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Globally, it is evident that vaccination and social media significantly influence the spread of diseases. Research has demonstrated that the spread of diseases can be affected by unforeseen events. Therefore, a stochastic hepatitis B virus (HBV) dynamical model is constructed that incorporates media coverage, while also Lévy noise is included. Itô's formula and the Lyapunov function approach are employed to analyze the existence of a positive global solution. Furthermore, the necessary conditions for disease eradication as well as long-term survival are also established to facilitate the general understanding. The statistics indicate that the media's impact is not immediate and does not lead to disease eradication. To effectively manage the spread of diseases, it is essential to employ a combination of significant noise disruption and a low rate of decline in vaccine effectiveness. Numerical simulations are conducted to demonstrate the analytical findings.

Nanofluids garner significant scientific interest due to their exceptional heat-conducting abilities and potential to enhance heat transfer efficiency. This manuscript investigates the behavior of a two-dimensional fractional Carreau fluid model on a stretched sheet over time, incorporating convection, magnetic fields, nanoparticles, diffusion, and thermal radiations. The model elucidates viscoelastic nanofluids’ memory and inheritance properties, employing non-integer Caputo fractional derivatives innovatively. Fundamental equations are transformed into dimensionless form and solved using an explicit finite difference approach. Essential parameters like Skin friction coefficient, Nusselt number, and Sherwood number are accurately determined. Rigorous stability and convergence criteria ensure effective solution convergence. Visual representations demonstrate the significant impact of each parameter on fluid flow. It is noted that temperature gradient increases 49.38% with the increase of fractional exponent α while it decreases 13.39% with the increase of magnetic parameter M. Moreover, concentration gradient increases 66.48% with the increase of thermophoresis parameter Nt and 94.71% with the increase of pedesis parameter Nb.

Abstract Satellite laser ranging (SLR) is a well‐established geodetic technique for measuring the low‐degree time‐variable gravity field for decades. However, its application in mass change estimation is limited by low spatial resolution, even for global mean ocean mass (GMOM) change which represents one of the largest spatial scales. After successfully correcting for signal leakage, for the first time, we can infer realistic GMOM changes using SLR‐derived gravity fields up to only degree and order 5. Our leakage‐corrected SLR GMOM estimates are compared with those from the Gravity Recovery and Climate Experiment (GRACE) for the period 2005 to 2015. Our results show that the GMOM rate estimates from SLR are in remarkable agreement with those from GRACE, at 2.23 versus 2.28 mm/year, respectively. This proof‐of‐concept study opens the possibility of directly quantifying GMOM change using SLR data prior to the GRACE era.

To validate gravity recovery and climate experiment (GRACE)/ GRACE follow-on (GRACE-FO) gravity solutions, we compare satellite altimetry observations of Caspian Sea level (CSL) change with CSL estimates from satellite gravity from April 2002 to December 2020. We use GRACE/GRACE-FO Release 6 GSM fields [spherical harmonics (SH)] from the three processing centers [Center for Space Research (CSR), Jet Propulsion Laboratory (JPL), and Geoscience Research Center (GFZ)] and three mascon solutions from CSR, JPL, and Goddard Space Flight Center (GSFC). CSL change is a regional scale signal that should be reasonably well resolved by satellite gravity measurements, but spatial leakage and other corrections are still required. We computed an average of smoothed SH solutions and those that are both smoothed and decorrelation filtered (to remove north–south stripe noise). Averaging mitigates attenuating effects of decorrelation filtering on the north–south oriented Caspian Sea Signal. After spatial leakage, terrestrial water storage, and steric corrections, most GRACE/GRACE-FO CSL estimates agree remarkably well with the altimetry series over a range of time scales as measured by trend and seasonal components and at other frequencies. The linear CSL trend from altimetry is −7.55 ± 0.17 cm/yr, while GRACE/GRACE-FO values range from −7.30 ± 0.17 to −8.66 ± 0.20 cm/yr. Annual amplitudes from altimetry are (17.75 ± 1.28 cm) with GRACE/GRACE-FO values in the range 17.05 ± 1.49 to 19.16 ± 1.55 cm, with good phase agreement. The GSFC mascon solution shows substantially smaller annual amplitude (11.62 ± 1.04 cm) than others. We found no bias between GRACE and GRACE-FO, but GRACE-FO shows larger root-mean-square differences from altimetry. Among the three standard SH solutions, those from CSR show the best agreement with altimetry.

