Higher Eigenvalues Research Articles

Eigenbin compression for reducing photon-counting CT data size.

Photon-counting CT (PCCT) systems acquire multiple spectral measurements at high spatial resolution, providing numerous image quality benefits while also increasing the amount of data that must be transferred through the gantry slip ring. This study proposes a lossy method to compress photon-counting CT data using eigenvector analysis, with the goal of providing image quality sufficient for applications that require a rapid initial reconstruction, such as to confirm anatomical coverage, scan quality, and to support automated advanced applications. The eigenbin compression method was experimentally evaluated on a clinical silicon PCCT prototype system. The proposed eigenbin method performs principal component analysis (PCA) on a set of PCCT calibration measurements. PCA finds the orthogonal axes or eigenvectors, which capture the maximum variance in the N dimensional photon-count data space, where N is the number of acquired energy bins. To reduce the dimensionality of the PCCT data, the data are linearly transformed into a lower dimensional space spanned by the M<N eigenvectors with highest eigenvalues (i.e., the vectors that account for most of the information in the data). Only M coefficients are then transferred per measurement, which we term eigenbin values. After transmission, the original N energy-bin measurements are estimated as a linear combination of the M eigenvectors. Two versions of the eigenbin method were investigated: pixel-specific and pixel-general. The pixel-specific eigenbin method determines eigenvectors for each individual detector pixel, while the more practically realizable pixel-general eigenbin method finds one set of eigenvectors for the entire detector array. The eigenbin method was experimentally evaluated by scanning a 20cm diameter Gammex Multienergy phantom with different material inserts on a clinical silicon-based PCCT prototype. The method was evaluated with the number of eigenbins varied between two and four. In each case, the eigenbins were used to estimate the original 8-bin data, after which material decomposition was performed. The mean, standard deviation, and contrast-to-noise ratio (CNR) of values in the reconstructed basis and virtual monoenergetic images (VMI) were compared for the original 8-bin data and for the eigenbin data. The pixel-specific eigenbin method reduced photon-counting CT data size by a factor of four with<5% change in mean values and a small noise penalty (mean change in noise of<12%, maximum change in noise of 20% for basis images). The pixel-general eigenbin compression method reduced data size by a factor of 2.67 with<5% change in mean values and a less than 10% noise penalty in the basis images (average noise penalty≤5%). The noise penalty and errors were less for the VMIs than for the basis images, resulting in<5% change in CNR in the VMIs. The eigenbin compression method reduced photon-counting CT data size by a factor of two to four with less than 5% change in mean values, noise penalty of less than 10%-20%, and change in CNR ranging from 15% decrease to 24% increase. Eigenbin compression reduces the data transfer time and storage space of photon-counting CT data for applications that require rapid initial reconstructions.

Genetic polymorphism amongst moth bean (Vigna aconitifolia (Jacq.) Marechal) accessions evaluated using various molecular markers

This study presents genetic level diversity of 50 moth bean legume accessions (Vigna aconotifolia (Jacq.) Marechal). Despite seeds being a rich source of soluble nutritional proteins, it still remains an underutilized crop commercially. To assess the molecular diversity amongst accessions, RAPD, ISSR, DAMD, SCoT and SSR were employed as PCR markers. Of the total 5064 polymorphic bands shown with these makers, DAMD1 and SCoT1 presented higher levels of polymorphism with 407 and 262 polymorphic bands respectively. These genotypes revealed logical similarity and variation under UPGMA clustering. The PCA analysis of IC-258167, IC-415167, and IC-402286 present three highest eigen values, hence seem fit to be considered as parents for moth bean breeding programme. The polymorphic bands as produced by SCoT and DAMD primers can serve unique genotypic identifiers. This study seems to present a maiden report in labelling genetic marker based polymorphism amongst the accessions of moth bean.

