Mean Eigenvalue Research Articles

Unidimensional community detection: A monte carlo simulation, grid search, and comparison.

Unidimensionality is fundamental to psychometrics. Despite the recent focus on dimensionality assessment in network psychometrics, unidimensionality assessment remains a challenge. Community detection algorithms are the most common approach to estimate dimensionality in networks. Many community detection algorithms maximize an objective criterion called modularity. A limitation of modularity is that it penalizes unidimensional structures in networks, favoring two or more communities (dimensions). In this study, this penalization is discussed and a solution is offered. Then, a Monte Carlo simulation using one- and two-factor models is performed. Key to the simulation was the condition of model error or the misfit of the population factor model to the generated data. Based on previous simulation studies, several community detection algorithms that have performed well with unidimensional structures (Leading Eigenvalue, Leiden, Louvain, and Walktrap) were compared. A grid search was performed on the tunable parameters of these algorithms to determine the optimal trade-off between unidimensional and bidimensional recovery. The best-performing parameters for each algorithm were then compared against each other as well as maximum likelihood factor analysis and parallel analysis (PA) with mean and 95th percentile eigenvalues. Overall, the Leiden and Louvain algorithms and PA methods were the most accurate methods to recover unidimensional and bidimensional structures and were the most robust to model error. More nuanced method recommendations for specific unidimensional and bidimensional conditions are provided. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Evaluation of potential factors affecting the success of Cisco re-introduction and re-establishment in Lake Huron

Recent food web changes led to an opportunity to reintroduce (fingerling stocking) Cisco in central Lake Huron. We examined 9 factors affecting the ability of stocked Cisco fingerlings to survive, and reproduce and for their progeny to survive and reproduce. These values (obtained from the literature) were applied to a stochastic Leslie Matrix model and projected forward 30 years. The mean terminal eigenvalue (λ) of the final 10 years was used to indicate if the resulting wild population would continue to increase or decrease and thresholds for each variable. Recovery success was sensitive to survival rates especially in early life stages. Numbers stocked and the rate of homing by hatchery fish only affected the rate of recovery. Adult survival, if adjusted up, helped compensate for many of the earlier life stages lower survival rates. Simulations indicated the likelihood of successful establishment of ongoing natural reproduction if periodicity of boom years of reproduction were at least once every 5 years on average, but higher adult survival rates can relax this requirement allowing for an expanding population at less frequent periodicities.

Cardiac Phase and Flow Compensation Effects on REnal Flow and Microstructure AnisotroPy MRI in Healthy Human Kidney.

Renal diffusion-weighted imaging (DWI) involves microstructure and microcirculation, quantified with diffusion tensor imaging (DTI), intravoxel incoherent motion (IVIM), and hybrid models. A better understanding of their contrast may increase specificity. To measure modulation of DWI with cardiac phase and flow-compensated (FC) diffusion gradient waveforms. Prospective. Six healthy volunteers (ages: 22-48 years, five females), water phantom. 3-T, prototype DWI sequence with 2D echo-planar imaging, and bipolar (BP) or FC gradients. 2D Half-Fourier Single-shot Turbo-spin-Echo (HASTE). Multiple-phase 2D spoiled gradient-echo phase contrast (PC) MRI. BP and FC water signal decays were qualitatively compared. Renal arteries and velocities were visualized on PC-MRI. Systolic (peak velocity), diastolic (end stable velocity), and pre-systolic (before peak velocity) phases were identified. Following mutual information-based retrospective self-registration of DWI within each kidney, and Marchenko-Pastur Principal Component Analysis (MPPCA) denoising, combined IVIM-DTI analysis estimated mean diffusivity (MD), fractional anisotropy (FA), and eigenvalues (λi) from tissue diffusivity (Dt ), perfusion fraction (fp ), and pseudodiffusivity (Dp , Dp,axial , Dp,radial ), for each tissue (cortex/medulla, segmented on b0/FA respectively), phase, and waveform (BP, FC). Monte Carlo water diffusion simulations aided data interpretation. Mixed model regression probed differences between tissue types and pulse sequences. Univariate general linear model analysis probed variations among cardiac phases. Spearman correlations were measured between diffusion metrics and renal artery velocities. Statistical significance level was set at P < 0.05. Water BP and FC signal decays showed no differences. Significant pulse sequence dependence occurred for λ1 , λ3 , FA, Dp , fp , Dp,axial , Dp,radial in cortex and medulla, and medullary λ2 . Significant cortex/medulla differences occurred with BP for all metrics except MD (systole [P= 0.224]; diastole [P= 0.556]). Significant phase dependence occurred for Dp , Dp,axial , Dp,radial for BP and medullary λ1 , λ2 , λ3 , MD for FC. FA correlated significantly with velocity. Monte Carlo simulations indicated medullary measurements were consistent with a 34 μm tubule diameter. Cardiac gating and flow compensation modulate of measurements of renal diffusion. 2 TECHNICAL EFFICACY STAGE: 2.

