Iterative Algorithm Research Articles

A new method for synthesis and designing transmissive linear-to-circular polarization converters based on branch line circuit model

ABSTRACT This paper proposes a new design method of a linear-to-circular polarization converter based on the branch line circuit model. The series branches are implemented by dielectric spacers and the shunt branches are implemented by anisotropic admittance sheets. The admittance matrix of the anisotropic admittance sheets is derived by even and odd mode analysis. A unit cell consisting of two metal layers and a dielectric spacer is then designed using an iterative algorithm for operation from 15.5 to 23 GHz. Results indicate that the axial ratio and insertion loss of the designed polarizer are better than 3 and 1.5 dB respectively, for incident angles between ±45°. To validate the simulation results, a waveguide-based test setup is designed and fabricated, with measurement results indicating good agreement with simulations. The proposed method can be potentially applied to design other anisotropic structures such as half-plate polarizers and polarization rotators.

Fungal microtubule organizing centers are evolutionarily unstable structures

For most Eukaryotic species the requirements of cilia formation dictate the structure of microtubule organizing centers (MTOCs). In this study we find that loss of cilia corresponds to loss of evolutionary stability for fungal MTOCs. We used iterative search algorithms to identify proteins homologous to those found in saccharomyces cerevisiae, and schizosaccharomyces pombe MTOCs, and calculated site-specific rates of change for those proteins that were broadly phylogenetically distributed. Our results indicate that both the protein composition of MTOCs as well as the sequence of MTOC proteins are poorly conserved throughout the fungal kingdom. To begin to reconcile this rapid evolutionary change with the rigid structure and essential function of the s. cerevisiae MTOC we further analyzed how structural interfaces among proteins influence the rates of change for specific residues within a protein. We find that a more stable protein may stabilize portions of an interacting partner where the two proteins are in contact. In summary, while the protein composition and sequences of the MTOC may be rapidly changing the proteins within the structure have a stabilizing effect on one another. Further exploration of fungal MTOCs will expand our understanding of how changes in the functional needs of a cell have affected physical structures, proteomes, and protein sequences throughout fungal evolution.

NUMERICAL TREATMENT OF LINEAR VOLTERRA INTEGRO DIFFERENTIAL EQUATIONS USING VARIATIONAL ITERATION ALGORITHM WITH COLLOCATION

To numerically solve the linear Volterra integro-differential equation, this study employs fourth-kind Chebyshev polynomials and the variational iteration algorithm with collocation, which is a combination of the variational iteration strategy and collocation technique. By applying fourth-kind Chebyshev polynomials to the variational iteration method with collocation for solving Volterra integro-differential equations, mathematical problems with a broad range of multidisciplinary applications are addressed, and numerical techniques that produce more accurate and efficient results are developed. The recommended method is then used, and the fourth-kind Chebyshev polynomials generated for the given integro-differential equation serve as the trial functions for the approximation. As a result, the suggested method's significance probably goes beyond a particular equation or application, as it contributes to the larger field of mathematical modeling and numerical analysis. Research methods employing a variational iteration algorithm with collocation aim to provide general techniques that can be applied to a wide range of problems. Additionally, numerical examples were provided to highlight the applicability and dependability of the proposed methodology. The mathematical computations were carried out using the Maple 18 software.

HPETC: History Priority Enhanced Tensor Completion for Network Distance Measurement

In network distance measurement, how to estimate the whole network distance data from partially observed samples has attracted lots of attention because of its significance for network performance evaluation. Matrix completion becomes the most effective approach. However, the two-dimension matrix can only capture the spatial features in the network distance data while ignoring the temporal features. To conquer the problem, few recent studies begin to model the network distance data as a three-dimension tensor and propose tensor completion approaches for distance estimation. Although promising, existing tensor completion approaches still suffer the problem of low recovery accuracy and high measurement cost because they ignore the history priority information. To fully utilize both spatial and temporal features hidden in the distance data, this paper formulates a novel History Priority Enhanced Tensor Completion (HPETC) for distance estimation as a weighted tensor nuclear norm minimization problem where the weight is defined based on the history subspaces information. To solve the weighted tensor nuclear norm minimization problem, we firstly transform it into a factorization-based Frobenius norm minimization problem to avoid costly T-SVD computations, and then propose an iterative algorithm to solve the transformed problem. We further derive a theoretical sampling bound that is lower than the existing sampling bound, thus leads a lower measurement cost. We demonstrate the effectiveness of the proposed algorithm by conducting extensive experiments using two real network distance datasets. The result shows that the proposed algorithm can not only improve the estimation accuracy but also reduce the sampling complexity compared to the state-of-the-art approaches.

