towards net-zero greenhouse gas (GHG) emissions. However, it remains unclear how to effectively deploy and operate public charging infrastructure to best serve an electrified transportation system within a multi-modal context while maximizing the benefits of decarbonization. This is especially true when considering the GHG emitted by generating one kWh of electricity, i.e. the electricity carbon intensity, varies across a day due the change of generation mix between renewable and fossil fueled resources. To address this question, we propose a mechanism of shared charging hubs that can provide holistic energy management for both electric buses (EBs) and passenger electric vehicles (EVs). The deployment and operation of shared charging hubs is determined by a new spatio-temporal optimization model which aims to minimize GHG emission given a budget limit while avoiding the occurrence of massive spikes in peak power demand. This is achieved by coherently accommodating the charging demand of EBs and EVs, and explicitly integrating the time-varying electricity carbon intensity and vehicle-to-grid (V2G) technology. To demonstrate its effectiveness, the model is applied to the bus fleets operated by seven transit agencies and the park-and-ride facilities (for EVs) near twelve rail transit stations in Contra Costa County, California, USA. The results show that the shared charging hubs can lead to significant GHG emission reduction while mitigating the peak electricity demand. This research will help policymakers and transportation agencies make more informed decisions regarding the planning and design of charging infrastructure.

Lymphography method based on time-autocorrelated optical coherence tomography.

Lymphatic vessels are structurally similar to blood vessels, and the lymphatic fluid flowing within the lymphatic vessels is distributed throughout the body and plays a vital role in the human immune system. Visualization of the lymphatic vessels is clinically important in the diagnosis of tumor cell metastasis and related immune system diseases, but lymph is difficult to image due to its near-transparent nature and low flow rate. In this paper, we present a lymphography method based on time-autocorrelated optical coherence tomography. By using the minimum value difference of the autocorrelation function of the time-varying interference intensity between the lymph and the surrounding tissues, the non-invasive and high-sensitivity imaging of lymph vessels can be achieved. The method proposed in this paper has potential significance for the research and treatment of immune system diseases.

Study on the time-varying extreme value characteristic of the transient loads on a 5:1 rectangular cylinder subjected to a thunderstorm-like wind

A reasonable extreme probability model to estimate the transient loads is essential for structural wind resistance design. The transient aerodynamic characteristics of a 5:1 rectangular cylinder under thunderstorm-like wind are experimentally studied based on the multiple-fan active wind tunnel technique. In this paper, the non-Gaussian characteristics of the transient pressures are analyzed with emphasis on the time-varying skewness and time-varying kurtosis. A generalized time-varying extreme value model for uniformly modulated nonstationary stochastic processes is proposed, which is adopted to study the extreme value of transient loads on a 5:1 rectangular cylinder under a thunderstorm-like wind. Compared with the stationary flow condition, the results show that the non-Gaussian features of the transient pressures is noticeable, which is determined by the time-varying turbulence intensity. The greater the time-varying turbulence intensity, the stronger the non-Gaussian characteristic of the transient loads is, which is consistent with the stationary wind case. Notably, the presented work confirms that the conventional mean extreme value model may seriously underestimate the extreme value of transient loads. Moreover, the extreme values under stationary flow are slightly higher than those under transient wind pressures. The results show that the peak factors in the suction region are significantly greater than that in the reattachment region, and the time-varying peak factors under transient wind pressures are slightly less than in the stationary flow case.

A low power 50 Hz argon plasma for surface modification of polytetrafluoroethylene

The characteristics of a low power 50 Hz argon plasma for surface treatment of polytetrafluoroethylene (PTFE) film is presented in this article. The current–voltage behavior of the discharge and time-varying intensity of the discharge showed that a DC glow discharge was generated in reversed polarity at every half-cycle. At discharge power between 0.5 and 1 W, the measured electron temperature and density were 2–3 eV and ∼108 cm−3, respectively. The optical emission spectrum of the argon plasma showed presence of some ‘impurity species’ such as OH, N2 and H, which presumably originated from the residual air in the discharge chamber. On exposure of PTFE films to the argon glow plasma at pressure 120 Pa and discharge power 0.5 to 1 W, the water contact angle reduced by 4% to 20% from the original 114° at pristine condition, which confirms improvement of its surface wettability. The increase in wettability was attributed to incorporation of oxygen-containing functional groups on the treated surface and concomitant reduction in fluorine as revealed by the XPS analysis and increase in surface roughness analyzed from the atomic force micrographs. Ageing upon storage in ambient air showed retention of the induced increase in surface wettability.

