Minimum Eigenvalue Research Articles

Learner experiences of safety at public high schools in three South African townships: Baseline findings from the National School Safety Framework learner surveys.

Despite progressive policies and frameworks on school safety by the Department of Basic Education, safety remains a concern in South African schools. A cross-sectional descriptive design was employed using the National School Safety Framework (NSSF) 152-question learner survey, exploring perceptions and experiences pertaining to eight safety domains: dangerous objects, drugs and alcohol, bullying, verbal abuse, physical violence, discrimination, sexual violence, and journey to and from school. Grade 9-11 learners from 15 government-funded high schools in the Girls Achieve Power trial in Khayelitsha, Soweto, and Thembisa townships were surveyed (March 2018 - April 2019), sampling 10% of the school population. Data analysis included Principal Component Analysis (PCA), reducing correlated variables into fewer questions, then analysis on a scree plot by calculating eigenvalues; repeated PCA with those that had a minimum eigenvalue of 1 and Cronbach Alpha test for internal reliability. Eleven composite variables were included in the final analysis. In total, 1034 learners completed the NSSF learner survey; 52.9% were female and the mean age was 16 years (SD=1.36). Results show statistically significant associations between four of the 11 composite variables in relation to sex. Over half (55%) of males have experienced peer provocation and relational aggression (p<0.001). Fifty-eight percent of females reported feeling unsafe on their way to and from school (p<0.003). Over half of males reported that their school was not effective in enforcing discipline (p=0.002) while 58% of females noted they could comfortably report any form of experienced or witnessed violence at school, to their educators (p<0.000). Violence continues to be a concern in South African schools. Interventions should work across the ecological model to effectively prevent and reduce violence at school and community levels. Strengthened NSSF implementation is critical to achieving this. We recommend NSSF learner survey adaptations to increase utility and implementation.

Free Metaplectic Wigner Distribution: Definition and Heisenberg’s Uncertainty Principles

Inspired by a definition of the closed-form instantaneous cross-correlation Wigner distribution (Zhang in IEEE Trans Signal Process 67(21):5527–5542, 2019), we generalize the notion of Wigner distribution to the so-called free metaplectic Wigner distribution (FMWD) through three free metaplectic transforms, in order to tackle a challenge in high-dimensional complex features information processing. We provide some representative special cases for this general form, including the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -dimensional nonseparable affine characteristic Wigner distribution, kernel function Wigner distribution, convolution representation Wigner distribution and instantaneous cross-correlation Wigner distribution. We establish the standard Heisenberg’s uncertainty principles (HUPs) of the real-valued function for the FMWD. We also establish the standard HUPs of the complex-valued function for some specific (i.e., the orthogonal, the orthonormal, the minimum eigenvalue commutative and the maximum eigenvalue commutative) FMWDs. In view of the one-dimensional case of our results, we solve a burning question regarding the limit of time-frequency superresolution triggered by the linear canonical transform free parameters.

Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error analysis

A computer-assisted proof is proposed for the Laplacian eigenvalue minimization problems over triangular domains under diameter constraints. The paper provides an elementary analysis to derive the Hadamard shape derivative formula for complicated problem settings that allow non-homogeneous Neumann boundary conditions. Moreover, an algorithm to rigorously evaluate the Hadamard formula is proposed by utilizing the guaranteed computation for both eigenvalues and eigenfunctions of differential operators, which is recently developed by the second author. Besides the model homogeneous Dirichlet eigenvalue problem, the eigenvalue problem associated with a non-homogeneous Neumann boundary condition, which is related to the Crouzeix–Raviart interpolation error constant, is considered. The computer-assisted proof tells that among the triangles with the unit diameter, the equilateral triangle minimizes the first eigenvalue for each concerned eigenvalue problem.