In this study, we explore the concept of symmetry as it applies to the dynamics of the Hepatitis B Virus (HBV) epidemic model. By incorporating symmetric principles in the stochastic model, we ensure that the control strategies derived are not only effective but also consistent across varying conditions, and ensure the reliability of our predictions. This paper presents a stochastic optimal control analysis of an HBV epidemic model, incorporating vaccination as a pivotal control measure. We formulate a stochastic model to capture the complex dynamics of HBV transmission and its progression to acute and chronic stages. By leveraging stochastic differential equations, we examine the model’s stationary distribution and asymptotic behavior, elucidating the impact of random perturbations on disease dynamics. Optimal control theory is employed to derive control strategies aimed at minimizing the disease burden and vaccination costs. Through rigorous numerical simulations using the fourth-order Runge–Kutta method, we demonstrate the efficacy of the proposed control measures. Our findings highlight the critical role of vaccination in controlling HBV spread and provide insights into the optimization of vaccination strategies under stochastic conditions. The symmetry within the proposed model equations allows for a balanced approach to analyzing both acute and chronic stages of HBV.

In this paper, we study a split-step Galerkin finite element (FE) method for the two-dimensional Riesz space-fractional coupled nonlinear Schrödinger equations (CNLSs). The proposed method adopts a second-order split-step technique to handle the nonlinearity and FE approximation to discretize the fractional derivatives in space, which avoids iteration at each time layer. The analysis of mass conservative and convergent properties for this split-step FE scheme is performed. To test its capability, some numerical tests and the simulation of the double solitons intersection and plane wave are carried out. The results and comparisons with the algorithm combined with Newton’s iteration illustrate its effectiveness and advantages in computational efficiency.

People’s ability to easily travel across cities is thought to play a major role in the spread of infectious diseases. This research develops and analyzes a new Susceptible-Infected-Recovered-Susceptible (SIRS) model that accounts for transport-related infection, media coverage, and three types of noise (white, telegraph, and Lévy) to examine the role of transport in disease transmission. Thus, several theoretical and numerical uses of the revised model are investigated. Using Lyapunov functions, we check whether or not the model has a positive global solution. The infection either dies out or stays put beyond that point. The researched analytical results are validated by developing and using a numerical scheme to analyze and simulate the effects of various factors on the model’s dynamics.

This work proposes a novel stochastic model describing the propagation dynamics of the hepatitis B virus. The model takes into account numerous disease characteristics, and environmental disturbances were collected using Lévy jumps and the conventional Brownian motions. Initially, the deterministic model is developed, and the asymptotic behavior of the model’s solution near the equilibria is examined. The deterministic model is transformed into a stochastic model while retaining the Lévy jumps and conventional Brownian motions. Under specific assumptions, the stochastic system is shown to have a unique solution. The study further investigates the conditions that ensure the extinction and persistence of the infection. The numerical solutions to both stochastic and deterministic systems were obtained using the well-known Milstein and RK4 techniques, and the analytical findings are theoretically confirmed. The simulation suggests that the noise intensities have a direct relationship with the amplitudes of the stochastic curves around the equilibria of the deterministic system. Smaller values of the intensities imply negligible fluctuations of trajectories around the equilibria and, hence, better describe the extinction and persistence of the infection. It has also been found that both Brownian motions and the Lévy jump had a significant influence on the oscillations of these curves. A discussion of the findings of the study reveals other important aspects as well as some future research guidelines. In short, this study proposes a novel stochastic model to describe the propagation dynamics of the hepatitis B virus.

Finite Gaussian mixture models are powerful tools for modeling distributions of random phenomena and are widely used for clustering tasks. However, their interpretability and efficiency are often degraded by the impact of redundancy and noise, especially on high-dimensional datasets. In this work, we propose a generative graphical model for parsimonious modeling of the Gaussian mixtures and robust unsupervised learning. The model assumes that the data are generated independently and identically from a finite mixture of robust factor analyzers, where the features’ salience is adjusted by an active set of latent factors to allow a violation of the local independence assumption. For the model inference, we propose a structured variational Bayes inference framework to realize simultaneous clustering, model selection and outlier processing. Performance of the proposed algorithm is evaluated by conducting experiments on artificial and real-world datasets. Moreover, an application on the high-dimensional machine learning task of handwritten alphabet recognition is introduced.