Assessment of Myocardial Microstructure in a Murine Model of Obesity-Related Cardiac Dysfunction by Diffusion Tensor Magnetic Resonance Imaging at 7T.

BackgroundObesity exerts multiple deleterious effects on the heart that may ultimately lead to cardiac failure. This study sought to characterize myocardial microstructure and function in an experimental model of obesity-related cardiac dysfunction.MethodsMale C57BL/6N mice were fed either a high-fat diet (HFD; 60 kcal% fat, n = 12) or standard control diet (9 kcal% fat, n = 10) for 15 weeks. At the end of the study period, cardiac function was assessed by ultra-high frequency echocardiography, and hearts were processed for further analyses. The three-dimensional myocardial microstructure was examined ex vivo at a spatial resolution of 100 × 100 × 100 μm3 by diffusion tensor magnetic resonance imaging (DT-MRI) at 7T. Myocardial deformation, diffusion metrics and fiber tract geometry were analyzed with respect to the different myocardial layers (subendocardium/subepicardium) and segments (base/mid-cavity/apex). Results were correlated with blood sample analyses, histopathology, and gene expression data.ResultsHFD feeding induced significantly increased body weight combined with a pronounced accumulation of visceral fat (body weight 42.3 ± 5.7 vs. 31.5 ± 2.2 g, body weight change 73.7 ± 14.8 vs. 31.1 ± 6.6%, both P < 0.001). Obese mice showed signs of diastolic dysfunction, whereas left-ventricular ejection fraction and fractional shortening remained unchanged (E/e’ 41.6 ± 16.6 vs. 24.8 ± 6.0, P < 0.01; isovolumic relaxation time 19 ± 4 vs. 14 ± 4 ms, P < 0.05). Additionally, global longitudinal strain was reduced in the HFD group (−15.1 ± 3.0 vs. −20.0 ± 4.6%, P = 0.01), which was mainly driven by an impairment in basal segments. However, histopathology and gene expression analyses revealed no myocardial fibrosis or differences in cardiomyocyte morphology. Mean diffusivity and eigenvalues of the diffusion tensor were lower in the basal subepicardium of obese mice as assessed by DT-MRI (P < 0.05). The three-dimensional fiber tract arrangement of the left ventricle (LV) remained preserved.ConclusionFifteen weeks of high-fat diet induced alterations in myocardial diffusion properties in mice, whereas no remodeling of the three-dimensional myofiber arrangement of the LV was observed. Obese mice showed reduced longitudinal strain and lower mean diffusivity predominantly in the left-ventricular base, and further investigation into the significance of this regional pattern is required.

Diffusion tensor imaging indices of acute muscle damage are augmented after exercise in peripheral arterial disease.

Although it is known that peripheral arterial disease (PAD) is associated with chronic myopathies, the acute muscular responses to exercise in this population are less clear. This study used diffusion tensor imaging (DTI) to compare acute exercise-related muscle damage between PAD patients and healthy controls. Eight PAD patients and seven healthy controls performed graded plantar flexion in the bore of a 3T MRI scanner. Exercise began at 2kg and increased by 2kg every 2min until failure, or completion of 10min of exercise. DTI images were acquired from the lower leg pre- and post-exercise, and were analyzed for mean diffusivity, fractional anisotropy (FA), and eigenvalues 1-3 (λ1-3) of the medial gastrocnemius (MG) and tibialis anterior (TA). Results indicated a significant leg by time interaction for mean diffusivity, explained by a significantly greater increase in diffusivity of the MG in the most affected legs of PAD patients (11.1 × 10-4 ± 0.5 × 10-4 mm2/s vs. 12.7 × 10-4 ± 1.2 × 10-4 mm2/s at pre and post, respectively, P = 0.02) compared to healthy control subjects (10.8 × 10-4 ± 0.3 × 10-4 mm2/s vs. 11.2 × 10-4 ± 0.5 × 10-4 mm2/s at pre and post, respectively, P = 1.0). No significant differences were observed for the TA, or λ1-3 (all P ≥ 0.06). Moreover, no reciprocal changes were observed for FA in either group (all P ≥ 0.29). These data suggest that calf muscle diffusivity increases more in PAD patients compared to controls after exercise. These findings are consistent with the notion that acute exercise results in increased muscle damage in PAD.