Dynamic Interaction Analysis and Damping Control Strategy of Hybrid System With Grid-Forming and Grid-Following Control Modes

The dynamic behavior of converters with different synchronous control modes is significantly different. Therefore, the renewable energy grid-connected system cannot be equivalent as the same type of power electronics equipment. There are dynamic interactions among the multiple time scale controllers of each equipment, which may lead to the small signal instability of the hybrid system. In this paper, a hybrid grid-connected system with phase-locked loop (PLL) controlled doubly fed induction generator (DFIG) and virtual synchronous generator (VSG) controlled converter is studied. On the basis of the open-loop modal resonance theory, the mechanism of small signal instability of hybrid system is revealed from the perspective of mode interaction. Furthermore, a design method of additional damping controller is proposed based on normal matrix, which can achieve the minimum eigenvalue sensitivity of the hybrid system and avoid the interaction between different control loops. Finally, a hybrid system including a grid-forming VSG system and a grid-following DFIG wind farm is investigated in this paper. The correctness and effectiveness of interaction analysis and damping control strategy are confirmed by the results of modal analysis and simulation.

Quantitative Prediction of Sling Events in Turbulence at High Reynolds Numbers.

Collisional growth of droplets, such as occurring in warm clouds, is known to be significantly enhanced by turbulence. Whether particles collide depends on their flow history, in particular on their encounters with highly intermittent small-scale turbulent structures, which despite their rarity can dominate the overall collision rate. Here, we develop a quantitative criterion for sling events based on the velocity gradient history along particle paths. We show by a combination of theory and simulations that the problem reduces to a one-dimensional localization problem as encountered in condensed matter physics. The reduction demonstrates that the creation of slings is controlled by the minimal real eigenvalue of the velocity gradient tensor. We use fully resolved turbulence simulations to confirm our predictions and study their Stokes and Reynolds number dependence. We also discuss extrapolations to the parameter range relevant for typical cloud droplets, showing that sling events at high Reynolds numbers are enhanced by an order of magnitude for small Stokes numbers. Thus, intermittency could be a significant ingredient in the collisional growth of rain droplets.

Hypergraph partitioning using tensor eigenvalue decomposition.

Hypergraphs have gained increasing attention in the machine learning community lately due to their superiority over graphs in capturing super-dyadic interactions among entities. In this work, we propose a novel approach for the partitioning of k-uniform hypergraphs. Most of the existing methods work by reducing the hypergraph to a graph followed by applying standard graph partitioning algorithms. The reduction step restricts the algorithms to capturing only some weighted pairwise interactions and hence loses essential information about the original hypergraph. We overcome this issue by utilizing tensor-based representation of hypergraphs, which enables us to capture actual super-dyadic interactions. We extend the notion of minimum ratio-cut and normalized-cut from graphs to hypergraphs and show that the relaxed optimization problem can be solved using eigenvalue decomposition of the Laplacian tensor. This novel formulation also enables us to remove a hyperedge completely by using the "hyperedge score" metric proposed by us, unlike the existing reduction approaches. We propose a hypergraph partitioning algorithm inspired from spectral graph theory and also derive a tighter upper bound on the minimum positive eigenvalue of even-order hypergraph Laplacian tensor in terms of its conductance, which is utilized in the partitioning algorithm to approximate the normalized cut. The efficacy of the proposed method is demonstrated numerically on synthetic hypergraphs generated by stochastic block model. We also show improvement for the min-cut solution on 2-uniform hypergraphs (graphs) over the standard spectral partitioning algorithm.

An Adaptive Method for Likelihood Optimization in Linear Mixed Models Under Constrained Search Spaces

Linear mixed effects models are highly flexible in handling correlated data by considering covariance matrices that explain variation patterns between and within clusters. For these covariance matrices, there exist a wide list of possible structures proposed by researchers in multiple scientific areas. Maximum likelihood is the most common estimation method in linear mixed models and it depends on the structured covariance matrices for random effects and errors. Classical methods used to optimize the likelihood function, such as Newton-Raphson or Fisher's scoring, require analytical procedures to obtain parametrical restrictions to guarantee positive definiteness for the structured matrices and it is not, in general, an easy task. To avoid dealing with complex restrictions, we propose an adaptive method that incorporates the so-called Hybrid Genetic Algorithms with a penalization technique based on minimum eigenvalues to guarantee positive definiteness in an evolutionary process which discards non-viable cases. The proposed method is evaluated through simulations and its performance is compared with that of Newton-Raphson algorithm implemented in SAS® PROC MIXED V9.4.