Computing multi-eigenpairs of high-dimensional eigenvalue problems using tensor neural networks

In this paper, we propose a type of tensor-neural-network-based machine learning method to compute multi-eigenpairs of high dimensional eigenvalue problems without Monte-Carlo procedure. Solving multi-eigenvalues and their corresponding eigenfunctions is one of the basic tasks in mathematical and computational physics. With the help of tensor neural network, the high dimensional integrations included in the loss functions of the machine learning process can be computed with high accuracy. The high accuracy of high dimensional integrations can improve the accuracy of the machine learning method for computing multi-eigenpairs of high dimensional eigenvalue problems. Here, we introduce the tensor neural network and design the machine learning method for computing multi-eigenpairs of the high dimensional eigenvalue problems. The proposed numerical method is validated with plenty of numerical examples.

Eigenvalue asymptotic expansion for non-Hermitian tetradiagonal Toeplitz matrices with real spectrum

In this paper we consider a family of tetradiagonal (= four non-zero diagonals) Toeplitz matrices with a limiting set consisting in one analytic arc only and obtain individual asymptotic expansions for all the eigenvalues, as the matrix size goes to infinity. Additionally, we provide specific expansions for the extreme eigenvalues which are the eigenvalues approaching the extreme points of the limiting set. In contrast to previous related works, we study non-Hermitian Toeplitz matrices having non-canonical distribution and a real limiting set. The considered family does not belong to the so-called simple-loop class, nevertheless we manage to extend the theory to this case. The achieved formulas reveal the fine details of the eigenvalue structure and allow us to directly calculate high accuracy eigenvalues, even for matrices of relatively small size.

Deep learning techniques for securing cyber-physical systems in supply chain 4.0

The fourth industrial revolution's transformation utilizes a Cyber-Physical System (CPS) to secure Supply Chain 4.0. It integrates manufacturing information with internet communication technology to create a smart CPS that tracks products from manufacture to customer delivery using the Internet of Things (IoT). This research uses a Machine Learning (ML) approach for network anomaly detection and constructing data-driven models to detect DDoS attacks on Industry 4.0 CPSs. Limitations of existing techniques, such as artificial data and small datasets, are addressed by capturing network traffic data from a real-world semiconductor production factory. 45 bidirectional network flow features are extracted, and labeled datasets are constructed for training and testing ML models. The proposed PCA-BSO algorithm is employed to select the most relevant features based on their eigenvalues, as the feature with the highest eigenvalues may not always improve classification accuracy. Supervised ML algorithms are evaluated through simulations to assess their performance.

Meaningful local signalling in sinoatrial node identified by random matrix theory and PCA

The sinoatrial node (SAN) is the pacemaker of the heart. Recently calcium signals, believed to be crucially important in rhythm generation, have been imaged in intact SAN and shown to be heterogeneous in various regions of the SAN with a lot of analysis relying on visual inspection rather than mathematical tools. Here we apply methods of random matrix theory (RMT) developed for financial data and various biological data sets including β-cell collectives and electroencephalograms (EEG) to analyse correlations in SAN calcium signals using eigenvalues and eigenvectors of the correlation matrix. We use principal component analysis to locate signalling modules corresponding to localization properties the eigenvectors corresponding to high eigenvalues. We find that the top eigenvector captures the global behaviour of the SAN i.e. action potential (AP) induced calcium transient. In some cases, the eigenvector corresponding to the second highest eigenvalue yields a pacemaker region whose calcium signals predict the AP. Furthermore, using new analytic methods, we study the relationship between covariance coefficients and distance, and find that even inside the central zone, there are non-trivial long range correlations, indicating intercellular interactions in most cases. Lastly, we perform an analysis of nearest-neighbour eigenvalue distances and find that it coincides with universal Wigner surmise under all available experimental conditions, while the number variance, which captures eigenvalue correlations, is sensitive to experimental conditions. Thus RMT application to SAN allows to remove noise and the global effects of the AP-induced calcium transient and thereby isolate the local and meaningful correlations in calcium signalling.