Time-varying intensity of oxygen exposure is associated with mortality in critically ill patients with mechanical ventilation

BackgroundThere is no consensus exists regarding the association between oxygen exposure (arterial oxygen tension or fraction of inspired oxygen) and outcomes for patients with mechanical ventilation. Additionally, whether the association remains persistent over time is unknown. We aimed to explore the association between exposure to different intensities of oxygen exposure over time and 28-day mortality in patients with mechanical ventilation.MethodsWe obtained data from the Medical Information Mart for Intensive Care IV (MIMIC-IV), which included adult (≥ 18 years) patients who received invasive mechanical ventilation for at least 48 h. We excluded patients who received extracorporeal membrane oxygenation (ECMO) or who initiated ventilation more than 24 h after ICU admission. The primary outcome was 28-day mortality. Piece-wise exponential additive mixed models were employed to estimate the strength of associations over time.ResultsA total of 7784 patients were included in the final analysis. Patients had a median duration of invasive mechanical ventilation of 8.1 days (IQR: 3.8–28 days), and the overall 28-day mortality rate was 26.3%. After adjustment for baseline and time-dependent confounders, both daily time-weighted average (TWA) arterial oxygen tension (PaO2) and fraction of inspired oxygen (FiO2) were associated with increased 28-day mortality, and the strength of the association manifested predominantly in the early-middle course of illness. A significant increase in the hazard of death was found to be associated with daily exposure to TWA-PaO2 ≥ 120 mmHg (Hazard ratio 1.166, 95% CI 1.059–1.284) or TWA-FiO2 ≥ 0.5 (Hazard ratio 1.496, 95% CI 1.363–1.641) during the entire course. A cumulative effect of harmful exposure (TWA-PaO2 ≥ 120 mmHg or TWA-FiO2 ≥ 0.5) was also observed.ConclusionPaO2 and FiO2 should be carefully monitored in patients with mechanical ventilation, especially during the early-middle course after ICU admission. Cumulative exposure to higher intensities of oxygen exposure was associated with an increased risk of death.

Impact of Time-Varying Intensity of Mechanical Ventilation on 28-Day Mortality Depends on Fluid Balance in Patients With Acute Respiratory Distress Syndrome: A Retrospective Cohort Study.

BackgroundRecent studies have mainly focused on the association between baseline intensity of mechanical ventilation (driving pressure or mechanical power) and mortality in acute respiratory distress syndrome (ARDS). It is unclear whether the association between the time-varying intensity of mechanical ventilation and mortality is significant and varies according to the fluid balance trajectories.MethodsWe conducted a secondary analysis based on the NHLBI ARDS Network’s Fluid and Catheter Treatment Trial (FACTT). The primary outcome was 28-day mortality. The group-based trajectory modeling (GBTM) was employed to identify phenotypes based on fluid balance trajectories. Bayesian joint models were used to account for informative censoring due to death during follow-up.ResultsA total of 1,000 patients with ARDS were included in the analysis. Our study identified two phenotypes of ARDS, and compared patients with Early Negative Fluid Balance (Early NFB) and patients with Persistent-Positive Fluid Balance (Persistent-PFB) accompanied by higher tidal volume, higher static driving pressure, higher mechanical power, and lower PaO2/FiO2, over time during mechanical ventilation. The 28-day mortality was 14.8% in Early NFB and 49.6% in Persistent-PFB (p < 0.001). In the Bayesian joint models, the hazard ratio (HR) of 28-day death for time-varying static driving pressure [HR 1.03 (95% CI 1.01–1.05; p < 0.001)] and mechanical power [HR 1.01 (95% CI 1.002–1.02; p = 0.01)] was significant in patients with Early NFB, but not in patients with Persistent-PFB.ConclusionTime-varying intensity of mechanical ventilation was associated with a 28-day mortality of ARDS in a patient with Early NFB but not in patients with Persistent-PFB.

News Arrival, Time-Varying Jump Intensity, and Realized Volatility: Conditional Testing Approach

Abstract This paper introduces new econometric tests to identify stochastic intensity jumps in high-frequency data. Our approach exploits the behavior of a time-varying stochastic intensity and allows us to assess how intensely stock market reacts to news. We describe the asymptotic properties of our test statistics, derive the associated central limit theorem and show in simulations that the tests have good size and reasonable power in finite-sample cases. Implementing our testing procedures on the S&amp;P 500 exchange-traded fund data, we find strong evidence for the presence of intensity jumps surrounding the scheduled Federal Open Market Committee (FOMC) policy announcements. Intensity jumps occur very frequently, trigger sharp increases in realized volatility and arrive when differences in opinion among market participants are large at times of FOMC press releases. Unlike intensity jumps, volatility jumps fail to explain the variation in news-induced realized volatility.

