Linear Basis Research Articles

Simple vertex algebras arising from congruence subgroups

For any congruence subgroup Γ, we consider the vertex algebra of Γ-invariant global sections of chiral de Rham complex on the upper half plane that are meromorphic at the cusps. We give a description of the linear structure of the Γ-invariant vertex algebra by exhibiting a linear basis determined by meromorphic modular forms, and generalize the Rankin-Cohen bracket of modular forms to meromorphic modular forms. We also show that the Γ-invariant vertex algebra is simple.

MEDEA: A New Model for Emulating Radio Antenna Beam Patterns for 21 cm Cosmology and Antenna Design Studies

In 21 cm experimental cosmology, accurate characterization of a radio telescope’s antenna beam response is essential to measure the 21 cm signal. Computational electromagnetic (CEM) simulations estimate the antenna beam pattern and frequency response by subjecting the EM model to different dependencies, or beam hyperparameters, such as soil dielectric constant or orientation with the environment. However, it is computationally expensive to search all possible parameter spaces to optimize the antenna design or accurately represent the beam to the level required for use as a systematic model in 21 cm cosmology. We therefore present the Model for Emulating Directivities and Electric fields of Antennas (MEDEA), an emulator that rapidly and accurately generates far-field radiation patterns over a large hyperparameter space. MEDEA takes a subset of beams simulated by CEM software, spatially decomposes them into coefficients on a complete, linear basis, and then interpolates them to form new beams at arbitrary hyperparameters. We test MEDEA on an analytical dipole and two numerical beams motivated by upcoming lunar lander missions, and then employ MEDEA as a model to fit mock radio spectrometer data to extract covariances on the input beam hyperparameters. We find that the interpolated beams have rms relative errors of at most 10−2 using 20 input beams or less, and that fits to mock data are able to recover the input beam hyperparameters when the model and mock are derived from the same set of beams. When a systematic bias is introduced into the mock data, extracted beam hyperparameters exhibit bias, as expected. We propose several extensions to MEDEA to potentially account for such bias.

Analysis of influencing factors of traffic accidents on urban ring road based on the SVM model optimized by Bayesian method.

Based on small scale sample of accident data from specific scenarios, fully exploring the potential influencing factors of the severity of traffic accidents has become a key and effective research method. In order to analyze the factors mentioned above in the scenario of urban ring roads, this paper collected data records of 1250 traffic accidents involving different severity on urban ring road of a central city in northwest China in the past 3 years. Firstly, the Support Vector Machine (SVM) model of non-parametric method is utilized to analyze the data above, and three kernel functions of linear, inhomogeneous polynomial and Gaussian radial basis are constructed respectively. Considering comprehensively 16 potential influencing factors covering the driver-vehicle-road-environment integrated system, the SVM models of above three kernel functions are verified, accuracy reaches 0.771 and F1 reaches 0.841. Then, Bayesian Optimization (BO), Grids Search (GS) and Rough Set (RS) are utilized as optimizer to adjust the parameters of Gaussian radial basis function SVM model, the performance of BO-SVM is further improved and reaches the optimum, with an average accuracy of 0.875 on the test set and a F1 of 0.886, completely outperforming the benchmark models of GS-SVM, RS-SVM, Bilayer-LSTM and BP. Finally, the sensitivity analysis method is utilized to quantify the sensitivity of the potential influencing factors to the severity of road accidents, and the backward selection method is utilized to screen the core influencing factors that influence the severity of accident, concluded that core influencing factors are age, driving mileage and vehicle type. This paper will provide reference for the analysis of the significant influencing factors for road accidents severity, and to provide theoretical support for the precise formulation of accident improvement strategies.

Ultrafast Polarization-Resolved Phonon Dynamics in Monolayer Semiconductors.

Monolayer transition metal dichalcogenide semiconductors exhibit unique valleytronic properties interacting strongly with chiral phonons that break time-reversal symmetry. Here, we observed the ultrafast dynamics of linearly and circularly polarized E'(Γ) phonons at the Brillouin zone center in single-crystalline monolayer WS2, excited by intense, resonant, and polarization-tunable terahertz pulses and probed by time-resolved anti-Stokes Raman spectroscopy. We separated the coherent phonons producing directional sum-frequency generation from the incoherent phonon population emitting scattered photons. The longer incoherent population lifetime than what was expected from coherence lifetime indicates that inhomogeneous broadening and momentum scattering play important roles in phonon decoherence at room temperature. Meanwhile, the faster depolarization rate in circular bases than in linear bases suggests that the eigenstates are linearly polarized due to lattice anisotropy. Our results provide crucial information for improving the lifetime of chiral phonons in two-dimensional materials and potentially facilitate dynamic control of spin-orbital polarizations in quantum materials.

