Average Vector Research Articles

A Kernel-Based Meshless Conservative Galerkin Method for Solving Hamiltonian Wave Equations

We propose a meshless conservative Galerkin method for solving Hamiltonian wave equations. We first discretize the equation in space using radial basis functions in a Galerkin-type formulation. Differ from the traditional RBF Galerkin method that directly uses nonlinear functions in its weak form, our method employs appropriate projection operators in the construction of the Galerkin equation, which will be shown to conserve global energies. Moreover, we provide a complete error analysis to the proposed discretization. We further derive the fully discretized solution by a second order average vector field scheme. We prove that the fully discretized solution preserved the discretized energy exactly. Finally, we provide some numerical examples to demonstrate the accuracy and the energy conservation.

Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables

We present a novel numerical method for solving ODEs while preserving polynomial first integrals. The method is based on introducing multiple quadratic auxiliary variables to reformulate the ODE as an equivalent but higher-dimensional ODE with only quadratic integrals to which the midpoint rule is applied. The quadratic auxiliary variables can subsequently be eliminated yielding a midpoint-like method on the original phase space. The resulting method is shown to be a novel discrete gradient method. Furthermore, the averaged vector field method can be obtained as a special case of the proposed method. The method can be extended to higher-order through composition and is illustrated through a number of numerical examples.

Blood Flow Quantification with High-Frame-Rate, Contrast-Enhanced Ultrasound Velocimetry in Stented Aortoiliac Arteries: In Vivo Feasibility.

Local flow patterns influence stent patency, while blood flow quantification in stents is challenging. The aim of this study was to investigate the feasibility of 2-D blood flow quantification using high-frame-rate, contrast-enhanced ultrasound (HFR-CEUS) and particle image velocimetry (PIV), or echoPIV, in patients with aortoiliac stents. HFR-CEUS measurements were performed at 129 locations in 62 patients. Two-dimensional blood flow velocity fields were obtained using echoPIV. Visual inspection was performed by five observers to evaluate feasibility. The contrast-to-background ratio and average vector correlation were calculated and compared between stented and native vessel segments. Flow quantification with echoPIV was feasible in 128 of 129 locations (99%), with optimal quantification in 40 of 129 locations (31%). Partial quantification was achieved in 88 of 129 locations (68%), where one or multiple limiting issues occurred (not related to the stent) including loss of correlation during systole (57/129), short vessel segments (20/129), loss of contrast during diastole (20/129) and shadow regions (20/129). The contrast-to-background ratio and vector correlation were lower downstream in the imaged blood vessel, independent of the location of the stent. In conclusion, echoPIV was feasible in stents placed in the aortoiliac region, and the stents did not adversely affect flow tracking.

A Gas Concentration Prediction Method Driven by a Spark Streaming Framework

In the traditional coal-mine gas-concentration prediction process, problems such as low timeliness of data and low efficiency of the prediction model in learning data features result in low accuracy of the final prediction. To solve these problems, a gas-concentration prediction method driven by the Spark Streaming framework is proposed. In this research study, the Spark Streaming framework, autoregressive integrated moving average (ARIMA) model and support vector machine (SVM) model are used to construct a new prediction model called the SPARS model. The Spark Streaming framework is used to process large batches of real-time streaming data in a short period of time, and the model can be used to intermittently update and optimize the prediction model so that the model can fully learn the characteristics of the data. At the same time, the advantages of the ARIMA model and SVM model for processing linear data and nonlinear data are combined to improve the model’s prediction efficiency and fully reflect the timeliness of gas prediction. Finally, the proposed prediction model is verified using gas data collected on site. The optimal learning time for the SPARS model in predicting this set of data is determined, and a comparative analysis of the prediction results obtained from the ARIMA, SVM and other models fully confirms that high-precision prediction results can be obtained using the SPARS model. The proposed model can be used to realize scientific and accurate real-time prediction and analyses of coal-mine gas concentrations and provides a new idea for realizing real-time and accurate gas prediction in coal mines.