Communication area estimation for decentralized control of nanosatellites swarm

The problem of relative drift elimination between the satellites in the swarm is considered in the paper. The proposed decentralized control takes into account a communication constraint such as limited size of communication area. Only the satellites within the communication area can be identified by relative motion determination system. The control aim is to eliminate the mean relative drift between all the satellites inside the communication area. The purpose of the work is to study the performance of the proposed decentralized control algorithm. It is shown that the system matrix of differential equations for the vector of relative drifts is related to the Laplacian matrix of the communication graph. In the case of the connected swarm, all but one eigenvalues of the system are negative, and the remaining one is equal to zero. It means that all the relative drifts converge to the same value under the proposed control. The speed of convergence is defined by the minimum absolute eigenvalue that depends on the graph topology. The initial drift and the convergence speed make it possible to estimate the communication distance that provides the connectivity of the graph. Considering normally distributed errors of the initial velocity after the launch, it is possible to estimate the distance between any two satellites after the convergence. It allows us to estimate the communication distance that ensures the relative drift elimination between all the satellites in the swarm. The obtained estimations are validated using Monte Carlo simulations. In numerical simulations the swarm of 3U CubeSats in low-Earth orbit is considered. The decentralized control is implemented by differential aerodynamic drag via the change of cross-sectional area using onboard reaction wheels.

Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems I: regularity and error analysis

Abstract Stochastic partial differential equation (PDE) eigenvalue problems are useful models for quantifying the uncertainty in several applications from the physical sciences and engineering, e.g., structural vibration analysis, the criticality of a nuclear reactor or photonic crystal structures. In this paper we present a multilevel quasi-Monte Carlo (MLQMC) method for approximating the expectation of the minimal eigenvalue of an elliptic eigenvalue problem with coefficients that are given as a series expansion of countably-many stochastic parameters. The MLQMC algorithm is based on a hierarchy of discretizations of the spatial domain and truncations of the dimension of the stochastic parameter domain. To approximate the expectations, randomly shifted lattice rules are employed. This paper is primarily dedicated to giving a rigorous analysis of the error of this algorithm. A key step in the error analysis requires bounds on the mixed derivatives of the eigenfunction with respect to both the stochastic and spatial variables simultaneously. Under stronger smoothness assumptions on the parametric dependence, our analysis also extends to multilevel higher-order quasi-Monte Carlo rules. An accompanying paper (Gilbert, A. D. &amp; Scheichl, R. (2023) Multilevel quasi-Monte Carlo methods for random elliptic eigenvalue problems II: efficient algorithms and numerical results. IMA J. Numer. Anal.) focusses on practical extensions of the MLQMC algorithm to improve efficiency and presents numerical results.

Mixed convective-quadratic radiative MoS 2–SiO 2/H 2 O hybrid nanofluid flow over an exponentially shrinking permeable Riga surface with slip velocity and convective boundary conditions: Entropy and stability analysis

In this work, the flow of a hybrid Mo S 2 − Si O 2 /water nanofluid across a porous exponentially diminishing Riga surface with the effects of quadratic heat radiation is taken into account. We also considered the effects of mixed convection, slip velocity, and convective thermal boundary conditions. Before numerically solving the governing partial differential equations, the MATLAB function bvp4c was used to get a comprehensive description of all relevant flow characteristics. The ramifications of physical characteristics concerning fluid flow and thermal profile are investigated using graphs and tables. The primary objective of this study is to investigate the Nusselt number, skin friction coefficient, and entropy production. Using the second law of thermodynamics, the irreversibility factor is computed. For a given value of the mass suction parameter, the findings also indicate the occurrence of dual-nature solutions in the shrinking sheet area, with a stable upper solution branch and unstable bottom solution branch. In addition, the first solution produces a positive minimum eigenvalue, whereas the second solution produces a negative eigenvalue, showing the stability of the first solution. For heat transfer enhancement, the existence of quadratic thermal radiative parameter impacts is more advantageous. With a larger value for the modified Hartman number, the velocity field has expanded. Also, recent research demonstrates that raising the thermal Biot number enhances the thermal gradient. Increases in nanoparticle volume fraction and thermal radiation parameters lead to a commensurate rise in entropy production. Because of these findings, we can better regulate the temperature of various environments by controlling the flow of heat.