Automatic Classification of Conclusions from Multi-Tracer Reports of PET Brain Imaging in Cognitive Impairment.

The goal of this paper is to build an automatic way to interpret conclusions from brain molecular imaging reports performed for investigation of cognitive disturbances (FDG, Amyloid and Tau PET) by comparing several traditional machine learning (ML) techniques-based text classification methods. Two purposes are defined: to identify positive or negative results in all three modalities, and to extract diagnostic impressions for Alzheimer's Disease (AD), Fronto-Temporal Dementia (FTD), Lewy Bodies Dementia (LBD) based on metabolism of perfusion patterns. A dataset was created by manual parallel annotation of 1668 conclusions of reports from the Nuclear Medicine and Molecular Imaging Division of Geneva University Hospitals. The 6 Machine Learning (ML) algorithms (Support Vector Machine (Linear and Radial Basis function), Naive Bayes, Logistic Regression, Random Forrest, and K-Nearest Neighbors) were trained and evaluated with a 5-fold cross-validation scheme to assess their performance and generalizability. The best classifier was SVM showing the following accuracies: FDG (0.97), Tau (0.94), Amyloid (0.98), Oriented Diagnostic (0.87 for a diagnosis among AD, FTD, LBD, undetermined, other), paving the way for a paradigm shift in the field of data handling in nuclear medicine research.

Numerical analysis for nonlinear wave equations with boundary conditions: Dirichlet, Acoustics and Impenetrability

In this article, we present an error estimation in the L2 norm referring to three wave models with variable coefficients, supplemented with initial and boundary conditions. The first two models are nonlinear wave equations with Dirichlet, Acoustics, and nonlinear dissipative impenetrability boundary conditions, while the third model is a linear wave equation with Dirichlet, Acoustics, and linear dissipative impenetrability boundary conditions. In the field of numerical analysis, we establish two key theorems for estimating errors to the semi-discrete and totally discrete problems associated with each model. Such theorems provide theoretical results on the convergence rate in both space and time. For conducting numerical simulations, we employ linear, quadratic, and cubic polynomial basis functions for the finite element spaces in the Galerkin method, in conjunction with the Crank-Nicolson method for time discretization. For each time step, we apply Newton's method to the resulting nonlinear problem. The numerical results are presented for all three models in order to corroborate with the theoretical convergence order obtained.

CIELAB Color Space as a Field for Tracking Color-Changing Chemical Reactions of Polymeric pH Indicators.

Two types of cross-linked polymeric dye films that exhibit reversible color changes in response to pH were prepared. Upon protonation, films with a nitrophenol dye moiety (NP) changed from yellow to colorless, whereas films with an azobenzene dye moiety (AB) changed from yellow to reddish-purple. The colored light transmitted through these films from a D65 white-light source was measured colorimetrically, and the transition of the chromaticity point in CIELAB upon protonation of the polymeric dyes was observed. At low dye concentrations ([NP] < 4.7 × 10-5 and [AB] < 2.7 × 10-5 mol L-1), linear loci of the chromaticity points were displayed for both polymeric dye films, indicating perceptual linearity. This linearity is caused by the avoidance of nonlinear perceptual phenomena such as the Abney effect and the Bezold-Brücke phenomenon. The perceptual linearity of space is a necessary condition for achieving stoichiometric linearity, which requires an additional linear relationship between the dye concentration and each component, a*, b*, and L*. A geometric equation that included the AB concentration and the protonation ratio of AB was used to successfully depict, on the basis of stoichiometric linearity, the protonation of the polymeric AB films three-dimensionally in the restricted area of CIELAB.

Predictive algorithm of instrument health condition based on linear regression and radial basis function neural network

Abstract Enterprises and institutions engaged in social production activities need to apply for mandatory verification of general instruments and meters on production equipment according to law, and its verification period is determined by national or local verification and calibration procedures, but the health condition in the calibration intervals is difficult to know. To improve equipment reliability, this paper relies on the linear regression model to research the health condition of general instruments and meters, uses MATLAB tools to analyze the data samples of typical equipment pressure gauge, and combines radial basis function neural network to form a complete algorithm, and finally provides a complete implementation scheme for the health condition prediction of general instruments and meters in service.

