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AbstractWe propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series p is large in relation to the length of time series n. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed curve series can be segmented into several groups such that any two subseries from any two different groups are uncorrelated both contemporaneously and serially. Consequently in our second step those groups are handled separately without the information loss on the overall linear dynamic structure. The second step is devoted to establishing a finite-dimensional dynamical structure for all the transformed functional time series within each group. Furthermore the finite-dimensional structure is represented by that of a vector time series. Modelling and forecasting for the original high-dimensional functional time series are realized via those for the vector time series in all the groups. We investigate the theoretical properties of our proposed methods, and illustrate the finite-sample performance through both extensive simulation and two real datasets. [ABSTRACT FROM AUTHOR]

Widespread interest in nondestructive biomarkers of aging has led to a multitude of biological ages that each proffers a "true" health-adjusted individual age. Although each measure provides salient information on the aging process, they are each univariate, in contrast to the "hallmark" and "pillar" theories of aging, which are explicitly multidimensional, multicausal, and multiscale. Fortunately, multiple biological ages can be systematically combined into a multidimensional network representation. The interaction network between these biological ages permits analysis of the multidimensional effects of aging, as well as quantification of causal influences during both natural aging and, potentially, after anti-aging intervention. The behavior of the system as a whole can then be explored using dynamical network stability analysis, which identifies new, efficient biomarkers that quantify long-term resilience scores on the timescale between measurements (years). We demonstrate this approach using a set of 8 biological ages from the longitudinal Swedish Adoption/Twin Study of Aging (SATSA). After extracting an interaction network between these biological ages, we observed that physiological age, a proxy for cardiometabolic health, serves as a central node in the network, implicating it as a key vulnerability for slow, age-related decline. We furthermore show that while the system as a whole is stable, there is a weakly stable direction along which recovery is slow—on the timescale of a human lifespan. This slow direction provides an aging biomarker, which correlates strongly with chronological age and predicts longitudinal decline in health—suggesting that it estimates an important driver of age-related changes. [ABSTRACT FROM AUTHOR]

The increasing integration of intermittent renewable sources (RSs) poses a dynamic frequency stability challenge for modern marine vessel microgrids. To address this issue, this paper proposes a novel control approach, specifically targeting frequency and tie-line power stabilization in a diverse source marine microgrid (MμG) with two intertied areas featuring renewable (wind-wave) sources. The suggested approach introduces a modified tilt-integral active disturbance rejection (TI-ADRC) controller designed to ensure effective damping of power frequency oscillations. As the control scheme depends on the optimal setting of the proposed controller, a recently developed marine predator technique (MPT) has been adopted. The performance of the proposed controller is compared with other recent controllers viz. PID, tilt-integral derivative (TID), two-degree-of-freedom (2DOF)-PID, fuzzy-PI, and ADRC to validate its superiority. To further enhance the system dynamics, a precise modeling of inertia emulated direct current (IEPDC) tie link is incorporated in microgrid system. The impact assessments, considering time delays with pre/post IEPDC link, demonstrate a substantial 57.79% and 81.53% reduction in peak frequency overshoot compared to DC link (conventional model) and AC link, respectively. The analysis of the eigen plot confirms the stability of the control system. Sensitivity assessments of the controller against ± 30% parametric variations and load fluctuations are conducted, affirming its robustness. Finally, the result from OPAL-RT confirm the practicality of the proposed method. It is asserted that the suggested controller is reliable and functions well in n the presence of diverse disruptions and parametric variations. • An integrated two-area inter-tied marine microgrid model based on intermittent renewable sources for secondary frequency control. • Novel MPT-tuned tilt integral-active disturbance rejection controller (TI-ADRC) for marine microgrid. • Comprehensive modelling of inertia emulated DC (IEPDC) link with parallel AC link. • Stability and dynamic response analysis of the proposed control strategy. • Sensitivity analysis to validate robustness of the proposed control strategy under uncertain parametric variation. [ABSTRACT FROM AUTHOR]

An innovative method of obtaining the weights for a Finite Impulse Response (FIR) notch filter using the Eigen-approach is proposed. The Eigen-approach was used to identify the frequencies of the source signals by determining the eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix. The FIR notch filter was constructed by shifting the root corresponding to the desired signal, which filtered out all other undesired signals. The obtained results indicate that using the Eigen-approach to generate a selective FIR notch filter is a viable solution. [ABSTRACT FROM AUTHOR]

We propose a new unsupervised learning method for clustering a large number of time series based on a latent factor structure. Each cluster is characterized by its own cluster-specific factors in addition to some common factors which impact on all the time series concerned. Our setting also offers the flexibility that some time series may not belong to any clusters. The consistency with explicit convergence rates is established for the estimation of the common factors, the cluster-specific factors, and the latent clusters. Numerical illustration with both simulated data as well as a real data example is also reported. As a spin-off, the proposed new approach also advances significantly the statistical inference for the factor model of Lam and Yao. for this article are available online. [ABSTRACT FROM AUTHOR]