The role of time-varying viral shedding in modelling environmental surveillance for public health: revisiting the 2013 poliovirus outbreak in Israel.

Environmental pathogen surveillance is a sensitive tool that can detect early-stage outbreaks, and it is being used to track poliovirus and other pathogens. However, interpretation of longitudinal environmental surveillance signals is difficult because the relationship between infection incidence and viral load in wastewater depends on time-varying shedding intensity. We developed a mathematical model of time-varying poliovirus shedding intensity consistent with expert opinion across a range of immunization states. Incorporating this shedding model into an infectious disease transmission model, we analysed quantitative, polymerase chain reaction data from seven sites during the 2013 Israeli poliovirus outbreak. Compared to a constant shedding model, our time-varying shedding model estimated a slower peak (four weeks later), with more of the population reached by a vaccination campaign before infection and a lower cumulative incidence. We also estimated the population shed virus for an average of 29 days (95% CI 28-31), longer than expert opinion had suggested for a population that was purported to have received three or more inactivated polio vaccine (IPV) doses. One explanation is that IPV may not substantially affect shedding duration. Using realistic models of time-varying shedding coupled with longitudinal environmental surveillance may improve our understanding of outbreak dynamics of poliovirus, SARS-CoV-2, or other pathogens.

Time-varying capital intensities and the hump-shaped evolution of economic activity in manufacturing

Manufacturing’s share of employment is known to follow a hump-shaped pattern as economies structurally transform. Motivated by the observation that sectoral capital intensities evolve over time, this paper examines whether such changes are important in accounting for this pattern. It does this by putting forth a structural transformation theory that allows for time-varying capital intensities, heterogeneous TFP, Engel curves and trade. The model is calibrated to South Korea (1970–2010), a country for which the rise and decline of the manufacturing employment share occurred within four decades for which comprehensive measures of sectoral capital income shares are available. I show that whereas traditional drivers matter for various elements of development, time-varying capital intensities are critical for generating the complete hump-shaped pattern in manufacturing employment: Time-varying capital intensities trigger an additional “push” of labor out of manufacturing, generating differences between employment and value added shares that are in line with the observed patterns of structural transformation in South Korea.

Forecasting extreme financial risk: A score-driven approach

This paper develops a new class of dynamic models for forecasting extreme financial risk. This class of models is driven by the score of the conditional distribution with respect to both the duration between extreme events and the magnitude of these events. It is shown that the models are a feasible method for modeling the time-varying arrival intensity and magnitude of extreme events. It is also demonstrated how exogenous variables such as realized measures of volatility can easily be incorporated. An empirical analysis based on a set of major equity indices shows that both the arrival intensity and the size of extreme events vary greatly during times of market turmoil. The proposed framework performs well relative to competing approaches in forecasting extreme tail risk measures.

Robustification of Learning Observers to Uncertainty Identification via Time-Varying Learning Intensity

This brief studies the simultaneous estimation of states and uncertainties in general continuous-time systems. In particular, we present a novel time-varying learning intensity (TLI) learning observer (LO). It has the advantage of inheriting the valuable properties of conventional LOs with a simple structure, i.e., the uncertainty estimation is achieved using simply one algebraic equation with low computational costs. The foremost difference in comparison with conventional LOs is the utilization of the TLI approach, which attenuates the overshooting response in the case of large estimation errors and obtains decent performance improvement. Simulations for constant and time-varying signals demonstrate a notable performance boost of TLI-LO.

Framework for probabilistic simulation of power transmission network performance under hurricanes

Structures in a power transmission network, such as towers and conductors, are vulnerable to hurricanes. Failures of these structures trip transmission lines and usually result in large scale power outages in the region. This paper presents a technique for the probabilistic simulation of power transmission systems under hurricane events and provides fundamental insights on the modeling and quantification of power system performance and resilience. The study models the power transmission system as a network of connected individual components, which are subjected to wind-induced mechanical failure and power flow constraints. A realistic power transmission network is developed for the study region. The geographical data are obtained for all components in the network based on a data collection and image processing campaign to reflect the realistic properties of the network serving the Lehigh Valley, PA. A hurricane simulator is utilized to generate a hurricane scenario providing time-varying wind intensities and wind directions for the component failure analysis. The spatio-temporal impact of the hurricane is investigated: a pool of component fragilities is generated to effectively incorporate the uncertainties in structural capacities into the analysis; the spatial correlation among structures is modeled efficiently by a random field based technique. At the system level, Monte Carlo simulation is adopted to determine the failure probability of transmission lines. The unmet demand of the system is computed probabilistically, based on the alternate current optimal power flow analysis, capacity constraints and load shedding process of the system. The simulation results can be used to quantify and visualize the power network performance, and help decision makers to identify critical components in the network to optimize the short-term pre-event preparation for an approaching hurricane and long-term retrofit strategy to enhance system resilience.