All-optical complex field imaging using diffractive processors.

Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However, conventional image sensors are intensity-based and inherently lack the capability to directly measure the phase distribution of a field. This limitation can be overcome using interferometric or holographic methods, often supplemented by iterative phase retrieval algorithms, leading to a considerable increase in hardware complexity and computational demand. Here, we present a complex field imager design that enables snapshot imaging of both the amplitude and quantitative phase information of input fields using an intensity-based sensor array without any digital processing. Our design utilizes successive deep learning-optimized diffractive surfaces that are structured to collectively modulate the input complex field, forming two independent imaging channels that perform amplitude-to-amplitude and phase-to-intensity transformations between the input and output planes within a compact optical design, axially spanning ~100 wavelengths. The intensity distributions of the output fields at these two channels on the sensor plane directly correspond to the amplitude and quantitative phase profiles of the input complex field, eliminating the need for any digital image reconstruction algorithms. We experimentally validated the efficacy of our complex field diffractive imager designs through 3D-printed prototypes operating at the terahertz spectrum, with the output amplitude and phase channel images closely aligning with our numerical simulations. We envision that this complex field imager will have various applications in security, biomedical imaging, sensing and material science, among others.

A flexible time-varying coefficient rate model for panel count data.

Panel count regression is often required in recurrent event studies, where the interest is to model the event rate. Existing rate models are unable to handle time-varying covariate effects due to theoretical and computational difficulties. Mean models provide a viable alternative but are subject to the constraints of the monotonicity assumption, which tends to be violated when covariates fluctuate over time. In this paper, we present a new semiparametric rate model for panel count data along with related theoretical results. For model fitting, we present an efficient EM algorithm with three different methods for variance estimation. The algorithm allows us to sidestep the challenges of numerical integration and difficulties with the iterative convex minorant algorithm. We showed that the estimators are consistent and asymptotically normally distributed. Simulation studies confirmed an excellent finite sample performance. To illustrate, we analyzed data from a real clinical study of behavioral risk factors for sexually transmitted infections.

Optimal Voltage Recovery Learning Control for Microgrids with N-Distributed Generations via Hybrid Iteration Algorithm

Considering that the nonlinearity and uncertainty of the microgrid model complicate the derivation and design of the optimal controller, an adaptive dynamic programming (ADP) algorithm is designed to solve the model-free non-zero-sum game. By combining the advantages of policy iteration and value iteration, an optimal learning control scheme based on hybrid iteration is constructed to provide stringent real power sharing for the nonlinear and coupled microgrid systems with N-distributed generations. First, using non-zero-sum differential game strategy, a novel distributed secondary voltage recovery consensus optimal control protocol is built using a hybrid iteration method to realize the voltage recovery of microgrids. Then, the data of the system state and input are gathered along a dynamic system trajectory and a data-driven optimal controller learns the game solution without microgrid physics information, enhancing convenience and efficiency in practical applications. Furthermore, the convergence analysis is given in detail, and it is proved that the control protocol can converge to the optimal solution so as to ensure the stability of the voltage recovery of the microgrid system. Convergence analysis proves the convergence of the the protocol to the optimal solution, ensuring voltage recovery stability. Simulation results validate the feasibility and effectiveness of the proposed scheme.

Background-oriented schlieren experimental and simulation study of the effect of sidewalls on optical turbulence anisotropy in a thermal convection turbulence simulator

The anisotropic optical structure characteristics within the Rayleigh-Bénard (RB) turbulence simulator have been investigated through experiment and simulation. We collected data using background-oriented schlieren technology and extracted displacements using optical flow algorithms. The wavefront phase can be recovered using the conjugate gradient iterative algorithm. We analyzed the optical structural characteristics within the turbulence simulator under different temperature differences. It is observed that with an increased temperature difference, the spatial correlation of the refractive index field decreases at an accelerated rate as the separation distance increases, and the degree of anisotropy characterized by the phase structure function increases. Large eddy simulation and split-step beam propagation method complement experimental results. Numerical simulations demonstrate consistency with experimental data. The results show that the von Karman power spectral density fits the simulation and experimental phase structure function very well relative to the Kolmogorov power spectral density, which demonstrates that the simulation system combining dynamics simulation and optical simulation can achieve power spectral characteristics that are consistent with reality. The experimental and simulation results are crucial for understanding the flow field's optical structural properties inside the turbulence simulator. They will help to construct a suitable turbulence simulator for optical engineering applications and establish a rational scheme for analyzing its internal optical structural properties.