Density function of numerical solution of splitting AVF scheme for stochastic Langevin equation

In this article, we study the density function of the numerical solution of the splitting averaged vector field (AVF) scheme for the stochastic Langevin equation. We first show the existence of the density function of the numerical solution by proving its exponential integrability property, Malliavin differentiability and the almost surely non-degeneracy of the associated Malliavin covariance matrix. Then the smoothness of the density function is obtained through a lower bound estimate of the smallest eigenvalue of the corresponding Malliavin covariance matrix. Meanwhile, we derive the optimal strong convergence rate in every Malliavin–Sobolev norm of the numerical solution via Malliavin calculus. Combining the strong convergence result and the smoothness of the density functions, we prove that the convergence order of the density function of the numerical scheme coincides with its strong convergence order.

Machine Learning-Based Matching Medium Design for Implant Communications

Matching media are used in various applications to increase the power transmitted into the human body. The selection of the optimum matching medium (MM) permittivity is not a straightforward task, as the optimum value maximizing the transmitted power depends on the thickness of the MM and the electromagnetic properties of the target tissue. In this article, a computationally heavy empirical approach and a machine learning (ML)-based approach are utilized for the selection of the MM. The empirical approach demonstrates that the MM can increase the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$|S_{21}|$ </tex-math></inline-formula> values up to 8 dB, which is validated with measurements. Next, an ML-based tool is proposed to predict the optimum MM permittivity for any target tissue and any MM thickness. A 1-D convolutional neural network followed by a multilayer perceptron is trained with the simulated average Poynting vector magnitudes (APVMs) for muscle and fat as target tissues. The APVM and the dipole length for given system parameters are predicted by the trained artificial neural network. The accuracy is calculated by comparison with the results of the empirical analysis and found to be 1% and 12.3% mean absolute percentage error for dipole length and APVM, respectively. The proposed tool decreases the time required to milliseconds.

Single-branch self-supervised learning with hybrid tasks

Convolutional neural network (CNN)-based self-supervised visual representation learning (SSL) is a long-standing problem achieving significant successes with traditional handcrafted pretext tasks and contrastive learning. However, existing SSL methods typically suffer from high computational overhead and poor performance due to sluggish convergence speeds and poor detail extraction capabilities. In this work, to address these issues and improve the robustness, we provide a new self-supervised architecture for incorporating a single-branch backbone with hybrid tasks into the representation learning process. Specifically, our method takes advantage of features from both intra- and inter-images by using discrete montage images. Then a single backbone with a novel Adaptive Decouple Confusion (ADC) module is proposed to improve the feature extraction capabilities and alleviate the confusion regions in montage images. Besides, both concatenated discrete vectors and patch-based global average pooled vectors in latent space are utilized to learn local detailed features and maintain semantic consistency simultaneously. Moreover, our method is optimized by hybrid tasks and enjoys faster convergence speed due to these improvements. Extensive experiments on several datasets demonstrate the effectiveness and robustness of our method. The proposed method has 2.0% improved in linear classification to the conventional single-branch methods.

Texture analysis of myometrium-derived T2WI in the evaluation of placenta increta: An observational retrospective study

IntroductionMRI has demonstrated its potential in the diagnosis of placenta percreta. Texture analysis is a novel technique to quantify tissue heterogeneity. The study aimed to evaluate the feasibility of using texture analysis based on myometrium-derived T2WI to differentiate placenta accreta from increta. MethodsParticipants with MRI and clinical or histopathological diagnosis of placenta increta were retrospectively enrolled. Texture analysis of T2WI was implemented on normal myometrium and placenta increta by MaZda software. With the Fisher discriminant method, parameter selection and reduction were done automatically. Multivariate analysis was used for the comparison of response variables between two groups. The contours of multivariable average vectors were compared using profile analysis. Two-step clustering was performed to assess the importance of parameters. ResultsThere were a total of 23 participants (median age 29 years, range 22–43 years). The pixel intensity distribution was narrow and wide in two first-order histograms taken from normal myometrium and placenta increta, respectively. Multivariate analysis showed nine second-order parameters derived from the histogram were statistically significant (P < 0.05). The results of two-step clustering indicated that three second-order parameters (Mean, Percentile 90%, and Percentile 99%) were important (predictor importance > 0.8). Multivariate analysis of three second-order parameters further showed they were different between normal myometrium and placenta increta. DiscussionTexture analysis based on myometrium-derived T2WI may be a useful add-on to MRI in diagnosing placenta increta. Trial registrationRegistration number: ChiCTR2000038604 and name of registry: Evaluation of diagnostic accuracy of MRI multi-parameter imaging combined with texture analysis for placenta accreta spectrum disorders (PAD).