A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method

In this paper, we compare three methods for deriving a priority vector in the theoretical framework of pairwise comparisons—the Geometric Mean Method (GMM), Eigenvalue Method (EVM) and Best–Worst Method (BWM)—with respect to two features: sensitivity and order violation. As the research method, we apply One-Factor-At-a-Time (OFAT) sensitivity analysis via Monte Carlo simulations; the number of compared objects ranges from 3 to 8, and the comparison scale coincides with Saaty’s fundamental scale from 1 to 9 with reciprocals. Our findings suggest that the BWM is, on average, significantly more sensitive statistically (and thus less robust) and more susceptible to order violation than the GMM and EVM for every examined matrix (vector) size, even after adjustment for the different numbers of pairwise comparisons required by each method. On the other hand, differences in sensitivity and order violation between the GMM and EMM were found to be mostly statistically insignificant.

Determining the Number of Attributes in Cognitive Diagnosis Modeling.

Cognitive diagnosis models (CDMs) allow classifying respondents into a set of discrete attribute profiles. The internal structure of the test is determined in a Q-matrix, whose correct specification is necessary to achieve an accurate attribute profile classification. Several empirical Q-matrix estimation and validation methods have been proposed with the aim of providing well-specified Q-matrices. However, these methods require the number of attributes to be set in advance. No systematic studies about CDMs dimensionality assessment have been conducted, which contrasts with the vast existing literature for the factor analysis framework. To address this gap, the present study evaluates the performance of several dimensionality assessment methods from the factor analysis literature in determining the number of attributes in the context of CDMs. The explored methods were parallel analysis, minimum average partial, very simple structure, DETECT, empirical Kaiser criterion, exploratory graph analysis, and a machine learning factor forest model. Additionally, a model comparison approach was considered, which consists in comparing the model-fit of empirically estimated Q-matrices. The performance of these methods was assessed by means of a comprehensive simulation study that included different generating number of attributes, item qualities, sample sizes, ratios of the number of items to attribute, correlations among the attributes, attributes thresholds, and generating CDM. Results showed that parallel analysis (with Pearson correlations and mean eigenvalue criterion), factor forest model, and model comparison (with AIC) are suitable alternatives to determine the number of attributes in CDM applications, with an overall percentage of correct estimates above 76% of the conditions. The accuracy increased to 97% when these three methods agreed on the number of attributes. In short, the present study supports the use of three methods in assessing the dimensionality of CDMs. This will allow to test the assumption of correct dimensionality present in the Q-matrix estimation and validation methods, as well as to gather evidence of validity to support the use of the scores obtained with these models. The findings of this study are illustrated using real data from an intelligence test to provide guidelines for assessing the dimensionality of CDM data in applied settings.

Asymptotics of Fredholm Determinant Associated with the Pearcey Kernel

The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue density exhibits a cusp-like singularity. It appears in a variety of statistical physics models beyond matrix models as well. We consider the Fredholm determinant of a trace class operator acting on $L^2\left(-s, s\right)$ with the Pearcey kernel. Based on a steepest descent analysis for a $3\times 3$ matrix-valued Riemann-Hilbert problem, we obtain asymptotics of the Fredholm determinant as $s\to +\infty$, which is also interpreted as large gap asymptotics in the context of random matrix theory.

On the Detection of the Correct Number of Factors in Two-Facet Models by Means of Parallel Analysis.

