Iterative Approximation Research Articles

Investigation of neighborhood disadvantage in the context of APOE‐associated amyloid onset age risk

AbstractBackgroundExposome social determinants of health (SDoH), such as neighborhood disadvantage, have shown associations with accelerated cognitive decline, brain volume loss, and postmortem AD pathology. However, associations between neighborhood disadvantage and amyloid biomarker positivity (A+) onset remain understudied. This study uses estimated A+ onset age (EAOA) and the Area Deprivation Index (ADI; an exposome SDoH) to investigate associations between neighborhood disadvantage and A+ risk.MethodParticipants (n = 599, Table 1) from the Wisconsin Registry for Alzheimer’s Prevention (WRAP) and the Wisconsin Alzheimer’s Disease Research Center (WADRC) with available amyloid PET, address, and APOE genotype were included. EAOA was estimated using sampled iterative local approximation. Neighborhood disadvantage was categorized by national‐rank 2020 ADI (most disadvantaged = 80th percentile; least disadvantaged <80th percentile). APOE groups were established based on the number of e4 alleles. Cox proportional hazard models assessed A+ risk associated with APOE, ADI, and their interaction. Secondary Cox models used continuous ADI and a lower 70th ADI percentile for neighborhood groups. Kaplan‐Meier curves were generated to depict A‐ probability vs. age for combinations of APOE and ADI groups. A‐ were right censored.ResultA significant interaction (p = 0.015) between ADI and APOE groups was observed such that APOE‐e4 homozygotes who resided within a highly disadvantaged neighborhood had higher risk of becoming A+, but this group was limited to two participants. Secondary analyses indicated no significant effect of ADI or interaction with APOE on A+ risk (p>0.49). Plots of A+/‐ and EAOA by ADI and APOE group (Figure 1) and Kaplan‐Meier EAOA curves indicated EAOA overlap of ADI groups within APOE strata. A+ risk was significantly higher for APOE‐e4 homozygotes, followed by APOE‐e4 heterozygotes, and then APOE‐e4 non‐carriers.ConclusionIn this mostly unimpaired, highly educated sample, higher number of APOE‐e4 alleles was associated with higher A+ risk and earlier A+ onset. APOE‐associated A+ risk was similar for all ADI groups, but representation across APOE genotypes for individuals residing within highly disadvantaged neighborhoods was limited. Further work is needed in more diverse samples to investigate the possible influence of ADI and other exposome SDoH factors on AD biomarker timing and trajectories.

Estimating a clinically normal individual’s position along a preclinical Alzheimer’s disease continuum using cognitive and amyloid trajectories

AbstractBackgroundOptimizing longitudinal cognitive and biomarker trajectories can distill multiple observations from one individual into a single metric. Relative to other individuals, this metric can represent an individual’s distance from an anchor‐point based on their rate and non‐linearity of change. We have recently developed a cognitive time (c‐time) based on the cognitive trajectories of clinically normal older adults. We examined the association between c‐time and a previously published ‘time‐to‐Aβ+ threshold’ and how these metrics align with demographics and other biomarkers.MethodWe identified 135 clinically normal older adults from the Harvard Aging Brain Study (Agemean:73years(±5.9); Female:61%) with ≥3 neuropsychological assessments and PiB‐PET, ≥1 Flortaucipir‐PET, ≥2 volumetric MRI, and diagnostic follow up. We defined c‐time using iterative non‐linear least‐squares optimization to define a curvilinear function that described the group‐level Preclinical Alzheimer Cognitive Composite (PACC) trajectory (Fig1D). Each participant’s PACC trajectory was subsequently located on the curve using the same optimization framework (Fig1E). We identified the anchor‐point of cognitive decline (c‐time) using piecewise linear mixed‐effects models. Time‐to‐Aβ+ was calculated using the published sampled iterative local approximation (SILA; Fig1A) algorithm with the anchor‐point indicating Aβ+ threshold (Fig1B). We examined associations between c‐time and time‐to‐Aβ+ using linear regression. Individuals were subsequently placed into groups depending on their position relative to the anchor‐point on each axis, as well as the line‐of‐best‐fit (Fig2). We compared the groups on demographics, and both cross‐sectional and longitudinal indices of medial temporal (MTL) Flortaucipir‐PET (entorhinal, parahippocampal, amygdala) and ICV‐adjusted hippocampal volume.ResultC‐time and time‐to‐Aβ+ were significantly associated (r = 0.42,p<0.001). Only one participant (who progressed to MCI/dementia) was post‐c‐time and remained pre‐time‐to‐Aβ+, supporting the notion that time‐to‐Aβ+ occurs prior to cognitive inflection. Individuals post‐c‐time and post‐time‐to‐Aβ+ (Group 1) were more likely to be APOEε4 carriers, progressors to MCI/dementia, have significantly higher baseline MTL tau and lower hippocampal volume, and faster hippocampal atrophy (Fig3). Group 2 (post‐time‐to‐Aβ+/pre‐c‐time) were more likely APOEε4 carriers. Notably, no age or other effects were apparent between groups.ConclusionOptimizing longitudinal cognitive and biomarker data to estimate a preclinical disease continuum can provide unique, and potentially age‐independent, information about the distance an individual might be from disease‐relevant events.

