138 research outputs found

    Discrete Fourier analysis with lattices on planar domains

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    A discrete Fourier analysis associated with translation lattices is developed recently by the authors. It permits two lattices, one determining the integral domain and the other determining the family of exponential functions. Possible choices of lattices are discussed in the case of lattices that tile \RR^2 and several new results on cubature and interpolation by trigonometric, as well as algebraic, polynomials are obtained

    Discrete Fourier analysis, Cubature and Interpolation on a Hexagon and a Triangle

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    Several problems of trigonometric approximation on a hexagon and a triangle are studied using the discrete Fourier transform and orthogonal polynomials of two variables. A discrete Fourier analysis on the regular hexagon is developed in detail, from which the analysis on the triangle is deduced. The results include cubature formulas and interpolation on these domains. In particular, a trigonometric Lagrange interpolation on a triangle is shown to satisfy an explicit compact formula, which is equivalent to the polynomial interpolation on a planer region bounded by Steiner's hypocycloid. The Lebesgue constant of the interpolation is shown to be in the order of (logn)2(\log n)^2. Furthermore, a Gauss cubature is established on the hypocycloid.Comment: 29 page

    Discrete Fourier Analysis and Chebyshev Polynomials with G2G_2 Group

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    The discrete Fourier analysis on the 30°30^{\degree}-60°60^{\degree}-90°90^{\degree} triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group G2G_2, which leads to the definition of four families generalized Chebyshev polynomials. The study of these polynomials leads to a Sturm-Liouville eigenvalue problem that contains two parameters, whose solutions are analogues of the Jacobi polynomials. Under a concept of mm-degree and by introducing a new ordering among monomials, these polynomials are shown to share properties of the ordinary orthogonal polynomials. In particular, their common zeros generate cubature rules of Gauss type

    Theory and Design of Feasible Active Noise Control Systems for 3D Regions

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    This thesis advances Active Noise Control (ANC) over three-dimensional (3D) space using feasible loudspeaker and microphone array systems. By definition, ANC reduces unwanted acoustic noise by generating an anti-noise signal(s) from secondary loudspeakers. The concept of spatial ANC aims to reduce unwanted acoustic noise over a continuous 3D region, by utilizing multiple microphones and multiple secondary loudspeakers to create a large-sized quiet zone for listeners in three-dimensional space. However, existing spatial ANC techniques are usually impractical and difficult to implement due to their strict hardware requirements and high computation complexity. Therefore, this thesis explores various aspects of spatial ANC, seeking algorithms and techniques to promote the reliability and feasibility of ANC over space in real-life applications. The spherical harmonic analysis technique is introduced as the basis of conventional spatial ANC systems. This technique provides an accurate representation of a given spatial sound field using higher-order microphone (spherical microphone array) recordings. Hence, the residual noise field in a spatial ANC system can be effectively captured spatially by applying the spherical harmonic technique. Incorporating conventional spatial ANC methods, we developed a series of algorithms and methods that optimize conventional methods regarding array geometries and ANC algorithms, towards improving the feasibility of a conventional spatial ANC system involving the spherical harmonic analysis. Overall, motivated by feasible and realistic designs for spatial ANC systems, work included in this thesis mainly solves the three problems of: (i) the impracticality of realizing spherical microphone and loudspeaker arrays, (ii) achieving secondary channel estimation with microphones remote from their desired locations, and (iii) unreasonable delays inherent to frequency domain spatial ANC methods. Based on our work, we have stepped towards achieving a spatial ANC system in a real-world environment for people to enjoy silence in the control region with the reliable usage of resources and algorithms. Several contributions of this work are: (i) designing a 3D spatial ANC system using multiple circular microphone and loudspeaker arrays instead of spherical arrays, (ii) proposing a 3D spatial ANC method with remote microphone technique such that noise reduction over a region is achieved with microphones remote from the region, (iii) proposing a secondary channel estimation method using a moving higher-order microphone such that usage of an error microphone array is not necessary, (iv) deriving a time domain spherical harmonic analysis method for open spherical microphone array recording with less delay than in the frequency domain, and (v) designing a feed-forward adaptive spatial ANC algorithm incorporating the time domain spherical harmonic analysis technique to better minimize the noise in the region of interest