Methods for optimal factor rotation of two-facet loading matrices have recently been proposed. However, the problem of the correct number of factors to retain for rotation of two-facet loading matrices has rarely been addressed in the context of exploratory factor analysis. Most previous studies were based on the observation that two-facet loading matrices may be rank deficient when the salient loadings of each factor have the same sign. It was shown here that full-rank two-facet loading matrices are, in principle, possible, when some factors have positive and negative salient loadings. Accordingly, the current simulation study on the number of factors to extract for two-facet models was based on rank-deficient and full-rank two-facet population models. The number of factors to extract was estimated from traditional parallel analysis based on the mean of the unreduced eigenvalues as well as from nine other rather traditional versions of parallel analysis (based on the 95th percentile of eigenvalues, based on reduced eigenvalues, based on eigenvalue differences). Parallel analysis based on the mean eigenvalues of the correlation matrix with the squared multiple correlations of each variable with the remaining variables inserted in the main diagonal had the highest detection rates for most of the two-facet factor models. Recommendations for the identification of the correct number of factors are based on the simulation results, on the results of an empirical example data set, and on the conditions for approximately rank-deficient and full-rank two-facet models.

A novel fault detection location method under noise environments based on random matrix theory

Fault detection and location is a critically significant application of a supervisory control system in smart grid. The methods based on random matrix theory (RMT) have been practiced using measurements to detect short circuit faults occurring on transmission lines. However, the diagnostic accuracy is influenced by the noise signal in measurements. The relationship between mean eigenvalue of a random matrix and noise is deduced in this paper, and the defects of the Mean Spectral Radius (MSR) as an indicator to detect fault are pointed out theoretically. Therefore, a novel indicator of the shifting degree of maximum eigenvalue and its threshold are deduced theoretically. By comparing the indicator and the threshold, the occurrence of a fault can be assessed. Finally, an augmented matrix is constructed to locate the fault area. The proposed method can effectively achieve the fault detection via the RMT without any influence of noise. Also, it does not depend on system models. The experiment results have been done based on the IEEE 39-bus system. Also, actual provincial grid data is applied to validate the effectiveness of the proposed method.

An analytical solution of Reynolds equation for evaluating the characteristics of surface textured bearing

PurposeCurrently, there is a lack of fast and highly accurate on analytical solution of Reynolds equation for evaluating the characteristics of surface textured bearing. This paper aims to develop such an analytical solution of Reynolds equation for an effective analysis of the characteristics of surface textured bearings.Design/methodology/approachBy using the separation of variables method and mean eigenvalue method, the analytical solution is constructed. The CFD simulations and experimental results are used to validate the correctness of the analytical solution.FindingsThe analytical solution can accurately evaluate the characteristics of textured bearings. It is found that the larger the eccentricity ratio and aspect ratio, the greater the oil film force. It also found that the smaller the eccentricity ratio, the larger the Sommerfeld number S. When eccentricity ratio e = 0.65, the attitude angles of different oil boundaries are same. The effect of different aspect ratios on dynamic stiffness and damping coefficient generally follows a same trend. It is numerically shown that the critical speed of rotor-bearing is 3500 rpm.Originality/valueThe analytical solution provides a simple yet effective way to study the characteristics of surface textured bearings.

A Convergent $$\varvec{\frac{1}{N}}$$ 1 N Expansion for GUE

We show that the asymptotic 1 / N expansion for the averages of linear statistics of the GUE is convergent when the test function is an entire function of order two and finite type. This allows to fully recover the mean eigenvalue density function for finite N from the coefficients of the expansion thus providing a resummation procedure. As an intermediate result, we compute the bilateral Laplace transform of the GUE reproducing kernel in the half-sum variable, generalizing a formula of Haagerup and Thorbjornsen.

Capacity analysis for free space coherent optical MIMO transmission systems: with and without adaptive optics.

This paper analyzes the capacity of the free space coherent optical MIMO transmission system. Two scenarios are considered (i.e., with and without the adaptive optics compensation). It is generally accepted that the adaptive optics compensation can significantly improve the system performance, which is rigorously true when the MIMO algorithm is not implemented. However, it might not be the case in the coherent MIMO systems. When the turbulence strength is weak or moderate, this work demonstrates that the phase-only wave-front corrector will increase the mean eigen value of the coherent system capacity matrix HHH and make the eigen value distribution more even, i.e. it will decrease the maximal eigen value while increasing the average eigen value. Hence, the capacity of the system with adaptive optics increases when the channel information is not available, because the sub-channels are placed with equal powers. When the channel information is perfectly available and the water filling algorithm is used to optimize the power allocation, the system with adaptive optics could have a deteriorated performance as the capacity is more related to the large eigen values especially in the low signal to noise ratio (SNR) regime. When the turbulence strength is strong, it is found that adaptive optics will decrease both the mean and maximal eigen values for the capacity matrix HHH, and therefore the system capacity degrades, whether the channel information is available or not.