Online defect detection method of optical cable pitch based on machine vision technology and deep learning algorithms

In the field of optical cable manufacturing, the pitch error of finished optical cable exceeding 2 % is considered a defect. Currently, there is no method for online detection of pitch defect in optical cable. Therefore, this paper proposes an online intelligent detection method for cable pitch defects. This method utilizes a multi-sensor fusion image acquisition platform consisting of a Doppler laser velocimeter and an industrial line scan CCD to achieve visual information acquisition of ultra long measured objects. A mathematical model that integrates cascaded dual deep convolutional networks and iterative approximation algorithms based on deep learning technology is proposed for defect detection of optical cable pitch. In order to verify the accuracy and stability of the on-line detection method, 6 types of optical cables were prepared for experimental testing. The experimental results show that the method is robust in the field of engineering detection, and the detection results meet the accuracy requirements.

Curve fitting by GLSPIA

We develop the generalized B-splines least square progressive iterative approximation (GLSPIA) method to improve LSPIA method (Deng and Lin, 2014) from the perspective of its equivalent neural network framework. We replace the B-spline basis function in standard LSPIA method with the generalized B-spline basis function (Juhász and Róth, 2013) in the GLSPIA method. By adjusting the control points as well as the parameter in the core function, higher precision fitting is achieved. Moreover, in order to solve the over-fitting problem of GLSPIA method when dealing with noise data, we propose three kinds of regularizations using the geometric properties of control polygon. Numerical examples are presented to show the effectiveness of our method.

An Elastic-Window-Based Method for the Underdetermined Problem in Linear Spectral Unmixing to Enhance the Spatial Resolution of the Normalized Difference Vegetation Index Time Series

Inverting land cover reflectance or derived indices from low-spatial-resolution images to refine the spatial resolution of this data is cost-effective for land surface monitoring applications that face technical or budget limitations. Based on the linear spectral mixing model, many approaches have successfully unmixed coarse mixed pixels using high-spatial-resolution land cover maps in the past decades. However, in some cases, the solutions of linear systems composed of several mixed pixels may not be acquired due to the underdetermined problem. This study presents the causes of this problem and proposes an iterative approximation strategy to address it. An elastic-window-based algorithm was developed, where the initial size of the window was calculated based on the land cover of the mixed pixel. Mixed pixels of neighborhoods with similar land covers were then selected to form the unmixing linear system, which was examined through a simulation test to ensure it was not underdetermined. Otherwise, the window would expand to include more adjacent pixels. This process was repeated until a successful solution was obtained. A statistical analysis of sixty land cover maps from around the globe shows that the underdetermined problem exists at a low level but becomes more serious with an increase in mixed scale. The results demonstrate that the proposed algorithm effectively prevents the underdetermined problem for mixed pixels of different scales and can be integrated into the coarse NDVI downscaling procedure to refine spatial resolution. This study provides a reference for estimating underdetermined mixed pixels and benefits applications that require dealing with the inversion of land cover values directly.

