Approximation Technique Research Articles

Surface-Enhanced Raman Scattering Combined with Machine Learning for Rapid and Sensitive Detection of Anti-SARS-CoV-2 IgG

This work reports an efficient method to detect SARS-CoV-2 antibodies in blood samples based on SERS combined with a machine learning tool. For this purpose, gold nanoparticles directly conjugated with spike protein were used in human blood samples to identify anti-SARS-CoV-2 antibodies. The comprehensive database utilized Raman spectra from all 594 blood serum samples. Machine learning investigations were carried out using the Scikit-Learn library and were implemented in Python, and the characteristics of Raman spectra of positive and negative SARS-CoV-2 samples were extracted using the Uniform Manifold Approximation and Projection (UMAP) technique. The machine learning models used were k-Nearest Neighbors (kNN), Support Vector Machine (SVM), Decision Trees (DTs), logistic regression (LR), and Light Gradient Boosting Machine (LightGBM). The kNN model led to a sensitivity of 0.943, specificity of 0.9275, and accuracy of 0.9377. This study showed that combining Raman spectroscopy and a machine algorithm can be an effective diagnostic method. Furthermore, we highlighted the advantages and disadvantages of each algorithm, providing valuable information for future research.

Distributed Photovoltaic Communication Anomaly Detection Based on Spatiotemporal Feature Collaborative Modeling

As distributed photovoltaic (PV) technology rapidly develops and is widely applied, the methods of cyberattacks are continuously evolving, posing increasingly severe threats to the communication networks of distributed PV systems. Recent studies have shown that the Transformer model, which effectively integrates global information and handles long-distance dependencies, has garnered significant attention. Based on this, our research proposes a model named STformer, which is applied to the task of attack detection in distributed PV communication. Specifically, we propose a temporal attention mechanism and a variable attention mechanism. The temporal attention mechanism focuses on capturing subtle changes and trends in data sequences over time, ensuring a highly sensitive recognition of patterns inherent in time-series data. In contrast, the variable attention mechanism analyzes the intrinsic relationships and interactions between different variables, uncovering critical correlations that may indicate abnormal behavior or potential attacks. Additionally, we incorporate the Uniform Manifold Approximation and Projection (UMAP) dimensionality reduction technique. This technique not only helps reduce computational complexity but, in certain cases, can enhance anomaly detection performance. Finally, compared to classical and advanced methods, STformer demonstrates satisfactory performance in simulation experiments.

Optimizing Methane Uptake on N/O Functionalized Graphene via DFT, Machine Learning, and Uniform Manifold Approximation and Projection (UMAP) Techniques

Optimizing Methane Uptake on N/O Functionalized Graphene via DFT, Machine Learning, and Uniform Manifold Approximation and Projection (UMAP) Techniques

A type II radio burst associated with solar filament–filament interaction

Aims. Solar radio type II bursts are often associated with coronal shocks driven by solar eruptions. In this study, we report a type II burst associated with filament–filament interaction. Methods. Combining the high-quality multiwavelength observations from CHASE, SDO, STEREO, and CALLISTO, we conducted a detailed study of the type II burst associated with filament–filament interaction. Results. On 2023 September 11, an erupting filament (F1) likely disturbed a nearby long filament (F2), causing F2 to subsequently erupt. As a result of possible magnetic reconnection between ejective materials from the two filaments, loop-like structures formed perpendicular to them. Subsequently, the expansion of these loop-like structures triggered a strong coronal mass ejection (CME). Interestingly, a type II burst appeared on the solar spectrum around the time when the loop-like structures formed and the CME appeared above the occulting disk of STEREO/COR1. By converting the frequency of the type II burst to the coronal height using polarization brightness data recorded by the COR1 coronagraph and the spherically symmetric polynomial approximation technique, we determined the formation height of the type II burst to be around 1.45 R⊙, with a speed of approximately 440 km s−1. This is comparable to the observed height of the CME (∼1.43 R⊙), although slightly lower in speed (540 km s−1). Conclusions. All these results indicate that the type II burst was closely associated with filament–filament interactions and was possibly excited by the accompanying CME at the flank. We suggest that the filament–filament interactions played an important role in producing the type II burst by acting as a piston to trigger a strong CME.