Classification of LAMOST spectra of B-type and hot subdwarf stars using kernel support vector machine

Machine learning has emerged as a leading field in artificial intelligence, demonstrating expert-level performance in various domains. Astronomy has benefited from machine learning techniques, particularly in classifying and identifying stars based on their features. This study focuses on the spectra-based classification of 11,408 B-type and 2422 hot subdwarf stars. The study employs baseline correction using Asymmetric Least Squares (ALS) to enhance classification accuracy. It applies the Pan-Core concept to identify 500 unique patterns or ranges for both types of stars. These patterns are the foundation for creating Support Vector Machine (SVM) models, including the linear (L-SVM), polynomial (P-SVM), and radial basis (R-SVM) kernels. Parameter tuning for the SVM models is achieved through cross-validation. Evaluation of the SVM models on test data reveals that the linear kernel SVM achieves the highest accuracy (87.0%), surpassing the polynomial kernel SVM (84.1%) and radial kernel SVM (80.1%). The average calibrated accuracy falls within the range of 90–95%. These results demonstrate the potential of using spectrum-based classification to aid astronomers in improving and expanding their understanding of stars, with a specific focus on the identification of hot subdwarf stars. This study presents a valuable investigation for astronomers, as it enables the classification of stars based on their spectra, leveraging machine learning techniques to enhance their knowledge and insights in astronomy.

A proof of the Lewis-Reiner-Stanton conjecture for the Borel subgroup

For each parabolic subgroup P \mathrm {P} of the general linear group GL n ⁡ ( F q ) \operatorname {GL}_n(\mathbb {F}_q) , a conjecture due to Lewis, Reiner and Stanton [Proc. Roy. Soc. Edinburgh Sect. A 147 (2017), pp. 831–873] predicts a formula for the Hilbert series of the space of invariants Q m ( n ) P \mathcal {Q}_m(n)^\mathrm {P} where Q m ( n ) \mathcal {Q}_m(n) is the quotient ring F q [ x 1 , … , x n ] / ( x 1 q m , … , x n q m ) \mathbb {F}_q[x_1,\ldots ,x_n]/(x_1^{q^m},\ldots ,x_n^{q^m}) . In this paper, we prove the conjecture for the Borel subgroup B \mathrm {B} by constructing a linear basis for Q m ( n ) B \mathcal {Q}_m(n)^\mathrm {B} . The construction is based on an operator δ \delta which produces new invariants from old invariants of lower ranks. We also upgrade the conjecture of Lewis, Reiner and Stanton by proposing an explicit basis for the space of invariants for each parabolic subgroup.

MODELLING DOMESTIC WATER DEMAND IN MALAYSIA TO IDENTIFY INFLUENCING FACTORS: A COMPARATIVE ANALYSIS

Water crises are often experienced by many developing countries worldwide. Predicting future domestic water demand and identifying the influential factors are vital to managing water supply effectively. This study aims to determine the best predictive models among Multiple Linear Regression (MLR), Multi-layer Perceptron (MLP), and Radial Basis Function (RBF) Neural Networks as well as to identify the significant influential factors towards domestic water demand. Based on the yearly records from 2000 to 2018 obtained from the Malaysian Water Association, the Department of Environment, and the Department of Statistics Malaysia the analysis results indicate an increasing pattern of domestic water in Malaysia with the demand for non-domestic water twice lower than domestic water. Based on RMSE and R-squared, Multi-layer Perceptron is the best model for predicting domestic water demand. The MLR model shows that the two most significant influential factors towards domestic water demand are price and design capacity, with negative and positive relationships. The results describe that an increase in price affects a decrease in water demand, while an increase in design capacity will reduce the water demand. The findings suggest that the water utilities in Malaysia should focus more on these identified factors.

Speech Emotion Recognition Method Based on Support Vector Machine and Suprasegmental Acoustic Features

The problem of recognizing emotions in a speech signal using mel-frequency cepstral coefficients using a classifier based on the support vector machine has been studied. The RAVDESS data set was used in the experiments. A model is proposed that uses a 306-component suprasegmental feature vector as input to a support vector machine classifier. Model quality was assessed using unweighted average recall (UAR). The use of linear, polynomial and radial basis functions as a kernel in a classifier based on the support vector machine is considered. The use of different signal analysis frame sizes (from 23 to 341 ms) at the stage of extracting mel-frequency cepstral coefficients was investigated. The research results revealed significant accuracy of the resulting model (UAR = 48 %). The proposed approach shows potential for applications such as voice assistants, virtual agents, and mental health diagnostics.