Conceptualizing the Iterative method of Newton-Raphson for systems with two equations

In numerical analysis, Newton-Raphson method is a root-finding algorithm which generates iterative approximations to the zeroes (or roots) of a real-valued function. This paper describes in a detailed way the mathematical background around the iterative method of Newton-Raphson for systems with two equations. Next, an algorithmic implementation of the iterative method of Newton-Raphson for systems with two equations is developed in Pascal Programming Language, to represent the steps of this method with a procedural programming language with special emphasis on the use of computing in the scientific area of mathematics.

Constrained least square progressive and iterative approximation (CLSPIA) for B-spline curve and surface fitting

Constrained least square progressive and iterative approximation (CLSPIA) for B-spline curve and surface fitting

Elasticity and Characteristic Stress Thresholds of Shale under Deep In Situ Geological Conditions.

The mechanical properties of shale are generally influenced by in situ geological conditions. However, the understanding of the effects of in situ geological conditions on the mechanical properties of shale is still immature. To address this problem, this paper provides insight into the elasticity and characteristic stress thresholds (i.e., the crack closure stress σcc, crack initiation stress σci, and crack damage stress σcd) of shales with differently oriented bedding planes under deep in situ geological conditions. To accurately determine the elastic parameters and crack closure and initiation thresholds, a new method-i.e., the bidirectional iterative approximation (BIA) method-which iteratively approaches the upper and lower limit stresses of the linear elastic stress-strain regime, was proposed. Several triaxial compression experiments were performed on Longmaxi shale samples under coupled in situ stress and temperature conditions reflecting depths of 2000 and 4000 m in the study area. The results showed that the peak deviatoric stress (σp) of shale samples with the same bedding plane orientation increases as depth increases from 2000 m to 4000 m. In addition, the elastic modulus of the shale studied is more influenced by bedding plane orientation than by burial depth. However, the Poisson's ratios of the studied shale samples are very similar, indicating that for the studied depth conditions, the Poisson's ratio is not influenced by the geological conditions and bedding plane orientation. For the shale samples with the two typical bedding plane orientations tested (i.e., perpendicular and parallel to the axial loading direction) under 2000 and 4000 m geological conditions, the ratio of crack closure stress to peak deviatoric stress (σcc/σp) ranges from 24.83% to 25.16%, and the ratio of crack initiation stress to peak deviatoric stress (σci/σp) ranges from 34.78% to 38.23%, indicating that the σcc/σp and σci/σp ratios do not change much, and are less affected by the bedding plane orientation and depth conditions studied. Furthermore, as the in situ depth increases from 2000 m to 4000 m, the increase in σcd is significantly greater than that of σcc and σci, indicating that σcd is more sensitive to changes in depth, and that the increase in depth has an obvious inhibitory effect on crack extension. The expected experimental results will provide the background for further constitutive modeling and numerical analysis of the shale gas reservoirs.

Energy-Efficient Joint Collaborative and Passive Beamforming for Intelligent-Reflecting-Surface-Assisted Wireless Sensor Networks

Intelligent reflecting surface (IRS) provides a promising technology that can improve the energy efficiency of wireless communications, by building the controllable wireless propagation environment with the utilization of massive passive reflecting elements. Motivated by this, we apply the IRS to assist the data collection based on collaborative beamforming in Wireless Sensor Networks (WSNs). With the objective to maximize the network lifetime, we present an energy efficient joint collaborative and passive beamforming design for an IRS-assisted WSN, which jointly optimizes the beamforming vector for all nodes and phase shifts for IRS’s reflecting elements. To efficiently resolve the joint optimization problem, we develop a penalty dual decomposition (PDD) based algorithm combined with augmented Lagrangian method, penalty-based method and block coordinate descent algorithm, which decomposes the joint optimization problem into four simplified subproblems. Especially in solving IRS’s phase shifts optimization subproblem, we formulate this subproblem as a quadratically constrained quadratic programming (QCQP) problem and further propose a low computational complexity approximate iteration algorithm to resolve this QCQP problem, which iteratively linearizes this QCQP problem to a sequence of approximate programming with linear equality constraints, whose closed-form solution is presented. Theoretical analysis indicates the proposed algorithm can converge to a KKT solution. Simulation results indicate that the IRS-assisted design and proposed algorithm improve the energy efficiency and prolong the network lifetime as compared to alternative algorithms.