Long-Term Orthopaedic and Radiological Outcomes of Symphysis Approximation without Osteotomy in Primary Bladder Exstrophy Repair.

Previous assumptions suggested that the technique of approximation without osteotomy in primary exstrophy repair (PER) could only be applied in newborns and anticipated poorer outcomes. Recent studies indicated that this technique can be successfully executed not only in immediate PER but also yields favorable long-term results. Therefore, we evaluated and compared the orthopaedic and radiological long-term outcomes after pubic symphysis approximation without osteotomy in immediate and delayed PER. From March 2018 to December 2020, individuals with PER and approximation of the symphysis without osteotomy were recruited. Patients <12 years and with a history of orthopaedic surgery of the bony pelvis were excluded. Orthopaedic examinations and magnetic resonance imaging (MRI) of the bony pelvis including the hip joints were performed and pubic diastasis, the acetabulum angle (ACA), and the center-edge angle (CEA) were evaluated. Twenty-nine patients were included, 11 of them had an immediate and 18 had a delayed PER. Between the two groups, no significant differences could be observed concerning hip pain (p = 0.419), mobility impairment (p = 0.543), sports impairment (p = 0.543), hip impingement (p = 1.000), leg length discrepancy (p = 0.505), and width of the pubic diastasis as measured by MRI (p = 0.401). There were also no significant differences with regard to CEA right (median 30 degrees, p = 0.976), CEA left (median 31.5 degrees, p = 0.420), ACA right (median 19 degrees, p = 0.382), and ACA left (median 17 degrees, p = 0.880). There were no significant differences in clinical orthopaedic or radiological long-term outcomes between bladder exstrophy patients after immediate and delayed bladder closure with symphysis approximation without osteotomy. Establishing core outcome sets is essential to get robust and comparable results, further advancing and substantiating our initial insights.

Oblique Wave Scattering by a Pair of Asymmetric Inverse Π-Shaped Breakwater

Abstract The topic of wave scattering by different breakwaters has unfolded over the past few decades, largely driven by the profound impacts of global climate change. In this study, a completely new type of breakwater, inverse Π-shaped breakwater, has been taken into account for serving both purposes from analytical as well as an application point of view. During the formulation, the actual physical problem is transferred into a boundary value problem by employing the small amplitude water wave theory. With the aid of eigenfunction expansion, the problem is reduced to a set of integral equations having square-root singularities at the submerged edges of thin structures. To address such singularities, a multi-term Galerkin approximation technique is used along with Chebyshev polynomials (multiplied with suitable weights) as basis functions. The numerical methodology employed here validates with different previous literatures as special cases. Then, numerical solutions of the reflection and transmission coefficients, hydrodynamic forces are graphically illustrated across various dimensionless structural parameters. In summary, the present paper offers valuable insights into the dynamics of wave scattering by a pair of asymmetric inverse bottom-mounted Π-shaped breakwater, emphasizing the role of different non-dimensional parameters in this system.

The Synthesis of Spherical Four-bars for Biomimetic Motion through Complete Solutions for Approximate Rigid Body Guidance

Abstract In this paper, we form a constrained optimization problem for spherical four-bar motion generation. Instead of using local optimization methods, all critical points are found using homotopy continuation solvers. The complete solution set provides a full view of the optimization landscape and gives the designer more freedom in selecting a mechanism. The motion generation problem admits 61 critical points, of which two must be selected for each four-bar mechanism. We sort solutions by objective value and perform a second order analysis to determine if the solution is a minimum, maximum, or saddle point. We apply our approximate synthesis technique to two applications: a hummingbird wing mechanism and a sea turtle flipper gait. Suitable mechanisms were selected from the respective solution sets and used to build physical prototypes.