Blind image quality assessment utilising local mean eigenvalues

Eigenvalues are intrinsic and representative values of a square matrix. They have thus been used in many image processing areas due to their important application value, but not in the image quality assessment (IQA) field. In this Letter, the authors study the correlation between local mean eigenvalues (LMEs) and perceptual quality of images, and demonstrate the applicability of LMEs in IQA. The LMEs are related to structural complexity of images. The LMEs and natural scene statistics features are utilised for a sparse dictionary learning. Experimental results conducted on promising IQA databases show their method's superiority in comparison with top-performing blind IQA metrics.

3D MIMO for 5G NR: Several Observations from 32 to Massive 256 Antennas Based on Channel Measurement

By placing active antennas in a 2D grid at a BS, 3D MIMO is considered as a promising and practical technique for 5G New Radio (NR). So far, 3D MIMO studies reported are mostly done with antenna elements from 32 up to 128 in the limited scenario at one frequency. To gain further insights into the 3D massive MIMO channel and performance, field measurements from 32 to 256 antenna elements at the transmitter and 16 antenna elements at the receiver are performed in three typical deployment scenarios, including outdoor to indoor, urban microcell, and urban macrocell at both 3.5 and 6 GHz frequencies with 200 MHz bandwidth. Based on the extracted channel information from measured data, power angle spectrum, root mean square angle spread, channel capacity, and eigenvalue spread have been studied. Several observations, including 3D MIMO channel spatial dispersive properties and multi-user performance varying with antenna number, scenario, and frequency are given. These findings can provide valuable experimental insights for efficient utilization of 3D MIMO with massive antenna elements.

Analysis of electrocardiosignals for formation of the diagnostic features of post-traumatic myocardial dystrophy

The possibilities of high-resolution electrocardiography (HR ECG) application for diagnostics of post-traumatic myocardial dystrophy having multifactorial genesis is considered in this paper. Numerical processing and analysis of electrocardiograms that belong to patients from armed forces after explosive-driven injuries have been performed based on clinical studies. Complex method of cardiosignal analysis based on combination of wavelet analysis, eigenvector decomposition and principal component analysis is developed. This method revealed that low-amplitude deviations in ECG signal in case of post-traumatic myocardial dystrophy have low-frequency nature that is linked to slow electro-physiological processes. It is shown that these low-frequency, low-amplitude components appear at a high levels (8th and 9th) of decomposition in case of 9-level wavelet decomposition of averaged cardio cycles. Integral parameters for identification of post-traumatic myocardial dystrophy features are suggested and determined on the basis of principal component analysis. These parameters are squared sum of signal projections to eigenspaces H k and mean eigenvalues of covariance matrices of electrocardiosignals ensembles λmean.

High dimensional covariance matrix estimation by penalizing the matrix-logarithm transformed likelihood

It is well known that when the dimension of the data becomes very large, the sample covariance matrix S will not be a good estimator of the population covariance matrix Σ. Using such estimator, one typical consequence is that the estimated eigenvalues from S will be distorted. Many existing methods tried to solve the problem, and examples of which include regularizing Σ by thresholding or banding. In this paper, we estimate Σ by maximizing the likelihood using a new penalization on the matrix logarithm of Σ (denoted by A) of the form: ‖A−mI‖F2=∑i(log(di)−m)2, where di is the ith eigenvalue of Σ. This penalty aims at shrinking the estimated eigenvalues of A toward the mean eigenvalue m. The merits of our method are that it guarantees Σ to be non-negative definite and is computational efficient. The simulation study and applications on portfolio optimization and classification of genomic data show that the proposed method outperforms existing methods.

Reduced Field-of-View Diffusion Tensor Imaging of the Optic Nerve in Retinitis Pigmentosa at 3T.