We propose a contemporaneous bilinear transformation for a p × q matrix time series to alleviate the difficulties in modeling and forecasting matrix time series when p and/or q are large. The resulting transformed matrix assumes a block structure consisting of several small matrices, and those small matrix series are uncorrelated across all times. Hence, an overall parsimonious model is achieved by modeling each of those small matrix series separately without the loss of information on the linear dynamics. Such a parsimonious model often has better forecasting performance, even when the underlying true dynamics deviates from the assumed uncorrelated block structure after transformation. The uniform convergence rates of the estimated transformation are derived, which vindicate an important virtue of the proposed bilinear transformation, that is, it is technically equivalent to the decorrelation of a vector time series of dimension max(p, q) instead of p × q. The proposed method is illustrated numerically via both simulated and real data examples. for this article are available online. [ABSTRACT FROM AUTHOR]

The accurate prediction of rotating stall inception is critical for determining the stable operating regime of a compressor. Among the two widely accepted pathways to stall, namely, modal and spike, the former is plausibly believed to originate from a global linear instability, and experiments have partially confirmed it. As for the latter, recent computational and experimental findings have shown it to exhibit itself as a rapidly amplified flow perturbation. However, rigorous analysis has yet to be performed to prove that this is due to global linear instability. In this work, an eigenanalysis approach is used to investigate the rotating stall inception of a transonic annular cascade. Steady analyses were performed to compute the performance characteristics at a given rotational speed. A numerical stall boundary was first estimated based on the residual convergence behavior of the steady solver. Eigenanalyses were then performed for flow solutions at a few near-stall points to determine their global linear stability. Once the relevant unstable modes were identified according to the signs of real parts of eigenvalues, they were examined in detail to understand the flow destabilizing mechanism. Furthermore, time-accurate unsteady simulations were performed to verify the obtained eigenvalues and eigenvectors. The eigenanalysis results reveal that at the rotating stall inception condition, multiple unstable modes appear almost simultaneously with a leading mode that grows most rapidly. In addition, it was found that the unstable modes are continuous in their nodal diameters, and are members of a particular family of modes typical of a dynamic system with cyclic symmetries. This is the first time such an interesting structure of the unstable modes is found numerically, which to some extent explains the rich and complex results constantly observed from experiments but have never been consistently explained. The verified eigenanalysis method can be used to predict the onset of a rotating stall with a CPU time cost orders of magnitude lower than time-accurate simulations, thus making compressor stall onset prediction based on the global linear instability approach feasible in engineering practice. [ABSTRACT FROM AUTHOR]

For any graph G, the modified Sombor index is defined as the reciprocal of the well-known Sombor Index. The girth of G, by short g(G), is the length of the smallest cycle in G. A graph with exactly one cycle is a unicyclic graph. If it is further, connected, it is a connected unicyclic graph. In this article, we achieved the modified Sombor index for a collection of graphs, connected unicyclic graphs and also obtained the maximum modified Sombor index for the class of unicyclic graphs based on the restrictions by a fixed girth. [ABSTRACT FROM AUTHOR]

Purpose: There is inherent variability of the structural parameters due to various changing environmental conditions, such as ambient temperature, wind speed, traffic load, etc. in an updating procedure. This concept is considered in this paper, where a Finite Element (FE) model updating methodology in a Hierarchical Bayesian framework using the modal data is presented. The modal data consists of multiple sets of Most Probable Values (MPVs) and covariance matrices of the modal parameters obtained at different instances. Methods: The dynamic condensation technique is utilized to avoid direct matching between the experimental and analytical modes while solving the Eigen equation. The system eigenvalues and partial system mode shapes corresponding to the measured Degrees of Freedom (DOFs) are incorporated into the reduced-order Eigen equation to establish the relation between the modal data and the structural parameters. The Metropolis-within-Gibbs (MWG) sampler is proposed to sample from the posterior PDF. Another solution methodology is also presented to obtain the Maximum a Posteriori (MAP) estimate of the uncertain parameters. Results: Two numerical examples are presented to demonstrate the effectiveness of the proposed approach. The effectiveness of the proposed approach is also validated using an experimental example based on a laboratory structure. Both the MWG sampler and the estimation of MAP using the optimization method are utilized while updating the two structures and almost similar results are obtained from both methods. Conclusion: Although similar results were obtained using both the methods, the simplified approach for MAP estimation is found to be more computationally efficient than the MWG sampler. Besides, it has been observed that the updating performance has been much better in case of the second numerical example as compared with the first numerical example and the laboratory example. This is due to the higher modeling error in case of the first numerical example and significant modeling and measurement errors associated with the updating exercise of the experimental example. [ABSTRACT FROM AUTHOR]

