Auxiliary Functions Research Articles

Accelerating Analytic-Continuation GW Calculations with a Laplace Transform and Natural Auxiliary Functions.

We present a simple and accurate GW implementation based on a combination of a Laplace transform (LT) and other acceleration techniques used in post-self-consistent field quantum chemistry, namely, natural auxiliary functions and the frozen-core approximation. The LT-GW approach combines three major benefits: (a) a small prefactor for computational scaling, (b) easy integration into existing molecular GW implementations, and (c) significant performance improvements for a wide range of possible applications. Illustrating these advantages for systems consisting of up to 352 atoms and 7412 basis functions, we further demonstrate the benefits of this approach combined with an efficient implementation of the Bethe-Salpeter equation.

Fixed-time nonsingular terminal sliding mode control for trajectory tracking of uncertain robot manipulators

Fixed-time nonsingular terminal sliding mode control for trajectory tracking of uncertain robot manipulators

Adaptive Bipartite Consensus of Multi-agent Systems with Parameter Uncertainty and Leader of Nonzero Input under Signed Digraph

This article investigates the bipartite consensus problem for a class of multi-agent systems (MASs) with parameter uncertainty and leader of nonzero input under a signed digraph. Due to the unknown and time-varying input signal of the leader, followers are unable to obtain accurate information about the leader. For this purpose, a distributed adaptive observer is designed based on parameterization theory. Then, considering the existence of parameter uncertainty in the MASs, an auxiliary function is designed to compensate for the impact of uncertainty. Afterwards, an adaptive controller with dynamic coupling gain is designed based on observation errors and auxiliary function. Subsequently, it is demonstrated that the MASs with parameter uncertainty and leader of nonzero input can achieve bipartite consensus by stability analysis. Finally, the effectiveness of the proposed scheme is verified through simulation.

A Dexterous Hand-Arm Teleoperation System Based on Hand Pose Estimation and Active Vision.

Markerless vision-based teleoperation that leverages innovations in computer vision offers the advantages of allowing natural and noninvasive finger motions for multifingered robot hands. However, current pose estimation methods still face inaccuracy issues due to the self-occlusion of the fingers. Herein, we develop a novel vision-based hand-arm teleoperation system that captures the human hands from the best viewpoint and at a suitable distance. This teleoperation system consists of an end-to-end hand pose regression network and a controlled active vision system. The end-to-end pose regression network (Transteleop), combined with an auxiliary reconstruction loss function, captures the human hand through a low-cost depth camera and predicts joint commands of the robot based on the image-to-image translation method. To obtain the optimal observation of the human hand, an active vision system is implemented by a robot arm at the local site that ensures the high accuracy of the proposed neural network. Human arm motions are simultaneously mapped to the slave robot arm under relative control. Quantitative network evaluation and a variety of complex manipulation tasks, for example, tower building, pouring, and multitable cup stacking, demonstrate the practicality and stability of the proposed teleoperation system.

Investigating the entry of symmetric/asymmetric elastic wedge into water

Understanding the impact of fluid–structure interaction during the entry of a marine vessel into water is crucial for its design. While numerous models have been proposed to investigate the penetration of symmetric elastic wedges into water, in this study, we propose a numerical model that combines the fully nonlinear boundary element method with a mode superposition method to analyze the penetration of symmetric and asymmetric elastic wedges into water. We derive the boundary conditions of the acceleration potential within the flow field for the problem of fluid–structure interaction and use auxiliary functions to decompose the acceleration potential and extract the instantaneous added mass. Following this, the differential equations of the modes of rigid motion and elastic deformation of the body are established and solved. This approach enables the simultaneous solution of the motion and vibrations of the wedge as well as the hydrodynamic pressure. The proposed model also accounts for flow separation while the wedge is submerged, thereby prolonging the simulation. We confirmed the validity of the model through comprehensive examinations based on semi-analytical, computational, and experimental data on the problem of the entry of a symmetric body into water. We then extended our study to encompass the free-falling entry of an asymmetric elastic wedge into water. The results revealed notable discrepancies in the evolution of deformation and jet flow between the right and left boundaries during the entry of the wedge into water.