Optimization of the electric vehicle charging strategy problem for sustainable intercity travels with multiple refueling stops

Electric vehicle (EV) drivers considering long-distance trips still face range anxiety due to the limited range of EVs and the scarcity of charging stations. Thus, it becomes important to ensure the feasibility of the selected route and determine an optimal charging strategy. As a crucial aspect of decision support for EV drivers, this study proposes a mixed integer linear programming (MILP) approach for the EV charging strategy problem (EVCSP), incorporating a piecewise linear approximation technique to address the challenges posed by nonlinear charging times. The proposed optimization model, namely CSPM determines where, when, and how much to charge an EV for a specified route to minimize travel time and cost. The solution time of large-scale test problems and a case study on Türkiye reveal the robustness and reliability of the CSPM. Furthermore, two multi-objective optimization methods (the weighted sum and the lexicographic method) are applied to the case study, and the results are analyzed. The results indicate that the travel cost is more sensitive to the selected charging strategy, with a range of 46.09 % across the applied charging strategies, whereas travel time remains more resilient, with a maximum fluctuation of 19.77 %. A comparative analysis with a full charging strategy reveals that the CSPM reduces the travel time by 60.1 % and improves the cost efficiency by 105.72 %.

Advanced classification of hot subdwarf binaries using artificial intelligence techniques and Gaia DR3 data

Hot subdwarf stars are compact blue evolved objects, burning helium in their cores surrounded by a tiny hydrogen envelope. In the Hertzsprung-Russell Diagram they are located by the blue end of the Horizontal Branch. Most models agree on a quite probable common envelope binary evolution scenario in the Red Giant phase. However, the current binarity rate for these objects is yet unsolved, but key, question in this field. This study aims to develop a novel classification method for identifying hot subdwarf binaries within large datasets using Artificial Intelligence techniques and data from the third Gaia data release (GDR3). The results will be compared with those obtained previously using Virtual Observatory techniques on coincident samples. The methods used for hot subdwarf binary classification include supervised and unsupervised machine learning techniques. Specifically, we have used Support Vector Machines (SVM) to classify 3084 hot subdwarf stars based on their colour-magnitude properties. Among these, 2815 objects have Gaia DR3 BP/RP spectra, which were classified using Self-Organizing Maps (SOM) and Convolutional Neural Networks (CNN). In order to ensure spectral quality, previously to SOM and CNN classification, our 2815 BP/RP set were pre-analysed with two different approaches: the cosine similarity technique and the Uniform Manifold Approximation and Projection (UMAP) technique. Additional analysis onto a golden sample of 88 well-defined objects, is also presented. The findings demonstrate a high agreement level (sim 70-90&lt;!PCT!&gt;) with the classifications from the Virtual Observatory Sed Analyzer (VOSA) tool. This shows that the SVM, SOM, and CNN methods effectively classify sources with an accuracy comparable to human inspection or non-AI techniques. Notably, SVM in a radial basis function achieves 70.97&lt;!PCT!&gt; reproducibility for binary targets using photometry, and CNN reaches 84.94&lt;!PCT!&gt; for binary detection using spectroscopy. We also found that the single--binary differences are especially observable on the infrared flux in our Gaia DR3 BP/BR spectra, at wavelengths larger than $ sim $700 nm. We find that all the methods used are in fairly good agreement and are particularly effective to discern between single and binary systems. The agreement is also consistent with the results previously obtained with VOSA. In global terms, considering all quality metrics, CNN is the method that provides the best accuracy. The methods also appear effective for detecting peculiarities in the spectra. While promising, challenges in dealing with uncertain compositions highlight the need for caution, suggesting further research is needed to refine techniques and enhance automated classification reliability, particularly for large-scale surveys.