Under the spin–position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra substitutes the vector–matrix spin model built on the Pauli spin operator. The standard quantum operator‐state spin formalism is replaced with vectors transforming by proper and improper rotations in the same 3D space—isomorphic to the space of Pauli matrices. In the single‐spin case, the novel spin 1/2 representation (1) is Hermitian, (2) shows handedness, (3) yields all the standard results and its modulus equals the total spin angular momentum Stot=3ℏ/2, (4) formalizes irreversibility in measurement, and (5) permits adaptive imbedding of the 2D spin space in 3D. Maximally entangled spin pairs (1) are in phase and have opposite handedness, (2) relate by one of the four basic improper rotations in 3D: plane reflections (triplets) and inversion (singlet), (3) yield the standard total angular momentum, and (4) all standard expectation values for bipartite and partial observations follow. Depending on whether proper and improper rotors act one—or two—sided, the formalism appears in two complementary forms, the "spinor" or the "vector" form, respectively. The proposed scheme provides a clear geometric picture of spin correlations and transformations entirely in the 3D physical orientation space. [ABSTRACT FROM AUTHOR]

This work presents a deep neural network (DNN)-based approach for identifying the modal field distributions of closed non-radiating waveguides. Specifically, physics-informed neural networks (PINNs) are used to solve the Helmholtz partial differential equation. The PINN architecture includes incorporation of boundary conditions and selection of initial conditions to obtain required modes inside the waveguides. In this paper, furthermore, the use of this method is illustrated for waveguides consisting of inhomogeneous and anisotropic media, where we apply a domain decomposition-based deep learning method. Our approach successfully identifies all eigenmode distributions with an error of less than −12 dB as compared to analytical and full-wave simulation results. Notably, we further enhance the efficiency of our approach by utilizing transfer learning, achieving a 23 times reduction in solution time. Our results demonstrate PINNs as an alternative to traditional methods in accurately calculating waveguide modal field distributions and its applicability to other partial differential equation based EM problems.

This study uses data for >3300 business and economics journals to explore the relationships between 5 subjective (expert) journal ratings and 10 citation metrics including 5IF (5-year Impact Factor), Article Influence (AI) score, CiteScore, Eigenfactor, Impact per Publication, SJR, and SNIP. Overall, AI and SJR are the citation metrics most closely related to the expert journal ratings. Comparisons of paired citation metrics that are similar in all but a single key characteristic confirm that expert journal ratings are more closely related to size-independent citation metrics than to size-dependent metrics, more closely related to weighted metrics than to unweighted metrics, and more closely related to normalized metrics than to non-normalized metrics. These results, which are consistent across the 5 expert ratings, suggest that evaluators consider the average impact of an article in each journal rather than the total impact of the journal as a whole, that they give more credit for citations in high-impact journals than for citations in lesser journals, and that they assess each journal's relative standing within its own field or subfield rather than its broader scholarly impact. No single citation metric is a good substitute for any of the expert ratings considered here. [ABSTRACT FROM AUTHOR]

We study first-passage percolation on random simple triangulations and their dual maps with independent identically distributed link weights. Our main result shows that the first-passage percolation distance concentrates in an op(n1/4) window around a constant multiple of the graph distance. Our approach follows the proof strategy by Curien and Le Gall (Ann. Sci. Éc. Norm. Supér., 2019), but we have to overcome several obstacles specific to simple triangulations. [ABSTRACT FROM AUTHOR]

We give in this paper two characterizations of the minimal exponential rate of survival θ* of the M/M/∞ queue. The first one is a derivation of a known result on the duration of excursions of this process. The second one was conjectured by Martínez and Ycart (2001) and is proved using complex analysis by establishing a connection with the first characterization in terms of the incomplete gamma function. [ABSTRACT FROM AUTHOR]

In the paper we find sufficient conditions on the coefficients of a class of third order quasi-elliptic operator pencils providing the completeness of the part of eigen and associated vectors in a separable Hilbert space. The completeness of the system of decreasing elementary solutions of the corresponding homogeneous equation in the space of solutions of this equation is proved. All these conditions are expressed by the coefficients of the operator pencil. [ABSTRACT FROM AUTHOR]