Comparative study of fractional Newell–Whitehead–Segel equation using optimal auxiliary function method and a novel iterative approach

This research explores the solution of the time-fractional Newell–Whitehead–Segel equation using two separate methods: the optimal auxiliary function method and a new iterative method. The Newell–Whitehead–Segel equation holds significance in modeling nonlinear systems, particularly in delineating stripe patterns within two-dimensional systems. Employing the Caputo fractional derivative operator, we address two case study problems pertaining to this equation through our proposed methods. Comparative analysis between the numerical results obtained from our techniques and an exact solution reveals a strong alignment. Graphs and tables illustrate this alignment, showcasing the effectiveness of our methods. Notably, as the fractional orders vary, the results achieved at different fractional orders are compared, highlighting their convergence toward the exact solution as the fractional order approaches an integer. Demonstrating both interest and simplicity, our proposed methods exhibit high accuracy in resolving diverse nonlinear fractional order partial differential equations.

Predefined-time sliding mode attitude control for liquid-filled spacecraft with large amplitude sloshing

In the present study, a predefined-time attitude stabilization for liquid-filled spacecraft with large liquid sloshing is investigated under input saturation and external disturbance. First, the large slosh of the liquid is equivalent to the motion pulsating ball model (MPBM), and the dynamic model of the rigid-liquid coupling system is established. Then, liquid sloshing state quantity-related items and external disturbances are combined to form a lumped disturbance. A predefined-time disturbance observer is proposed to accurately reconstruct the lumped disturbance within a predefined-time regardless of the initial estimated state. Based on the proposed predefined-time disturbance observer, a predefined-time sliding mode surface is designed. The predefined-time stability of the proposed observer and controller is proved using the Lyapunov function. Finally, a variable-speed reaching law and exponential reaching law are combined to suppress the chattering caused by sliding mode control. To this end, a new auxiliary function is developed to consider the effects of input saturation. The simulation results show that the proposed controller can effectively stabilize the attitude stability of the liquid-filled spacecraft.

The Utility Model Relates to a Structure Design of a Drawbar Trolley with a Telescopic Stool

As a convenient handling tool, the pull rod car can use people's pushing and pulling to easily carry heavy objects, achieve the handling tasks that people need to complete, and reduce the burden on the shoulders and arms. The use of a trolley can reduce people's physical consumption, avoid overwork, especially suitable for long walks or need to carry a large number of items. Its biggest advantage is that it can complete different handling tasks through simple operations, so as to help people easily move items. The main design task of this paper is to transform the traditional draw-bar car, so that it has the function of telescopic stool and upstairs power. The design aims to solve the problem of carrying items and needing rest during shopping, providing a more convenient shopping experience. The specific design idea is to take the stool as the main body, and the shopping cart becomes its auxiliary function; The slider is used as a telescopic mechanism to realize the smooth expansion and contraction of the stool; Add the upstairs power function to drive the shopping cart upstairs through the motor and remote control. In terms of technical implementation, the base is welded with steel, the stool is made of high-strength polymer materials, and the telescopic mechanism is made of sliders. This paper mainly uses UG to carry out 3D modeling.

Implementation of intelligent healthcare image detection system based on OpenCV

As an interface between image processing technology and the real world, image detection can achieve real-time capture of information such as images and movements. It has wide applications in fields such as medical rehabilitation, military simulation, and intelligent recognition. This article aims to achieve autonomous medical detection and assist doctors in diagnosis. Based on a detailed analysis of the principles of image detection technology and the current development status of image detection technology, a comprehensive medical detection system solution is designed. Addressing issues such as the tension of hospital registration queues, lengthy doctor-patient consultations, lack of auxiliary diagnostic functions, and non-visualizable diagnosis and treatment results, this study utilizes literature analysis and modeling to simulate the collection and intelligent analysis of surface images of the human body and limb movements. This enables the realization of functions such as image detection, image capture, image transmission, image processing, and medical feedback. This article has completed the design of an intelligent medical system, solving the problem of low medical diagnosis efficiency. At the same time, it has been found that the clarity of infrared thermal imaging images is not high, which affects the accuracy of collecting human surface images and limb movements. The processing of infrared thermal imaging images has become a direction that needs further research.