SVR and ARIMA models as machine learning solutions for solving the latency problem in real-time clock corrections

Real-time precise point positioning (PPP) has become a prevalent technique in global navigation satellite systems (GNSS). However, GNSS real-time users must receive space state representation (SSR) products to correct for satellite clock, orbit, and phase biases. The International GNSS Service (IGS) provides GNSS users with real-time services (RTSs) through different real-time correction SSR products. These products arrive at the GNSS users with some latency, which affects the quality of real-time PPP positioning. The autoregressive integrated moving average (ARIMA) and support vector regression (SVR) models are used in this research to predict those corrections to eliminate the latency effect. ARIMA model reduces the standard deviation by 28% and 13% for GPS and GLONASS constellations, respectively, compared to the real-time solution, which includes the latency effect, the research simulated the latency effect and named it a forced-latency solution, and the SVR model reduces the standard deviation by 28% and 23% for GPS and GLONASS constellations, respectively. The results for the permanent GNSS stations used in this study across different years 2013, 2014, 2015, 2019, and 2021 show a mean reduction in the 3D positioning standard deviation by 13% compared with the forced-latency solution for the ARIMA solution and 9% for the SVR solution. The potential of both models to overcome the latency effect is apparent based on the findings.

News topic detection based on capsule semantic graph

Most news topic detection methods use word-based methods, which easily ignore the relationship among words and have semantic sparsity, resulting in low topic detection accuracy. In addition, the current mainstream probability methods and graph analysis methods for topic detection have high time complexity. For these reasons, we present a news topic detection model on the basis of capsule semantic graph (CSG). The keywords that appear in each text at the same time are modeled as a keyword graph, which is divided into multiple subgraphs through community detection. Each subgraph contains a group of closely related keywords. The graph is used as the vertex of CSG. The semantic relationship among the vertices is obtained by calculating the similarity of the average word vector of each vertex. At the same time, the news text is clustered using the incremental clustering method, where each text uses CSG; that is, the similarity among texts is calculated by the graph kernel. The relationship between vertices and edges is also considered when calculating the similarity. Experimental results on three standard datasets show that CSG can obtain higher precision, recall, and F1 values than several latest methods. Experimental results on large-scale news datasets reveal that the time complexity of CSG is lower than that of probabilistic methods and other graph analysis methods.

Energy-Preserving Continuous-Stage Exponential Runge--Kutta Integrators for Efficiently Solving Hamiltonian Systems

As one of the most important properties, energy preservation is a natural requirement for numerical integrators of Hamiltonian systems. Considering the limited second-order accuracy of the existing exponential average vector filed (or discrete gradient) method, this paper is devoted to developing high-order energy-preserving exponential integrators for general semilinear Hamiltonian systems. To this end, we first formulate and analyze the continuous-stage exponential Runge--Kutta (ERK) method. After deriving the order conditions, energy-preserving conditions, and symmetric conditions for the continuous-stage ERK method, we construct a novel class of fourth-order symmetric energy-preserving continuous-stage ERK methods with a free parameter based on the established conditions and present a convergence theorem for the fixed-point iteration associated with the continuous-stage ERK method. Furthermore, we extend the proposed continuous-stage ERK method to noncanonical Hamiltonian systems and discuss implementation issues in detail. Finally, numerical results from the FPU problem, the charged-particle dynamics, and the Klein--Gordon equation demonstrate the high efficiency, good energy-preserving behavior, and applicability of large time stepsizes of the proposed fourth-order energy-preserving continuous-stage ERK method.