This note presents an exact analytical solution of Fredlund–Hasan consolidation for unsaturated soils under an arbitrary loading using the mode superposition method. Air pressure and water pressure are expressed in a series of products of Eigen functions with respect to depth and normal coordinates with respect to time, respectively. A pressure function substitutes for the related homogeneous problem. Eigen functions can be first obtained based on two pairs of drainage condition. Then, the nonhomogeneous governing equations of unsaturated soils under constant loading, exponential loading, and sine loading are considered. After matrix algebraic manipulation, the normal coordinates can be obtained based on the initial conditions that compose the final solutions of the Fredlund–Hasan unsaturated consolidation. This solution can avoid inconvenient Laplace transform and inverse Laplace transform. Through comparisons with a classic example, the validation of the proposed analytical solution is verified against other analytical solutions and the finite difference method solutions. [ABSTRACT FROM AUTHOR]

In this paper, we give a simple sufficient condition for the eigenvalue-separation properties of real tridiagonal matrices T. This result is much more than the statement that the pertinent eigenvalues are distinct. Its derivation is based on recurrence formulae satisfied by the polynomials made up by the minors of the characteristic polynomial det(xE - T) that are proven to form a Sturm sequence. This is a new result, and it proves the simple spectrum property of a symmetric tridiagonal matrix studied in a Grünbaum paper. Two numerical examples underpin the theoretical findings. The style of the paper is expository in order to address a large readership. [ABSTRACT FROM AUTHOR]

The Intelligent Fault Diagnosis of rotating machinery currently proposes some captivating challenges. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open issues. Models' interpretation is still buried under the foundations of data driven science, thus requiring attention to the development of new opportunities also for machine learning theories. This study proposes a machine learning diagnosis model, based on intelligent spectrogram recognition, via image processing. The approach is characterized by the employment of the eigen-spectrograms and randomized linear algebra in fault diagnosis. Randomized algebra and eigen-spectrograms enable the construction of a significant feature space, which nonetheless emerges as a viable device to explore models' interpretations. The computational efficiency of randomized approaches provides reading keys of well-established statistical learning theories such as the Support Vector Machine (SVM). Machine learning applied to spectrogram recognition shows to be extremely accurate and efficient as compared to state of the art results. [ABSTRACT FROM AUTHOR]

An Eigen root analysis is fulfilled for a high-speed rail vehicle concerning suspension parameters variation and active control using a simplified lateral-dynamics-intended model. The model is verified to be capable of reflecting the modal features of both carbody suspension modes and hunting modes. Subsequently, the effects of suspension parameters and the active yaw damper (AYD) on the vehicle modes are examined with various wheel/rail conicities. It shows that the frequency of hunting motion does not linearly increase with the vehicle speed but saturates to a value over 300 km/h. The crucial influential suspension parameters of the vehicle modes include the series stiffness and damping coefficient of the yaw damper, the longitude positioning stiffness on the wheelset, the series damping of the lateral damper, and the lateral stiffness of air springs. Sky-hook damping/stiffness control of AYD helps to increase the modal damping for bogie hunting concerns. For a large conicity of 0.37 case, a minimum of 400 kN·s/m is suggested for the damping control and 10 MN/m for stiffness control. Moreover, the damping control would adequately relieve the carbody hunting with a conicity of 0.11, and the stiffness control still works fine even with an extremely small conicity of 0.07. [ABSTRACT FROM AUTHOR]

A novel method of combination of wavelet‐based boundary element method (WBEM) with frequency‐independent fundamental solutions is proposed to determine the band structures of fluid–solid phononic crystals (PCs) with square and triangular lattices. Integral equations established are based on the frequency‐independent fundamental solutions, which can avoid nonlinear eigenvalue problems and reduce computing time. Domain integral terms arising from the use of frequency‐independent fundamental solutions are handled with the radial integration method (RIM) and dual reciprocity method (DRM), respectively. The results show the lower precision in high frequency domain of using RIM to handle domain integral terms than that of using DRM, which can be solved by increasing Gauss point. The B‐spline wavelet on the interval and wavelet coefficients are applied to approximate the physical boundary conditions. It is proved that coupling conditions between matrix and scatterers and Bloch theorem are also applicable to wavelet coefficients. Some small matrix entries generated by wavelet vanishing moment characteristics are truncated by the provided matrix compression technique, and the influence of compressed matrices on the results is studied. Furthermore, the final Eigen equations constructed are modified to avoid numerical instability. Some examples are provided to demonstrate the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A direct method for simultaneously updating mass and stiffness matrices of the undamped piezoelectric smart structural models based on incomplete modal measured data is presented. By applying the generalized singular value decomposition and some matrix derivatives, the optimal approximate mass and stiffness matrices which satisfy the required eigenvalue equation and the orthogonality relation are found under the Frobenius norm sense. The method is computationally efficient as neither iteration nor eigenanalysis is required. Numerical results are included to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The shear behavior of corrugated web beams can be highly sensitive to the presence of initial imperfections. The designer has, in general, no prior information about the mechanical and geometric imperfections of welded elements. As a solution, in a FEM‐based design, the eigen buckling deformations with an equivalent maximum magnitude are included as an equivalent initial imperfection in a nonlinear analysis to account for the simultaneous effects of geometric imperfections and residual stresses. Previous researchers investigated the effects of initial imperfections in the form of different eigenmodes found via linear buckling analysis. They concluded that the shear strength rises with mode number, with the first mode providing the most crucial condition. However, it is shown in this paper that such a methodology is not applicable to stainless steel corrugated web beams in the medium slenderness ratio range when shear yielding precedes shear buckling. It is observed that, unlike in elastic buckling, in plastic buckling the first buckling mode does not result in the minimum strength. The results show that in FEM‐based design, using the first mode instead of the critical mode as the shape of the initial imperfection can result in a maximum of 19% and 31% overestimation of the ultimate shear capacity for the imperfection amplitudes of tw and hw/200, respectively. [ABSTRACT FROM AUTHOR]