Abstract Geodetic applications of Low Earth Orbit (LEO) satellites requires accurate satellite orbits. Instead of using onboard Global Navigation Satellite System observations, this contribution treats the LEO satellite constellation independently, using Inter-Satellite Links and the measurements of different ground networks. Due to geopolitical and geographical reasons, a ground station network cannot be well distributed. We compute the impact of different ground networks (i.e., global networks with different numbers of stations and regional networks in different areas and latitudes) on LEO satellite orbit determination with and without the inter-satellite links. The results are based on a simulated constellation of 90 LEO satellites. We find that the orbits determined using a high latitude network is worse than using a middle or low latitude network. This is because the high latitude network has a poorer geometry even if the availability of satellite measurements is higher than for the other two cases. Also, adding more stations in a regional network shows almost no improvements on the satellite orbits if the number of stations is more than 16. With the help of ISL observations, however, the satellite orbits determined with a small regional network can reach the same accuracy as that with the global network of 60 stations. Furthermore, satellite biases can be well estimated (less than 0.6 mm) and have nearly no impact on satellite orbits. It does thus not matter if they are not physically calibrated for estimating precise orbits.

In this paper, we present and analyze two linearized Galerkin finite element schemes, which are constructed by employing the H2N2 formula and its fast version in time direction, for solving the nonlinear time-fractional diffusion-wave equation. By utilizing mathematical induction, the optimal error estimates in H1-norm are derived without any ratio restrictions between the time step size τ and the space mesh size h. The key point in our argument is the application of Sobolev’s embedding inequality to the fully discrete solution uhn. On the other hand, additional time-discrete elliptic system and the inverse inequality, which play a vital role in the temporal–spatial error splitting technique, are avoided in our numerical analysis. Finally, two numerical experiments are given to demonstrate the theoretical findings.

In this paper, an SVIR epidemic model with temporary immunities and general incidence rates is constructed and analyzed. By utilizing Lyapunov functions, we prove the existence and uniqueness of the positive global solution of the constructed model, as well as the sufficient conditions of extinction and persistence of disease, are provided. Due to the difficulty of obtaining the analytical solution to our model, we construct two numerical schemes to generate an approximate solution to the model. The first one is called the split-step θ-Milstein (SSTM) method, and the second one is called the stochastic split-step θ-nonstandard finite difference (SSSNSFD) method, which is designed by merging split-step θ method with stochastic nonstandard finite difference method for the first time in this paper. Further, we prove the positivity, boundedness, and stability of the SSSTNSFD method. By employing the two mentioned methods, we support the validity of the studied theoretical results, as well, the effect of the length of immunity periods, parameters values of the incidence rates, and noise on the dynamics of the model are discussed and simulated. The increase in the size of time step size plays a vital role in revealing the method that preserves positivity, boundedness, and stability. To this end, a comparison between the proposed numerical methods is carried out graphically.

Abstract In quantum physics, fractional Schrödinger equation is of particular interest in the research of particles on stochastic fields modeled by the Lévy processes, which was derived by extending the Feynman path integral over the Brownian paths to a path integral over the trajectories of Lévy fights. In this work, a fully discrete finite element method (FEM) is developed for the Riesz space-fractional coupled nonlinear Schrödinger equations (CNLS), conjectured with a linearized Crank–Nicolson discretization. The error estimate and mass conservative property are discussed. It is showed that the proposed method is decoupled and convergent with optimal orders in L2 $L^{2}$-sense. Numerical examples are performed to support our theoretical results.