    Comparison and optimization of cordon and area pricings for managing travel demand

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    This paper analyses both the cordon and area pricings from the perspective of travel demand management. Sensitivity analysis of various performance measures with respect to the toll rate and demand elastic parameter is performed on a virtual grid network. The analysis shows that cordon pricing mainly affects those trips with origins outside of the Central Business District and destinations inside, while area pricing imposes additional cost on the trips with either origins or destinations in the Central Business District. Though both pricing strategies are able to alleviate traffic congestion in the charging area, area pricing seems more effective, however, area pricing owns the risk to detour too much traffic and thus cause severe congestion to the network outside of the Central Business District. Following the sensitivity analysis, a unified framework is proposed to optimize the designs of the both pricing strategies, which is flexible to account for various practical concerns. The optimization models are formulated as mixed-integer nonlinear programs with complementarity constraints, and the solution procedure is composed of solving a series of nonlinear programs and mixed-integer linear programs. Results from the numerical examples are in line with the findings in the sensitivity analysis. Under the specific network settings, cordon pricing achieves the best system performance when the toll rate reaches the maximum allowed, while area pricing finds the optimal design scheme when the toll rate equals half of the maximum allowed. First published online: 28 May 201

    Multifactor dimensionality reduction analysis of syndrome characteristics of chronic persistent asthma

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    AbstractObjectiveTo analyze the syndrome characteristics in patients with chronic persistent asthma.Methods365 patients (121 males, 244 females, 60.8 ± 29.1 years old) with chronic persistent asthma were enrolled in this cross-sectional study. The information of syndrome, symptoms, signs, tongue coating and pulse were collected from all patients. The syndrome characteristics of chronic persistent asthma were examined through the multifactor dimensionality reduction (MDR) analysis and the results were verified by the Chi-square test.ResultsThe results of the MDR analysis and the Chi-square test showed the following positive correlation of the interaction among: the deficiency syndrome of the lung and spleen and deep pulse, disinclination to talk due to lack of qi, fatigue, lassitude and thick tongue coating; the deficiency syndrome of the lung and kidney and dizziness and disinclination to talk due to lack of qi, fatigue, lassitude and pallid complexion; the syndrome of phlegm-heat obstructing the lung and rapid pulse, abdominal distension, disinclination to talk due to lack of qi, frequent urination and lassitude; the syndrome of phlegm-dampness obstructing the lung and disinclination to talk due to lack of qi, greasy coating, fatigue and lassitude. (P < .05 for all).ConclusionThe syndrome of chronic persistent asthma is characterized by fatigue and lassitude due to dysfunction of the lung, spleen and kidney

    MCCFNet: multi-channel color fusion network for cognitive classification of traditional Chinese paintings.

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    The computational modeling and analysis of traditional Chinese painting rely heavily on cognitive classification based on visual perception. This approach is crucial for understanding and identifying artworks created by different artists. However, the effective integration of visual perception into artificial intelligence (AI) models remains largely unexplored. Additionally, the classification research of Chinese painting faces certain challenges, such as insufficient investigation into the specific characteristics of painting images for author classification and recognition. To address these issues, we propose a novel framework called multi-channel color fusion network (MCCFNet), which aims to extract visual features from diverse color perspectives. By considering multiple color channels, MCCFNet enhances the ability of AI models to capture intricate details and nuances present in Chinese painting. To improve the performance of the DenseNet model, we introduce a regional weighted pooling (RWP) strategy specifically designed for the DenseNet169 architecture. This strategy enhances the extraction of highly discriminative features. In our experimental evaluation, we comprehensively compared the performance of our proposed MCCFNet model against six state-of-the-art models. The comparison was conducted on a dataset consisting of 2436 TCP samples, derived from the works of 10 renowned Chinese artists. The evaluation metrics employed for performance assessment were Top-1 Accuracy and the area under the curve (AUC). The experimental results have shown that our proposed MCCFNet model significantly outperform all other benchmarking methods with the highest classification accuracy of 98.68%. Meanwhile, the classification accuracy of any deep learning models on TCP can be much improved when adopting our proposed framework
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