We explore a hierarchical generalized latent factor model for discrete and bounded response variables and in particular, binomial responses. Specifically, we develop a novel two‐step estimation procedure and the corresponding statistical inference that is computationally efficient and scalable for the high dimension in terms of both the number of subjects and the number of features per subject. We also establish the validity of the estimation procedure, particularly the asymptotic properties of the estimated effect size and the latent structure, as well as the estimated number of latent factors. The results are corroborated by a simulation study and for illustration, the proposed methodology is applied to analyze a dataset in a gene–environment association study. [ABSTRACT FROM AUTHOR]

A geometric intrinsic pre-processing algorithm(GPA for short) for solving large-scale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun (in 2022–2023). Different from traditional preconditioning, the authors apply the intrinsic geometric invariance, the Grid matrix G and the discrete PDE mass matrix B, stiff matrix A satisfies commutative operator BG = GB and AG = GA, where G satisfies Gm = I, m ≪ dim(G). A large scale system solvers can be replaced to a more smaller block-solver as a pretreatment in real or complex domain. In this paper, the authors expand their research to 2-D and 3-D mathematical physical equations over more wide polyhedron grids such as triangle, square, tetrahedron, cube, and so on. They give the general form of pre-processing matrix, theory and numerical test of GPA. The conclusion that "the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron" is obtained through research, and it is further found that "commutative of grid mesh matrix and mass matrix is an important basis for the feasibility and reliability of GPA algorithm". [ABSTRACT FROM AUTHOR]

One of the key goals of geodesy is to study the fine structure of the Earth's gravity field and construct a high-resolution gravity field model (GFM). Aiming at the current insufficient resolution problem of the EIGEN_6C4 model, the refined ultra-high degree models EIGEN_3660 and EIGEN_5480 are determined with a spectral expansion approach in this study, which is to augment EIGEN_6C4 model using topographic potential models (TPMs). A comparative spectral evaluation for EIGEN_6C4, EIGEN_3660, and EIGEN_5480 models indicates that the gravity field spectral powers of EIGEN_3660 and EIGEN_5480 models outperform the EIGEN_6C4 model after degree 2000. The augmented models EIGEN_3660 and EIGEN_5480 are verified using the deflection of the vertical (DOV) of China and Colorado, gravity data from Australia and mainland America, and GNSS/leveling in China. The validation results indicate that the accuracy of EIGEN_3660 and EIGEN_5480 models in determining height anomaly, DOV, and gravity anomaly outperform the EIGEN_6C4 model, and the EIGEN_5480 model has optimal accuracy. The accuracy of EIGEN_5480 model in determining south–north component and east–west component of the DOV in China has been improved by about 21.1% and 23.1% compared to the EIGEN_6C4 model, respectively. In the mountainous Colorado, the accuracy of EIGEN_5480 model in determining south–north component and east–west component of the DOV has been improved by about 28.2% and 35.2% compared to EIGEN_6C4 model, respectively. In addition, gravity value comparison results in Australia and mainland America indicate that the accuracy of the EIGEN_5480 model for deriving gravity anomalies is improved by 16.5% and 11.3% compared to the EIGEN_6C4 model, respectively. [ABSTRACT FROM AUTHOR]

In this investigation, an ultra-compact dual-mode bandpass filter (BPF) with a wide stopband response is realized by using a half-mode substrate-integrated rectangular cavity (HMSIRC). The HMSIRC resonator is designed with a cavity that is rectangular in shape and has metallic vias along three of the sides. The fourth side is open-ended and contains microstrip feed lines. For the purpose of constructing a magnetic wall, a rectangular slot is cut into each of the HMSIRC's three edges. In order to produce an electrical wall that may generate a variety of resonances, the side with the open edges is provided with a single metallic via in the center. After that, a second-order BPF is generated by loading a transverse slot in the middle of the BPF, which enables independent frequency regulation of the mode frequencies. The eigen-mode analysis; field distributions; coupling matrix; and full-wave simulation of the proposed HMSIRC filter topology are used to develop the working principle of the filter. A second-order BPF is realized, constructed, and experimentally validated in order to provide evidence that the theory is correct. The BPF prototype achieves satisfactory performance thanks to its compact footprint of 0.028 λg2; its broad passband of 15.9%; its low insertion loss of 0.41 dB; and its wide stopband of 4.36 f0 with a rejection level greater than 20 dB. Both the measured and EM-simulated responses of the BPF are very consistent with one another. [ABSTRACT FROM AUTHOR]