Abstract Fractional differential equations (FDEs) of distributed-order are important in depicting the models where the order of differentiation distributes over a certain range. Numerically solving this kind of FDEs requires not only discretizations of the temporal and spatial derivatives, but also approximation of the distributed-order integral, which brings much more difficulty. In this paper, based on the mid-point quadrature rule and composite two-point Gauss–Legendre quadrature rule, two finite difference schemes are established. Different from the previous works, which concerned only one- or two-dimensional problems with linear source terms, time-fractional wave equations of distributed-order whose source term is nonlinear in two and even three dimensions are considered. In addition, to improve the computational efficiency, the technique of alternating direction implicit (ADI) decomposition is also adopted. The unique solvability of the difference scheme is discussed, and the unconditional stability and convergence are analyzed. Finally, numerical experiments are carried out to verify the effectiveness and accuracy of the algorithms for both the two- and three-dimensional cases.

Abstract In this article, we propose an exponential B-spline approach to obtain approximate solutions for the fractional sub-diffusion equation of Caputo type. The presented method is established via a uniform nodal collocation strategy by using an exponential B-spline based interpolation in conjunction with an effective finite difference scheme in time. The unique solvability is rigorously proved. The unconditional stability is well illustrated via a procedure closely resembling the classic von Neumann technique. A series of numerical examples are carried out, and by contrast to other algorithms available in the open literature, numerical results confirm the validity and superiority of our method.

In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS) with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.

Individuals with Internet gaming disorder (IGD) show deficits in face processing due to long-term Internet-game social activities based on cartoon faces in the popular online game "Strike of Kings." However, the abnormal neurocognitive mechanism of face recognition and processing in individuals with IGD has not been systematically explored. This study used event-related potential (ERP) methods and the reversed deviant-standard oddball paradigm to comprehensively compare four ERP components, namely, P100, N170, P200, and mismatch negativity (MMN), induced in the unconscious and automatic processing of realistic and cartoon faces in individuals with IGD. Results showed that, with respect to cartoon faces, individuals with IGD exhibited not only P100, P200 and MMN enhancements but also the absence of the N170 dominance effect in the left hemisphere. Our results also demonstrated that individuals with IGD had the advantages of early automatic perception of cartoon faces and automatic detection of changes in "cartoon" features. This study enhances our understanding of the mechanism of IGD from the neurocognitive perspective and provides candidate electrophysiological indicators for the clinical diagnosis of IGD.

The loop cutset solving algorithm in the Bayesian network is particularly important for Bayesian inference. This paper proposes an algorithm for solving the approximate minimum loop cutset based on the loop-cutting contribution index. Compared with the existing algorithms, the algorithm uses the loop-cutting contribution index of nodes and node-pairs to analyze nodes from a global perspective, and select loop cutset candidates with node-pair as the unit. The algorithm uses the parameter μ to control the range of node-pairs, and the parameter ω to control the selection conditions of the node-pairs, so that the algorithm can adjust the parameters according to the size of the Bayesian networks, which ensures computational efficiency. The numerical experiments show that the calculation efficiency of the algorithm is significantly improved when it is consistent with the accuracy of the existing algorithm; the experiments also studied the influence of parameter settings on calculation efficiency using trend analysis and two-way analysis of variance. The loop cutset solving algorithm based on the loop-cutting contribution index uses the node-pair as the unit to solve the loop cutset, which helps to improve the efficiency of Bayesian inference and Bayesian network structure analysis.

Bayesian Network is one of the famous network models, and the loop cutset is one of the crucial structures for Bayesian Inference. In the Bayesian Network and its inference, how to measure the relationship between nodes is very important, because the relationship between different nodes has significant influence on the node-probability of the loop cutset. To analyse the relationship between two nodes in a graph, we define the shared node, prove the upper and lower bounds of the shared nodes number, and affirm that the shared node influences the node-probability of the loop cutset according to the theorems and experiments. These results can explain the problems that we found in studying on the statistical node-probability belonging to the loop cutset. The shared nodes are performed not only to improve the theoretical analysis on the loop cutset, but also to the loop cutset solving algorithms, especially the heuristic algorithms, in which the heuristic strategy can be optimized by a shared node. Our results provide a new tool to gauge the relationship between different nodes, a new perspective to estimate the loop cutset, and it is helpful to the loop cutset algorithm and network analysis.