Diffusion tensor imaging may reflect pathology of the optic nerve; however, the ability of DTI to evaluate alterations of the optic nerve in retinitis pigmentosa has not yet been assessed, to our knowledge. The aim of this study was to investigate the diagnostic potential of reduced FOV-DTI in optic neuropathy of retinitis pigmentosa at 3T. Thirty-eight patients and thirty-five healthy controls were enrolled in this study. Measures of visual field and visual acuity of both eyes in all subjects were performed. A reduced FOV-DTI sequence was used to derive fractional anisotropy, apparent diffusion coefficient, principal eigenvalue, and orthogonal eigenvalue of the individual optic nerves. Mean fractional anisotropy, ADC, and eigenvalue maps were obtained for quantitative analysis. Further analyses were performed to determine the correlation of fractional anisotropy, ADC, principal eigenvalue, and orthogonal eigenvalue with optic nerves in patients with mean deviation of the visual field and visual acuity, respectively. The optic nerves of patients with retinitis pigmentosa compared with control subjects showed significantly higher ADC, principal eigenvalue, and orthogonal eigenvalue and significantly lower fractional anisotropy (P < .01). For patients with retinitis pigmentosa, the mean deviation of the visual field of the optic nerve was significantly correlated with mean fractional anisotropy (r = 0.364, P = .001) and orthogonal eigenvalue (r = -0.254, P = .029), but it was not correlated with mean ADC (P = .154) and principal eigenvalue (P = .337). Moreover, no correlation between any DTI parameter and visual acuity in patients with retinitis pigmentosa was observed (P > .05). Reduced FOV-DTI measurement of the optic nerve may serve as a biomarker of axonal and myelin damage in optic neuropathy for patients with retinitis pigmentosa.

WE‐G‐BRD‐03: Real‐Time Tumor Motion Tracking in Low Field Cine‐MR Images

Purpose:ViewRay's MRIdian system acquires cine‐MR images during treatment, allowing for real‐time visualization of the tumor without additional dose. We propose a novel method for tracking the tumor target on these cine‐MR images in real‐time.Methods:9 patients with mobile abdominal tumors (3 stomach, 1 pancreas, 1 adrenal, 2 mesenteric, 2 peritoneal) were imaged on ViewRay (0.3T, open‐bore; TrueFISP). Sagittal slice cine‐MR images (3.5×3.5mm pixels) were acquired at 4 frames per second. A 25‐second training period was used to collect 100 images during normal breathing. PCA was used to bin the images using the first 2 eigenvalues. Manual contouring of the target was performed on the first eigenimage. The mean eigenvalues in each bin were used to reconstruct 15 images, on which template matching was used to locate the target. A linear fit of the pixel locations was used to create the motion model. For each subsequently acquired image, the 2‐component PCA model was inverted and the values plugged into the motion model to get the corresponding pixel location. Finally, this location and the user‐drawn contour were used as the initialization for an active contouring algorithm to refine the edges of the tracked target. 100 images for each patient were manually contoured and used as the gold standard for comparison using the Dice similarity coefficient (DSC) and the modified Hausdorff distance (MHD).Results:The mean DSC is 0.87±0.09 and MHD is 2.6±0.9mm, which is less than the pixel size. The algorithm takes 100ms per image using Matlab, and is therefore more than fast enough for real‐time use.Conclusion:We have developed a robust method for real‐time tumor motion tracking in low‐resolution, low‐field cine‐MR images. We foresee our method being used for automated gating and dosimetric measurement purposes with the ViewRay system.

Simulation and experimental validation of powertrain mounting bracket design obtained from multi-objective topology optimization

A framework of multi-objective topology optimization for vehicle powertrain mounting bracket design with consideration of multiple static and dynamic loading conditions is developed in this article. Incorporating into the simplified isotropic material with penalization model, compromise programming method is employed to describe the multi-objective and multi-stiffness topology optimization under static loading conditions, whereas mean eigenvalue formulation is proposed to analyze vibration optimization. To yield well-behaved optimal topologies, minimum member size and draw constraint are settled for meeting manufacturing feasibility requirements. The ultimate mounting bracket is reconstructed based on the optimum results. Numerical analyses of the bracket are performed, followed by physical tests. It is proven that topology optimization methodology is promising and effective for vehicle component design.