Measurement and Calculation Techniques of Complex Permeability Applied to Mn-Zn Ferrites Based on Iterative Approximation Curve Fitting and Modified Equivalent Inductor Model

In many cases, power inductors are responsible for most of the power loss, volume, and cost if applied to high-frequency power electronics applications. It is desirable to optimize their design by the proper calculation of winding and core loss. It allows faster and cheaper commercial product release, which is the key to being successful in a highly competitive market. This is only possible if existing calculation techniques and technical data given by, e.g., core manufacturers, are verified and correct; otherwise, the inductor optimization process is less precise and requires several iterations to achieve good convergence. This paper addresses existing and proposes improved measurement and calculation techniques with regard to complex permeability, one of the key quantities that define inductor behavior in the frequency domain. This is done through impedance measurement and improved definition of the equivalent inductor model. Moreover, the proposed calculation techniques fulfill the need for the simple, accurate analytical methods required in commercial designs.

Krasnoselskij-type algorithms for fixed point problems and variational inequality problems in Banach spaces

Existence and uniqueness as well as the iterative approximation of fixed points of enriched almost contractions in Banach spaces are studied. The obtained results are generalizations of the great majority of metric fixed point theorems, in the setting of a Banach space. The main tool used in the investigations is to work with the averaged operator Tλ instead of the original operator T. The effectiveness of the new results thus derived is illustrated by appropriate examples. An application of the strong convergence theorems to solving a variational inequality is also presented.

A family of hybrid iterative approximation methods for fitting blending curves

A family of hybrid iterative approximation methods for fitting blending curves

Novel Multistep Implicit Iterative Methods for Solving Common Solution Problems with Asymptotically Demicontractive Operators and Applications

It is very meaningful and challenging to efficiently seek common solutions to operator systems (CSOSs), which are widespread in pure and applied mathematics, as well as some closely related optimization problems. The purpose of this paper is to introduce a novel class of multistep implicit iterative algorithms (MSIIAs) for solving general CSOSs. By using Xu’s lemma and Maingé’s fundamental and important results, we first obtain strong convergence theorems for both one-step and multistep implicit iterative schemes for CSOSs, involving asymptotically demicontractive operators. Finally, for the applications and profits of the main results presented in this paper, we give two numerical examples and present an iterative approximation to solve the general common solution to the variational inequalities and operator equations.

Robust Reconstruction of Closed Parametric Curves by Topological Understanding with Persistent Homology

Curve reconstruction is a fundamental problem in reverse engineering, which has intrigued researchers for decades. In this paper, we propose a topological understanding based method for reconstructing parametric curves robustly from unorganized point clouds. Given a point cloud, we firstly understand the number of closed curves which need to be reconstructed using persistent homology. Then, by calculating the persistent 1-cycles of the point cloud, the initial shapes of the reconstructed parametric curves are generated. Finally, the closed parametric curves are reconstructed with the weighted least-squares progressive iterative approximation (W-LSPIA) method. Due to the topological understanding, the reconstructed parametric curves are faithful to the salient topological structure of the point cloud. Moreover, the developed reconstruction method is robust, and the reconstructed curve is much less affected by noise points and outliers, compared with the conventional parametric curve reconstruction algorithms. Experimental results demonstrated in this paper show the effectiveness of the developed curve reconstruction method.

Range ambiguity suppression under high-resolution estimation using the MUSIC-AP algorithm for pulse-Doppler radar

Range ambiguity is a significant challenge in conventional pulse-Doppler radar systems with medium or high pulse repetition frequencies, greatly impacting radar detection and imaging capabilities. The classic approaches such as waveform diversity and compressed sensing are based on the isolation between pulses. However, these methods encounter issues like residual ambiguity and grid mismatch, resulting in poor range ambiguity suppression performance. In this paper, the multiple signal classification-alternating projection (MUSIC-AP) method is proposed to address these challenges and achieve high-resolution estimation. The proposed method converts the range-velocity estimate into a spectrum estimate, enabling the utilization of the MUSIC algorithm to solve the grid mismatch problem and improve echo reconstruction. Then, to mitigate the effect of ambiguous energy on reconstruction, the MUSIC reconstruction subprocess is embedded into the AP framework. Through iterative approximation, the method gradually suppresses ambiguous and noise energy, thereby further enhancing the echo reconstruction accuracy and range ambiguity suppression performance. Simulations demonstrate the effectiveness of the proposed method. Moreover, algorithm analysis is conducted, considering aspects such as resolution, robustness, and sparsity, which provides a basis for parameter selection and applicability conditions.