Improved Automatic Classification of Litho-Geomorphological Units by Using Raster Image Blending, Vipava Valley (SW Slovenia)

Automatic landslide classification based on digital elevation models has become a powerful complementary tool to field mapping. Many studies focus on the automatic classification of landslides’ geomorphological features, such as their steep main scarps, but in many cases, the scarps and other morphological features are difficult for algorithms to detect. In this study, we performed an automatic classification of different litho-geomorphological units to differentiate slope mass movements in field maps by using Maximum Likelihood Classification. The classification was based on high-resolution lidar-derived DEM of the Vipava Valley, SW Slovenia. The results show an improvement over previous approaches as we used a blended image (VAT, which included four different raster layers with different weights) along with other common raster layers for morphometric analysis of the surface (e.g., slope, elevation, aspect, TRI, curvature, etc.). The newly created map showed better classification of the five classes we used in the study and recognizes alluvial deposits, carbonate cliffs (including landslide scarps), carbonate plateaus, flysch, and slope deposits better than previous studies. Multivariate statistics recognized the VAT layer as the most important layer with the highest eigenvalues, and when combined with Aspect and Elevation layers, it explained 90% of the total variance. The paper also discusses the correlations between the different layers and which layers are better suited for certain geomorphological surface analyses.

The Determining Factors of Generation Z Purchase Decision for the Local Brand T-Shirt

The study aims to determine the determinants factors on T-shirt purchasing decision for the local brand. The sampling technique used purposive sampling with a total of 310 respondents proportionally male and female each of 155 respondents. Analysis data used exploratory factor analysis technique with Principal component analysis method. Regarding BEKRAF data of the creative economy that has not been spread evenly and supported by the number of Indonesians aged 15-24 years as the target consumers of local brand t-shirts, the objective of this study is to determine the determinant factors of generation Z purchase decision for local brand T-shirts. This study found six determinant factors. They are the trend, digital channel, social media influencer, brand originality, simplicity, and motif. The trend factor has the highest eigenvalues. Independent T-test indicates a different perception between males and females in the decision to buy the local brand t-shirt

Maladaptive Cognitions in Adolescents and Young Adults When They Play: The Dysfunctional Cognitions in Gaming Scale (DCG)

Gaming is increasingly prevalent among young people, and Gaming Disorders are a growing concern. Maladaptive cognitions related to gaming may affect the psychological development of young people. We examined psychometric properties of the Dysfunctional Cognitions Gaming (DCG) Scale in Spanish adolescents and young adults. We applied 16 items of the DCG Scale in a sample of 2173 video gamers (age from 12 to 22; 28.8% female), extracted from random sampling in educational institutions. Three factors emerged from exploratory analysis (EFA): Preoccupation, Self-esteem, and Compulsion, accounting for 51.92% of the scale’s total variance. Confirmatory analysis (CFA) yielded a good fit, RMSEA = 0.040, 90% CI [0.034, 0.046]. However, several results (factor cross-loadings in EFA, a high eigenvalue for the first factor in parallel analysis, high correlation between latent factors in CFA, and high hierarchical omega and explained common variance—ECV—in a bifactor model) suggested the convenience of using the total score for evaluation and other applied purposes. The scale showed adequate reliability, ω = 0.908, 95% CI [0.900, 0.914], Rxx = 0.91. No gender or age invariance was found. The scale converged with the severity of internet gaming disorder scores, r = 0.697, p &lt; 0.05; higher frequency of video gaming, F(1, 2165) = 474.9, p &lt; 0.001, η2 = 0.176; poorer mental health, r = 0.20, p &lt; 0.05. We provided percentile ranks separated by gender and age. The DCG Scale seems to be a reliable and valid instrument to identify maladaptive cognitions about gaming in Spanish youth. These cognitions are a health-related problem; identifying and addressing them would be desirable to promote positive youth development.