Measure of perceived social support from family, friends, and healthcare providers for Korean adolescents and young adults with cancer

ObjectiveAssessing the perceived social support (PSS) that adolescents and young adults (AYAs) with cancer receive from family, friends, and healthcare providers is critical to promoting their adjustment. This study developed a reliable and comprehensive self-report PSS assessment tool that measures various aspects of social support by translating existing measurements into Korean. MethodsThe translation was completed in accordance with international guidelines. To focus on cultural adaptation, the main ideas associated with items were translated to reflect the differences between Western and Eastern culture. In total, 144 Korean AYAs with cancer (mean age: 17.0 years; 45.8% female) completed the translated version. A separate principal component analysis (PCA) with an orthogonal quartimax rotation, a minimum eigenvalue of 1.0, and minimum factor loadings of 0.50 was used for each subscale. Cronbach's alpha coefficients were calculated for each PCA-derived subscale. ResultsFour subscales with 46 items were identified. Two subscales represented perceived emotional support within the family (PSS-ESF, 14 items) and the AYA's perceived helpfulness within the family (PSS-HWF, 3 items). The third scale represented the perceived support of friends (PSS-Friends, 14 items). The final scale represented the perceived support of healthcare providers (PSS-HCPs, 15 items). Excellent reliability per subscale was demonstrated (Cronbach's alpha: 0.93 for PSS-ESF, 0.73 for PSS-HWF, and 0.92 each for PSS-Friends and PSS-HCPs). ConclusionsA culturally adapted and reliable Korean version questionnaire with four independent subscales was developed. Further assessment of the Korean PSS is required and will contribute to the development of culturally adapted and tailored interventions.

Target Local Matching Recognition Algorithm based on Improved Harris Key Point Detection Operator

In the process of attacking fighters, helicopters and other targets, infrared imaging guided air-to-air missiles once they find themselves intercepted, they will release interference to induce the missile to deviate from the trajectory, which brings great difficulties to the missile to successfully destroy the target. When infrared interference occludes aircraft targets, a target local matching recognition algorithm based on the improved Harris key point detection operator is proposed. The algorithm first uses the Gaussian smoothing window to count the gradients in the x direction and y direction of each pixel, forms an autocorrelation feature matrix and calculates its feature values. Because smaller eigenvalues can be used to characterize the prominence of the curve, the minimum eigenvalue is used as the corner response function value, and the point when greater than the given threshold is marked as the key point of the aircraft target. In the process of interference occlusion of aircraft targets, the local matching recognition of targets is achieved by calculating the Euclidean distance of the feature descriptors between key points. Experimental results show that the proposed improved algorithm can achieve local matching recognition of infrared aircraft targets when infrared interference occludes aircraft targets.

Cooperative output feedback tracking control of stochastic nonlinear heterogeneous multi‐agent systems

SummaryWe study cooperative output feedback tracking control of stochastic nonlinear heterogeneous leader‐following multi‐agent systems. Each agent has a continuous‐time stochastic nonlinear heterogeneous dynamics with an unmeasurable state, and there are additive and multiplicative noises along with information exchange among agents. We propose admissible distributed observation strategies for estimating the leader's and the followers' states, and admissible cooperative output feedback control strategies based on the certainty equivalence principle. By output regulation theory and stochastic analysis, we show if the dynamics of each agent satisfies the Lipschitz condition, and the product of the leader's Lipschitz coefficient, the intensity of multiplicative measurement noises, and the constant related to the leader's Lipschitz coefficient and dimension is less than the minimum nonzero eigenvalue of graph Laplacian, then there exist admissible distributed observation and cooperative control strategies to ensure mean square bounded output tracking. Finally, the effectiveness of our control strategies is demonstrated by a numerical simulation.

Data-Efficient Active Weighting Algorithm for Composite Adaptive Control Systems

We propose an active weighting algorithm for composite adaptive control to reduce the state and estimate errors while maintaining the estimation quality. Unlike previous studies that construct the composite term by simply stacking, removing, and pausing observed data, the proposed method efficiently utilizes the data by providing a theoretical set of weights for observations that can actively manipulate the composite term to have desired characteristics. As an example, a convex optimization formulation is provided, which maximizes the minimum eigenvalue while keeping other constraints, and an illustrative numerical simulation is also presented.