Electromagnetic forces play a critical role in shaping the trajectories of charged particles, affecting their movement across scales ranging from subatomic dimensions to distances smaller than astronomical ones. This study focuses on the behaviour of a charged spin-half particle exposed to a perpendicular electric and magnetic field. We analyze the associated eigenfunctions and eigenvalues using the Landau gauge. The non-relativistic and classical limits align with the standard results. [ABSTRACT FROM AUTHOR]

The structural health monitoring (SHM) technique is a highly competent operative process dedicated to improving the resilience of an infrastructure by evaluating its system state. SHM is performed to identify any modification in the dynamic properties of an infrastructure by evaluating the acceleration, natural frequencies, and damping ratios. Apart from the vibrational measurements, SHM is employed to assess the displacement. Consequently, sensors are mounted on the investigated framework aiming to collect frequent readings at regularly spaced time intervals during and after being induced. In this study, a LabVIEW program was developed for vibrational monitoring and system evaluation. In a case study reported herein, it calculates the natural frequencies as well as the damping and displacement parameters of a cantilever steel beam after being subjected to excitation at its free end. For that purpose, a Bridge Diagnostic Inc. (BDI) accelerometer and a displacement transducer were parallelly mounted on the free end of the beam. The developed program was capable of detecting the eigenfrequencies, the damping properties, and the displacements from the acceleration data. The evaluated parameters were estimated with the ARTeMIS modal analysis software for comparison purposes. The reported response confirmed that the proposed system strongly conducted the desired performance as it successfully identified the system state and modal parameters. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study the elastic seismic response of simplified building models that include considerations of the vertical lateral force resisting system (walls) and the horizontal lateral force resisting system (floor diaphragms) through parametric study. The assumption of rigid diaphragms is often used in the seismic design of buildings; however, research suggests that the diaphragm may influence the fundamental building period and the seismic building response. In this paper, a simplified model is presented for single and multi‐story buildings utilizing two degrees of freedom per story for the vertical system, for example, the walls, and one degree of freedom per story for the floor diaphragm. The number of stories, the stiffness of the walls and diaphragm(s), and the mass distribution between the walls and diaphragm are varied to represent a large range of potential building compositions. Eigen analyses of the models indicate that the wall and diaphragm interact when at similar periods resulting in elongation of the overall building period. Response of elastic time‐history analyses of the building models are presented in this paper where it is shown that the force demands in both the wall and diaphragm(s) are dependent on the relative stiffness of the walls and diaphragm(s), and the mass‐distribution between these two systems. In the companion paper "Wall‐Diaphragm Interactions in Seismic Response of Building System II: Inelastic Response and Design" the parametric building study is extending to nonlinear time‐history analyses including different levels of assumed inelasticity in both the walls and diaphragm. [ABSTRACT FROM AUTHOR]

Frequency estimation plays a critical role in vital sign monitoring. Methods based on Fourier transform and eigen-analysis are commonly adopted techniques for frequency estimation. Because of the nonstationary and time-varying characteristics of physiological processes, time-frequency analysis (TFA) is a feasible way to perform biomedical signal analysis. Among miscellaneous approaches, Hilbert–Huang transform (HHT) has been demonstrated to be a potential tool in biomedical applications. However, the problems of mode mixing, unnecessary redundant decomposition and boundary effect are the common deficits that occur during the procedure of empirical mode decomposition (EMD) or ensemble empirical mode decomposition (EEMD). The Gaussian average filtering decomposition (GAFD) technique has been shown to be appropriate in several biomedical scenarios and can be an alternative to EMD and EEMD. This research proposes the combination of GAFD and Hilbert transform that is termed the Hilbert–Gauss transform (HGT) to overcome the conventional drawbacks of HHT in TFA and frequency estimation. This new method is verified to be effective for the estimation of respiratory rate (RR) in finger photoplethysmography (PPG), wrist PPG and seismocardiogram (SCG). Compared with the ground truth values, the estimated RRs are evaluated to be of excellent reliability by intraclass correlation coefficient (ICC) and to be of high agreement by Bland–Altman analysis. [ABSTRACT FROM AUTHOR]