New Perturbation–Iteration Algorithm for Nonlinear Heat Transfer of Fractional Order

New Perturbation–Iteration Algorithm for Nonlinear Heat Transfer of Fractional Order

Uniqueness and numerical inversion in bioluminescence tomography with time-dependent boundary measurement

In the paper, an inverse source problem in bioluminescence tomography (BLT) is investigated. BLT is a method of light imaging and offers many advantages such as sensitivity, cost-effectiveness, high signal-to-noise ratio and non-destructivity. It thus has promising prospects for many applications such as cancer diagnosis, drug discovery and development as well as gene therapies. In the literature, BLT is extensively studied based on the (stationary) diffusion approximation (DA) equation, where the distribution of peak sources is reconstructed and no solution uniqueness is guaranteed without proper a priori information. In this work, motivated by solution uniqueness, a novel dynamic coupled DA model is proposed. Theoretical analysis including the well-posedness of the forward problem and the solution uniqueness of the inverse problem are given. Based on the new model, iterative inversion algorithms under the framework of regularizing schemes are introduced and applied to reconstruct the smooth and non-smooth sources. We discretize the regularization functional with the finite element method and give the convergence rate of numerical solutions. Several numerical examples are implemented to validate the effectiveness of the new model and the proposed algorithms.

Harmonic impedance optimization scheme for multi‐resonance systems to suppress resonance

AbstractHarmonic resonance is caused by harmonic source matching resonance frequency and presents the characteristics of decentralization and whole network in modern grids. The current resonance suppression methods mainly focus on reducing the harmonic source, and are suitable for single‐site and small‐scale grids. This paper presents a new method for suppressing parallel resonance at system level. The holistic harmonic resonance is suppressed by reducing the harmonic impedance. In addition, new resonances are prevented by weakening the coupling between resonance and non‐resonance frequencies. The resonance modal analysis and resonance frequency shift (RFS) are employed to optimize harmonic impedance. Simulation results indicate that the capacitance parameter has higher sensitivity and is theoretically more suitable for RFS. Considering the accuracy of modal frequency sensitivity, a variable‐limit genetic algorithm for iteration is proposed. The validity of the proposed method was verified using an IEEE 14‐bus test network.

Numerical Investigation on a High-Speed Transom Stern Ship Advancing in Shallow Water

A high-speed advancing ship will cause significant squats in shallow water, which could increase the risk of grounding. To this end, a program based on the Rankine higher-order boundary element method (HOBEM) is developed to investigate a high-speed displacement ship with a transom stern moving in shallow water. The nonlinear free surface condition is satisfied by adopting an iterative algorithm on the real free surface. The transom condition is considered by implementing a modified transom condition. Computations of wave-making resistance, sinkage and trim in deep water are first performed, and satisfactory agreement is achieved by comparing with the experimental results; the simulations are then extended to the shallow water case. It indicates that the present method can provide a suitable balance of practicability and robustness, which can be considered as an efficient tool for the guidance in ship design stage.

Reconstruction of inhomogeneous media by an iteration algorithm with a learned projector

Reconstruction of inhomogeneous media by an iteration algorithm with a learned projector

Robust Spherical Laplacian Embedding.

Laplacian embedding (LE) aims to project high-dimensional input data samples, which often contain nonlinear structures, into a low-dimensional space. However, existing distance functions used in the embedding space fail to provide discriminative representations for real-world datasets, especially those related to text analysis or image processing. Cosine similarity measurements are advantageous in dealing with sparse data but are fragile to the impact of outliers and noise from samples or data features. In this work, we propose robust spherical LE (RS-LE), a powerful method that builds the LE on a novel metric that unifies the Euclidean distance and cosine similarity in a spherical space using a robust lp,p -norm. We introduce an efficient iterative algorithm, the proximal alternating linearized minimization (ALM) method, to solve the difficult optimization problem that arises from the new metric, which is neither convex nor smooth. This algorithm allows the solution to achieve both global and objective convergence. Our findings are presented in rigorous theoretical analysis and validated in experiments.

Enhancing voxel-based dosimetry accuracy with an unsupervised deep learning approach for hybrid medical image registration.