Free commutative two-step-associative algebras

We construct linear bases for free commutative two-step-associative algebras and study their automorphisms. It turns out that every automorphism of a polynomial algebra without unit can be lifted to an automorphism of a free commutative two-step-associative algebra. Moreover, for any n ≥ 2 , a wild automorphism is constructed for the n-generated free commutative two-step-associative algebra which is not stably tame and cannot be lifted to an automorphism of the n-generated free commutative nonassociative algebra.

Machine learning models predicts risk of proliferative lupus nephritis.

This study aims to develop and validate machine learning models to predict proliferative lupus nephritis (PLN) occurrence, offering a reliable diagnostic alternative when renal biopsy is not feasible or safe. This study retrospectively analyzed clinical and laboratory data from patients diagnosed with SLE and renal involvement who underwent renal biopsy at West China Hospital of Sichuan University between 2011 and 2021. We randomly assigned 70% of the patients to a training cohort and the remaining 30% to a test cohort. Various machine learning models were constructed on the training cohort, including generalized linear models (e.g., logistic regression, least absolute shrinkage and selection operator, ridge regression, and elastic net), support vector machines (linear and radial basis kernel functions), and decision tree models (e.g., classical decision tree, conditional inference tree, and random forest). Diagnostic performance was evaluated using ROC curves, calibration curves, and DCA for both cohorts. Furthermore, different machine learning models were compared to identify key and shared features, aiming to screen for potential PLN diagnostic markers. Involving 1312 LN patients, with 780 PLN/NPLN cases analyzed. They were randomly divided into a training group (547 cases) and a testing group (233 cases). we developed nine machine learning models in the training group. Seven models demonstrated excellent discriminatory abilities in the testing cohort, random forest model showed the highest discriminatory ability (AUC: 0.880, 95% confidence interval(CI): 0.835-0.926). Logistic regression had the best calibration, while random forest exhibited the greatest clinical net benefit. By comparing features across various models, we confirmed the efficacy of traditional indicators like anti-dsDNA antibodies, complement levels, serum creatinine, and urinary red and white blood cells in predicting and distinguishing PLN. Additionally, we uncovered the potential value of previously controversial or underutilized indicators such as serum chloride, neutrophil percentage, serum cystatin C, hematocrit, urinary pH, blood routine red blood cells, and immunoglobulin M in predicting PLN. This study provides a comprehensive perspective on incorporating a broader range of biomarkers for diagnosing and predicting PLN. Additionally, it offers an ideal non-invasive diagnostic tool for SLE patients unable to undergo renal biopsy.

An information field theory approach to Bayesian state and parameter estimation in dynamical systems

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable the seamless fusion of different experimental modalities. When the dynamics are discrete and stochastic, one may employ powerful techniques such as Kalman, particle, or variational filters. Practitioners commonly apply these methods to continuous-time, deterministic dynamical systems after discretizing the dynamics and introducing fictitious transition probabilities. However, approaches based on time-discretization suffer from the curse of dimensionality since the number of random variables grows linearly with the number of time-steps. Furthermore, the introduction of fictitious transition probabilities is an unsatisfactory solution because it increases the number of model parameters and may lead to inference bias. To address these drawbacks, the objective of this paper is to develop a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. Our methodology builds upon information field theory. Specifically, we parameterize the dynamical system state path using a linear basis. Then, we construct a physics-informed prior probability measure for the coefficients of the linear basis such that functions that satisfy the physics are more likely. This prior allows us to quantify model form errors. We connect the system's response to observations through a probabilistic model of the measurement process. The joint posterior over the system responses and all parameters is given by Bayes' rule. To approximate the intractable posterior, we develop a stochastic variational inference algorithm. In summary, the developed methodology offers a powerful framework for Bayesian estimation in dynamical systems.