Many flexible structures are characterized by a small number of compliant modes, i.e., large-deformation paths that can be traversed with little mechanical effort, whereas resistance to other deformations is much stiffer. Predicting the compliant modes for a given flexible structure, however, is challenging. While linear eigenmodes capture the small-deformation behavior, they quickly divert into states of unrealistically high energy for larger displacements. Moreover, they are inherently unable to predict nonlinear phenomena such as buckling, stiffening, multistability, and contact. To address this limitation, we propose Nonlinear Compliant Modes—a physically principled extension of linear eigenmodes for large-deformation analysis. Instead of constraining the entire structure to deform along a given eigenmode, our method only prescribes the projection of the system's state onto the linear mode while all other degrees of freedom follow through energy minimization. We evaluate the potential of our method on a diverse set of flexible structures, ranging from compliant mechanisms to topology-optimized joints and structured materials. As validated through experiments on physical prototypes, our method correctly predicts a broad range of nonlinear effects that linear eigenanalysis fails to capture. [ABSTRACT FROM AUTHOR]

Based on a Gaussian mixture type model of K components, we derive eigen selection procedures that improve the usual spectral clustering algorithms in high-dimensional settings, which typically act on the top few eigenvectors of an affinity matrix (e.g., X ⊤ X ) derived from the data matrix X. Our selection principle formalizes two intuitions: (i) eigenvectors should be dropped when they have no clustering power; (ii) some eigenvectors corresponding to smaller spiked eigenvalues should be dropped due to estimation inaccuracy. Our selection procedures lead to new spectral clustering algorithms: ESSC for K = 2 and GESSC for K > 2. The newly proposed algorithms enjoy better stability and compare favorably against canonical alternatives, as demonstrated in extensive simulation and multiple real data studies. for this article are available online. [ABSTRACT FROM AUTHOR]

Topological indices are an important method for understanding the fundamental topology of chemical structures. Quantitative structure properties relationship (QSPR) is an analytical approach for breaking down a molecule into a sequence of numerical values that describe the chemical and physical characteristics of the molecule. In this article, we have developed the QSPR analysis between eigenvalue‐based topological indices and physical properties of COVID‐19 drugs to predict the significance level of eigenvalue based indices. We have to use MATLAB for the computation of indices and SPSS for analysis. We show that positive interia index, signless Laplacian Estrada index and Randić energy are the best predictors of molar reactivity, polar surface area and molecular weight, respectively. [ABSTRACT FROM AUTHOR]

We consider to model matrix time series based on a tensor canonical polyadic (CP)-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further refined approach which projects it into a lower-dimensional full-ranked eigenequation. This refined method can significantly improve the finite-sample performance. We show that all the component coefficient vectors in the CP-decomposition can be estimated consistently. The proposed model and the estimation method are also illustrated with both simulated and real data, showing effective dimension-reduction in modelling and forecasting matrix time series. [ABSTRACT FROM AUTHOR]

The current paper is a trial to investigate the Eigen functions appears through mathematical treatment of 2nd kind of Fredholm integral equations by making use a new developed an Inverse Iterative Numerical Scheme (IINS). To test the applicability and accuracy of the proposed IINS, two numerical examples were solved and compared with previous results. The discussion of the results gave a good coincides up to some decimal places of results with the available ones. [ABSTRACT FROM AUTHOR]

In nodal-based finite element method (FEM), degrees of freedom are associated with the nodes of the element whereas, for edge FEM, degrees of freedom are assigned to the edges of the element. Edge element is constructed based on Whitney spaces. Nodal elements impose both tangential and normal continuity of vector or scalar fields across interface boundaries. But in edge elements, only tangential continuity is imposed across interface boundaries, which is consistent with electromagnetic field problems. Therefore the required continuities in the electromagnetic analysis are directly obtained with edge elements whereas in nodal elements they are attained through potential formulations. Hence, while using edge elements, field variables are directly calculated but with nodal elements, post-processing is required to obtain the field variables from the potentials. Here, we present the finite element formulations with the edge element as well as with nodal elements. Thereafter, we have demonstrated the relative performances of different nodal and edge elements through a series of examples. All possible complexities like curved boundaries, non-convex domains, sharp corners, non-homogeneous domains have been addressed in those examples. The robustness of edge elements in predicting the singular eigen values for the domains with sharp edges and corners is evident in the analysis. A better coarse mesh accuracy has been observed for all the edge elements as compared to the respective nodal elements. Edge elements are also not susceptible to mesh distortion. [ABSTRACT FROM AUTHOR]