Finite-time synchronization control scheme for underactuated satellite formation reconfiguration

A synchronization control scheme for underactuated satellite formation reconfiguration in circular orbits is proposed in this paper. The main idea of the synchronization scheme is to control the satellite without radial or along-track thrust to track its desired configuration while synchronizing its motion with that of other underactuated satellites to maintain the predefined or time-varying formation. Firstly, a new underactuated control approach is presented for either underactuated case. Based on the inherent coupling of the system states, the finite-time convergence of the system trajectory could be guaranteed by the sliding mode-based underactuated controller. Secondly, to synchronize the reconfiguration motion between followers, the sum of the sliding mode errors of every two neighbor followers is defined as the synchronization control. The Lyapunov-based method proves the finite-time convergence of synchronization control. More importantly, the minimum nonzero eigenvalue of the Laplace matrix can reduce the system state convergence region. Numerical simulations also verify the performance of the proposed underactuated synchronization controller.

Machine Learning Methods for Inferring the Number of UAV Emitters via Massive MIMO Receive Array

To provide important prior knowledge for the direction of arrival (DOA) estimation of UAV emitters in future wireless networks, we present a complete DOA preprocessing system for inferring the number of emitters via a massive multiple-input multiple-output (MIMO) receive array. Firstly, in order to eliminate the noise signals, two high-precision signal detectors, the square root of the maximum eigenvalue times the minimum eigenvalue (SR-MME) and the geometric mean (GM), are proposed. Compared to other detectors, SR-MME and GM can achieve a high detection probability while maintaining extremely low false alarm probability. Secondly, if the existence of emitters is determined by detectors, we need to further confirm their number. Therefore, we perform feature extraction on the the eigenvalue sequence of a sample covariance matrix to construct a feature vector and innovatively propose a multi-layer neural network (ML-NN). Additionally, the support vector machine (SVM) and naive Bayesian classifier (NBC) are also designed. The simulation results show that the machine learning-based methods can achieve good results in signal classification, especially neural networks, which can always maintain the classification accuracy above 70% with the massive MIMO receive array. Finally, we analyze the classical signal classification methods, Akaike (AIC) and minimum description length (MDL). It is concluded that the two methods are not suitable for scenarios with massive MIMO arrays, and they also have much worse performance than machine learning-based classifiers.

Replica method for eigenvalues of real Wishart product matrices

We show how the replica method can be used to compute the asymptotic eigenvalue spectrum of a real Wishart product matrix. For unstructured factors, this provides a compact, elementary derivation of a polynomial condition on the Stieltjes transform first proved by Müller [IEEE Trans. Inf. Theory. 48, 2086-2091 (2002)]. We then show how this computation can be extended to ensembles where the factors are drawn from matrix Gaussian distributions with general correlation structure. For both unstructured and structured ensembles, we derive polynomial conditions on the average values of the minimum and maximum eigenvalues, which in the unstructured case match the results obtained by Akemann, Ipsen, and Kieburg [Phys. Rev. E 88, 052118 (2013)] for the complex Wishart product ensemble.

ICA’s bug: How ghost ICs emerge from effective rank deficiency caused by EEG electrode interpolation and incorrect re-referencing