Patient Satisfaction With Healthcare Service Quality and Its Associated Factors at One Polyclinic in Hanoi, Vietnam.

Introduction: Patient satisfaction is one of the most important components of measuring healthcare quality. Objectives: The study aimed to evaluate the validity and reliability of the patient satisfaction scale with the quality of health services and its associated factors. Methods: A cross-sectional study was conducted to collect data on patient satisfaction with 301 outpatients at one polyclinic in Hanoi, Vietnam. Results: The overall outpatient satisfaction was 53.5%. There were five factors (facilities, services provision results, information transparency and administrative procedures, accessibility, and interaction and communication of staff) including one major factor with high Eigenvalues coefficient, 22.5 for satisfaction with facility, and four others with lower Eigenvalues coefficient, 3.2, 2.0, 1.5, and 1.2 for satisfaction with service provision results, information transparency and administrative procedures, accessibility, and interaction and communication of staff respectively. All satisfaction-factors show internal consistency reliability, with a Cronbach's Alpha of over 0.9. The insured are 3.5 times (95% CI: 1.9-6.2) more likely to be satisfied with health services than the uninsured. Conclusion: The patient satisfaction measurement tool should be used for intervention to improve the quality of health services at the clinic.

Sharp eigenvalue asymptotics of fourth-order differential operators

Two-term self-adjoint fourth-order differential operator with summable potential on the unit interval is considered. High energy eigenvalue asymptotics and the trace formula for this operator are obtained.

The high order spectrum of a graph and its applications in graph colouring and clique counting

D. Cvetković, M. Doob and H. Sachs considered the high order eigenvalue problems of graphs. The high order eigenvalues of a graph G are solutions of the high degree homogeneous polynomial equations derived from G. We propose the adjacency tensor of a graph G and show that the high order eigenvalues of G can be regarded as eigenvalues of . Some results of the spectrum of the adjacency matrix are extended to the spectrum of by using the spectral theory of nonnegative tensors. An upper bound of chromatic number is given via the spectral radius of . Our upper bound is a generalization of Wilf's bound (where is the spectral radius of the adjacency matrix of a graph G) and sharper than the bound of Wilf in some classes of graphs. A formula of the number of cliques of fixed size which involve the spectrum of is obtained.

Accurate Eigenvalues for the Sturm-Liouville Problems, Involving Generalized and Periodic Ones

In the paper, the eigenvalues of Sturm-Liouville problems (SLPs), generalized SLPs and periodic SLPs are solved. First, we propose a new method to transform the SLP with mixed boundary conditions to a {generalized} SLP for a transformed variable, for which the Dirichlet boundary conditions occur on two-side, but the coefficients are nonlinear functions of eigenvalue. To computing the eigenvalue and eigenfunction, we further recast the transformed system to an initial value problem for a new variable. In terms of the relative residual of two consecutive terminal values of the new variable a nonlinear equation is solved for seeking the eigenvalue by the fictitious time integration method (FTIM), which monotonically converges to the exact eigenvalue. We solve a numerically characteristic equation by the half-interval method (HIM) and a derivative-free iterative scheme LHL {(Liu, Hong $\&amp;amp;$ Li, 2021)} to achieve high precision eigenvalues. Next, the generalized SLP is transformed to a {new} one, so that the Dirichlet boundary condition happens on the right-end. By using the boundary shape function method and the uniqueness condition of the transformed variable, a definite initial value problem is derived for the new variable. To match the right-end Dirichlet boundary condition a numerically characteristic equation is {obtained and} solved by the HIM and LHL. Finally, new techniques for solving the periodic SLPs with three types periodic boundary conditions are proposed, which preserve the periodic boundary conditions with the aids of boundary shape functions. Three iterative algorithms are developed, which converge quickly.&amp;nbsp; All the proposed iterative algorithms are identified by testing some examples.