Prediction of elemental concentration using of laser induced breakdown spectroscopy aided by artificial neural network, statistical methods of autoregressive integrated moving average model and support vector regression and their combination

In this paper, by using of laser induced breakdown spectroscopy (LIBS) method, the elemental concentrations existed in standard aluminum alloys are measured quantitatively. Pulse laser of Nd:YAG at 1064 nm is irradiated on Al standard samples and analysis is performed by created plasma. Among different methods for estimation of concentration of existed elements in aluminum samples, artificial neural network (ANN), Support vector regression, autoregressive integrated moving average model (ARIMA), kernelized support vector regression (KSVR) and combined method of KSVR-ARIMA are utilized for prediction of element concentrations of Fe, Cu, Zn, Mg, Mn, and Si and obtained results from these methods are compared together. The extracted results show that the combined method of KSVR-ARIMA reports the best prediction values by the least error for the most of the elements.

Energy preserving reduced-order modeling of the rotating thermal shallow water equation

In this paper, reduced-order models (ROMs) are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with state-dependent Poisson matrix. The high fidelity full solutions are obtained by discretizing the RTSWE in space with skew-symmetric finite-differences, while preserving the Hamiltonian structure. The resulting skew-gradient system is integrated in time by the energy preserving average vector field (AVF) method. The ROM is constructed by applying proper orthogonal decomposition with the Galerkin projection, preserving the reduced skew-gradient structure, and integrating in time with the AVF method. The nonlinear terms of the Poisson matrix and Hamiltonian are approximated with the discrete empirical interpolation method to reduce the computational cost. The solutions of the resulting linear-quadratic reduced system are accelerated by the use of tensor techniques. The accuracy and computational efficiency of the ROMs are demonstrated for a numerical test problem. Preservation of the energy (Hamiltonian) and other conserved quantities, i.e., mass, buoyancy, and total vorticity, show that the reduced-order solutions ensure the long-term stability of the solutions while exhibiting several orders of magnitude computational speedup over the full-order model. Furthermore, we show that the ROMs are able to accurately predict the test and training data and capture the system behavior in the prediction phase.

P 37 Correlation of intra- and postoperative best active contact and its implication for STN-DBS outcome

Objective Deep brain stimulation is a well-established treatment for Parkinson’s Disease. The value of awake DBS to guide the implantation process is an ongoing debate. Intraoperative assessment of symptom control and side effect threshold are considered the gold standard for the decision of the final trajectory. Here we focus on a retrospective analysis of the intraoperative and one year follow up best active contacts and VTA-models. Methods We analyzed 46 patients (15 female) with 92 STN leads who received STN-DBS between 2014-2018. Intraoperative best active contact was defined as the contact with the lowest current to achieve maximum therapeutic effect. To determine stimulation location intraoperative semimacro-teststimulation settings were applied to Guide XT software after fusion of the individual MRi and postoperative CT scan. Same procedure was repeated for the stimulation settings used one year after implantation. Results 96 intraoperative and 96 postoperative leads and VTAs were calculated. Average AC-PC coordinates for the best intraoperative contact were 12.4/2.9/3.1mm (lat./post./inf.) and 12.7/2.2/2mm for the one year follow up. Average vector distance was 2.4mm between intraoperative best contact and chronically used contact (range 0.2 – 7.7mm). The distance between centers of gravity of intra- vs. postoperative VTAs did not show any correlation with motor outcome. Discussion Our findings show a significant location difference between the best contact at intraoperative stimulation and the best active contact at one year follow up. VTA-modelling showed no correlation for the therapeutic effect and the overlap of intra- and postoperative VTAs. Since intraoperative testing is mostly limited to rigidity assessment, a more inferior / caudal stimulation could selectively detect best rigidity control but not achieve the full scope of mobility improvement by STN-DBS. Interestingly, center of gravity for groups lied within the delineations of former published sweet spots. For the implantation process of directional leads, the placement of one directional pole 1-2mm superior to the best intraoperative spot appears advisable.