An almost sure limit theorem for the maximum interpoint distance of random vectors in spaces of growing dimension

Let { p n ; n ≥ 1 } be a sequence of positive integers. Let X 1 , … , X p n be i.i.d. random vectors in ℝ n with i.i.d. components that are centered and have variance 1. Consider the maximum interpoint distance M n = max 1 ≤ i < j ≤ p n ‖ X i − X j ‖ 2 . This article presents the almost sure limit theorem for M n under the polynomial and the exponential growth regimes for the dimension. The proofs rely on the moderate deviation principle of the partial sum of i.i.d. random variables, the Chen–Stein Poisson approximation method, and Gaussian approximation techniques.

Distance preserving machine learning for uncertainty aware accelerator capacitance predictions

Abstract Accurate uncertainty estimations are essential for producing reliable machine learning models, especially in safety-critical applications such as accelerator systems. Gaussian process models are generally regarded as the gold standard for this task; however, they can struggle with large, high-dimensional datasets. Combining deep neural networks with Gaussian process approximation techniques has shown promising results, but dimensionality reduction through standard deep neural network layers is not guaranteed to maintain the distance information necessary for Gaussian process models. We build on previous work by comparing the use of the singular value decomposition against a spectral-normalized dense layer as a feature extractor for a deep neural Gaussian process approximation model and apply it to a capacitance prediction problem for the High Voltage Converter Modulators in the Oak Ridge Spallation Neutron Source. Our model shows improved distance preservation and predicts in-distribution capacitance values with less than 1% error.

Robust adaptive impedance control of coordinated electrically driven robots: An engineering application for the (p,q)-analogue of Bernstein-Stancu operators

Function approximation techniques have emerged as influential mathematical tools for designing compliant motion controllers capable of managing objects using multiple electrical manipulators without the need for exact models. However, their effectiveness often relies on having access to velocity signals, which may not always be practical in real-world situations. This paper introduces an observer-based robust adaptive impedance control strategy that employs the (p,q)-analogue of Bernstein-Stancu operators as uncertainty estimators to tackle uncertainties in collaborative multiple electrical manipulators. This approach leverages visual task-space information and doesn’t depend on velocity feedback, enhancing cost-effectiveness and applicability in practical robotic systems. The lumped uncertainty is first modeled by this operator. The adaptation laws, derived from stability analysis, are then employed to tune its coefficients, which are not presented in the previous literature. By applying the Lyapunov lemma, the paper ensures that error signals in the controlled system are uniformly ultimately bounded (UUB). The suggested controller is evaluated in a system featuring two arms managing a rigid load. Simulation results showcase the effectiveness and versatility of the proposed approach. The outcomes are also compared with two advanced approximation techniques to demonstrate the precision and effectiveness of the suggested controller design.

Convergence rates and central limit theorem for 3-D stochastic fractional Boussinesq equations with transport noise

This work investigates the 3-D stochastic modified fractional Boussinesq equations driven by transport noise on the torus. The existence of weak solutions is initially established through Galerkin approximation and compactness techniques. Subsequently, we demonstrate that the weak solutions of stochastic modified fractional Boussinesq equations converge to the unique solution of a deterministic Boussinesq model with fractional dissipation, subject to an appropriate noise scaling, along with providing the quantitative estimates with explicit convergent rates. Finally, the central limit theorem with an explicit convergence rate is established based on the aforementioned scaling limit. It is noteworthy that the scaling limit result of stochastic modified fractional Boussinesq equations to deterministic Boussinesq models with additional fractional dissipation implies that the transport noise regularizes the modified fractional Boussinesq equations, thus leading to “approximate weak uniqueness”.