Oral Administration of Fermented Milk from Co-Starter Containing Lactobacillus plantarum Y44 Shows an Ameliorating Effect on Hypertension in Spontaneously Hypertensive Rats.

Fermented dairy foods such as yogurt exhibit some beneficial effects on consumers, including relieving the symptoms of hypertension. This study aims to obtain fermented dairy products from a co-starter that have a great flavor and the auxiliary function of reducing blood pressure after longtime consumption. Commercial starter cultures composed of Lactobacillus delbrueckii subsp. bulgaricus CICC 6047 and Streptococcus thermophilus CICC 6038 were combined with Lactobacillus plantarum strains Y44, Y12, and Y16, respectively, as a combined starter culture to ferment the mixed milk of skim milk and soybean milk. The fermented milk produced using the combined starter culture mixed with L. plantarum Y44 showed an angiotensin-converting-enzyme (ACE) inhibitory activity (53.56 ± 0.69%). Some peptides that regulate blood pressure were released in the fermented milk, such as AMKPWIQPK, GPVRGPFPII, LNVPGEIVE, NIPPLTQTPV, and YQEPVL. In spontaneously hypertensive rat (SHR) oral-administration experiments compared with the gavage unfermented milk group, the gavage feeding of SHRs with the fermented milk produced using the combined starter culture mixed with L. plantarum Y44 significantly reduced the blood pressure of the SHRs after long-term intragastric administration, shown with the systolic blood pressure (SBP) and diastolic blood pressure (DBP) decreasing by 23.67 ± 2.49 mmHg and 15.22 ± 2.62 mmHg, respectively. Moreover, the abundance of short-chain fatty acids (SCFA), bacterial diversity in the gut microbiota, and SCFA levels including acetic acid, propionic acid, and butyric acid in the feces of the SHRs were increased via oral administration of the fermented milk produced using the combined starter culture containing L. plantarum Y44. Furthermore, the ACE-angiotensin II (Ang II)-angiotensin type 1 (AT 1) axis was downregulated, the angiotensin-converting-enzyme 2 (ACE 2)-angiotensin(1-7) (Ang1-7)-Mas receptor axis of the SHRs was upregulated, and then the RAS signal was rebalanced. The fermented milk obtained from the combined starter culture shows the potential to be a functional food with antihypertension properties.

Fractional Heat Conduction with Heat Absorption in a Solid with a Spherical Cavity under Time-Harmonic Heat Flux

The central-symmetric time-fractional heat conduction equation with heat absorption is investigated in a solid with a spherical hole under time-harmonic heat flux at the boundary. The problem is solved using the auxiliary function, for which the Robin-type boundary condition with a prescribed value of a linear combination of a function and its normal derivative is fulfilled. The Laplace and Fourier sine–cosine integral transformations are employed. Graphical representations of numerical simulation results are given for typical values of the parameters.

Parasitic Reflection Eliminating for Planar Elements Based on Multi-Frequency Phase-Shifting in Phase Measuring Deflectometry.

Phase measuring deflectometry (PMD) stands as an extremely important technique for specular surface measurement. However, the parasitic reflection from the rear surface poses a challenge for PMD. To solve this problem, this paper proposes an effective method based on multi-frequency and phase-shifting to search for the correct phase. Firstly, the relationship between the phase error and fringe frequency is adequately investigated. Subsequently, an auxiliary function is established to find the special frequency at which the phase error is zero theoretically and the unwrapped phase is the phase of the top surface exactly. Then, the shape of the top surface can be reconstructed correctly. A standard plane element with a thickness of 40 mm and a flat glass with 19 mm were measured. The experimental results verify the feasibility of the proposed method. Considering the result of the interferometer as a reference, the RMSE of the error map is up to 20 nm for the standard plane element. The experimental results demonstrate that the proposed method can successfully untangle the superposed reflections and reliably reconstruct the top surface of the object under test.

MISNet: multi-source information-shared EEG emotion recognition network with two-stream structure.