FAKTOR-FAKTOR YANG MEMPENGARUHI KEPUTUSAN KONSUMEN DALAM MEMILIH PRODUK YAMAHA LEXI DI DEALER ISTANA MOTOR KLUNGKUNG-BALI

This study aims to analyze the factors that determine consumer decisions in choosing Yamaha Lexi products at the Istana Motor Dealer Klungkung-Bali. Sampling was done by using purposive sampling technique, where the number of samples used in this study was 85 respondents. In this study, statistical analysis was carried out with the help of the computer program SPSS (Statistical for Social Science) 24 for windows. The results of this study indicate that; the marketing factor has the highest eigenvalue, which is 2.819 and is able to explain the total variance of 16.585%. The superiority factor has a fairly high eigenvalue of 2.536% and is able to explain the total variance of 14,917. The supporting factor has an eigenvalue of 1.909 and is able to explain the total variance of 11.232. The Technology factor has an eigenvalue of 1,485 and is able to explain the total variance of 8,734. The supporting factor has an eigenvalue of 1,308 and is able to explain the total variance of 7,695 and the Service Factor has an eigenvalue of 1,141 and is able to explain the total variance of 6,714.

Enterprise Management Performance Evaluation Model Using Improved Fuzzy Clustering Algorithm in IoT Networks

Enterprise core competence is closely related to enterprise management performance, and it is important to evaluate enterprise management performance. However, the current enterprise management performance evaluation model has the problems of high eigenvalues of sample data, low cumulative contribution and correlation, high error rate in the calculation of business management performance evaluation index weights, low evaluation accuracy, and long evaluation time. Therefore, the enterprise management performance evaluation model using improved fuzzy clustering algorithm in Internet of things (IoT) networks is proposed. First, in the IoT architecture, the enterprise management performance evaluation index system is established by using the balanced scorecard theory. Second, the evaluation index system is reduced in dimensionality by combining principal component analysis and kernel-independent component analysis, the fuzzy C-mean clustering algorithm based on the objective function is designed, and finally, the improved fuzzy clustering algorithm is obtained to establish the enterprise management performance evaluation model, the reduced evaluation index system is input, and the evaluation results are output. The results show that the sample data eigenvalue of this model is low. The maximum error rate of weight calculation is 2.3%, the accuracy is always more than 95%, and the average value of evaluation time is 0.57 s, which effectively realize enterprise management performance evaluation in IoT networks.

Graphs with high second eigenvalue multiplicity

Jiang, Tidor, Yao, Zhang, and Zhao recently showed that connected bounded degree graphs have sublinear second eigenvalue multiplicity (always referring to the adjacency matrix). This result was a key step in the solution to the problem of equiangular lines with fixed angles. It led to the natural question: what is the maximum second eigenvalue multiplicity of a connected bounded degree $n$-vertex graph? The best known upper bound is $O(n/\log\log n)$. The previously known best known lower bound is on the order of $n^{1/3}$ (for infinitely many $n$), coming from Cayley graphs on $\text{PSL}(2,q)$. Here we give constructions showing a lower bound on the order of $\sqrt{n/\log n}$. We also construct Cayley graphs with second eigenvalue multiplicity at least $n^{2/5}-1$. Earlier techniques show that there are at most $O(n/\log\log n)$ eigenvalues (counting multiplicities) within $O(1/\log n)$ of the second eigenvalue. We give a construction showing this upper bound on approximate second eigenvalue multiplicity is tight up to a constant factor. This demonstrates a barrier to earlier techniques for upper bounding eigenvalue multiplicities.

Validity of the Web-Based, Self-Directed, NeuroCognitive Performance Test in Mild Cognitive Impairment.