Adaptive model-free disturbance rejection for continuum robots

This paper presents two model-free control strategies for the rejection of unknown disturbances in continuum robots. The strategies utilize a neural network-based approximation technique to estimate the uncertain Jacobian matrix using position measurements. The first strategy is designed for periodic disturbances and employs an adaptive model-free controller in conjunction with an adaptive disturbance observer. The second strategy is designed for robustness against arbitrary disturbances and employs time-varying input and update law gains that grow monotonically, resulting in the achievement of asymptotic, exponential, and prescribed-time reference trajectory tracking. The notion of fixed-time stabilization in prescribed time is particularly noteworthy, as it allows for the predefinition of a terminal time, independent of initial conditions and system parameters. A formal stability analysis is presented for each strategy, and the strategies are both tested experimentally with a concentric tube robot subject to unknown disturbances.

РАЗРАБОТКА ПРОГРАММЫ РАСЧЕТА ПАРАМЕТРОВ СХЕМЫ ЗАМЕЩЕНИЯ ТРЕХФАЗНОГО АСИНХРОННОГО ЭЛЕКТРОДВИГАТЕЛЯ

The article is devoted to developing a program for calculating the parameters of a T-shaped equivalent circuit of three-phase asynchronous electric motors. The relevance of this work is due to the need to obtain reliable results of computer simulation modelling of electric drive systems in software packages. The aim of the study is to implement in a convenient software interface an analytical technique for calculating the parameters of an asynchronous motor equivalent circuit with minimal deviations from the catalogue data. For the software calculation of the equivalent circuit parameters the paper considers analytical approximation and iterative counting techniques, since they do not require experiments on industrial electrical equipment. A comparative analysis of such techniques is performed using the example of a three-phase asynchronous motor brand BA280S4 with a power of 110 kW. The results of the compar-ative analysis show that the highest reliability of the mechanical and electromechanical characteristics is achieved in the case of using the iterative counting technique with minimizing the objective function of the sum of the weighted squares of the deviations of the control point values from the catalogue data. The authors implement the program for calculating the equivalent circuit parameters according to the selected calculation method in the Embarcadero Delphi environment. The reliable values of the electric motor parameters calculated by the program will allow for computer to model electric drive systems that best matches real objects.

Iterative Numerical Approximation Technique for 3D Eddy Current Models in Harmonic Regime Based on the Electromagnetic T-Formulation and the Finite Element Method

In this paper, an iterative numerical approximation technique is used for analyzing the distribution of eddy currents density in conductive materials plates by using the electromagnetic T-formulation and the Biot-Savart law, solved by the finite element method. The proposed approach allows for the meshing of the different parts of the studied system separately, including the sensor and the conductive plate, without the need for an air region. Firstly, this approach reduces the number of unknown variables by avoiding the air region of the system's mesh. Secondly, it simplifies the consideration of the sensor's motion without the need to remesh the system. For this purpose, a calculation code has been developed for solving an electromagnetic three-dimensional non-destructive testing model. This latter permits the resolution of JSEAM # 6 Benchmark problem to validate the proposed method. The impedance variation due to the presence of a defect are evaluated. The obtained results are compared with the experimental ones found in the literature. These results reveal a good agreement, which proves the validity of the proposed method.

Comparison of Adams-Bashforth-Moulton and Dormand-Prince Methods in Lengyel-Epstein Reaction Model Forming Zinc Oxide Nanostructures

This study adopts a numerical approach in the Lengyel-Epstein reaction model for forming zinc oxide (ZnO) nanostructures. It aims to determine the optimal approximation technique to analyze the growth of ion concentrations in ZnO nanostructures. For this purpose, ordinary differential equations are developed using the Dormand-Prince method in the Lengyel-Epstein reaction model. The results obtained from this technique are compared with the results obtained from the Adams-Bashforth-Moulton (ABM) method. After a comparative analysis of both methods, the results showed that the ABM method performs better than the Dormand-Prince method. The accuracy and stability of the ABM method are higher than those of the Dormand-Prince method. Furthermore, error analysis for both methods confirms that the results obtained from the former are more optimized. Moreover, this method also validates the results obtained from the experimental procedure by using the aqueous chemical growth (ACG) method to form the nanostructures of ZnO.