Pearl’s conditioning method is one of the basic algorithms of Bayesian inference, and the loop cutset is crucial for the implementation of conditioning. There are many numerical algorithms for solving the loop cutset, but theoretical research on the characteristics of the loop cutset is lacking. In this paper, theoretical insights into the size and node probability of the loop cutset are obtained based on graph theory and probability theory. It is proven that when the loop cutset in a p-complete graph has a size of p − 2 , the upper bound of the size can be determined by the number of nodes. Furthermore, the probability that a node belongs to the loop cutset is proven to be positively correlated with its degree. Numerical simulations show that the application of the theoretical results can facilitate the prediction and verification of the loop cutset problem. This work is helpful in evaluating the performance of Bayesian networks.

The present study investigated the unsteady magnetohydrodynamic (MHD) nanofluid flow over a radially nonlinear stretching sheet along with the viscosity dependent on temperature, convective boundary condition, thermo-diffusion, and the radiation effects. Moreover, the nanofluid’s viscous effects were considered dependent on temperature and the exponential Reynolds model was considered in this context. It was additionally assumed that a uniform suspension of nanoparticles is present in the base fluid. The Buongiorno model, which involves the thermophoresis and Brownian motion effects, was considered. For the sake of a solution, the variational finite element method was selected with coding in MATLAB and the numerical results were contrasted with the published articles. The influence of various physical parameters on the velocity, temperature, and concentration profiles are discussed by the aid of graphs and tables. It was detected that the nanofuid viscosity parameter declines the fluid flow velocity, while, for the temperature and the concentration profiles, it accomplished the reverse phenomenon.

In this paper, a two-stage filter for removing salt-and-pepper noise using noise detector based on characteristic difference parameter and adaptive directional mean filter is proposed. The first stage firstly detects the noise corrupted pixels by combining characteristic difference parameter and gray level extreme, then develops an improved adaptive median filter to firstly restore them. The second stage introduces a restoration scheme to further restore the noise corrupted pixels, which firstly divides them into two types and then applies different restoration skills for the pixels based on the classification result. One type of pixels is restored by the mean filter and the other type of pixels is restored by the proposed adaptive directional mean filter. The new filter firstly adaptively selects the optimal filtering window and direction template, then replaces the gray level of noise corrupted pixel by the mean value of pixels on the optimal template. Experimental results show that the proposed filter outperforms many existing main filters in terms of noise suppression and detail preservation.

The present article investigates the effect of multiple slips on axisymmetric magnetohydrodynamics (MHD) buoyant nano-fluid flow over a stretching sheet with radiation and chemical effect. The non-linear partial differential equations were transformed to a non-linear control equation using an appropriate similarity transformation. The governing equations were solved through the finite element method. The influence of physical parameters such as multiple slips, magnetic, thermal radiation, Prandtl number, stretching, Brownian motion, thermophoresis, Schmidt number, Lewis number and chemical reaction on the radial velocity, temperature, solutal concentration and nano-fluid volume fraction profile were investigated. We noted that the boundary layers increases in the presence of multiple slip effects whereas, the effect of thermal slip on Nusselt number increases with the increasing values of magnetic and thermal radiation. To verify the convergence of the numerical solution, the computations were made by reducing the mesh size. Finally, our results are parallel to previous scholarly contributions.

In this paper we propose an outlier detection approach for GNSS vector networks based on the specific direction (i.e., SD approach), along which the test statistic constructed reaches the maximum. We derive the unit vector of this specific direction in detail, and prove that the unit vector is the same as that determined by the outlier estimates in three-dimensional (3D) approach, while the distribution of the maximum test statistic in this direction is the square root of Chi-squared distribution. Therefore, eliminating an outlier along this specific direction can get the same result as that of eliminating all three components of outlier vector in 3D approach. The mathematical equivalence of SD approach and 3D approach is further demonstrated by a real GNSS network. Moreover, preliminary application of the SD approach to detect the abnormal antenna height measurement is carried out in terms of numerical simulations of multiple baseline solutions, and it shows that the SD approach can effectively detect baselines that are directly infected by corresponding receiver antenna height errors.