Boosting power density of photocatalytic fuel cells with integrated supercapacitive photoanode

The photocatalytic fuel cell (PFC) is a promising energy conversion technology for effective solar energy utilization, wastewater treatment, and electricity generation by photoelectrochemical reactions. Nevertheless, the discharging current output and stability of the PFC are still plagued by the low photoelectron conversion efficiency and time-varying light intensity, respectively. Herein, we integrated a RuO2 capacitive layer and a TiO2 photocatalytic layer into a capacitive photoanode, finally designing a PFC with the capacitive photoanode. Not only can the successful integration of the capacitive layer augment the discharging current, but it can also balance the solar intensity fluctuation by the ability of electron storage. The capacitive photoanode showed a high areal capacitance of 1040.7 mFcm−2 at a current density of 0.5 mAcm−2, was continuously charged and discharged for 1000 cycles, and maintained 87 % of the original capacitance after cycles. The superior rate capability, high capacitance, and good cycle performance of the capacitive photoanode originate from the “crack mud” structure in the capacitive layer. The discharging current of the capacitive photoanode was 32.0 mAcm−2 under one sun illumination, and the electrochemical performance of the capacitive photoanode was better than that of the conventional TiO2 photoanode. The capacitive photoanode PFC possessed a maximum short-circuit current of 300.0 μA⋅cm−2 at the beginning of discharge, which is independent of the light intensity. The capacitive photoanode PFC adopts a new working mode and provides a unique solution for the practical application of PFC.

Hawkes-based models for high frequency financial data

Compared with low frequency data, high frequency data exhibit distinct empirical properties, including, for instance, essentially discontinuous evolution paths, time-varying intensities, and self-exciting features. All these make it more challenging to model appropriately the dynamics associated with high frequency data such as order arrival and price formation. To capture more accurately the microscopic structures and properties pertaining to the limit order books, this paper focuses on modeling high frequency data using Hawkes processes. Two models, one with exponential kernels and the other with power-law kernels, are introduced systematically, algorithmized precisely, and compared with each other extensively from various perspectives, including the goodness of fit to the original data and the computational time in searching for the maximum likelihood estimator, with search algorithm being taken into consideration as well. To measure the goodness of fit, a number of quantities are proposed. Studies based on both multiple-trading-day data of one stock and multiple-stock data on one trading day indicate that Hawkes processes with slowly-decaying kernels are able to reproduce the intensity of jumps in the price processes more accurately. The results suggest that Hawkes processes with power-law kernels and their implied long memory nature of self-excitation phenomena could, on the level of microstructure, serve as a realistic model for high frequency data.

Numerical investigation of the mechanism of interfacial dynamics of the melt pool and defects during laser powder bed fusion

The occurrence of structural defects during laser powder bed fusion (LPBF) impairs the mechanical properties of components fabricated by the technique. Therefore, having a good grasp of the mechanism of various structural defects is useful for guiding process maps. However, investigating melt-pool dynamics and corresponding defects using experiments is challenging. Numerical simulation thus represents a promising and visual way to reproduce these phenomena. In this study, predicated to first ensure accuracy, a two-dimensional (2D) model was numerically implemented by a phase field with a finite element method (FEM). Our model emphasises the interaction between neighbouring powders during heat duration with time-varying maximum intensity under different deposition parameters. Our simulation results indicate that the reinforcement of liquidity can significantly enhance the wettability of the neighbouring powder to release gas bubbles and extend the melt pool. Similarly, the remelting process also effectively eliminates porosity, which yields a smooth surface deposited in the previous layers to improve deposit densification. Our simulation also provided detailed insights into the evolution of liquid metal droplets away from “the elongated neck” and investigated the effect of scanning speed on the width of the melt pool of single tracks. Additionally, our model implemented a discrete FEM method with extremely refined free-triangle elements, which was accompanied by a decrease in computational cost and expressed good agreement with the experiments.