Prediction of s^{±}-Wave Superconductivity Enhanced by Electronic Doping in Trilayer Nickelates La_{4}Ni_{3}O_{10} under Pressure.

Motivated by the recently reported signatures of superconductivity in trilayer La_{4}Ni_{3}O_{10} under pressure, we comprehensively study this system using abinitio and random-phase approximation techniques. Without electronic interactions, the Ni d_{3z^{2}-r^{2}} orbitals show a bonding-antibonding and nonbonding splitting behavior via the O p_{z} orbitals inducing a "trimer" lattice in La_{4}Ni_{3}O_{10}, analogous to the dimers of La_{3}Ni_{2}O_{7}. The Fermi surface consists of three electron sheets with mixed e_{g} orbitals, and a hole and an electron pocket made up of the d_{3z^{2}-r^{2}} orbital, suggesting a Ni two-orbital minimum model. In addition, we find that superconducting pairing is induced in the s^{±}-wave channel due to partial nesting between the M=(π,π) centered pockets and portions of the Fermi surface centered at the Γ=(0,0) point. With changing electronic density n, the s^{±} instability remains leading and its pairing strength shows a domelike behavior with a maximum around n=4.2 (∼6.7% electron doping). The superconducting instability disappears at the same electronic density as that in the new 1313 stacking La_{3}Ni_{2}O_{7}, correlated with the vanishing of the hole pocket that arises from the trilayer sublattice, suggesting that the high-T_{c} superconductivity of La_{3}Ni_{2}O_{7} does not originate from a trilayer and monolayer structure. Furthermore, we confirm the experimentally proposed spin state in La_{4}Ni_{3}O_{10} with an in-plane (π, π) order and antiferromagnetic coupling between the top and bottom Ni layers, and spin zero in the middle layer.

Investigation of the Sigma Approximation Technique for the Solution of the Time Spectral Equation System

Abstract The time spectral method is commonly utilized to analyze periodic unsteady flows within turbomachines. However, the time spectral solutions in regions with large temporal and spatial gradients, such as wakes, shocks, and boundary layers, can be plagued with unphysical oscillations, known as the Gibbs phenomenon. This paper presents an investigation into the sigma approximation technique, which is capable of significantly attenuating the Gibbs phenomenon by dampening high-frequency nonlinear components in the time spectral solutions. However, the optimal combination of the sigma factors remains to be ascertained considering the trade-off between the accuracy of solutions and the reduction of unphysical oscillations. In this study, a two-row compressor configuration is first selected, and numerical simulations are performed to evaluate the efficacy of this technique under near peak-efficiency and near-stall operating conditions. It is found that Gibbs-type unphysical oscillations can be effectively mitigated without notably compromising solution accuracy through an optimal combination of sigma factors. The NASA Stage 35 case study further verifies the effectiveness of the proposed optimal sigma factor combination in preserving the accuracy of time spectral solutions based on the data from test rig. Moreover, the von Neumann analysis reveals that the sigma approximation technique can enhance the numerical stability of the time spectral equation system, thereby allowing the use of aggressive numerical parameters to accelerate convergence. The stability analysis results are verified by a two-dimension bump under two different flow conditions and further assessed using the two-row compressor.

Total-current population-dependent branching processes: analysis via stochastic approximation

We consider continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. We assume finite second-moment conditions and use the stochastic approximation technique for the analysis. In particular, we identify an appropriate ordinary differential equation (ODE) and show that either of the two events occurs with a certain probability: (a) the time-asymptotic proportion of the populations converges to the attractors or saddle points of the ODE, (b) it enters every neighbourhood and exits some neighbourhood of a saddle point infinitely often. We also prove a finite time approximation result for the stochastic trajectory. Further, we analyse a branching process with attack and acquisition, which captures the competition in online viral markets; for this case, the probability of approximation equals one.