Thanks to the unprecedented success of Gravity Recovery and Climate Experiment (GRACE), its successive mission GRACE Follow-On (GFO) has been in orbit since May 2018 to continue measuring the Earth’s mass transport. In order to possibly enhance GFO in terms of mass transport estimates, four orbit configurations of future polar-type gravity mission (FPG) (with the same payload accuracy and orbit parameters as GRACE, but differing in orbit inclination) are investigated by full-scale simulations in both standalone and jointly with GFO. The results demonstrate that the retrograde orbit modes used in FPG are generally superior to prograde in terms of gravity field estimation in the case of a joint GFO configuration. Considering the FPG’s independent capability, the orbit configurations with 89- and 91-degree inclinations (namely FPG-89 and FPG-91) are further analyzed by joint GFO monthly gravity field models over the period of one-year. Our analyses show that the FPG-91 basically outperforms the FPG-89 in mass change estimates, especially at the medium- and low-latitude regions. Compared to GFO & FPG-89, about 22% noise reduction over the ocean area and 17% over land areas are achieved by the GFO & FPG-91 combined model. Therefore, the FPG-91 is worthy to be recommended for the further orbit design of FPGs.

In this study, we analyzed the three-dimensional flow of Williamson (pseudoplastic) fluids upon a linear porous stretching sheet. The thermal radiation impact was taken into account. The transformed non-linear equations were solved by the homotopy analysis method (HAM). The influence of the embedded parameters tretching parameter, Williamson parameter, porosity parameter, thermal radiation parameter, thermophoresis parameter, Brownian motion parameter, Prandtl number and Biot number are presented on velocity, temperature and concentration functions in the graphs and explained in detail. The velocity function along the x-direction reduces with the impact of the stretching, porosity and Williamson parameters. Velocity along the y-direction increases with the stretching parameter, while it reduces with the porosity and Williamson parameters. The effect of Skin friction, heat transfer and mass transfer are shown numerically. The numerical values of surface drag force and the impact of different parameters are calculated and it is observed that increasing the stretching parameter and the porosity parameter reduces the surface drag force, while increasing the Williamson parameter augments the surface drag force. Higher values of the stretching parameter, the Prandtl number and the radiation parameter enhance the heat transfer rate, while the augmented value of the thermophoresis and Brownian motion parameters reduces the heat transfer rate, where higher values of the stretching parameter, thermophoresis and Brownian motion parameters enhance the mass transfer rate.

A novel graphene-based nanocomposite particles (NH2-rGO/WS2), composed of reduced graphene oxide (rGO) and tungsten disulfide (WS2) grafted with active amino groups (NH2-rGO/WS2), was successfully synthesized by an effective and facile method. NH2-rGO/WS2 nanoparticles were then used to fabricate new bismaleimide (BMI) composites (NH2-rGO/WS2/BMI) via a casting method. The results demonstrated that a suitable amount of NH2-rGO/WS2 nanoparticles significantly improved the mechanical properties of the BMI resin. When the loading of NH2-rGO/WS2 was only 0.6 wt %, the impact and flexural strength of the composites increased by 91.3% and 62.6%, respectively, compared to the neat BMI resin. Rare studies have reported such tremendous enhancements on the mechanical properties of the BMI resin with trace amounts of fillers. This is attributable to the unique layered structure of NH2-rGO/WS2 nanoparticles, fine interfacial adhesion, and uniform dispersion of NH2-rGO/WS2 in the BMI resin. Besides, the thermal gravimetrical analysis (TGA) revealed that the addition of NH2-rGO/WS2 could also improve the stability of the composites.

Surface modification of graphene oxide (GO) is one of the most important issues to produce high performance GO/epoxy composites. In this paper, the imidazole ionic liquid (IMD-Si) was introduced onto the surface of GO sheets by a cheap and simple method, to prepare a reinforcing filler, as well as a catalyst in epoxy resin. The interlayer spacing of GO sheets was obviously increased by the intercalation of IMD-Si, which strongly facilitated the dispersibility of graphene oxide in organic solvents and epoxy matrix. The addition of 0.4 wt % imidazolium ionic liquid modified graphene oxide (IMD-Si@GO), yielded a 12% increase in flexural strength (141.3 MPa), a 26% increase in flexural modulus (4.69 GPa), and a 52% increase in impact strength (18.7 kJ/m2), compared to the neat epoxy. Additionally the IMD-Si@GO sheets could catalyze the curing reaction of epoxy resin-anhydride system significantly. Moreover, the improved thermal conductivities and thermal stabilities of epoxy composites filled with IMD-Si@GO were also demonstrated.