Independent component analysis (ICA) has been widely used for electroencephalography (EEG) analyses. However, ICA performance relies on several crucial assumptions about the data. Here, we focus on the granularity of data rank, i.e., the number of linearly independent EEG channels. When the data are rank-full (i.e., all channels are independent), ICA produces as many independent components (ICs) as the number of input channels (rank-full decomposition). However, when the input data are rank-deficient, as is the case with bridged or interpolated electrodes, ICA produces the same number of ICs as the data rank (forced rank deficiency decomposition), introducing undesired ghost ICs and indicating a bug in ICA. We demonstrated that the ghost ICs have white noise properties, in both time and frequency domains, while maintaining surprisingly typical scalp topographies, and can therefore be easily missed by EEG researchers and affect findings in unknown ways. This problem occurs when the minimum eigenvalue λmin of the input data is smaller than a certain threshold, leading to matrix inversion failure as if the rank-deficient inversion was forced, even if the data rank is cleanly deficient by one. We defined this problem as the effective rank deficiency. Using sound file mixing simulations, we first demonstrated the effective rank deficiency problem and determined that the critical threshold for λmin is 10−7 in the given situation. Second, we used empirical EEG data to show how two preprocessing stages, re-referencing to average without including the initial reference and non-linear electrode interpolation, caused this forced rank deficiency problem. Finally, we showed that the effective rank deficiency problem can be solved by using the identified threshold (λmin = 10−7) and the correct re-referencing procedure described herein. The former ensures the achievement of effective rank-full decomposition by properly reducing the input data rank, and the latter allows avoidance of a widely practiced incorrect re-referencing approach. Based on the current literature, we discuss the ambiguous status of the initial reference electrode when re-referencing. We have made our data and code available to facilitate the implementation of our recommendations by the EEG community.

A computer vision approach to identifying the manufacturer of posterior thoracolumbar instrumentation systems.

Knowledge of the manufacturer of the previously implanted pedicle screw systems prior to revision spinal surgery may facilitate faster and safer surgery. Often, this information is unavailable because patients are referred by other centers or because of missing information in the patients' records. Recently, machine learning and computer vision have gained wider use in clinical applications. The authors propose a computer vision approach to classify posterior thoracolumbar instrumentation systems. Lateral and anteroposterior (AP) radiographs obtained in patients undergoing posterior thoracolumbar pedicle screw implantation for any indication at the authors' institution (2015-2021) were obtained. DICOM images were cropped to include both the pedicle screws and rods. Images were labeled with the manufacturer according to the operative record. Multiple feature detection methods were tested (SURF, MESR, and Minimum Eigenvalues); however, the bag-of-visual-words technique with KAZE feature detection was ultimately used to construct a computer vision support vector machine (SVM) classifier for lateral, AP, and fused lateral and AP images. Accuracy was tested using an 80%/20% training/testing pseudorandom split over 100 iterations. Using a reader study, the authors compared the model performance with the current practice of surgeons and manufacturer representatives identifying spinal hardware by visual inspection. Among the three image types, 355 lateral, 379 AP, and 338 fused radiographs were obtained. The five pedicle screw implants included in this study were the Globus Medical Creo, Medtronic Solera, NuVasive Reline, Stryker Xia, and DePuy Expedium. When the two most common manufacturers used at the authors' institution were binarily classified (Globus Medical and Medtronic), the accuracy rates for lateral, AP, and fused images were 93.15% ± 4.06%, 88.98% ± 4.08%, and 91.08% ± 5.30%, respectively. Classification accuracy decreased by approximately 10% with each additional manufacturer added. The multilevel five-way classification accuracy rates for lateral, AP, and fused images were 64.27% ± 5.13%, 60.95% ± 5.52%, and 65.90% ± 5.14%, respectively. In the reader study, the model performed five-way classification on 100 test images with 79% accuracy in 14 seconds, compared with an average of 44% accuracy in 20 minutes for two surgeons and three manufacturer representatives. The authors developed a KAZE feature detector with an SVM classifier that successfully identified posterior thoracolumbar hardware at five-level classification. The model performed more accurately and efficiently than the method currently used in clinical practice. The relative computational simplicity of this model, from input to output, may facilitate future prospective studies in the clinical setting.

Minimum eigenvalue based adaptive fault compensation for hypersonic vehicles

The attitude tracking control problem is addressed for hypersonic vehicles under actuator faults that may cause an uncertain time-varying control gain matrix. An adaptive compensation scheme is developed to ensure system stability and asymptotic tracking properties, including a kinematic control signal and a dynamic control signal. To deal with the uncertainties of the control gain matrix, a new positive definite one is constructed. The minimum eigenvalue of such a new control gain matrix is estimated. Simulation results of application to an X-33 vehicle model verify the effectiveness of the proposed minimum eigenvalue based adaptive fault compensation scheme.