This article presents a novel Vector Quantized Eigen technique for effective classification of Power Quality (PQ) events. The Stockwell Transform (ST), and Empirical Mode Decomposition (EMD) are used as baselines to develop individual feature matrices. The MATLAB platform has been used to generate the PQ events synthetically. Several statistical parameters along with the Vector Quantized Coefficients and Eigenvectors are computed from each matrix for further analysis. Finally, a novel Vector Quantized Eigen Mapping algorithm (VQEM) is proposed in a combinational platform for better efficacy. The lower-order Eigencoefficients (LECs) are more revealing as compared to the Principal Coefficients, hence are contemplated. The reliability of the proposed VQEM is attributed to the vector dimensionality, correlation, and Probability Density Function (PDF) of VQ to cluster irrelevant data and the feature selection ability of eigenvectors. For classification, the Cost-Sensitive Decision Tree (CSDT) algorithm is chosen as it assumes implicitly the cost of all the recognition errors to be different. Results reveal an improved classification accuracy, the highest %Best cost savings, and a lower Friedman Ranking (F-Rank) with the proposed technique as compared to other cited works of literature in this field. [ABSTRACT FROM AUTHOR]

In this article, an efficient control scheme is proposed to enhance the voltage regulation and stability of the power system. The proposed control scheme is the combination of both the Harris Hawks Optimization Algorithm (HHOA) and the Tabu Search Algorithm (TSA). The HHOA searching process is improved by utilising the TSA algorithm based on the minimal error objective function and named the HHO-TSA control scheme. The proposed HHO-TSA ensures adequate swing damping through minimising the mutual influence during transient stability with voltage regulation. An optimisation complex for tuning the parameters of power system stabilisers (PSSs) is designed to increase the damping ratio of electro-mechanical systems and the HHO-TSA control system has been employed for searching optimum parameters. The analysis of the Eigenvalue investigates the dynamic behaviour of the power system at dissimilar characteristic frequencies by utilising the HHO-TSA control scheme. The proposed technique is activated in the MATLAB/Simulink site and the performance is assessed using other existing techniques. The Eigen value for two area systems using the proposed technique achieves −1.31 ± 2.18i, −1.42 ± 1.36i, −1.61 ± 1.53i, −4.50 ±.027i, −10.4 ± 12.6i, −13.7 ± 25.1i and −14.5 ± 55.6i. The Eigen value for nine bus systems using the proposed technique achieves −1.2 ± 2.41i, −2.5 ± 2.62i, −2.11 ± 2.68i, −2.15 ±.2.71i, −4.4 ± 3.76i, −4.7 ± 3.94i and −5.5 ± 6.99i. [ABSTRACT FROM AUTHOR]

To analytically measure the vibratory characteristics of the cable-stayed bridge with beam-tower constraint during the dual-cantilever erection, the isolating/assembling technique is used to derive the global equation. Eigen-equation governing the frequencies/modes is obtained by applying the coefficients vectors transferring between adjacent cable-beams and the boundary/matching conditions. An illustrative example of the dual-cantilever erection system is given to verify the effectiveness of the analytical method by comparing with the finite element method. The influences of the vertical/rotational beam-tower constraint stiffness and the beam/cable relative stiffness on the frequencies/modes are studied; the sensitive interval and unstable/veering regions in frequency spectrum are ascertained. The twin frequencies are analytically measured and it is found that the symmetry plays a fundamental role in its existence and distribution range. The measuring method supplies reference for similar cable-supported structures; the results provide suggestions to avoid unstable/veering zone depending on the designed parameters combination in cable-stayed bridge. [ABSTRACT FROM AUTHOR]

Principal component regression (PC regression) is a useful method developed for prediction based on a dimension‐reducing strategy. Generally, the principal components (PCs) are added to the regression model one by one based on the eigenvalue (PC‐Eigen). Considering that some PCs with large eigenvalues may be poorly associated with the response variable, the PC‐Eigen may not be the best framework. Researchers previously tried to add PCs to the model based on their contribution to the sum of squares of the regression (PC‐SS) and they found that the performance of PC‐SS is generally lower than that of the PC‐Eigen. A standard approach for selecting the optimal set of PCs remains a challenge. Here, from the cosine similarity theory, we postulated that we could rank the PCs by dot product, and this framework (we called PC‐DOT) could help to preferentially extract PCs that are highly correlated with the response variable and meanwhile have a large eigenvalue. Based on one simulated and three real genomic datasets (a total of 15 traits), we tested the prediction ability of different frameworks. In general, the PC‐DOT method showed a better performance than both PC‐Eigen and PC‐SS. To facilitate the application of PC, we attached a series of R codes for different frameworks (https://github.com/SUNHAO‐JLU/Genome%5fPrediction‐PC%5fDOT). In addition, the HAT matrix was used to reduce the compute complex in reference data during the cross‐validation process. Our work may help researchers to better understand and carry out the PC regression model. [ABSTRACT FROM AUTHOR]