Dynamics of the Three-Compartment Financial Bubble Model under the Mittag-Leffler Operator

This paper presents an investigation into the dynamics of the emerging three-compartment financial bubble problem using a new non-singular kernel Atangana–Baleanu derivative operator. The problem is tested for at least one solution, and a unique root is determined using an iterative Newton approximation method, providing a globally stable fractional analysis technique. Curve sketches of the globalized model are provided, considering integers and other conformable orders. Sensitivities of the fractional order and other model parameters are examined, offering insights into their impact on the system dynamics. This research contributes to understanding financial bubbles and lays the groundwork for future studies in this field.

Improving geometric iterative approximation methods using local approximations

In this study, we propose improvements to Geometric Iterative Methods (GIM) for curve and surface approximation. Our key contributions include introducing an error vector function and deriving new error vectors, which enhance the approximation quality compared to the Least Squared Progressive and Iterative Approximation (LSPIA) methods. Additionally, we integrate parameter correction and control points update based on local approximations, achieving comparable accuracy to Geometric Approximation (GA) methods while being more computationally efficient. Extensive experiments demonstrate the superior accuracy and computational efficiency of our method.

Application of Broadband Receptivity Data to the Amplitude Method for Transition Prediction

Conventional hypersonic transition prediction relies upon the highly empirical method, which is predicated on theoretical approximations of relative disturbance growth. This does not account for the receptivity mechanism and the high degree of variability present in experimental wind-tunnel conditions, which itself leads to high degrees of variability in transition factors. The amplitude method, which better approximates the broadband nature of boundary-layer disturbances, was previously proposed to account for the effects of receptivity. In this study, high-fidelity simulated second-mode receptivity data for two blunt cones at Mach 10 to broadband disturbances are applied to an iterative approximation of the amplitude method tuned for second-mode dominated flows. The studied geometries consist of 9.525- and 5.080-mm-nose-radius 7 deg half-angle straight cones based on experimental cases from Arnold Engineering Development Center’s wind tunnel 9. Amplitude method predictions show improvement over the accuracy of estimates using standard threshold factors. In particular, the less blunt 5.080 mm cone demonstrates the best agreement due to its stronger second-mode response. The results of this work provide a preliminary framework for applying high-fidelity receptivity simulations to the amplitude method for transition prediction in hypersonic flows.

A new Chinese text clustering algorithm based on WRD and improved K-means

Text clustering has been widely used in data mining, document management, search engines, and other fields. The K-means algorithm is a representative algorithm of text clustering. However, traditional K-means algorithm often uses Euclidean distance or cosine distance to measure the similarity between texts, which is not effective in face of high-dimensional data and cannot retain enough semantic information. In response to the above problems, we combine word rotator’s distance with the K-means algorithm, and propose the WRDK-means algorithm, which use word rotator’s distance to calculate the similarity between texts and preserve more text features. Furthermore, we define a new cluster center initialization method that improves cluster instability during random initial cluster center selection. And, to solve the problem of inconsistent length between texts, we propose a new iterative approximation method of cluster centers. We selected three suitable datasets and five evaluation indicators to verify the feasibility of the proposed algorithm. Among them, the RI value of our algorithm exceeds 90%. And for Marco_F1, our scheme was about 37.77%, 23.2%, 13.06% and 20.12% better than other four methods, respectively.

A switching MPC-based power management strategy for DC microgrids with SOC consistency and energy loss

The DC microgrids equipped with photovoltaic and energy storage systems have increasingly been applied to unmanned vehicles, and energy management is attracted much more attention. In this work, a power management strategy based on switching model predictive control is proposed to tackle energy loss and inconsistency of energy storage systems. The dynamic characteristic of the battery are fully addressed, and the non-affine equation constraints are dealt with by the iterative approximation method. The proposed strategy balances energy loss and state-of-charge consistency of the energy storage system and can operate when future environmental information is unavailable. Finally, comparative examples with existing schemes verify the effectiveness of the proposed strategy.