When constructing machine learning and deep neural networks, the domain shift problem on different subjects complicates the subject independent electroencephalography (EEG) emotion recognition. Most of the existing domain adaptation methods either treat all source domains as equivalent or train source-specific learners directly, misleading the network to acquire unreasonable transfer knowledge and thus resulting in negative transfer. This paper incorporates the individual difference and group commonality of distinct domains and proposes a multi-source information-shared network (MISNet) to enhance the performance of subject independent EEG emotion recognition models. The network stability is enhanced by employing a two-stream training structure with loop iteration strategy to alleviate outlier sources confusing the model. Additionally, we design two auxiliary loss functions for aligning the marginal distributions of domain-specific and domain shared features, and then optimize the convergence process by constraining gradient penalty on these auxiliary loss functions. Furthermore, the pre-training strategy is also proposed to ensure that the initial mapping of shared encoder contains sufficient emotional information. We evaluate the proposed MISNet to ascertain the impact of several hyper-parameters on the domain adaptation capability of network. The ablation experiments are conducted on two publically accessible datasets SEED and SEED-IV to assess the effectiveness of each loss function. The experimental results demonstrate that by disentangling private and shared emotional characteristics from differential entropy features of EEG signals, the proposed MISNet can gain robust subject independent performance and strong domain adaptability.

H[formula omitted] finite-time prescribed performance trajectory tracking control of MSVs with self-adjusting neural networks

The paper proposes a robust adaptive finite-time prescribed performance trajectory tracking control scheme for marine surface vessels (MSVs) under unknown external disturbance and model uncertainty, based on H∞ control and self-adjusting neural networks (SANN). Firstly, to tackle the challenge of unknown velocity, a high-gain observer is introduced. Secondly, SANN is designed to tackle model uncertainty, achieving a balance between the optimal number of neurons and the best expected performance, thus saving network resources. Simultaneously, finite-time (FT) auxiliary functions, error transformation functions, and H functions are introduced, ensuring a bounded expected decay level with L2 norm within FT. Finally, by combining backstepping, SANN, prescribed performance control and FTH∞ control methods, the system ensures the achievement of practically finite-time stable using fewer network resources under prescribed performance conditions. Simulation results validate the effectiveness of the proposed controller.

GradDFT. A software library for machine learning enhanced density functional theory.

Density functional theory (DFT) stands as a cornerstone method in computational quantum chemistry and materials science due to its remarkable versatility and scalability. Yet, it suffers from limitations in accuracy, particularly when dealing with strongly correlated systems. To address these shortcomings, recent work has begun to explore how machine learning can expand the capabilities of DFT: an endeavor with many open questions and technical challenges. In this work, we present GradDFT a fully differentiable JAX-based DFT library, enabling quick prototyping and experimentation with machine learning-enhanced exchange-correlation energy functionals. GradDFT employs a pioneering parametrization of exchange-correlation functionals constructed using a weighted sum of energy densities, where the weights are determined using neural networks. Moreover, GradDFT encompasses a comprehensive suite of auxiliary functions, notably featuring a just-in-time compilable and fully differentiable self-consistent iterative procedure. To support training and benchmarking efforts, we additionally compile a curated dataset of experimental dissociation energies of dimers, half of which contain transition metal atoms characterized by strong electronic correlations. The software library is tested against experimental results to study the generalization capabilities of a neural functional across potential energy surfaces and atomic species, as well as the effect of training data noise on the resulting model accuracy.

Exploring the Feasibility of AI's Auxiliary Functions in the Field of Children's Painting

This paper aims to explore the feasibility of AI in the field of children’s painting education and to design AI-assisted applications to guide children’s painting. The group selected Liu Yichen, the younger brother of the group member Swan, as the research subject, and selected six of his paintings. Through interviews, we learned about his creative intentions and the details that he failed to complete due to his own limitations. Then, through AI technology, we would conduct image processing experiments on the six selected paintings (some are dominated by keywords, some are not). Finally, we would feed back the generated works to Liu Yichen, and found out through interviews whether these works meet his expectations and whether they can stimulate him to further creation. At the same time, Liu Yichen’s relatives, friends, and strangers will evaluate Liu Yichen’s original works and AI works through questionnaires to test the feasibility of applying AI painting to children’s painting. The results obtained from the interview of the experimental subject Liu and the questionnaire of friends, relatives and strangers showed positive results. However, 12 per cent of the strangers showed extremely negative attitudes in the questionnaire. Therefore, the study concluded that the integration of AI into early art education is highly feasible in today’s market. However, in the face of the arrival of AI, we still need to leave a buffer period for human society, so as to realize the symbiosis between human and technology in a more peaceful way.