Early detection of breast cancer using robust back propagation neural network classifier

Breast cancer is the most widely recognized malignancy in women and is the second most common and important cause of cancer death in women. Currently, there is no e􀵵 ective approach to avoid breast cancer, as its motivation is not yet fully understood. The common problems of women in recent years are breast cancer. The problem of breast cancer classification has been the main problem in recent years. This article gives a reasonable idea of the readiness of the mammogram image to find out the area a􀵵 ected by cancer, which is a vital advance in breast cancer detection. Therefore, the research focuses on examining and analyzing the image processing of cancerous diseases, especially breast cancer. When detecting breast cancer, images are obtained from a mammogram and subjected to treatment. The artificial neural network (ANN) plays an important role in this regard, in particular in the application of biomedical image processing for the early diagnosis of breast cancer. It is actually detected by these steps. Preprocessing, image splitting, attribute extraction and categorization. An average vector filter is used to perform the preprocessing operation. Helps eliminate noise and turn RGB image into grayscale image. Vessel segmentation is used to segment the image. To perform entity extraction, the technique of the Binary Local Scale Model (MLBP) method is used and optimized using the Robust Propagation Neural Network Classifier (RBPNN). Using MLBP, 12 functional derivatives were extracted. The extraction is performed on the basis of color, texture and shape. It plays an important role in detection. Finally, for the classi􀂿 cation of the extracted function, RBPNN is performed and then analyzes the test data with the trained data. To prove its usefulness, it produces great precision compared to other current games. The accuracy of this suggested analysis is 97%.

The Hamiltonian structure and fast energy-preserving algorithms for the fractional Klein-Gordon equation

In this paper, an energy-preserving difference scheme is proposed for solving the space fractional Klein-Gordon equation based on the Hamiltonian form of the equation. First, we study some properties of the fractional Laplacian operator and reformulate the equation as an infinite-dimension canonical Hamiltonian system. Then, we use the fractional centered difference formula to discrete the equation and derive a semi-discrete Hamiltonian system that can conserve the semi-discrete energy. Subsequently, a fully-discrete scheme is obtained by applying the averaged vector field method to the semi-discrete system. The resulting scheme's unconditional point-wise error estimate is discussed by using the “cut-off” technique. Furthermore, a fast solver is presented to reduce the computational complexity of the scheme based on the fast Fourier transformation technique in practical computation. Finally, some numerical experiments are displayed to demonstrate the efficiency and conservation of the constructed scheme in long time simulation.

Energy-preserving methods for guiding center system based on averaged vector field

We propose a family of energy-preserving methods for guiding center dynamics by perceiving its Hamiltonian nature based on the averaged vector field. The energy conservation, symmetric property, and algebraic order of these methods are studied. Furthermore, higher order energy-preserving methods are systematically introduced by using a composition technique. Two second order and two fourth order symmetric energy-preserving methods are constructed and applied to simulate the guiding center motion in both the dipole magnetic field and the tokamak magnetic field. Numerical results show that these methods have significant superiorities in energy conservation compared with the existing canonicalized symplectic methods of the corresponding orders. The numerical case of the guiding center motion in the toroidal acceleration electric field exhibits favorable long-term conservative properties of the new methods to the particle-field system, while the kinetic energy of guiding centers keeps increasing. These energy-preserving methods based on the averaged vector field can be applied to any non-canonical Hamiltonian system.