Deformable registration is required to generate a time-integrated activity (TIA) map which is essential for voxel-based dosimetry. The conventional iterative registration algorithm using anatomical images (e.g., computed tomography (CT)) could result in registration errors in functional images (e.g., single photon emission computed tomography (SPECT) or positron emission tomography (PET)). Various deep learning-based registration tools have been proposed, but studies specifically focused on the registration of serial hybrid images were not found. In this study, we introduce CoRX-NET, a novel unsupervised deep learning network designed for deformable registration of hybrid medical images. The CoRX-NET structure is based on the Swin-transformer (ST), allowing for the representation of complex spatial connections in images. Its self-attention mechanism aids in the effective exchange and integration of information across diverse image regions. To augment the amalgamation of SPECT and CT features, cross-stitch layers have been integrated into the network. Two different 177 Lu DOTATATE SPECT/CT datasets were acquired at different medical centers. 22 sets from Seoul National University and 14 sets from Sunway Medical Centre are used for training/internal validation and external validation respectively. The CoRX-NET architecture builds upon the ST, enabling the modeling of intricate spatial relationships within images. To further enhance the fusion of SPECT and CT features, cross-stitch layers have been incorporated within the network. The network takes a pair of SPECT/CT images (e.g., fixed and moving images) and generates a deformed SPECT/CT image. The performance of the network was compared with Elastix and TransMorph using L1 loss and structural similarity index measure (SSIM) of CT, SSIM of normalized SPECT, and local normalized cross correlation (LNCC) of SPECT as metrics. The voxel-wise root mean square errors (RMSE) of TIA were compared among the different methods. The ablation study revealed that cross-stitch layers improved SPECT/CT registration performance. The cross-stitch layers notably enhance SSIM (internal validation: 0.9614vs. 0.9653, external validation: 0.9159vs. 0.9189) and LNCC of normalized SPECT images (internal validation: 0.7512vs. 0.7670, external validation: 0.8027vs. 0.8027). CoRX-NET with the cross-stitch layer achieved superior performance metrics compared to Elastix and TransMorph, except for CT SSIM in the external dataset. When qualitatively analyzed for both internal and external validation cases, CoRX-NET consistently demonstrated superior SPECT registration results. In addition, CoRX-NET accomplished SPECT/CT image registration in less than 6s, whereas Elastix required approximately 50s using the same PC's CPU. When employing CoRX-NET, it was observed that the voxel-wise RMSE values for TIA were approximately 27% lower for the kidney and 33% lower for the tumor, compared to when Elastix was used. This study represents a major advancement in achieving precise SPECT/CT registration using an unsupervised deep learning network. It outperforms conventional methods like Elastix and TransMorph, reducing uncertainties in TIA maps for more accurate dose assessments.

Iterative smoothing for change-point regression function estimation

Understanding wildfire spread in Canada is critical to promoting forest health and protecting human life and infrastructure. Quantifying fire spread from noisy images, where change-point boundaries separate regions of fire, is critical to accurately estimating fire spread rates. The challenge lies in denoising the fire images and accurately identifying highly non-linear fire lines without smoothing over boundaries. In this paper, we develop an iterative smoothing algorithm for change-point data that utilizes oversmoothed estimates of the underlying data generating process to inform re-smoothing. We demonstrate its effectiveness on simulated one- and two-dimensional change-point data, and robustness to response outliers. Then, we apply the methodology to fire spread images from laboratory micro-fire experiments and show that the regions fuel, burning and burnt-out are smoothed while boundaries are preserved.

On Mean-Optimal Robust Linear Discriminant Analysis

Linear discriminant analysis (LDA) is widely used for dimensionality reduction under supervised learning settings. Traditional LDA objective aims to minimize the ratio of the squared Euclidean distances that may not perform optimally on noisy datasets. Multiple robust LDA objectives have been proposed to address this problem, but their implementations have two major limitations. One is that their mean calculations use the squared \(\ell_{2}\) -norm distance to center the data, which is not valid when the objective depends on other distance functions. The second problem is that there is no generalized optimization algorithm to solve different robust LDA objectives. In addition, most existing algorithms can only guarantee the solution to be locally optimal, rather than globally optimal. In this paper, we review multiple robust loss functions and propose a new and generalized robust objective for LDA. Besides, to better remove the mean value within data, our objective uses an optimal way to center the data through learning. As one important algorithmic contribution, we derive an efficient iterative algorithm to optimize the resulting non-smooth and non-convex objective function. We theoretically prove that our solution algorithm guarantees that both the objective and the solution sequences converge to globally optimal solutions at a sub-linear convergence rate. The results of comprehensive experimental evaluations demonstrate the effectiveness of our new method, achieving significant improvements compared to the other competing methods.