Use of 3D printing models for donor tooth extraction in autotransplantation cases

ObjectiveTo clarify whether the 3D printing model has auxiliary functions in toto extraction of donor tooth in autotransplantation cases.MethodsTwo hundred and sixty patients who would have operation of ATT were divided into two groups. In group 1, determination of the tooth extraction in toto was predicted only according to the clinical and imaging examination. In group 2, the prediction was performed according to the clinical and imaging examination as well as the 3D model of donor tooth pre-extraction. A prespctive clinical study was designed on intra-group comparison between the predicted and actual donor teeth situation when extraction in cases of ATT. The consistent rate for the predicted results and the actual results were compared with the two groups.ResultsA remarkable difference was observed between the predicted results and the actual results of tooth positions and root numbers in group without model (p < 0,05). The consistency rate of the model group (94.62%) was significantly higher than that of non 3D model group (86.15%) (p = 0.034).ConclusionThe 3D printing model for the donor tooth is helpful for dentists to predict the accuracy of toto extraction of donor teeth in autotransplantation cases.

Fully distributed adaptive cooperative output regulation of heterogeneous multi-agent systems with hybrid event-triggering mechanism

This study focuses on the event-triggered cooperative output regulation problem (CORP) of multi-agent systems with heterogeneous dynamics. Two design criteria are required be achieved: event-triggered communication between agents has strictly positive minimum inter-event time (MIET), and global information with respect to communication topology is not needed to implement the event-triggered control strategy. These two criteria are significant, but cannot be simultaneously satisfied using the relevant existing results. In this work, two event-triggered observers with hybrid triggering conditions are developed to estimate the matrix and state of the exosystem, the MIET is enforced to be positive by incorporating an auxiliary function with decreasing dynamics into the event-triggering mechanism (ETM). This is more stringent than simply removing Zeno behavior and is more useful in engineering applications. Additionally, distributed controllers are developed based on the estimated state and regulator equation. The proposed method, which is better and more useful than the up-to-date results in literature, and can satisfy the two design criteria as mentioned before. Finally, numerical examples are provided to demonstrate the effectiveness.

Generalization of Homotopy Analysis Method for q-Fractional Non-linear Differential Equations

This paper presents a generalization of the Homotopy analysis method (HAM) for finding the solutions of nonlinear q-fractional differential equations (q-FDEs). This method shows that the series solution in the case of generalized HAM is more likely to converge than that on HAM. In order that it is applicable to solve immensely non-linear problems and also address a few issues, such as the impact of varying the auxiliary parameter, auxiliary function, and auxiliary linear operator on the order of convergence of the method. The generalized HAM method is more accurate than the HAM.

A cross-model hierarchical interactive fusion network for end-to-end multimodal aspect-based sentiment analysis

For the aspect-based sentiment analysis task, traditional works are only for text modality. However, in social media scenarios, texts often contain abbreviations, clerical errors, or grammatical errors, which invalidate traditional methods. In this study, the cross-model hierarchical interactive fusion network incorporating an end-to-end approach is proposed to address this challenge. In the network, a feature attention module and a feature fusion module are proposed to obtain the multimodal interaction feature between the image modality and the text modality. Through the attention mechanism and gated fusion mechanism, these two modules realize the auxiliary function of image in the text-based aspect-based sentiment analysis task. Meanwhile, a boundary auxiliary module is used to explore the dependencies between two core subtasks of the aspect-based sentiment analysis. Experimental results on two publicly available multi-modal aspect-based sentiment datasets validate the effectiveness of the proposed approach.