A Three-Grid High-Order Immersed Finite Element Method for the Analysis of CAD Models

The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an efficient, robust, high-order immersed finite element method for complex CAD models. Our approach relies on three adaptive structured grids: a geometry grid for representing the implicit geometry, a finite element grid for discretising physical fields and a quadrature grid for evaluating the finite element integrals. The geometry grid is a sparse VDB (Volumetric Dynamic B+ tree) grid that is highly refined close to physical domain boundaries. The finite element grid consists of a forest of octree grids distributed over several processors, and the quadrature grid in each finite element cell is an octree grid constructed in a bottom-up fashion. The resolution of the quadrature grid ensures that finite element integrals are evaluated with sufficient accuracy and that any sub-grid geometric features, like small holes or corners, are resolved up to a desired resolution. The conceptual simplicity and modularity of our approach make it possible to reuse open-source libraries, i.e. openVDB and p4est for implementing the geometry and finite element grids, respectively, and BDDCML for iteratively solving the discrete systems of equations in parallel using domain decomposition. We demonstrate the efficiency and robustness of the proposed approach by solving the Poisson equation on domains described by complex CAD models and discretised with tens of millions of degrees of freedom. The solution field is discretised using linear and quadratic Lagrange basis functions.

Bridge Damage Detection with Support Vector Machine in Accelerometer-Based Wireless Sensor Network

Abstract Purpose This paper proposes an in-network vibration data processing using Wireless Sensor Network (WSN) leveraging Machine Learning (ML) for damage detection and localization. The study also presents the ML algorithms comparison that is suitable to be deployed in WSN and implemented the proposed cluster-based WSN topology on the bridge simulation test. Methods The bridge vibration data was acquired using accelerometer-based wireless sensor nodes. The data collected are transformed using Fast Fourier Transform (FFT) to obtain fundamental frequencies and their corresponding amplitudes. The machine learning method i.e., Support Vector Machine (SVM) with linear and Radial Basis Function (RBF) kernel was used to analyze the vibration data collected from the WSN. In-network data processing and cluster-based WSN topology is implemented and the programmable wireless sensor nodes is utilized in this study. Results The experiments were conducted using real programmable wireless sensor nodes and developed our test bed bridge which makes this work different from the previous studies. The classification and predicting results shows 97%, 96%, 97%, and 96% for accuracy, precision, recall rate, and f1-score, respectively. Conclusion Machine learning methods can potentially be combined with the vibration WSN for bridge damage detection and localization.

Mathematical analysis and numerical simulations for a nonlinear Klein Gordon equation in an exterior domain

In this study, the finite propogation speed properties investigated for a two dimensional exterior problem defined by nonlinear Klein-Gordon equation. Under some assumptions on the initial data and the nonlinearity, the solution is shown to have a finite propogation speed. Furthermore, it is demonstrated that the problem has a unique solution, and accurate numerical solutions have been produced by the use of the dual reciprocity boundary element approach with linear radial basis functions.

A framework for performance enhancement of classifiers in detection of prostate cancer from microarray gene

Prostate cancer is a major world health problem for men. This shows how important early detection and accurate diagnosis are for better treatment and patient outcomes. This study compares different ways to find Prostate Cancer (PCa) and label tumors as normal or abnormal, with the goal of speeding up current work in microarray gene data analysis. The study looks at how well several feature extraction methods work with three feature selection strategies: Harmonic Search (HS), Firefly Algorithm (FA), and Elephant Herding Optimization (EHO). The techniques tested are Expectation Maximization (EM), Nonlinear Regression (NLR), K-means, Principal Component Analysis (PCA), and Discrete Cosine Transform (DCT). Eight classifiers are used for the task of classification. These are Random Forest, Decision Tree, Adaboost, XGBoost, and Support Vector Machine (SVM) with linear, polynomial, and radial basis function kernels. This study looks at how well these classifiers work with and without feature selection methods. It finds that the SVM with radial basis function kernel, using DCT for feature extraction and EHO for feature selection, does the best of all of them, with an accuracy of 94.8 % and an error rate of 5.15 %.

Distributed Formation–Containment Tracking Control for Multi-Hovercraft Systems with Compound Perturbations

Aiming at the problem of hovercraft formation–containment control with compound perturbations including model uncertainties and ocean disturbances, a distributed control algorithm for underactuated hovercraft formation–containment is proposed by combining adaptive linear extended state observer (ALESO) and radial basis function neural network (RBFNN). Firstly, ALESO and RBFNN are designed to estimate the ocean disturbances and model uncertainties, respectively, for dynamic compensation in the controller. Then, the auxiliary variables are introduced into the formation error function, and the lateral and longitudinal error stabilization is transformed into the design of longitudinal force and rotational torque by using the skew-symmetric matrix transformation, which solves the lateral underactuated problem of the hovercraft. Finally, the uniform ultimate boundedness of formation–containment cooperative errors is proved by the Lyapunov stability theory. Digital simulation verifies the effectiveness of the proposed method.