Abstract MP27: Associations Of Accelerometer-measured Physical Activity And Sedentary Behavior With Incident Ischemic Stroke: The Women’s Health Study (WHS)

Introduction: Higher self-reported physical activity and lower sedentary behavior (SB) are associated with lower incidence of ischemic stroke (IS). Objective measurement by accelerometer allows for novel, in-depth examination of these relationships with IS. Objective: Assess the association of accelerometer-measured physical activity and SB with IS. Methods: We included 16,031 women adherent with accelerometer wear (≥ 10 hours/day for 4 days) from the WHS cohort (2011-2015) with no prior cardiovascular disease [age 71.4 (SD 5.6) years, BMI 26.2 (SD 5.0), and 67% hypertensive]. ActiGraph GT3X+ accelerometers measured total volume of physical activity (average vector magnitude [VM]/min), mins spent in light-high (LHPA) and moderate-to-vigorous (MVPA) intensity physical activity, and SB. We categorized all metrics as quartiles and residualized to account for accelerometer wear time. We produced adjusted hazard ratios (HR) and 95% confidence intervals (CI) that independently relate physical activity and SB with IS using Cox proportional hazards models. Sensitivity analyses excluded events in the first year and those with poor self rated health to assess reverse causality. Results: Over a mean of 7.1 (SD 1.6) years of follow-up, 181 IS were observed (30 in first year). Greater total volume of physical activity and more minutes spent in MPVA were associated with lower hazards of ischemic stroke (quartile 4 vs. ref: VM/min HR=0.51, 95% CI: 0.32, 0.82, MVPA HR=0.42, 95% CI: 0.26, 0.67). Minutes spent in LHPA were not associated with IS. Less time spent in SB was associated with lower hazards of IS, but was not statistically significant (Table). Results were robust when adjusted for clinical covariates. Exclusions for reverse causality did not alter inferences made and decreased precision. Conclusion: Greater total volume of physical activity and more minutes spent in MVPA were associated with lower occurrence of IS in this cohort. Less time spent in SB appeared to be protective against IS, but requires further investigation.

Comparison of Productivity of Sentul and Kampung Chickens until the Age of 3 Months in the First Generation Selection Population (G1)

This study aimed to compare the productivity of Sentul chickens and first-generation Kampung chickens (G1) until the age of 3 months. The research material were Sentul chicken and Kampung chicken. The method used was an experiment method or direct observation with a sample of 174 chickens from each strain. The data collected were egg weight, doc weight, body weight, body weight gain, body measurements, and selection response. Data on egg weight, body weight, and body measurements were analyzed using the average difference test (t-test), while the average value vector of body measurements Sentul chicken and Kampung chicken were analyzed using the T2-Hotelling statistical test. To identify the body size and body shape characteristics of Sentul chickens and Kampung chickens were analyzed using principal component analysis. Data processing used the statistical software Minitab version 18. The results of this study showed that egg weight, body weight at the age of DOC-3 months and body measurements of Sentul chickens were significantly different (P&lt;0.05) higher than the Kampung chickens. This study concludes that the egg weight, body weight, body weight gain, and body sizes of Sentul chickens are higher than Kampung chickens. The size characteristic of Sentul and Kampung chickens is chest circumference. The characteristic of the shape of the Sentul chicken is the length of the wings, while the shape of the native chicken is the width of the chest. The selection response and the heritability value of the Sentul chickens was higher than Kampung chikens.

Identification of Proper and Improper Signatures Using Graph Theory Techniques

Objectives: To propose an automatic signature identification for off-line signature utilising graph theory approaches. Methods: Scanned signatures (Kaggle, https://www.kaggle.com/divyanshrai/handwritten-signatures/data) are collected for off-line signature data. The method follows pre-processing, vertex point extraction by midpoint traverse method, features extraction using edge, average edge and average edge D-distance and Support Vector Machine (SVM) to classify and predict the true label for the genuine and forged signatures. False Acceptance Ratio (FAR) and False Rejection Ratio (FRR) give the accuracy of the proposed methods. This off-line signature verification method is compared with the deep learning techniques existing in the literature. Findings: Support Vector Machine (SVM) used for classification and results on standard signature datasets like ICDAR (International Conference on Document Analysis and Recognition). The results demonstrate how the proposed strategy outperforms the state-of-the-art already available. Novelty: The proposed approach use the edge distance, average edge distance, and average edge D-distance inbuilt graph structures to extract the feature points. Keywords: Signature images; grid approach; bipartite graph; complete bipartite graph; mid point traverse method