Normscan: open-source Python software to create average models from CT scans.

Age-matched average 3D models facilitate both surgical planning and intraoperative guidance of cranial birth defects such as craniosynostosis. We aimed to develop an algorithm that accepts any number of CT scans as input and generates highly accurate, average models with minimal user input that are ready for 3D printing and clinical use. Using a compiled database of 'normal' pediatric computed tomography (CT) scans, we report Normscan, an open-source platform built in Python that allows users to generate normative models of CT scans through user-defined landmarks. We use the basion, nasion, and left and right porions as anatomical landmarks for initial correspondence and then register the models using the iterative closest points algorithm before downstream averaging. Normscan is fast and easy to use via our user interface and also creates highly accurate average models of any number of input models. Additionally, it is highly repeatable, with coefficients of variance for the surface area and volume of the average model being less than 3% across ten independent trials. Average models can then be 3D printed and/or visualized in augmented reality. Normscan provides an end-to-end pipeline for the creation of average models of skulls. These models can be used for the generation of databases of specific demographic anatomical models as well as for intraoperative guidance and surgical planning. While Normscan was designed for craniosynostosis repair, due to the modular nature of the algorithm, Normscan has many applications in other areas of surgical planning and research.

Constrained Iterative Adaptive Algorithm for the Detection and Localization of RFI Sources Based on the SMAP L-Band Microwave Radiometer

The Soil Moisture Active Passive (SMAP) satellite carries an L-band microwave radiometer. This sensor can be used to observe global soil moisture (SM) and sea surface salinity (SSS) within the protected L-band spectrum (1400–1427 MHz). Owing to the complex effects of radio frequency interference (RFI), the SM and SSS data are missing or have low accuracy. In this paper, a constrained iterative adaptive algorithm for the detection, identification, and localization of RFI sources is designed, named MICA-BEID. The algorithm synthesizes antenna temperatures for the third and fourth Stokes parameters before RFI filtering, creating a new polarization parameter called WSPDA, designed to approximate the level of RFI interference on the L-band microwave radiometer. The algorithm then utilizes the WSPDA intensity and distribution density of RFI detection samples to enhance the identification and classification of RFI sources across various intensity levels. By utilizing statistical methods such as the probability density function (PDF) and the cumulative distribution function (CDF), the algorithm dynamically adjusts adaptive parameters, including the RFI detection threshold and the maximum effective radius of RFI sources. Through the application of multiple iterative clustering methods, the algorithm can adaptively detect and identify RFI sources at various satellite orbits and intensity levels. Through extensive comparative analysis with other localization results and known RFI sources, the MICA-BEID algorithm can achieve optimal localization accuracy of approximately 1.2 km. The localization of RFI sources provides important guidance for identifying and turning off illegal RFI sources. Moreover, the localization and long-time-series characteristic analysis of RFI sources that cannot be turned off is of significant value for simulating the spatial distribution characteristics of localized RFI source intensity in local areas.

Automatic extraction of facial median sagittal plane for patients with asymmetry based on the EDMA alignment algorithm.

We aimed to establish a novel method for automatically constructing three-dimensional (3D) median sagittal plane (MSP) for mandibular deviation patients, which can increase the efficiency of aesthetic evaluating treatment progress. We developed a Euclidean weighted Procrustes analysis (EWPA) algorithm for extracting 3D facial MSP based on the Euclidean distance matrix analysis, automatically assigning weight to facial anatomical landmarks. Forty patients with mandibular deviation were recruited, and the Procrustes analysis (PA) algorithm based on the original mirror alignment and EWPA algorithm developed in this study were used to construct the MSP of each facial model of the patient as experimental groups 1 and 2, respectively. The expert-defined regional iterative closest point algorithm was used to construct the MSP as the reference group. The angle errors of the two experimental groups were compared to those of the reference group to evaluate their clinical suitability. The angle errors of the MSP constructed by the two EWPA and PA algorithms for the 40 patients were 1.39 ± 0.85°, 1.39 ± 0.78°, and 1.91 ± 0.80°, respectively. The two EWPA algorithms performed best in patients with moderate facial asymmetry, and in patients with severe facial asymmetry, the angle error was below 2°, which was a significant improvement over the PA algorithm. The clinical application of the EWPA algorithm based on 3D facial morphological analysis for constructing a 3D facial MSP for patients with mandibular deviated facial asymmetry deformity showed a significant improvement over the conventional PA algorithm and achieved the effect of a dental clinical expert-level diagnostic strategy.