Digital cognitive tests offer several potential advantages over established paper-pencil tests but have not yet been fully evaluated for the clinical evaluation of mild cognitive impairment. The NeuroCognitive Performance Test (NCPT) is a web-based, self-directed, modular battery intended for repeated assessments of multiple cognitive domains. Our objective was to examine its relationship with the Alzheimer's Disease Assessment Scale-Cognition Subscale (ADAS-Cog) and Mini-Mental State Examination (MMSE) as well as with established paper-pencil tests of cognition and daily functioning in mild cognitive impairment (MCI). We used Spearman correlations, regressions and principal components analysis followed by a factor analysis (varimax rotated) to examine our objectives. In MCI subjects, the NCPT composite is significantly correlated with both a composite measure of established tests (r = 0.78, p < 0.0001) as well as with the ADAS-Cog (r = -0.55, p < 0.0001). Both NCPT and paper-pencil test batteries had a similar factor structure that included a large "g" component with a high eigenvalue. The correlation for the analogous tests (e.g., Trails A and B, learning memory tests) were significant (p < 0.0001). Further, both the NCPT and established tests significantly (p < 0.0001) predicted the University of California San Diego Performance-Based Skills Assessment and Functional Activities Questionnaire, measures of daily functioning. The NCPT, a web-based, self-directed, computerized test, shows high concurrent validity with established tests and hence offers promise for use as a research or clinical tool in MCI. Despite limitations such as a relatively small sample, absence of control group and cross-sectional nature, these findings are consistent with the growing literature on the promise of self-directed, web-based cognitive assessments for MCI.

Enhanced interband tunneling in two-dimensional tunneling transistors through anisotropic energy dispersion

The unsatisfactory transmission probability in tunneling junction is a major challenge that restricts the performance and scaling of next-generation nanodevices, such as the tunnel field-effect transistors (TFETs). Here, we propose a strategy utilizing anisotropic electronic structures to enhance the inter-band tunneling performance. In the tunneling process, the sharp energy dispersion in transport direction ensures a high transmission eigenvalue, and the weak transverse energy state can broaden the transverse tunneling window, thus strengthening the tunneling probability. Furthermore, our quantum transport simulations demonstrate that in two-dimensional (2D) group VA-VA TFETs, the stronger anisotropic band structures make 2D BiAs and arsenene exhibit high on-state current several times higher than other systems, and the relative larger bandgap of arsenene also gives rise to a steep subthreshold slope below 60 mV/dec. This work provides a physical understanding of the tunneling transport performance, and the anisotropic 2D electronic structures can be regarded as a target feature to design tunneling transistors.

Real-Time Automated Epileptic Seizure Detection by Analyzing Time-Varying High Spatial Frequency Oscillations

Real-time seizure onset detection has been an active area of research in the study of epilepsy. Electroencephalography (EEG) measurements are widely used in seizure detection due to their high temporal resolution, cost-effective, and noninvasive nature. Various approaches based on machine learning are used for epileptic seizure detection, but these approaches do not explicitly reveal the underlying dynamics, require larger datasets for training, and are computationally demanding. Although high-frequency oscillations (HFOs) are the new biomarkers of epilepsy, they cannot be used with the existing data acquisition systems as they require high sampling rates and high cutoff frequency of the used filters. In this article, we present a novel approach for real-time seizure detection using high spatial frequencies. Since eigenvalues of the graph Laplacian represent spatial frequencies, we conjecture that higher eigenvalues and eigenvectors will contain the detailed information of seizure and non-seizure brain states. Hence, we have formed sub-band characteristic response vector (sub-band CRV) using weighted sum of eigenvectors corresponding to higher spatial frequencies and analyzed it over time. We have used a publicly available dataset to demonstrate the efficacy of the proposed approach. We observed that the proposed approach performs satisfactorily well in real-time automated seizure detection without requiring any kind of prior training. Moreover, our approach is not only accurate in seizure detection but also is independent of sampling rates, hence can be implemented easily in clinical realm for developing an automated seizure detection tool with the existing data acquisition systems operating at low sampling rates.

Fourth-order superlinear elliptic problems interacting with high eigenvalues

Fourth-order superlinear elliptic problems interacting with high eigenvalues